TI-84 Plus TI-84 Plus Silver Edition Guidebook
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Chapter 1: Operating the TI-84 Plus Silver Edition Documentation Conventions In the body of this guidebook, TI-84 Plus refers to the TI-84 Plus Silver Edition. Sometimes, as in Chapter 19, the full name TI-84 Plus Silver Edition is used to distinguish it from the TI-84 Plus. All the instructions and examples in this guidebook also work for the TI-84 Plus. All the functions of the TI-84 Plus Silver Edition and the TI-84 Plus are the same.
Scientific — Scientific calculator keys access the capabilities of a standard scientific calculator.
Using the Color. Color.Coded Keyboard The keys on the TI-84 Plus are color-coded to help you easily locate the key you need. The light colored keys are the number keys. The light gray keys along the right side of the keyboard are the common math functions. The light gray keys across the top set up and display graphs. The Πkey with the purple lettering provides access to applications such as the Inequality Graphing application. The primary function of each key is printed on the keys.
The y key accesses the second function printed in blue above each key. The ƒ key accesses the alpha function printed in green above each key. Turning On and Turning Off the TI-84 Plus Turning On the Graphing Calculator To turn on the TI-84 Plus, press É. • If you previously had turned off the graphing calculator by pressing y M, the TI-84 Plus displays the home screen as it was when you last used it and clears any error.
• If Automatic Power Down™ (APD™) had previously turned off the graphing calculator, the TI-84 Plus will return exactly as you left it, including the display, cursor, and any error. • If the TI-84 Plus is turned off and connected to another graphing calculator or personal computer, any communication activity will “wake up” the TI-84 Plus. To prolong the life of the batteries, APD turns off the TI-84 Plus automatically after about five minutes without any activity.
Setting the Display Contrast Adjusting the Display Contrast You can adjust the display contrast to suit your viewing angle and lighting conditions. As you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current level. You may not be able to see the number if contrast is too light or too dark. Note: The TI-84 Plus has 40 contrast settings, so each number 0 through 9 represents four settings.
When to Replace Batteries When the batteries are low, a low-battery message is displayed when you turn on the graphing calculator. To replace the batteries without losing any information in memory, follow the steps in Appendix C. Generally, the graphing calculator will continue to operate for one or two weeks after the low-battery message is first displayed. After this period, the TI-84 Plus will turn off automatically and the unit will not operate. Batteries must be replaced. All memory should be retained.
Displaying Entries and Answers When text is displayed, the TI-84 Plus screen can display a maximum of 8 lines with a maximum of 16 characters per line. If all lines of the display are full, text scrolls off the top of the display. If an expression on the home screen, the Y= editor (Chapter 3), or the program editor (Chapter 16) is longer than one line, it wraps to the beginning of the next line. In numeric editors such as the window screen (Chapter 3), a long expression scrolls to the right and left.
Busy Indicator When the TI-84 Plus is calculating or graphing, a vertical moving line is displayed as a busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line. Display Cursors In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.
Interchangeable Faceplates The TI-84 Plus Silver Edition has interchangeable faceplates that let you customize the appearance of your unit. To purchase additional faceplates, refer to the TI Online Store at education.ti.com. Removing a Faceplate 1. Lift the tab at the bottom edge of the faceplate away from the TI-84 Plus Silver Edition case. 2. Carefully lift the faceplate away from the unit until it releases. Be careful not to damage the faceplate or the keyboard.
Installing New Faceplates 1. Align the top of the faceplate in the corresponding grooves of the TI-84 Plus Silver Edition case. 2. Gently click the faceplate into place. Do not force. 3. Make sure you gently press each of the grooves to ensure the faceplate is installed properly. See the diagram for proper groove placement. Using the Clock Use the Clock to set the time and date, select the clock display format, and turn the clock on and off.
Displaying the Clock Settings 1. Press z 2. Press the † to move the cursor to SET CLOCK. 3. Press Í. Changing the Clock settings 1. Press the ~ or | to highlight the date format you want, example: M/D/Y. Press Í. 2. Press † to highlight YEAR. Press ‘ and type the year, example: 2004. 3. Press † to highlight MONTH. Press ‘ and type the number of the month (a number from 1– 12). 4. Press † to highlight DAY. Press ‘ and type the date. 5. Press † to highlight TIME.
7. Press † to highlight MINUTE. Press ‘ and type the minutes. A number from 0–59. 8. Press † to highlight AM/PM. Press ~ or | to highlight the format. Press Í. 9. To Save changes, press † to select SAVE. Press Í. Error Messages If you type the wrong date for the month, for example: June 31, June does not have 31 days, you will receive an error message with two choices: • To Quit the Clock application and return to the Home screen, select 1: Quit. Press Í.
Using the Mode Screen to turn the clock on 1. If the Clock is turned off, Press † to highlight TURN CLOCK ON. 2. Press Í Í. Using the Catalog to turn the clock on 1. If the Clock is turned off, Press y N 2. Press † or } to scroll the CATALOG until the selection cursor points to ClockOn. 3. Press Í Í. Turning the Clock Off 1. Press y N. 2. Press † or } to scroll the CATALOG until the selection cursor points to ClockOff. 3. Press Í. ClockOff will turn off the Clock display.
Entering Expressions and Instructions What Is an Expression? An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements. An expression evaluates to a single answer. On the TI-84 Plus, you enter an expression in the same order as you would write it on paper. For example, pR2 is an expression. You can use an expression on the home screen to calculate an answer. In most places where a value is required, you can use an expression to enter a value.
Calculate 3.76 P (L7.9 + ‡5) + 2 log 45. 3 Ë 76 ¥ £ Ì 7 Ë 9 Ã y C 5 ¤ ¤ Ã 2 « 45 ¤ Í Multiple Entries on a Line To enter two or more expressions or instructions on a line, separate them with colons (ƒ [:]). All instructions are stored together in last entry (ENTRY). Entering a Number in Scientific Notation To enter a number in scientific notation, follow these steps. 1. Enter the part of the number that precedes the exponent. This value can be an expression. 2. Press y D.
When you enter a number in scientific notation, the TI-84 Plus does not automatically display answers in scientific or engineering notation. The mode settings and the size of the number determine the display format. Functions A function returns a value. For example, ÷, L, +, ‡(, and log( are the functions in the example on the previous page. In general, the first letter of each function is lowercase on the TI-84 Plus.
When you interrupt a graph, a partial graph is displayed. • To return to the home screen, press ‘ or any nongraphing key. • To restart graphing, press a graphing key or select a graphing instruction. TI-84 Plus Edit Keys Keystrokes Result ~ or | Moves the cursor within an expression; these keys repeat. } or † Moves the cursor from line to line within an expression that occupies more than one line; these keys repeat.
Keystrokes Result y Changes the cursor to Þ; the next keystroke performs a 2nd operation (an operation in blue above a key and to the left); to cancel 2nd, press y again. ƒ Changes the cursor to Ø; the next keystroke pastes an alpha character (a character in green above a key and to the right) or executes SOLVE (Chapters 10 and 11); to cancel ƒ, press ƒ or press |, }, ~, or †.
To display the mode settings, press z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.
Setting a Mode from a Program You can set a mode from a program by entering the name of the mode as an instruction; for example, Func or Float. From a blank program command line, select the mode setting from the mode screen; the instruction is pasted to the cursor location. Normal, Sci, Eng Notation modes only affect the way an answer is displayed on the home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You can enter a number in any format.
Float, 0123456789 Float (floating) decimal mode displays up to 10 digits, plus the sign and decimal. 0123456789 (fixed) decimal mode specifies the number of digits (0 through 9) to display to the right of the decimal. Place the cursor on the desired number of decimal digits, and then press Í. The decimal setting applies to Normal, Sci, and Eng notation modes.
Func, Par, Pol, Seq Graphing modes define the graphing parameters. Chapters 3, 4, 5, and 6 describe these modes in detail. Func (function) graphing mode plots functions, where Y is a function of X (Chapter 3). Par (parametric) graphing mode plots relations, where X and Y are functions of T (Chapter 4). Pol (polar) graphing mode plots functions, where r is a function of q (Chapter 5). Seq (sequence) graphing mode plots sequences (Chapter 6).
Note: Regardless of which graphing mode is selected, the TI-84 Plus will sequentially graph all stat plots before it graphs any functions. Real, a+bi, re^q re^ i Real mode does not display complex results unless complex numbers are entered as input. Two complex modes display complex results. • a+bi (rectangular complex mode) displays complex numbers in the form a+bi. • re^qi (polar complex mode) displays complex numbers in the form re^qi.
Using TI-84 Plus Variable Names Variables and Defined Items On the TI-84 Plus you can enter and use several types of data, including real and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings. The TI-84 Plus uses assigned names for variables and other items saved in memory. For lists, you also can create your own five-character names. Variable Type Names Real numbers A, B, ... , Z Complex numbers A, B, ... , Z Matrices ãAä, ãBä, ãCä, ...
Variable Type Names Apps Applications AppVars Application variables Groups Grouped variables System variables Xmin, Xmax, and others Notes about Variables • You can create as many list names as memory will allow (Chapter 11). • Programs have user-defined names and share memory with variables (Chapter 16).
Storing Variable Values Storing Values in a Variable Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used. To store a value to a variable from the home screen or a program using the ¿ key, begin on a blank line and follow these steps. 1. Enter the value you want to store. The value can be an expression. 2. Press ¿. ! is copied to the cursor location. 3.
Archiving Variables (Archive, Unarchive) You can archive data, programs, or other variables in a section of memory called user data archive where they cannot be edited or deleted inadvertently. Archived variables are indicated by asterisks (ä) to the left of the variable names. Archived variables cannot be edited or executed. They can only be seen and unarchived.
• Press |, and then select the name of the program (in the program editor only). The variable name you selected is displayed on the bottom line and the cursor disappears. 3. Press Í. The variable contents are inserted where the cursor was located before you began these steps. Note: You can edit the characters pasted to the expression without affecting the value in memory.
To recall ENTRY, press y [. The last entry is pasted to the current cursor location, where you can edit and execute it. On the home screen or in an editor, the current line is cleared and the last entry is pasted to the line. Because the TI-84 Plus updates ENTRY only when you press Í, you can recall the previous entry even if you have begun to enter the next expression. 5Ã7 Í y[ Accessing a Previous Entry The TI-84 Plus retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes.
If you press y [ after displaying the oldest stored entry, the newest stored entry is displayed again, then the next-newest entry, and so on. y[ Reexecuting the Previous Entry After you have pasted the last entry to the home screen and edited it (if you chose to edit it), you can execute the entry. To execute the last entry, press Í. To reexecute the displayed entry, press Í again. Each reexecution displays an answer on the right side of the next line; the entry itself is not redisplayed.
When you press y [, all the expressions and instructions separated by colons are pasted to the current cursor location. You can edit any of the entries, and then execute all of them when you press Í. For the equation A=pr 2, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess. 8 ¿ ƒ R ƒ ã :ä yB ƒ R ¡Í y[ y | 7 y 6 Ë 95 Í Continue until the answer is as accurate as you want.
You can use the variable Ans to represent the last answer in most places. Press y Z to copy the variable name Ans to the cursor location. When the expression is evaluated, the TI-84 Plus uses the value of Ans in the calculation. Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate the yield per square meter if the plot produces a total of 147 tomatoes.
Calculate the area of a circle of radius 5 meters. Next, calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V. yB 5 ¡ Í ¯3Ë3 Í ¿ƒ V Í TI-84 Plus Menus Using a TI-84 Plus Menu You can access most TI-84 Plus operations using menus. When you press a key or key combination to display a menu, one or more menu names appear on the top line of the screen. • The menu name on the left side of the top line is highlighted.
• When an asterisk (ä) appears to the left of a menu item, that item is stored in user data archive (Chapter 18). To display any other menu listed on the top line, press ~ or | until that menu name is highlighted. The cursor location within the initial menu is irrelevant. The menu is displayed with the cursor on the first item. Displaying a Menu While using your TI-84 Plus, you often will need to access items from its menus.
Moving from One Menu to Another Some keys access more than one menu. When you press such a key, the names of all accessible menus are displayed on the top line. When you highlight a menu name, the items in that menu are displayed. Press ~ and | to highlight each menu name. Scrolling a Menu To scroll down the menu items, press †. To scroll up the menu items, press }. To page down six menu items at a time, press ƒ †. To page up six menu items at a time, press ƒ }.
Selecting an Item from a Menu You can select an item from a menu in either of two ways. • Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen. • Press † or } to move the cursor to the item you want, and then press Í. After you select an item from a menu, the TI-84 Plus typically displays the previous screen.
Leaving a Menu without Making a Selection You can leave a menu without making a selection in any of four ways. • Press y 5 to return to the home screen. • Press ‘ to return to the previous screen. • Press a key or key combination for a different menu, such as or y 9. • Press a key or key combination for a different screen, such as o or y 0. VARS and VARS Y-VARS Menus VARS Menu You can enter the names of functions and system variables in an expression or store to them directly.
VARS Y-VARS 3: GDB... Graph database variables 4: Picture... Picture variables 5: Statistics... XY, G, EQ, TEST, and PTS variables 6: Table... TABLE variables 7: String... String variables Selecting a Variable from the VARS Menu or VARS Y-VARS Menu To display the VARS Y-VARS menu, press ~. 1:Function, 2:Parametric, and 3:Polar display secondary menus of the Y= function variables. VARS Y-VARS 1: Function... Yn functions 2: Parametric... XnT, YnT functions 3: Polar... rn functions 4: On/Off.
Press ~ to display the VARS Y-VARS menu. • 2. Select the type of variable, such as 2:Zoom from the VARS menu or 3:Polar from the VARS Y-VARS menu. A secondary menu is displayed. 3. If you selected 1:Window, 2:Zoom, or 5:Statistics from the VARS menu, you can press ~ or | to display other secondary menus. 4. Select a variable name from the menu. It is pasted to the cursor location.
Order Number Function 7 Relational functions, such as > or 8 Logic operator and 9 Logic operators or and xor Note: Within a priority level, EOS evaluates functions from left to right. Calculations within parentheses are evaluated first. Implied Multiplication The TI-84 Plus recognizes implied multiplication, so you need not press ¯ to express multiplication in all cases. For example, the TI-84 Plus interprets 2p, 4sin(46), 5(1+2), and (2…5)7 as implied multiplication.
You can omit the close parenthesis ( ) ) at the end of an expression. All open parenthetical elements are closed automatically at the end of an expression. This is also true for open parenthetical elements that precede the store or display-conversion instructions. Note: An open parenthesis following a list name, matrix name, or Y= function name does not indicate implied multiplication.
Special Features of the TI-84 Plus Flash – Electronic Upgradability The TI-84 Plus uses Flash technology, which lets you upgrade to future software versions without buying a new graphing calculator. As new functionality becomes available, you can electronically upgrade your TI-84 Plus from the Internet.
Applications Applications can be installed to customize the TI-84 Plus to your classroom needs. The big 1.5 M archive space lets you store up to 94 applications at one time. Applications can also be stored on a computer for later use or linked unit-to-unit. There are 30 App slots for the TI-84 Plus. For details, refer to: Chapter 18 Archiving You can store variables in the TI-84 Plus user data archive, a protected area of memory separate from RAM.
Graphing You can store, graph, and analyze up to 10 functions, up to six parametric functions, up to six polar functions, and up to three sequences. You can use DRAW instructions to annotate graphs. The graphing chapters appear in this order: Function, Parametric, Polar, Sequence, and DRAW. For graphing details, refer to: Chapters 3, 4, 5, 6, 8 Sequences You can generate sequences and graph them over time. Or, you can graph them as web plots or as phase plots.
For details, refer to: Chapter 9 Matrices You can enter and save up to 10 matrices and perform standard matrix operations on them. For details, refer to: Chapter 10 Lists You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves.
Inferential Statistics You can perform 16 hypothesis tests and confidence intervals and 15 distribution functions. You can display hypothesis test results graphically or numerically. For details, refer to: Chapter 13 Applications Press Πto see the complete list of applications that came with your graphing calculator. Documentation for TI Flash applications are on the product CD. Visit education.ti.com/calc/guides for additional Flash application guidebooks.
For details, refer to: Chapter 16 Archiving Archiving allows you to store data, programs, or other variables to user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory. Archived variables are indicated by asterisks (ä) to the left of the variable names.
As future software upgrades become available on the TI Web site, you can download the software to your PC and then use the TI Connect™ software and a USB computer cable to upgrade your TI-84 Plus. For details, refer to: Chapter 19 Error Conditions Diagnosing an Error The TI-84 Plus detects errors while performing these tasks.
Note: If a syntax error occurs in the contents of a Y= function during program execution, then the Goto option returns to the Y= editor, not to the program. Correcting an Error To correct an error, follow these steps. 1. Note the error type (ERR:error type). 2. Select 2:Goto, if it is available. The previous screen is displayed with the cursor at or near the error location. 3. Determine the error. If you cannot recognize the error, refer to Appendix B. 4. Correct the expression.
Chapter 2: Math, Angle, and Test Operations Getting Started: Coin Flip Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this simulation 40 times. With a fair coin, the probability of a coin flip resulting in heads is 0.5 and the probability of a coin flip resulting in tails is 0.5. 1. Begin on the home screen.
3. Press ~ or | to view the additional counts in the list. Ellipses (...) indicate that the list continues beyond the screen. 4. Press ¿ y d Í to store the data to the list name L1. You then can use the data for another activity, such as plotting a histogram (Chapter 12). Note: Since randBin( generates random numbers, your list elements may differ from those in the example.
Addition, Subtraction, Multiplication, Division You can use + (addition, Ã), N (subtraction, ¹), … (multiplication, ¯), and à (division, ¥) with real and complex numbers, expressions, lists, and matrices. You cannot use à with matrices. valueA N valueB valueA à valueB valueA+valueB valueA…valueB Trigonometric Functions You can use the trigonometric (trig) functions (sine, ˜; cosine, ™; and tangent, š) with real numbers, expressions, and lists. The current angle mode setting affects interpretation.
Power, Square, Square Root You can use ^ (power, ›), 2 (square, ¡), and ‡( (square root, y C) with real and complex numbers, expressions, lists, and matrices. You cannot use ‡( with matrices. value^power È value2 ‡(value) È Inverse You can use L1 (inverse, œ) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1àx.
Exponential e^( (exponential, y J) returns the constant e raised to a power. You can use e^( with real or complex numbers, expressions, and lists. e^(power) Constant e (constant, y [e]) is stored as a constant on the TI-84 Plus. Press y [e] to copy e to the cursor location. In calculations, the TI-84 Plus uses 2.718281828459 for e. Negation M (negation, Ì) returns the negative of value. You can use M with real or complex numbers, expressions, lists, and matrices.
Note: On the TI-84 Plus, the negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press ¹. Pi p (Pi, y B) is stored as a constant in the TI-84 Plus. In calculations, the TI-84 Plus uses 3.1415926535898 for p.
MATH Operations MATH Menu To display the MATH menu, press . MATH NUM CPX PRB 1: 4Frac Displays the answer as a fraction. 2: 4Dec Displays the answer as a decimal. 3: 3 Calculates the cube. 4: 3 5: x‡ Calculates the xth root. 6: fMin( Finds the minimum of a function. 7: fMax( Finds the maximum of a function. 8: nDeriv( Computes the numerical derivative. 9: fnInt( Computes the function integral. 0: Solver... Displays the equation solver. ‡( Calculates the cube root.
cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use 4Frac following value. value 4Frac 4Dec (display as a decimal) displays an answer in decimal form. You can use 4Dec with real or complex numbers, expressions, lists, and matrices. You can only use 4Dec following value. value 4Dec Cube, Cube Root 3 (cube) returns the cube of value. You can use 3 with real or complex numbers, expressions, lists, and square matrices.
x‡ (Root) x ‡ (xth root) returns the xth root of value. You can use x‡ with real or complex numbers, expressions, and lists. xthrootx‡value fMin(, fMax( fMin( (function minimum) and fMax( (function maximum) return the value at which the local minimum or local maximum value of expression with respect to variable occurs, between lower and upper values for variable. fMin( and fMax( are not valid in expression. The accuracy is controlled by tolerance (if not specified, the default is 1âL5).
nDeriv( nDeriv( (numerical derivative) returns an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1âL3). nDeriv( is valid only for real numbers. nDeriv(expression,variable,value[,H]) nDeriv( uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.
fnInt( fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of expression with respect to variable, given lower limit, upper limit, and a tolerance (if not specified, the default is 1âL5). fnInt( is valid only for real numbers. fnInt(expression,variable,lower,upper[,tolerance]) Note: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press s.
Entering an Expression in the Equation Solver To enter an expression in the equation solver, assuming that the variable eqn is empty, follow these steps. 1. Select 0:Solver from the MATH menu to display the equation editor. 2. Enter the expression in any of three ways. • Enter the expression directly into the equation solver. • Paste a Y= variable name from the VARS Y-VARS menu to the equation solver. • Press y K, paste a Y= variable name from the VARS Y-VARS menu, and press Í.
• Variables in the equation are listed in the order in which they appear in the equation. Any values stored to the listed variables also are displayed. • The default lower and upper bounds appear in the last line of the editor (bound={L1â99,1â99}). • A $ is displayed in the first column of the bottom line if the editor continues beyond the screen. Note: To use the solver to solve an equation such as K=.5MV2, enter eqn:0=KN.5MV2 in the equation editor.
Solving for a Variable in the Equation Solver To solve for a variable using the equation solver after an equation has been stored to eqn, follow these steps. 1. Select 0:Solver from the MATH menu to display the interactive solver editor, if not already displayed. 2. Enter or edit the value of each known variable. All variables, except the unknown variable, must contain a value. To move the cursor to the next variable, press Í or †. 3. Enter an initial guess for the variable for which you are solving.
( upper + lower ) The default guess is calculated as ----------------------------------------- . 2 4. Edit bound={lower,upper}. lower and upper are the bounds between which the TI-84 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is bound={L1â99,1â99}. 5. Move the cursor to the variable for which you want to solve and press ƒ \. • The solution is displayed next to the variable for which you solved.
leftNrt indicates that the equation has been evaluated at the new value of the variable for which you solved. Editing an Equation Stored to eqn To edit or replace an equation stored to eqn when the interactive equation solver is displayed, press } until the equation editor is displayed. Then edit the equation. Equations with Multiple Roots Some equations have more than one solution. You can enter a new initial guess or new bounds to look for additional solutions.
Using solve( on the Home Screen or from a Program The function solve( is available only from CATALOG or from within a program. It returns a solution (root) of expression for variable, given an initial guess, and lower and upper bounds within which the solution is sought. The default for lower is L1â99. The default for upper is L1â99. solve( is valid only for real numbers. solve(expression,variable,guess[,{lower,upper}]) expression is assumed equal to zero.
MATH NUM (Number) Operations MATH NUM Menu To display the MATH NUM menu, press ~. MATH NUM CPX PRB 1: abs( Absolute value 2: round( Round 3: iPart( Integer part 4: fPart( Fractional part 5: int( Greatest integer 6: min( Minimum value 7: max( Maximum value 8: lcm( Least common multiple 9: gcd( Greatest common divisor abs( abs( (absolute value) returns the absolute value of real or complex (modulus) numbers, expressions, lists, and matrices.
Note: abs( is also available on the MATH CPX menu. round( round( returns a number, expression, list, or matrix rounded to #decimals (9). If #decimals is omitted, value is rounded to the digits that are displayed, up to 10 digits. round(value[,#decimals]) iPart(, fPart( iPart( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices.
fPart(value) int( int( (greatest integer) returns the largest integer real or complex numbers, expressions, lists, and matrices. int(value) Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative numbers and negative integers, but one integer less than the result of iPart( for negative noninteger numbers. min(, max( min( (minimum value) returns the smaller of valueA and valueB or the smallest element in list.
max( (maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared, max( returns a list of the larger of each pair of elements. If list and value are compared, max( compares each element in list with value. min(valueA,valueB) min(list) min(listA,listB) min(list,value) max(valueA,valueB) max(list) max(listA,listB) max(list,value) Note: min( and max( also are available on the LIST MATH menu.
each pair of elements. If list and value are specified, gcd( finds the gcd of each element in list and value. lcm(valueA,valueB) lcm(listA,listB) lcm(list,value) gcd(valueA,valueB) gcd(listA,listB) gcd(list,value) Entering and Using Complex Numbers Complex-Number Modes The TI-84 Plus displays complex numbers in rectangular form and polar form. To select a complex-number mode, press z, and then select either of the two modes.
On the TI-84 Plus, complex numbers can be stored to variables. Also, complex numbers are valid list elements. In Real mode, complex-number results return an error, unless you entered a complex number as input. For example, in Real mode ln(L1) returns an error; in a+bi mode ln(L1) returns an answer. Real mode a+bi mode $ $ Entering Complex Numbers Complex numbers are stored in rectangular form, but you can enter a complex number in rectangular form or polar form, regardless of the mode setting.
In degree mode, complex identities such as e^(iq) = cos(q) + i sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^() are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as e^(i45) = cos(p/4) + i sin(p/4). Complex identities are always true in radian mode.
Polar-Complex Mode Polar-complex mode recognizes and displays a complex number in the form re^qi, where r is the magnitude, e is the base of the natural log, q is the angle, and i is a constant equal to –1 . To enter a complex number in polar form, enter the value of r (magnitude), press y J (exponential function), enter the value of q (angle), press y V (constant), and then press ¤.
MATH CPX (Complex) Operations MATH CPX Menu To display the MATH CPX menu, press ~ ~. MATH NUM CPX PRB 1: conj( Returns the complex conjugate. 2: real( Returns the real part. 3: imag( Returns the imaginary part. 4: angle( Returns the polar angle. 5: abs( Returns the magnitude (modulus). 6: 4Rect Displays the result in rectangular form. 7: 4Polar Displays the result in polar form. conj( conj( (conjugate) returns the complex conjugate of a complex number or list of complex numbers.
real( real( (real part) returns the real part of a complex number or list of complex numbers. real(a+bi) returns a. real(re^(qi)) returns r†cos(q). imag( imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex numbers. imag(a+bi) returns b. imag(re^(qi)) returns r†sin(q). angle( angle( returns the polar angle of a complex number or list of complex numbers, calculated as tanL1 (b/a), where b is the imaginary part and a is the real part.
angle(a+bi) returns tanL1(b/a). angle(re^(qi)) returns q, where Lp
4Polar Polar 4Polar (display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Polar returns re^(qi). MATH PRB (Probability) Operations MATH PRB Menu To display the MATH PRB menu, press |.
rand rand (random number) generates and returns one or more random numbers > 0 and < 1. To generate a list of random-numbers, specify an integer > 1 for numtrials (number of trials). The default for numtrials is 1. rand[(numtrials)] Note: To generate random numbers beyond the range of 0 to 1, you can include rand in an expression. For example, rand5 generates a random number > 0 and < 5. With each rand execution, the TI-84 Plus generates the same random-number sequence for a given seed value.
nCr (number of combinations) returns the number of combinations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists. items nCr number Factorial ! (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. value must be ‚ L.5 and 69.
(The variable n equals value in the syntax description above.) randInt( randInt( (random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1. randInt(lower,upper[,numtrials]) randNorm( randNorm( (random Normal) generates and displays a random real number from a specified Normal distribution.
randBin( randBin( (random Binomial) generates and displays a random integer from a specified Binomial distribution. numtrials (number of trials) must be ‚ 1. prob (probability of success) must be ‚ 0 and 1. To generate a list of random numbers, specify an integer > 1 for numsimulations (number of simulations); if not specified, the default is 1. randBin(numtrials,prob[,numsimulations]) Note: The seed value stored to rand also affects randInt(, randNorm(, and randBin( instructions.
ANGLE Operations ANGLE Menu To display the ANGLE menu, press y ;. The ANGLE menu displays angle indicators and instructions. The Radian/Degree mode setting affects the TI-84 Plus’s interpretation of ANGLE menu entries.
For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to Degree, you must use ¡ so that the TI-84 Plus can interpret the argument as degrees, minutes, and seconds. Degree mode Radian mode Degree ¡ (degree) designates an angle or list of angles as degrees, regardless of the current angle mode setting. In Radian mode, you can use ¡ to convert degrees to radians. value¡ {value1,value2,value3,value4,...,value n}¡ ¡ also designates degrees (D) in DMS format.
valuer Degree mode 8DMS DMS 8DMS (degree/minute/second) displays answer in DMS format. The mode setting must be Degree for answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid only at the end of a line. answer8DMS R8P Pr (, R8P R Pq(( , P8Rx(, P Rx(, P8Ry( P Ry( R8Pr( converts rectangular coordinates to polar coordinates and returns r. R8Pq( converts rectangular coordinates to polar coordinates and returns q. x and y can be lists.
R8Pr(x,y), R8Pq(x,y) Note: Radian mode is set. P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry( converts polar coordinates to rectangular coordinates and returns y. r and q can be lists. P8Rx(r,q), P8Ry(r,q) Note: Radian mode is set.
TEST (Relational) Operations TEST Menu To display the TEST menu, press y :. This operator... TEST Returns 1 (true) if... LOGIC 1: = Equal 2: ƒ Not equal to 3: > Greater than 4: ‚ Greater than or equal to 5: < Less than 6: Less than or equal to Ä=, =, ƒ,, >, ‚,, <, Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false. valueA and valueB can be real numbers, expressions, or lists.
Relational operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values. valueA=valueB valueA>valueB valueA
TEST LOGIC (Boolean) Operations TEST LOGIC Menu To display the TEST LOGIC menu, press y : ~. This operator... TEST Returns a 1 (true) if... LOGIC 1: and Both values are nonzero (true). 2: or At least one value is nonzero (true). 3: xor Only one value is zero (false). 4: not( The value is zero (false). Boolean Operators Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values.
valueA and valueB valueA or valueB valueA xor valueB valueA valueB and or xor ƒ0 ƒ0 returns 1 1 0 ƒ0 0 returns 0 1 1 0 ƒ0 returns 0 1 1 0 0 returns 0 0 0 not( not( returns 1 if value (which can be an expression) is 0. not(value) Using Boolean Operations Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C.
Chapter 3: Function Graphing Getting Started: Graphing a Circle Getting Started is a fast-paced introduction. Read the chapter for details. Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSquare (zoom square) to adjust the display and make the functions appear as a circle. 1. In Func mode, press o to display the Y= editor.
2. Press q 6 to select 6:ZStandard. This is a quick way to reset the window variables to the standard values. It also graphs the functions; you do not need to press s. Notice that the functions appear as an ellipse in the standard viewing window. 3. To adjust the display so that each pixel represents an equal width and height, press q 5 to select 5:ZSquare. The functions are replotted and now appear as a circle on the display. 4.
Defining a Graph To define a graph in any graphing mode, follow these steps. Some steps are not always necessary. 1. Press z and set the appropriate graph mode. 2. Press o and enter, edit, or select one or more functions in the Y= editor. 3. Deselect stat plots, if necessary. 4. Set the graph style for each function. 5. Press p and define the viewing window variables. 6. Press y . and select the graph format settings. Displaying and Exploring a Graph After you have defined a graph, press s to display it.
• Window settings • Format settings You can store a picture of the current graph display to any of 10 graph picture variables (Pic1 through Pic9, and Pic0; Chapter 8). Then you can superimpose one or more stored pictures onto the current graph. Setting the Graph Modes Checking and Changing the Graphing Mode To display the mode screen, press z. The default settings are highlighted below.
Other mode settings affect graphing results. Chapter 1 describes each mode setting. • Float or 0123456789 (fixed) decimal mode affects displayed graph coordinates. • Radian or Degree angle mode affects interpretation of some functions. • Connected or Dot plotting mode affects plotting of selected functions. • Sequential or Simul graphing-order mode affects function plotting when more than one function is selected.
Defining or Editing a Function To define or edit a function, follow these steps. 1. Press o to display the Y= editor. 2. Press † to move the cursor to the function you want to define or edit. To erase a function, press ‘. 3. Enter or edit the expression to define the function. • You may use functions and variables (including matrices and lists) in the expression. When the expression evaluates to a nonreal number, the value is not plotted; no error is returned.
Defining a Function from the Home Screen or a Program To define a function from the home screen or a program, begin on a blank line and follow these steps. 1. Press ƒ [ã], enter the expression, and then press ƒ [ã] again. 2. Press ¿. 3. Press ~ 1 to select 1:Function from the VARS Y-VARS menu. 4. Select the function name, which pastes the name to the cursor location on the home screen or program editor. 5. Press Í to complete the instruction.
Yn(value) Yn({value1,value2,value3, . . .,value n}) Selecting and Deselecting Functions Selecting and Deselecting a Function You can select and deselect (turn on and turn off) a function in the Y= editor. A function is selected when the = sign is highlighted. The TI-84 Plus graphs only the selected functions. You can select any or all functions Y1 through Y9, and Y0. To select or deselect a function in the Y= editor, follow these steps. 1. Press o to display the Y= editor. 2.
Turning On or Turning Off a Stat Plot in the Y= Editor To view and change the on/off status of a stat plot in the Y= editor, use Plot1 Plot2 Plot3 (the top line of the Y= editor). When a plot is on, its name is highlighted on this line. To change the on/off status of a stat plot from the Y= editor, press } and ~ to place the cursor on Plot1, Plot2, or Plot3, and then press Í. Plot1 is turned on. Plot2 and Plot3 are turned off.
• To turn on or turn off all functions, do not enter a number after FnOn or FnOff. FnOn[function#,function#, . . .,function n] FnOff[function#,function#, . . .,function n] 5. Press Í. When the instruction is executed, the status of each function in the current mode is set and Done is displayed. For example, in Func mode, FnOff :FnOn 1,3 turns off all functions in the Y= editor, and then turns on Y1 and Y3.
Icon Style Description è Thick A thick solid line connects plotted points é Above Shading covers the area above the graph ê Below Shading covers the area below the graph ë Path A circular cursor traces the leading edge of the graph and draws a path ì Animate A circular cursor traces the leading edge of the graph without drawing a path í Dot A small dot represents each plotted point; this is the default in Dot mode Note: Some graph styles are not available in all graphing modes.
5. Press ~, }, or † when you have selected a style. Shading Above and Below When you select é or ê for two or more functions, the TI-84 Plus rotates through four shading patterns. • Vertical lines shade the first function with a é or ê graph style. • Horizontal lines shade the second. • Negatively sloping diagonal lines shade the third. • Positively sloping diagonal lines shade the fourth. • The rotation returns to vertical lines for the fifth é or ê function, repeating the order described above.
Note: When é or ê is selected for a Y= function that graphs a family of curves, such as Y1={1,2,3}X, the four shading patterns rotate for each member of the family of curves. Setting a Graph Style from a Program To set the graph style from a program, select H:GraphStyle( from the PRGM CTL menu. To display this menu, press while in the program editor. function# is the number of the Y= function name in the current graphing mode.
Setting the Viewing Window Variables The TI-84 Plus Viewing Window The viewing window is the portion of the coordinate plane defined by Xmin, Xmax, Ymin, and Ymax. Xscl (X scale) defines the distance between tick marks on the x-axis. Yscl (Y scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set Xscl=0 and Yscl=0. Displaying the Window Variables To display the current window variable values, press p.
Note: Small Xres values improve graph resolution but may cause the TI-84 Plus to draw graphs more slowly. Changing a Window Variable Value To change a window variable value from the window editor, follow these steps. 1. Press † or } to move the cursor to the window variable you want to change. 2. Edit the value, which can be an expression. • Enter a new value, which clears the original value. • Move the cursor to a specific digit, and then edit it. 3. Press Í, †, or }.
• Press ~ ~ to display the Seq window variables (U/V/W secondary menu). 5. Select the window variable to which you want to store a value. The name of the variable is pasted to the current cursor location. 6. Press Í to complete the instruction. When the instruction is executed, the TI-84 Plus stores the value to the window variable and displays the value.
Setting the Graph Format Displaying the Format Settings To display the format settings, press y .. The default settings are highlighted below. RectGC PolarGC Sets cursor coordinates. CoordOn CoordOff Sets coordinates display on or off. GridOff GridOn AxesOn LabelOff ExprOn AxesOff LabelOn ExprOff Sets grid off or on. Sets axes on or off. Sets axes label off or on. Sets expression display on or off. Format settings define a graph’s appearance on the display.
RectGC, PolarGC RectGC (rectangular graphing coordinates) displays the cursor location as rectangular coordinates X and Y. PolarGC (polar graphing coordinates) displays the cursor location as polar coordinates R and q. The RectGC/PolarGC setting determines which variables are updated when you plot the graph, move the free-moving cursor, or trace. • RectGC updates X and Y; if CoordOn format is selected, X and Y are displayed.
GridOn displays grid points. AxesOn, AxesOff AxesOn displays the axes. AxesOff does not display the axes. This overrides the LabelOff/ LabelOn format setting. LabelOff, LabelOn LabelOff and LabelOn determine whether to display labels for the axes (X and Y), if AxesOn format is also selected. ExprOn, ExprOff ExprOn and ExprOff determine whether to display the Y= expression when the trace cursor is active. This format setting also applies to stat plots.
Displaying Graphs Displaying a New Graph To display the graph of the selected function or functions, press s. TRACE, ZOOM instructions, and CALC operations display the graph automatically. As the TI-84 Plus plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated. Pausing or Stopping a Graph While plotting a graph, you can pause or stop graphing. • Press Í to pause; then press Í to resume. • Press É to stop; then press s to redraw.
• Changed the value of a variable in a selected function • Changed a window variable or graph format setting • Cleared drawings by selecting ClrDraw • Changed a stat plot definition Overlaying Functions on a Graph On the TI-84 Plus, you can graph one or more new functions without replotting existing functions. For example, store sin(X) to Y1 in the Y= editor and press s. Then store cos(X) to Y2 and press s again. The function Y2 is graphed on top of Y1, the original function.
{2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and 6 sin(X). {2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X) . Note: When using more than one list, the lists must have the same dimensions. Exploring Graphs with the Free-Moving Cursor Free-Moving Cursor When a graph is displayed, press |, ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or †, the cursor moves from the center of the viewing window.
As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if CoordOn format is selected. The Float/Fix decimal mode setting determines the number of decimal digits displayed for the coordinate values. To display the graph with no cursor and no coordinate values, press ‘ or Í. When you press |, ~, }, or †, the cursor moves from the same position. Graphing Accuracy The free-moving cursor moves from pixel to pixel on the screen.
Exploring Graphs with TRACE Beginning a Trace Use TRACE to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the Y= editor, at the middle X value on the screen. The cursor coordinates are displayed at the bottom of the screen if CoordOn format is selected.
Trace cursor on the curve If you move the trace cursor beyond the top or bottom of the screen, the coordinate values at the bottom of the screen continue to change appropriately. Moving the Trace Cursor from Function to Function To move the trace cursor from function to function, press † and }. The cursor follows the order of the selected functions in the Y= editor. The trace cursor moves to each function at the same X value. If ExprOn format is selected, the expression is updated.
value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor. Note: This feature does not apply to stat plots. Panning to the Left or Right If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right. Xmin and Xmax are updated to correspond to the new viewing window.
Using TRACE in a Program On a blank line in the program editor, press r. The instruction Trace is pasted to the cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function. As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press Í to resume program execution. Exploring Graphs with the ZOOM Instructions ZOOM Menu To display the ZOOM menu, press q.
ZOOM MEMORY 6: ZStandard Sets the standard window variables. 7: ZTrig Sets the built-in trig window variables. 8: ZInteger Sets integer values on the X and Y axes. 9: ZoomStat Sets the values for current stat lists. 0: ZoomFit Fits YMin and YMax between XMin and XMax. Zoom Cursor When you select 1:ZBox, 2:Zoom In, or 3:Zoom Out, the cursor on the graph becomes the zoom cursor (+), a smaller version of the free-moving cursor (+). ZBox To define a new viewing window using ZBox, follow these steps.
4. When you have defined the box, press Í to replot the graph. To use ZBox to define another box within the new graph, repeat steps 2 through 4. To cancel ZBox, press ‘. Zoom In, Zoom Out Zoom In magnifies the part of the graph that surrounds the cursor location. Zoom Out displays a greater portion of the graph, centered on the cursor location. The XFact and YFact settings determine the extent of the zoom. To zoom in on a graph, follow these steps. 1. Check XFact and YFact; change as needed. 2.
• To zoom in at the same point, press Í. • To zoom in at a new point, move the cursor to the point that you want as the center of the new viewing window, and then press Í. To zoom out on a graph, select 3:Zoom Out and repeat steps 3 through 5. To cancel Zoom In or Zoom Out, press ‘. ZDecimal ZDecimal replots the functions immediately. It updates the window variables to preset values, as shown below. These values set @X and @Y equal to 0.1 and set the X and Y value of each pixel to one decimal place.
ZStandard ZStandard replots the functions immediately. It updates the window variables to the standard values shown below. Xmin=L10 Xmax=10 Xscl=1 Ymin=L10 Ymax=10 Yscl=1 Xres=1 ZTrig ZTrig replots the functions immediately. It updates the window variables to preset values that are appropriate for plotting trig functions. Those preset values in Radian mode are shown below.
ZoomStat ZoomStat redefines the viewing window so that all statistical data points are displayed. For regular and modified box plots, only Xmin and Xmax are adjusted. ZoomFit ZoomFit replots the functions immediately. ZoomFit recalculates YMin and YMax to include the minimum and maximum Y values of the selected functions between the current XMin and XMax. XMin and XMax are not changed. Using ZOOM MEMORY ZOOM MEMORY Menu To display the ZOOM MEMORY menu, press q ~.
ZPrevious ZPrevious replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction. ZoomSto ZoomSto immediately stores the current viewing window. The graph is displayed, and the values of the current window variables are stored in the user-defined ZOOM variables ZXmin, ZXmax, ZXscl, ZYmin, ZYmax, ZYscl, and ZXres. These variables apply to all graphing modes. For example, changing the value of ZXmin in Func mode also changes it in Par mode.
Checking XFact and YFact To display the ZOOM FACTORS screen, where you can review the current values for XFact and YFact, select 4:SetFactors from the ZOOM MEMORY menu. The values shown are the defaults. Changing XFact and YFact You can change XFact and YFact in either of two ways. • Enter a new value. The original value is cleared automatically when you enter the first digit. • Place the cursor on the digit you want to change, and then enter a value or press { to delete it.
Using the CALC (Calculate) Operations CALCULATE Menu To display the CALCULATE menu, press y /. Use the items on this menu to analyze the current graph functions. CALCULATE 1: value Calculates a function Y value for a given X. 2: zero Finds a zero (x-intercept) of a function. 3: minimum Finds a minimum of a function. 4: maximum Finds a maximum of a function. 5: intersect Finds an intersection of two functions. 6: dy/dx Finds a numeric derivative of a function.
1. Select 1:value from the CALCULATE menu. The graph is displayed with X= in the bottom-left corner. 2. Enter a real value, which can be an expression, for X between Xmin and Xmax. 3. Press Í. The cursor is on the first selected function in the Y= editor at the X value you entered, and the coordinates are displayed, even if CoordOff format is selected. To move the cursor from function to function at the entered X value, press } or †. To restore the free-moving cursor, press | or ~.
1. Select 2:zero from the CALCULATE menu. The current graph is displayed with Left Bound? in the bottom-left corner. 2. Press } or † to move the cursor onto the function for which you want to find a zero. 3. Press | or ~ (or enter a value) to select the x-value for the left bound of the interval, and then press Í. A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left corner.
minimum, maximum minimum and maximum find a minimum or maximum of a function within a specified interval to a tolerance of 1âL5. To find a minimum or maximum, follow these steps. 1. Select 3:minimum or 4:maximum from the CALCULATE menu. The current graph is displayed. 2. Select the function and set left bound, right bound, and guess as described for zero.
2. Press † or }, if necessary, to move the cursor to the first function, and then press Í. Second curve? is displayed in the bottom-left corner. 3. Press † or }, if necessary, to move the cursor to the second function, and then press Í. 4. Press ~ or | to move the cursor to the point that is your guess as to location of the intersection, and then press Í. The cursor is on the solution and the coordinates are displayed, even if CoordOff format is selected. Intersection is displayed in the bottom-left corner.
3. Press | or ~ (or enter a value) to select the X value at which to calculate the derivative, and then press Í. The cursor is on the solution and the numerical derivative is displayed. To move to the same x-value for other selected functions, press } or †. To restore the free-moving cursor, press | or ~. ‰f(x)dx f(x)dx ‰f(x)dx (numerical integral) finds the numerical integral of a function in a specified interval. It uses the fnInt( function, with a tolerance of H=1âL3.
3. Set lower and upper limits as you would set left and right bounds for zero. The integral value is displayed, and the integrated area is shaded. Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area.
Chapter 4: Parametric Graphing Getting Started: Path of a Ball Getting Started is a fast-paced introduction. Read the chapter for details. Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level. How far does the ball travel? When does it hit the ground? How high does it go? Ignore all forces except gravity.
1. Press z. Press † † † ~ Í to select Par mode. Press † † ~ Í to select Simul for simultaneous graphing of all three parametric equations in this example. 2. Press o. Press 30 „ ™ 25 y ; 1 (to select ¡) ¤ Í to define X1T in terms of T. 3. Press 30 „ ˜ 25 y ; 1 ¤ ¹ 9.8 ¥ 2 „ ¡ Í to define Y1T. The vertical component vector is defined by X2T and Y2T. 4. Press 0 Í to define X2T. 5. Press ~ to display the VARS Y-VARS menu. Press 2 to display the PARAMETRIC secondary menu. Press 2 Í to define Y2T.
The horizontal component vector is defined by X3T and Y3T. 6. Press ~ 2, and then press 1 Í to define X3T. Press 0 Í to define Y3T. 7. Press | | } Í to change the graph style to è for X3T and Y3T. Press } Í Í to change the graph style to ë for X2T and Y2T. Press } Í Í to change the graph style to ë for X1T and Y1T. (These keystrokes assume that all graph styles were set to ç originally.) 8. Press p. Enter these values for the window variables. Tmin=0 Tmax=5 Tstep=.
10. Press s. The plotting action simultaneously shows the ball in flight and the vertical and horizontal component vectors of the motion. Note: To simulate the ball flying through the air, set graph style to ì (animate) for X1T and Y1T. 11. Press r to obtain numerical results and answer the questions at the beginning of this section. Tracing begins at Tmin on the first parametric equation (X1T and Y1T). As you press ~ to trace the curve, the cursor follows the path of the ball over time.
Setting Parametric Graphing Mode To display the mode screen, press z. To graph parametric equations, you must select Par graphing mode before you enter window variables and before you enter the components of parametric equations. Displaying the Parametric Y= Editor After selecting Par graphing mode, press o to display the parametric Y= editor. In this editor, you can display and enter both the X and Y components of up to six equations, X1T and Y1T through X6T and Y6T.
Defining and Editing Parametric Equations To define or edit a parametric equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is T. In Par graphing mode, you can enter the parametric variable T in either of two ways. • Press „. • Press ƒ [T]. Two components, X and Y, define a single parametric equation. You must define both of them.
Setting Window Variables To display the window variable values, press p. These variables define the viewing window. The values below are defaults for Par graphing in Radian angle mode. Tmin=0 Smallest T value to evaluate Tmax=6.2831853... Largest T value to evaluate (2p) Tstep=.1308996...
Displaying a Graph When you press s, the TI-84 Plus plots the selected parametric equations. It evaluates the X and Y components for each value of T (from Tmin to Tmax in intervals of Tstep), and then plots each point defined by X and Y. The window variables define the viewing window. As the graph is plotted, X, Y, and T are updated. Smart Graph applies to parametric graphs. Window Variables and Y. Y.VARS Menus You can perform these actions from the home screen or a program.
• Select or deselect parametric equations. • Store values directly to window variables. Exploring Parametric Graphs Free-Moving Cursor The free-moving cursor in Par graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. TRACE To activate TRACE, press r.
cursor is on the first selected function at Tmin. If ExprOn is selected, then the function is displayed. In RectGC format, TRACE updates and displays the values of X, Y, and T if CoordOn format is on. In PolarGC format, X, Y, R, q and T are updated; if CoordOn format is selected, R, q, and T are displayed. The X and Y (or R and q) values are calculated from T. To move five plotted points at a time on a function, press y | or y ~.
ZOOM ZOOM operations in Par graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. The T window variables (Tmin, Tmax, and Tstep) are only affected when you select ZStandard. The VARS ZOOM secondary menu ZT/Zq items 1:ZTmin, 2:ZTmax, and 3:ZTstep are the zoom memory variables for Par graphing. CALC CALC operations in Par graphing work the same as in Func graphing.
Chapter 5: Polar Graphing Getting Started: Polar Rose Getting Started is a fast-paced introduction. Read the chapter for details. The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B. 1. Press z to display the MODE screen. Press † † † ~ ~ Í to select Pol graphing mode. Select the defaults (the options on the left) for the other mode settings. 2. Press o to display the polar Y= editor. Press 8 ˜ 2.
4. Press p to display the window variables. Press † 4 y B to increase the value of qmax to 4p. 5. Press q 5 to select 5:ZSquare and plot the graph. 6. Repeat steps 2 through 5 with new values for the variables A and B in the polar equation r1=Asin(Bq). Observe how the new values affect the graph. Defining and Displaying Polar Graphs TI-84 Plus Graphing Mode Similarities The steps for defining a polar graph are similar to the steps for defining a function graph.
Setting Polar Graphing Mode To display the mode screen, press z. To graph polar equations, you must select Pol graphing mode before you enter values for the window variables and before you enter polar equations. Displaying the Polar Y= Editor After selecting Pol graphing mode, press o to display the polar Y= editor. In this editor, you can enter and display up to six polar equations, r1 through r6. Each is defined in terms of the independent variable q.
Defining and Editing Polar Equations To define or edit a polar equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a polar equation is q. In Pol graphing mode, you can enter the polar variable q in either of two ways. • Press „. • Press ƒ [q]. Selecting and Deselecting Polar Equations The TI-84 Plus graphs only the selected polar equations. In the Y= editor, a polar equation is selected when the = sign is highlighted.
Xmax=10 Largest X value to be displayed Xscl=1 Spacing between the X tick marks Ymin=L10 Smallest Y value to be displayed Ymax=10 Largest Y value to be displayed Yscl=1 Spacing between the Y tick marks Note: To ensure that sufficient points are plotted, you may want to change the q window variables. Setting the Graph Format To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings.
Window Variables and Y.VARS Menus You can perform these actions from the home screen or a program. • Access functions by using the name of the equation as a variable. • Store polar equations. • Select or deselect polar equations. • Store values directly to window variables.
Exploring Polar Graphs Free-Moving Cursor The free-moving cursor in Pol graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed. In PolarGC format, X, Y, R, and q are updated; if CoordOn format is selected, R and q are displayed. TRACE To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one qstep at a time.
Moving the Trace Cursor to Any Valid Theta Value To move the trace cursor to any valid q value on the current function, enter the number. When you enter the first digit, a q= prompt and the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the q= prompt. The value must be valid for the current viewing window. When you complete the entry, press Í to move the cursor. ZOOM ZOOM operations in Pol graphing work the same as in Func graphing.
Chapter 6: Sequence Graphing Getting Started: Forest and Trees Note: Getting Started is a fast-paced introduction. Read the chapter for details. A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted. Will the forest eventually disappear? Will the forest size stabilize? If so, in how many years and with how many trees? 1. Press z. Press † † † ~ ~ ~ Í to select Seq graphing mode. 2. Press y .
3. Press o. If the graph-style icon is not ç (dot), press | |, press Í until ç is displayed, and then press ~ ~. 4. Press ~ 3 to select iPart( (integer part) because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain. Press Ë 8 y [u] £ „ ¹ 1 ¤ to define the number of trees after each harvest. Press à 1000 ¤ to define the new trees. Press † 4000 to define the number of trees at the beginning of the program. 5. Press p 0 to set nMin=0. Press † 50 to set nMax=50.
Defining and Displaying Sequence Graphs TI-84 Plus Graphing Mode Similarities The steps for defining a sequence graph are similar to the steps for defining a function graph. Chapter 6 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 6 details aspects of sequence graphing that differ from function graphing. Setting Sequence Graphing Mode To display the mode screen, press z.
• The previous term or the term that precedes the previous term in another sequence function, such as u(nN1) or u(nN2) referenced in the sequence v(n). Note: Statements in this chapter about u(n) are also true for v(n) and w(n); statements about u(nN1) are also true for v(nN1) and w(nN1); statements about u(nN2) are also true for v(nN2) and w(nN2). Displaying the Sequence Y= Editor After selecting Seq mode, press o to display the sequence Y= editor.
Selecting Graph Styles The icons to the left of u(n), v(n), and w(n) represent the graph style of each sequence (Chapter 3). The default in Seq mode is í (dot), which shows discrete values. Dot, ç (line), and è (thick) styles are available for sequence graphing. Graph styles are ignored in Web format. Selecting and Deselecting Sequence Functions The TI-84 Plus graphs only the selected sequence functions.
• To enter the function name u, press y [u] (above ¬). • To enter the function name v, press y [v] (above −). • To enter the function name w, press y [w] (above ®). Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only at consecutive integer values. n is always a series of consecutive integers, starting at zero or any positive integer. Nonrecursive Sequences In a nonrecursive sequence, the nth term is a function of the independent variable n.
Recursive Sequences In a recursive sequence, the nth term in the sequence is defined in relation to the previous term or the term that precedes the previous term, represented by u(nN1) and u(nN2). A recursive sequence may also be defined in relation to n, as in u(n)=u(nN1)+n. For example, in the sequence below you cannot calculate u(5) without first calculating u(1), u(2), u(3), and u(4). Using an initial value u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, ... .
Enter the initial values as a list enclosed in braces ({ }) with commas separating the values. The value of the first term is 0 and the value of the second term is 1 for the sequence u(n). Setting Window Variables To display the window variables, press p. These variables define the viewing window. The values below are defaults for Seq graphing in both Radian and Degree angle modes.
Xmax=10 Largest X value to be displayed Xscl=1 Spacing between the X tick marks Ymin=L10 Smallest Y value to be displayed Ymax=10 Largest Y value to be displayed Yscl=1 Spacing between the Y tick marks nMin must be an integer | 0. nMax, PlotStart, and PlotStep must be integers | 1. nMin is the smallest n value to evaluate. nMin also is displayed in the sequence Y= editor. nMax is the largest n value to evaluate. Sequences are evaluated at u(nMin), u(nMin+1), u(nMin+2), ... , u(nMax).
Selecting Axes Combinations Setting the Graph Format To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in Seq mode.
Axes Setting x-axis y-axis uv u(n) v(n) vw v(n) w(n) uw u(n) w(n) Displaying a Sequence Graph To plot the selected sequence functions, press s. As a graph is plotted, the TI-84 Plus updates X, Y, and n. Smart Graph applies to sequence graphs (Chapter 3). Exploring Sequence Graphs Free-Moving Cursor The free-moving cursor in Seq graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is selected, X and Y are displayed.
When Time, uv, vw, or uw axes format is selected, TRACE moves the cursor along the sequence one PlotStep increment at a time. To move five plotted points at once, press y ~ or y |. • When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by PlotStart, even if it is outside the viewing window. • Quick Zoom applies to all directions. To center the viewing window on the current cursor location after you have moved the trace cursor, pressÍÍ.
value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor. ZOOM ZOOM operations in Seq graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. PlotStart, PlotStep, nMin, and nMax are only affected when you select ZStandard. The VARS Zoom secondary menu ZU items 1 through 7 are the ZOOM MEMORY variables for Seq graphing.
• When uv, vw, or uw axes format is selected, value displays X and Y according to the axes format setting. For example, for uv axes format, X represents u(n) and Y represents v(n). Evaluating u, v, and w To enter the sequence names u, v, or w, press y [u], [v], or [w]. You can evaluate these names in any of three ways. • Calculate the nth value in a sequence. • Calculate a list of values in a sequence. • Generate a sequence with u(nstart,nstop[,nstep]). nstep is optional; default is 1.
Valid Functions for Web Plots When Web axes format is selected, a sequence will not graph properly or will generate an error. • It must be recursive with only one recursion level (u(nN1) but not u(nN2)). • It cannot reference n directly. • It cannot reference any defined sequence except itself. Displaying the Graph Screen In Web format, press s to display the graph screen. The TI-84 Plus: • Draws a y=x reference line in AxesOn format.
2. It moves vertically (up or down) to the sequence. 3. It moves horizontally to the y=x reference line. 4. It repeats this vertical and horizontal movement as you continue to press ~. Using Web Plots to Illustrate Convergence Example: Convergence 1. Press o in Seq mode to display the sequence Y= editor. Make sure the graph style is set to í (dot), and then define nMin, u(n) and u(nMin) as shown below. 2. Press y . Í to set Time axes format. 3. Press p and set the variables as shown below.
5. Press y . and select the Web axes setting. 6. Press p and change the variables below. Xmin=L10 Xmax=10 7. Press s to graph the sequence. 8. Press r, and then press ~ to draw the web. The displayed cursor coordinates n, X (u(nN1)), and Y (u(n)) change accordingly. When you press ~, a new n value is displayed, and the trace cursor is on the sequence. When you press ~ again, the n value remains the same, and the cursor moves to the y=x reference line. This pattern repeats as you trace the web.
Graphing Phase Plots Graphing with uv, vw, and uw The phase-plot axes settings uv, vw, and uw show relationships between two sequences. To select a phase-plot axes setting, press y ., press ~ until the cursor is on uv, vw, or uw, and then press Í. Axes Setting x-axis y-axis uv u(n) v(n) vw v(n) w(n) uw u(n) w(n) Example: Predator-Prey Model Use the predator-prey model to determine the regional populations of a predator and its prey that would maintain population equilibrium for the two species.
W = number of foxes G = fox population growth rate with rabbits (.0002) D = fox population death rate without rabbits (.03) n = time (in months) Rn = R nN1(1+M NKW nN1) Wn = W nN1(1+GR nN1ND) 1. Press o in Seq mode to display the sequence Y= editor. Define the sequences and initial values for Rn and Wn as shown below. Enter the sequence Rn as u(n) and enter the sequence Wn as v(n). 2. Press y . Í to select Time axes format.
3. Press p and set the variables as shown below. nMin=0 nMax=400 PlotStart=1 PlotStep=1 Xmin=0 Xmax=400 Xscl=100 Ymin=0 Ymax=300 Yscl=100 4. Press s to graph the sequence. 5. Press r ~ to individually trace the number of rabbits (u(n)) and foxes (v(n)) over time (n). Note: Press a number, and then press Í to jump to a specific n value (month) while in TRACE. 6. Press y . ~ ~ Í to select uv axes format.
7. Press p and change these variables as shown below. Xmin=84 Xmax=237 Xscl=50 Ymin=25 Ymax=75 Yscl=10 8. Press r. Trace both the number of rabbits (X) and the number of foxes (Y) through 400 generations. Note: When you press r, the equation for u is displayed in the top-left corner. Press } or † to see the equation for v. Comparing TI-84 Plus and TI-82 Sequence Variables Sequences and Window Variables Refer to the table if you are familiar with the TI-82.
TI-84 Plus TI-82 v(n) Vn v(nMin) VnStart (window variable) w(n) not available w(nMin) not available In the window editor: nMin nStart nMax nMax PlotStart nMin PlotStep not available Keystroke Differences Between TI-84 Plus and TI-82 Sequence Keystroke Changes Refer to the table if you are familiar with the TI-82. It compares TI-84 Plus sequencename syntax and variable syntax with TI-82 sequence-name syntax and variable syntax.
TI-84 Plus / TI-82 On TI-84 Plus, press: On TI-82, press: v(n) / Vn y [v] £„¤ y ó ¶¦Á w(n) y [w] £„¤ u(nN1) / UnN1 y [u] £„¹À¤ yõ v(nN1) / VnN1 y [v] £„¹À¤ yö w(nN1) y [w] £„¹À¤ Chapter 6: Sequence Graphing not available not available 174
Chapter 7: Tables Getting Started: Roots of a Function Getting Started is a fast-paced introduction. Read the chapter for details. Evaluate the function Y = X3 N 2X at each integer between L10 and 10. How many sign changes occur, and at what X values? 1. Press z † † † Í to set Func graphing mode. 2. Press o. Press „ 3 to select 3. Then press ¹ 2 „ to enter the function Y1=X3N2X. 3. Press y - to display the TABLE SETUP screen. Press Ì 10 Í to set TblStart=L10. Press 1 Í to set @Tbl=1.
Press Í to select Indpnt: Auto (automatically generated independent values). Press † Í to select Depend: Auto (automatically generated dependent values). 4. Press y 0 to display the table screen. 5. Press † until you see the sign changes in the value of Y1. How many sign changes occur, and at what X values? Setting Up the Table TABLE SETUP Screen To display the TABLE SETUP screen, press y -.
TblStart, @Tbl Tbl TblStart (table start) defines the initial value for the independent variable. TblStart applies only when the independent variable is generated automatically (when Indpnt: Auto is selected). @Tbl (table step) defines the increment for the independent variable. Note: In Seq mode, both TblStart and @Tbl must be integers.
Setting Up the Table from the Home Screen or a Program To store a value to TblStart, @Tbl, or TbYZnput from the home screen or a program, select the variable name from the VARS TABLE secondary menu. TblZnput is a list of independent-variable values in the current table. When you press y - in the program editor, you can select IndpntAuto, IndpntAsk, DependAuto, and DependAsk.
3. Press Í. The cursor moves to the bottom line. Edit the function. 4. Press Í or †. The new values are calculated. The table and the Y= function are updated automatically. Note: You also can use this feature to view the function that defines a dependent variable without having to leave the table.
Displaying the Table The Table To display the table, press y 0. Note: The table abbreviates the values, if necessary. Current cell Dependent-variable values in the second and third columns Independent-variable values in the first column Current cell’s full value Independent and Dependent Variables The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1).
variable X and the dependent variables Y1 and Y2 are displayed because Func graphing mode is set. Independent Variable Graphing Mode Dependent Variable Func (function) X Y1 through Y9, and Y0 Par (parametric) T X1T/Y1T through X6T/Y6T Pol (polar) q r1 through r6 Seq (sequence) n u(n), v(n), and w(n) Clearing the Table from the Home Screen or a Program From the home screen, select the ClrTable instruction from the CATALOG. To clear the table, press Í.
values also are displayed. All dependent-variable values may not be displayed if Depend: Ask is selected. Note: You can scroll back from the value entered for TblStart. As you scroll, TblStart is updated automatically to the value shown on the top line of the table. In the example above, TblStart=0 and @Tbl=1 generates and displays values of X=0, …, 6; but you can press } to scroll back and display the table for X=M1, …, 5.
Note: To simultaneously display two dependent variables on the table that are not defined as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two you want to display. For example, to simultaneously display Y4 and Y7 on the table, go to the Y= editor and deselect Y5 and Y6.
Chapter 8: Draw Instructions Getting Started: Drawing a Tangent Line Getting Started is a fast-paced introduction. Read the chapter for details. 2 Suppose you want to find the equation of the tangent line at X = ------- for the function 2 Y=sin(X). Before you begin, select Radian and Func mode from the mode screen, if necessary. 1. Press o to display the Y= editor. Press ˜ „ ¤ to store sin(X) in Y1. 2. Press q 7 to select 7:ZTrig, which graphs the equation in the Zoom Trig window.
3. Press y < 5 to select 5:Tangent(. The tangent instruction is initiated. 4. Press y C 2 ¤ ¥ 2. 5. Press Í. The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph.
Using the DRAW Menu DRAW Menu To display the DRAW menu, press y <. The TI-84 Plus’s interpretation of these instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph. DRAW POINTS STO 1: ClrDraw Clears all drawn elements. 2: Line( Draws a line segment between 2 points. 3: Horizontal Draws a horizontal line. 4: Vertical Draws a vertical line. 5: Tangent( Draws a line segment tangent to a function. 6: DrawF Draws a function.
Before Drawing on a Graph The DRAW instructions draw on top of graphs. Therefore, before you use the DRAW instructions, consider whether you want to perform one or more of the following actions. • Change the mode settings on the mode screen. • Change the format settings on the format screen. • Enter or edit functions in the Y= editor. • Select or deselect functions in the Y= editor. • Change the window variable values. • Turn stat plots on or off. • Clear existing drawings with ClrDraw.
Clearing Drawings Clearing Drawings When a Graph Is Displayed All points, lines, and shading drawn on a graph with DRAW instructions are temporary. To clear drawings from the currently displayed graph, select 1:ClrDraw from the DRAW menu. The current graph is replotted and displayed with no drawn elements. Clearing Drawings from the Home Screen or a Program To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor.
Drawing Line Segments Drawing a Line Segment Directly on a Graph To draw a line segment when a graph is displayed, follow these steps. 1. Select 2:Line( from the DRAW menu. 2. Place the cursor on the point where you want the line segment to begin, and then press Í. 3. Move the cursor to the point where you want the line segment to end. The line is displayed as you move the cursor. Press Í. To continue drawing line segments, repeat steps 2 and 3. To cancel Line(, press ‘.
Line(X1,Y1,X2,Y2) To erase a line segment, enter Line(X1,Y1,X2,Y2,0) Drawing Horizontal and Vertical Lines Drawing a Line Directly on a Graph To draw a horizontal or vertical line when a graph is displayed, follow these steps. 1. Select 3:Horizontal or 4:Vertical from the DRAW menu. A line is displayed that moves as you move the cursor. 2. Place the cursor on the y-coordinate (for horizontal lines) or x-coordinate (for vertical lines) through which you want the drawn line to pass.
3. Press Í to draw the line on the graph. To continue drawing lines, repeat steps 2 and 3. To cancel Horizontal or Vertical, press ‘. Drawing a Line from the Home Screen or a Program Horizontal (horizontal line) draws a horizontal line at Y=y. y can be an expression but not a list. Horizontal y Vertical (vertical line) draws a vertical line at X=x. x can be an expression but not a list.
Drawing Tangent Lines Drawing a Tangent Line Directly on a Graph To draw a tangent line when a graph is displayed, follow these steps. 1. Select 5:Tangent( from the DRAW menu. 2. Press † and } to move the cursor to the function for which you want to draw the tangent line. The current graph’s Y= function is displayed in the top-left corner, if ExprOn is selected. 3. Press ~ and | or enter a number to select the point on the function at which you want to draw the tangent line. 4. Press Í.
Note: Change the fixed decimal setting on the mode screen if you want to see fewer digits displayed for X and the equation for Y. Drawing a Tangent Line from the Home Screen or a Program Tangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X2, at point X=value. X can be an expression. expression is interpreted as being in Func mode.
Drawing Functions and Inverses Drawing a Function DrawF (draw function) draws expression as a function in terms of X on the current graph. When you select 6:DrawF from the DRAW menu, the TI-84 Plus returns to the home screen or the program editor. DrawF is not interactive. DrawF expression Note: You cannot use a list in expression to draw a family of curves.
DrawInv expression Note: You cannot use a list in expression to draw a family of curves. Shading Areas on a Graph Shading a Graph To shade an area on a graph, select 7:Shade( from the DRAW menu. The instruction is pasted to the home screen or to the program editor. Shade( draws lowerfunc and upperfunc in terms of X on the current graph and shades the area that is specifically above lowerfunc and below upperfunc. Only the areas where lowerfunc < upperfunc are shaded.
pattern specifies one of four shading patterns. pattern=1 pattern=2 pattern=3 pattern=4 vertical (default) horizontal negative—slope 45¡ positive—slope 45¡ patres specifies one of eight shading resolutions.
Drawing Circles Drawing a Circle Directly on a Graph To draw a circle directly on a displayed graph using the cursor, follow these steps. 1. Select 9:Circle( from the DRAW menu. 2. Place the cursor at the center of the circle you want to draw. Press Í. 3. Move the cursor to a point on the circumference. Press Í to draw the circle on the graph. Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display.
Circle(X,Y,radius) Note: When you use Circle( on the home screen or from a program, the current window values may distort the drawn circle. Use ZSquare (Chapter 3) before drawing the circle to adjust the window variables and make the circle circular. Placing Text on a Graph Placing Text Directly on a Graph To place text on a graph when the graph is displayed, follow these steps. 1. Select 0:Text( from the DRAW menu. 2. Place the cursor where you want the text to begin. 3. Enter the characters.
Placing Text on a Graph from the Home Screen or a Program Text( places on the current graph the characters comprising value, which can include TI-84 Plus functions and instructions. The top-left corner of the first character is at pixel (row,column), where row is an integer between 0 and 57 and column is an integer between 0 and 94. Both row and column can be expressions. Text(row,column,value,value…) value can be text enclosed in quotation marks ( " ), or it can be an expression.
Using Pen to Draw on a Graph Using Pen to Draw on a Graph Pen draws directly on a graph only. You cannot execute Pen from the home screen or a program. To draw on a displayed graph, follow these steps. 1. Select A:Pen from the DRAW menu. 2. Place the cursor on the point where you want to begin drawing. Press Í to turn on the pen. 3. Move the cursor. As you move the cursor, you draw on the graph, shading one pixel at a time. 4. Press Í to turn off the pen.
Drawing Points on a Graph DRAW POINTS Menu To display the DRAW POINTS menu, press y < ~. The TI-84 Plus’s interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph. DRAW POINTS STO 1: Pt-On( Turns on a point. 2: Pt-Off( Turns off a point. 3: Pt-Change( Toggles a point on or off. 4: Pxl-On( Turns on a pixel. 5: Pxl-Off( Turns off a pixel. 6: Pxl-Change( Toggles a pixel on or off.
To continue drawing points, repeat steps 2 and 3. To cancel Pt-On(, press ‘. Erasing Points with PtPt-Off( To erase (turn off) a drawn point on a graph, follow these steps. 1. Select 2:Pt-Off( (point off) from the DRAW POINTS menu. 2. Move the cursor to the point you want to erase. 3. Press Í to erase the point. To continue erasing points, repeat steps 2 and 3. To cancel Pt-Off(, press ‘. Changing Points with PtPt-Change( To change (toggle on or off) a point on a graph, follow these steps. 1.
Drawing Points from the Home Screen or a Program Pt-On( (point on) turns on the point at (X=x,Y=y). Pt-Off( turns the point off. Pt-Change( toggles the point on or off. mark is optional; it determines the point’s appearance; specify 1, 2, or 3, where: 1 = ¦ (dot; default) 2 = › (box) 3 = + (cross) Pt-On(x,y[,mark]) Pt-Off(x,y[,mark]) Pt-Change(x,y) Note: If you specified mark to turn on a point with Pt-On(, you must specify mark when you turn off the point with Pt-Off(.
Turning On and Off Pixels with PxlPxl-On( and PxlPxl-Off( Pxl-On( (pixel on) turns on the pixel at (row,column), where row is an integer between 0 and 62 and column is an integer between 0 and 94. Pxl-Off( turns the pixel off. Pxl-Change( toggles the pixel on and off. Pxl-On(row,column) Pxl-Off(row,column) Pxl-Change(row,column) Using pxlpxl-Test( pxl-Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is turned off on the current graph.
Split Screen On a Horiz split screen, the maximum value for row is 30 for Pxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(. On a G-T split screen, the maximum value for row is 50 and the maximum value for column is 46 for Pxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(. Storing Graph Pictures (Pic) DRAW STO Menu To display the DRAW STO menu, press y < |. When you select an instruction from the DRAW STO menu, the TI-84 Plus returns to the home screen or the program editor.
Storing a Graph Picture You can store up to 10 graph pictures, each of which is an image of the current graph display, in picture variables Pic1 through Pic9, or Pic0. Later, you can superimpose the stored picture onto a displayed graph from the home screen or a program. A picture includes drawn elements, plotted functions, axes, and tick marks. The picture does not include axes labels, lower and upper bound indicators, prompts, or cursor coordinates.
1. Select 2:RecallPic from the DRAW STO menu. RecallPic is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the picture variable from which you want to recall a picture. For example, if you enter 3, the TI-84 Plus will recall the picture stored to Pic3. Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to RecallPic. 3. Press Í to display the current graph with the picture superimposed on it. Note: Pictures are drawings.
A GDB stores five elements of a graph. • Graphing mode • Window variables • Format settings • All functions in the Y= editor and the selection status of each • Graph style for each Y= function GDBs do not contain drawn items or stat plot definitions. Storing a Graph Database To store a graph database, follow these steps. 1. Select 3:StoreGDB from the DRAW STO menu. StoreGDB is pasted to the current cursor location. 2.
Recalling Graph Databases (GDB) Recalling a Graph Database CAUTION: When you recall a GDB, it replaces all existing Y= functions. Consider storing the current Y= functions to another database before recalling a stored GDB. To recall a graph database, follow these steps. 1. Select 4:RecallGDB from the DRAW STO menu. RecallGDB is pasted to the current cursor location. 2. Enter the number (from 1 to 9, or 0) of the GDB variable from which you want to recall a GDB.
Chapter 8: Draw Instructions 210
Chapter 9: Split Screen Getting Started: Exploring the Unit Circle Getting Started is a fast-paced introduction. Read the chapter for details. Use G-T (graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0¡ 30¡, 45¡, 60¡, 90¡, and so on. 1. Press z to display the mode screen. Press † † ~ Í to select Degree mode. Press † ~ Í to select Par (parametric) graphing mode.
3. Press o to display the Y= editor for Par graphing mode. Press ™ „ ¤ Í to store cos(T) to X1T. Press ÷ ˜ „ ¤ Í to store sin(T) to Y1T. 4. Press p to display the window editor. Enter these values for the window variables. Tmin=0 Xmin=L2.3 Tmax=360 Xmax=2.3 Tstep=15 Xscl=1 Ymin=L2.5 Ymax=2.5 Yscl=1 5. Press r. On the left, the unit circle is graphed parametrically in Degree mode and the trace cursor is activated.
Using Split Screen Setting a Split-Screen Mode To set a split-screen mode, press z, and then move the cursor to the next-to-last line on the mode screen. • Select Horiz (horizontal) to display the graph screen and another screen split horizontally. • Select G-T (graph-table) to display the graph screen and table screen split vertically. $ $ The split screen is activated when you press any key that applies to either half of the split screen.
If stat plots are turned on, the plots are shown along with the x-y plots in graphs. Press y 0 to make the table portion of the split screen active and to display the list data. Press † or } to highlight a value you want to edit, and then enter a new value directly in the table to overwrite the previous value. Press ~ repeatedly to display each column of data (both table and list data). Split-screen display with both x-y plots and stat plots Some screens are never displayed as split screens.
Horiz (Horizontal) Split Screen Horiz Mode In Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves. The top half displays the graph. The bottom half displays any of these editors.
• Press s or r. • Select a ZOOM or CALC operation. To use the bottom half of the split screen: • Press any key or key combination that displays the home screen. • Press o (Y= editor). • Press … Í (stat list editor). • Press p (window editor). • Press y 0 (table editor). Full Screens in Horiz Mode All other screens are displayed as full screens in Horiz split-screen mode.
The left half displays all active graphs and plots. The right half displays either table data corresponding to the graph at the left or list data corresponding to the plot at the left. Moving from Half to Half in G-T Mode To use the left half of the split screen: • Press s or r. • Select a ZOOM or CALC operation. To use the right half of the split screen, press y 0. If the values at the right are list data, these values can be edited similarly to using the Stat List Editor.
Note: When you trace in Par graphing mode, both components of an equation (XnT and YnT) are displayed in the two columns of the table. As you trace, the current value of the independent variable T is displayed on the graph. Full Screens in G-T Mode All screens other than the graph and the table are displayed as full screens in G-T splitscreen mode. To return to the G-T split screen from a full screen when in G-T mode, press any key or key combination that displays the graph or the table.
Note: Each set of numbers in parentheses above represents the row and column of a corner pixel, which is turned on. DRAW POINTS Menu Pixel Instructions For Pxl-On(, Pxl-Off(, Pxl-Change(, and pxl-Test(: • In Horiz mode, row must be {30; column must be {94. • In G-T mode, row must be {50; column must be {46. Pxl-On(row,column) DRAW Menu Text( Instruction For the Text( instruction: • In Horiz mode, row must be {25; column must be {94. • In G-T mode, row must be {45; column must be {46.
Output(row,column,"text") Note: The Output( instruction can only be used within a program. Setting a Split-Screen Mode from the Home Screen or a Program To set Horiz or G-T from a program, follow these steps. 1. Press z while the cursor is on a blank line in the program editor. 2. Select Horiz or G-T. The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution. It remains in effect after execution.
Chapter 10: Matrices Getting Started: Systems of Linear Equations Getting Started is a fast-paced introduction. Read the chapter for details. Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI-84 Plus, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form. 1. Press y . Press ~ ~ to display the MATRX EDIT menu. Press 1 to select 1: [A]. 2. Press 2 Í 4 Í to define a 2×4 matrix.
4. Press 2 Í 3 Í 3 Í to complete the first row for X + 2Y + 3Z = 3. 5. Press 2 Í 3 Í 4 Í 3 Í to enter the second row for 2X + 3Y + 4Z = 3. 6. Press y 5 to return to the home screen. If necessary, press ‘ to clear the home screen. Press y ~ to display the MATRX MATH menu. Press } to wrap to the end of the menu. Select B:rref( to copy rref( to the home screen. 7. Press y 1 to select 1: [A] from the MATRX NAMES menu. Press ¤ Í. The reduced row-echelon form of the matrix is displayed and stored in Ans.
Selecting a Matrix Before you can define or display a matrix in the editor, you first must select the matrix name. To do so, follow these steps. 1. Press y | to display the MATRX EDIT menu. The dimensions of any previously defined matrices are displayed. 2. Select the matrix you want to define. The MATRX EDIT screen is displayed. Accepting or Changing Matrix Dimensions The dimensions of the matrix (row × column) are displayed on the top line. The dimensions of a new matrix are 1 × 1.
The cursor moves to the column dimension, which you must accept or change the same way you accepted or changed the row dimension. When you press Í, the rectangular cursor moves to the first matrix element. Viewing and Editing Matrix Elements Displaying Matrix Elements After you have set the dimensions of the matrix, you can view the matrix and enter values for the matrix elements. In a new matrix, all values are zero. Select the matrix from the MATRX EDIT menu and enter or accept the dimensions.
Deleting a Matrix To delete matrices from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Viewing a Matrix The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the highlighted element is displayed on the bottom line. Select the matrix from the MATRX EDIT menu, and then enter or accept the dimensions.
Key Function Í ‘ Any entry character Switches to editing context; activates the edit cursor on the bottom line Switches to editing context; clears the value on the bottom line Switches to editing context; clears the value on the bottom line; copies the character to the bottom line y6 Nothing { Nothing Editing a Matrix Element In editing context, an edit cursor is active on the bottom line. To edit a matrix element value, follow these steps. 1.
5. Press Í, }, or † to move to another element.
Using Matrices with Expressions Using a Matrix in an Expression To use a matrix in an expression, you can do any of the following. • Copy the name from the MATRX NAMES menu. • Recall the contents of the matrix into the expression with y K (Chapter 1). • Enter the matrix directly (see below). Entering a Matrix in an Expression You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression. To enter a matrix in an expression, follow these steps. 1.
6. Press y [ ] ] to indicate the end of the matrix. Note: The closing ]] are not necessary at the end of an expression or preceding !. The resulting matrix is displayed in the form: [[element1,1,...,element1,n],...,[elementm,1,...,elementm,n]] Any expressions are evaluated when the entry is executed. Note: The commas that you must enter to separate elements are not displayed on output.
Copying One Matrix to Another To copy a matrix, follow these steps. 1. Press y > to display the MATRX NAMES menu. 2. Select the name of the matrix you want to copy. 3. Press ¿. 4. Press y > again and select the name of the new matrix to which you want to copy the existing matrix. 5. Press Í to copy the matrix to the new matrix name. Accessing a Matrix Element On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element.
[matrix](row,column) Using Math Functions with Matrices Using Math Functions with Matrices You can use many of the math functions on the TI-84 Plus keyboard, the MATH menu, the MATH NUM menu, and the MATH TEST menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same. Addition, Subtraction, Multiplication To add (Ã) or subtract (¹) matrices, the dimensions must be the same.
matrixA…matrixB Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is multiplied by value. matrix…value value…matrix Negation Negating a matrix (Ì) returns a matrix in which the sign of every element is changed (reversed).
abs( abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of each element of matrix. abs(matrix) round( round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded to 10 digits. round(matrix[,#decimals]) Inverse Use the L1 function (œ) to invert a matrix (^L1 is not valid). matrix must be square. The determinant cannot equal zero.
matrixL 1 Powers To raise a matrix to a power, matrix must be square. You can use 2 (¡), 3 (MATH menu), or ^power (›) for integer power between 0 and 255. matrix2 matrix3 matrix^power Relational Operations To compare two matrices using the relational operations = and ƒ (TEST menu), they must have the same dimensions. = and ƒ compare matrixA and matrixB on an element-byelement basis. The other relational operations are not valid with matrices.
matrixA=matrixB returns 1 if every comparison is true; it returns 0 if any comparison is false. matrixAƒmatrixB returns 1 if at least one comparison is false; it returns 0 if no comparison is false. iPart(, fPart(, int( iPart( (integer part), fPart( (fractional part), and int( (greatest integer) are on the MATH NUM menu. iPart( returns a matrix containing the integer part of each element of matrix. fPart( returns a matrix containing the fractional part of each element of matrix.
iPart(matrix) fPart(matrix) int(matrix) Using the MATRX MATH Operations MATRX MATH Menu To display the MATRX MATH menu, press y ~. NAMES MATH EDIT 1: det( Calculates the determinant. 2: T Transposes the matrix. 3: dim( Returns the matrix dimensions. 4: Fill( Fills all elements with a constant. 5: identity( Returns the identity matrix. 6: randM( Returns a random matrix. 7: augment( Appends two matrices. 8: Matr4list( Stores a matrix to a list.
NAMES MATH EDIT 9: List4matr( Stores a list to a matrix. 0: cumSum( Returns the cumulative sums of a matrix. A: ref( Returns the row-echelon form of a matrix. B: rref( Returns the reduced row-echelon form. C: rowSwap( Swaps two rows of a matrix. D: row+( Adds two rows; stores in the second row. E: …row( Multiplies the row by a number. F: …row+( Multiplies the row, adds to the second row. det( det( (determinant) returns the determinant (a real number) of a square matrix.
matrixT Accessing Matrix Dimensions with dim( dim( (dimension) returns a list containing the dimensions ({rows columns}) of matrix. dim(matrix) Note: dim(matrix)"Ln:Ln(1) returns the number of rows. dim(matrix)"Ln:Ln(2) returns the number of columns. Creating a Matrix with dim( Use dim( with ¿ to create a new matrixname of dimensions rows × columns with 0 as each element.
Redimensioning a Matrix with dim( Use dim( with ¿ to redimension an existing matrixname to dimensions rows × columns. The elements in the old matrixname that are within the new dimensions are not changed. Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted. {rows,columns}"dim(matrixname) Fill( Fill( stores value to every element in matrixname. Fill(value,matrixname) identity( identity( returns the identity matrix of dimension rows × dimension columns.
identity(dimension) randM( randM( (create random matrix) returns a rows × columns random matrix of integers ‚ L9 and 9. The seed value stored to the rand function controls the values (Chapter 2). randM(rows,columns) augment( augment( appends matrixA to matrixB as new columns. matrixA and matrixB both must have the same number of rows.
Matr4list( (matrix stored to list) fills each listname with elements from each column in matrix. Matr4list( ignores extra listname arguments. Likewise, Matr4list( ignores extra matrix columns. Matr4list(matrix,listnameA,...,listname n) Matr4list( also fills a listname with elements from a specified column# in matrix. To fill a list with a specific column from matrix, you must enter column# after matrix.
List4matr(listA,...,list n,matrixname) cumSum( cumSum( returns cumulative sums of the elements in matrix, starting with the first element. Each element is the cumulative sum of the column from top to bottom. cumSum(matrix) Row Operations MATRX MATH menu items A through F are row operations. You can use a row operation in an expression. Row operations do not change matrix in memory. You can enter all row numbers and values as expressions. You can select the matrix from the MATRX NAMES menu.
ref(, rref( ref( (row-echelon form) returns the row-echelon form of a real matrix. The number of columns must be greater than or equal to the number of rows. ref(matrix) rref( (reduced row-echelon form) returns the reduced row-echelon form of a real matrix. The number of columns must be greater than or equal to the number of rows. rref(matrix) rowSwap( rowSwap( returns a matrix. It swaps rowA and rowB of matrix.
row+( row+( (row addition) returns a matrix. It adds rowA and rowB of matrix and stores the results in rowB. row+(matrix,rowA,rowB) …row( row( …row( (row multiplication) returns a matrix. It multiplies row of matrix by value and stores the results in row. …row(value,matrix,row) …row+( row+( …row+( (row multiplication and addition) returns a matrix. It multiplies rowA of matrix by value, adds it to rowB, and stores the results in rowB.
…row+(value,matrix,rowA,rowB) Chapter 10: Matrices 245
Chapter 11: Lists Getting Started: Generating a Sequence Getting Started is a fast-paced introduction. Read the chapter for details. Calculate the first eight terms of the sequence 1/A2. Store the results to a user-created list. Then display the results in fraction form. Begin this example on a blank line on the home screen. 1. Press y 9 ~ to display the LIST OPS menu. 2. Press 5 to select 5:seq(, which pastes seq( to the current cursor location. 3.
5. Press Í to generate the list and store it in SEQ1. The list is displayed on the home screen. An ellipsis (...) indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements. 6. Press y 9 to display the LIST NAMES menu. Press 7 to select 7:seq( to paste ÙSEQ1 to the current cursor location. (If SEQ1 is not item 7 on your LIST NAMES menu, move the cursor to SEQ1 before you press Í.) 7.
Creating a List Name on the Home Screen To create a list name on the home screen, follow these steps. 1. Press y E, enter one or more list elements, and then press y F. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions. 2. Press ¿. 3. Press ƒ [letter from A to Z or q] to enter the first letter of the name. 4. Enter zero to four letters, q, or numbers to complete the name. 5. Press Í. The list is displayed on the next line.
• At an Xlist:, Ylist:, or Data List: prompt in the stat plot editor • At a List:, List1:, List2:, Freq:, Freq1:, Freq2:, XList:, or YList: prompt in the inferential stat editors • On the home screen using SetUpEditor You can create as many list names as your TI-84 Plus memory has space to store. Storing and Displaying Lists Storing Elements to a List You can store list elements in either of two ways. • Use braces and ¿ on the home screen. • Use the stat list editor (Chapter 12).
Displaying a List on the Home Screen To display the elements of a list on the home screen, enter the name of the list (preceded by Ù, if necessary, and then press Í. An ellipsis indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements. Copying One List to Another To copy a list, store it to another list. Accessing a List Element You can store a value to or recall a value from a specific list element.
Deleting a List from Memory To delete lists from memory, including L1 through L6, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Resetting memory restores L1 through L6. Removing a list from the stat list editor does not delete it from memory. Using Lists in Graphing You can use lists to graph a family of curves (Chapter 3). Entering List Names Using the LIST NAMES Menu To display the LIST NAMES menu, press y 9. Each item is a user-created list name except for L1 through L6.
Note: From the top of a menu, press } to move to the bottom. From the bottom, press † to move to the top. When you select a list name from the LIST NAMES menu, the list name is pasted to the current cursor location. • The list name symbol Ù precedes a list name when the name is pasted where nonlist name data also is valid, such as the home screen.
2. Select B:Ù, which pastes Ù to the current cursor location. Ù is not always necessary. Note: You also can paste Ù to the current cursor location from the CATALOG. 3. Enter the characters that comprise the list name. Attaching Formulas to List Names Attaching a Formula to a List Name You can attach a formula to a list name so that each list element is a result of the formula. When executed, the attached formula must resolve to a list.
For example, the first screen below shows that elements are stored to L3, and the formula L3+10 is attached to the list name ÙADD10. The quotation marks designate the formula to be attached to ÙADD10. Each element of ÙADD10 is the sum of an element in L3 and 10. The next screen shows another list, L4. The elements of L4 are the sum of the same formula that is attached to L3. However, quotation marks are not entered, so the formula is not attached to L4.
Attaching a Formula to a List on the Home Screen or in a Program To attach a formula to a list name from a blank line on the home screen or from a program, follow these steps. 1. Press ƒ [ã], enter the formula (which must resolve to a list), and press ƒ [ã] again. Note: When you include more than one list name in a formula, each list must have the same dimension. 2. Press ¿. 3. Enter the name of the list to which you want to attach the formula.
Detaching a Formula from a List You can detach (clear) an attached formula from a list in several ways. For example: • Enter ã ã !listname on the home screen. • Edit any element of a list to which a formula is attached. • Use the stat list editor (Chapter 12). • Use ClrList or ClrAllList to detach a formula from a list (Chapter 18). Using Lists in Expressions Using a List in an Expression You can use lists in an expression in any of three ways.
• Use y K to recall the contents of the list into an expression at the cursor location (Chapter 1). Note: You must paste user-created list names to the Rcl prompt by selecting them from the LIST NAMES menu. You cannot enter them directly using Ù. Using Lists with Math Functions You can use a list to input several values for some math functions. Other chapters and Appendix A specify whether a list is valid. The function is evaluated for each list element, and a list is displayed.
• When you use a list and a value with a two-argument function, the value is used with each element in the list. LIST OPS Menu LIST OPS Menu To display the LIST OPS menu, press y 9 ~. NAMES OPS MATH 1: SortA( Sorts lists in ascending order. 2: SortD( Sorts lists in descending order. 3: dim( Sets the list dimension. 4: Fill( Fills all elements with a constant. 5: seq( Creates a sequence. 6: cumSum( Returns a list of cumulative sums. 7: @List( Returns difference of successive elements.
NAMES OPS MATH 8: Select( Selects specific data points. 9: augment( Concatenates two lists. 0: List4matr( Stores a list to a matrix. A: Matr4list( Stores a matrix to a list. B: Ù Designates the list-name data type. SortA(, SortD( SortA( (sort ascending) sorts list elements from low to high values. SortD( (sort descending) sorts list elements from high to low values. Complex lists are sorted based on magnitude (modulus).
SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[,dependlist2,...,dependlist n]) Note: • In the example, 5 is the first element in L4, and 1 is the first element in L5. After SortA(L4,L5), 5 becomes the second element of L4, and likewise, 1 becomes the second element of L5. • SortA( and SortD( are the same as SortA( and SortD( on the STAT EDIT menu (Chapter 12).
Using dim( to Create a List You can use dim( with ¿ to create a new listname with dimension length from 1 to 999. The elements are zeros. length!dim(listname) Using dim( to Redimension a List You can use dim with ¿ to redimension an existing listname to dimension length from 1 to 999. • The elements in the old listname that are within the new dimension are not changed. • Extra list elements are filled by 0. • Elements in the old list that are outside the new dimension are deleted.
Fill( Fill( replaces each element in listname with value. Fill(value,listname) Note: dim( and Fill( are the same as dim( and Fill( on the MATRX MATH menu (Chapter 10). seq( seq( (sequence) returns a list in which each element is the result of the evaluation of expression with regard to variable for the values ranging from begin to end at steps of increment. variable need not be defined in memory. increment can be negative; the default value for increment is 1. seq( is not valid within expression.
cumSum( cumSum( (cumulative sum) returns the cumulative sums of the elements in list, starting with the first element. list elements can be real or complex numbers. cumSum(list) @List( List( @List( returns a list containing the differences between consecutive elements in list. @List subtracts the first element in list from the second element, subtracts the second element from the third, and so on. The list of differences is always one element shorter than the original list.
example, you can use Select( to select and then analyze a portion of plotted CBL 2™/CBL™ or CBR™ data. Select(xlistname,ylistname) Note: Before you use Select(, you must have selected (turned on) a scatter plot or xyLine plot. Also, the plot must be displayed in the current viewing window. Before Using Select( Before using Select(, follow these steps. 1. Create two list names and enter the data. 2.
2. Enter xlistname, press ¢, enter ylistname, and then press ¤ to designate list names into which you want the selected data to be stored. 3. Press Í. The graph screen is displayed with Left Bound? in the bottom-left corner. 4. Press } or † (if more than one stat plot is selected) to move the cursor onto the stat plot from which you want to select data points. 5. Press | and ~ to move the cursor to the stat plot data point that you want as the left bound. 6. Press Í.
7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press Í. The x-values and y-values of the selected points are stored in xlistname and ylistname. A new stat plot of xlistname and ylistname replaces the stat plot from which you selected data points. The list names are updated in the stat plot editor. Note: The two new lists (xlistname and ylistname) will include the points you select as left bound and right bound.
augment( augment( concatenates the elements of listA and listB. The list elements can be real or complex numbers. augment(listA,listB) List4matr( List matr( List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. If the dimensions of all lists are not equal, then List4matr( fills each extra matrixname row with 0. Complex lists are not valid. List4matr(list1,list2, ...
Matr4list( (matrix stored to lists) fills each listname with elements from each column in matrix. If the number of listname arguments exceeds the number of columns in matrix, then Matr4list( ignores extra listname arguments. Likewise, if the number of columns in matrix exceeds the number of listname arguments, then Matr4list( ignores extra matrix columns. Matr4list(matrix,listname1,listname2, . . . ,listname n) Matr4list( also fills a listname with elements from a specified column# in matrix.
Generally, Ù must precede a user-created list name when you enter a user-created list name where other input is valid, for example, on the home screen. Without the Ù, the TI-84 Plus may misinterpret a user-created list name as implied multiplication of two or more characters. Ù need not precede a user-created list name where a list name is the only valid input, for example, at the Name= prompt in the stat list editor or the Xlist: and Ylist: prompts in the stat plot editor.
min(, max( min( (minimum) and max( (maximum) return the smallest or largest element of listA. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB. For a complex list, the element with smallest or largest magnitude (modulus) is returned. min(listA[,listB]) max(listA[,listB]) Note: min( and max( are the same as min( and max( on the MATH NUM menu. mean(, median( mean( returns the mean value of list. median( returns the median value of list.
sum(, prod( sum( (summation) returns the sum of the elements in list. start and end are optional; they specify a range of elements. list elements can be real or complex numbers. prod( returns the product of all elements of list. start and end elements are optional; they specify a range of list elements. list elements can be real or complex numbers.
stdDev(, variance( stdDev( returns the standard deviation of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid. • variance( returns the variance of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid.
Chapter 12: Statistics Getting Started: Pendulum Lengths and Periods Getting Started is a fast-paced introduction. Read the chapter for details. A group of students is attempting to determine the mathematical relationship between the length of a pendulum and its period (one complete swing of a pendulum). The group makes a simple pendulum from string and washers and then suspends it from the ceiling. They record the pendulum’s period for each of 12 string lengths.
2. Press … 5 to select 5:SetUpEditor. SetUpEditor is pasted to the home screen. Press Í. This removes lists from stat list editor columns 1 through 20, and then stores lists L1 through L6 in columns 1 through 6. Note: Removing lists from the stat list editor does not delete them from memory. 3. Press … 1 to select 1:Edit from the STAT EDIT menu. The stat list editor is displayed. If elements are stored in L1 and L2, press } to move the cursor onto L1, and then press ‘ Í ~ } ‘ Í to clear both lists.
6. Press o to display the Y= editor. If necessary, press ‘ to clear the function Y1. As necessary, press }, Í, and ~ to turn off Plot1, Plot2, and Plot3 from the top line of the Y= editor (Chapter 3). As necessary, press †, |, and Í to deselect functions. 7. Press y , 1 to select 1:Plot1 from the STAT PLOTS menu. The stat plot editor is displayed for plot 1. 8. Press Í to select On, which turns on plot 1. Press † Í to select " (scatter plot). Press † y d to specify Xlist:L1 for plot 1.
Since the scatter plot of time-versus-length data appears to be approximately linear, fit a line to the data. 10. Press … ~ 4 to select 4:LinReg(ax+b) (linear regression model) from the STAT CALC menu. LinReg(ax+b) is pasted to the home screen. 11. Press y d ¢ y e ¢. Press ~ 1 to display the VARS Y-VARS FUNCTION secondary menu, and then press 1 to select 1:Y1. L1, L2, and Y1 are pasted to the home screen as arguments to LinReg(ax+b). 12. Press Í to execute LinReg(ax+b).
The regression line appears to fit the central portion of the scatter plot well. However, a residual plot may provide more information about this fit. 14. Press … 1 to select 1:Edit. The stat list editor is displayed. Press ~ and } to move the cursor onto L3. Press y 6. An unnamed column is displayed in column 3; L3, L4, L5, and L6 shift right one column. The Name= prompt is displayed in the entry line, and alpha-lock is on. 15. Press y 9 to display the LIST NAMES menu.
Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in L1. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in L1. Plotting the residuals will show this pattern more clearly. 18. Press y , 2 to select 2:Plot2 from the STAT PLOTS menu. The stat plot editor is displayed for plot 2. 19. Press Í to select On, which turns on plot 2. Press † Í to select " (scatter plot).
Notice the pattern of the residuals: a group of negative residuals, then a group of positive residuals, and then another group of negative residuals. The residual pattern indicates a curvature associated with this data set for which the linear model did not account. The residual plot emphasizes a downward curvature, so a model that curves down with the data would be more accurate. Perhaps a function such as square root would fit. Try a power regression to fit a function of the form y = a … xb. 22.
25. Press Í to calculate the power regression. Values for a and b are displayed on the home screen. The power regression equation is stored in Y1. Residuals are calculated and stored automatically in the list name RESID. 26. Press s. The regression line and the scatter plot are displayed. The new function y=.192x.522 appears to fit the data well. To get more information, examine a residual plot. 27. Press o to display the Y= editor. Press | Í to deselect Y1. Press } Í to turn off plot 1.
The new residual plot shows that the residuals are random in sign, with the residuals increasing in magnitude as the string length increases. To see the magnitudes of the residuals, continue with these steps. 29. Press r. Press ~ and | to trace the data. Observe the values for Y at each point. With this model, the largest positive residual is about 0.041 and the smallest negative residual is about L0.027. All other residuals are less than 0.02 in magnitude.
31. Press £ 20 ¤ to enter a string length of 20 cm. Press Í to calculate the predicted time of about 0.92 seconds. Based on the residual analysis, we would expect the prediction of about 0.92 seconds to be within about 0.02 seconds of the actual value. 32. Press y [ to recall the Last Entry. Press | | | 5 to change the string length to 50 cm. 33. Press Í to calculate the predicted time of about 1.48 seconds.
can store data for statistical calculations. Also, you can store data to list names that you create (Chapter 11). Setting Up a Statistical Analysis To set up a statistical analysis, follow these steps. Read the chapter for details. 1. Enter the statistical data into one or more lists. 2. Plot the data. 3. Calculate the statistical variables or fit a model to the data. 4. Graph the regression equation for the plotted data. 5. Graph the residuals list for the given regression model.
The top line displays list names. L1 through L6 are stored in columns 1 through 6 after a memory reset. The number of the current column is displayed in the top-right corner. The bottom line is the entry line. All data entry occurs on this line. The characteristics of this line change according to the current context. The center area displays up to seven elements of up to three lists; it abbreviates values when necessary. The entry line displays the full value of the current element.
2. Enter a valid list name in any of four ways. • Select a name from the LIST NAMES menu (Chapter 11). • Enter L1, L2, L3, L4, L5, or L6 from the keyboard. • Enter an existing user-created list name directly from the keyboard. • Enter a new user-created list name. 3. Press Í or † to store the list name and its elements, if any, in the current column of the stat list editor.
To begin entering, scrolling, or editing list elements, press †. The rectangular cursor is displayed. Note: If the list name you entered in step 2 already was stored in another stat list editor column, then the list and its elements, if any, move to the current column from the previous column. Remaining list names shift accordingly. Creating a Name in the Stat List Editor To create a name in the stat list editor, follow these steps. 1. Display the Name= prompt. 2.
Removing a List from the Stat List Editor To remove a list from the stat list editor, move the cursor onto the list name and then press {. The list is not deleted from memory; it is only removed from the stat list editor. Notes: • To delete a list name from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). • If you archive a list, it will be removed from the stat list editor.
• On the home screen or in the program editor, enter 0!dim(listname) to set the dimension of listname to 0 (Chapter 11). • Use ClrAllLists to clear all lists in memory (Chapter 18). Editing a List Element To edit a list element, follow these steps. 1. Move the rectangular cursor onto the element you want to edit. 2. Press Í to move the cursor to the entry line. Note: If you want to replace the current value, you can enter a new value without first pressing Í.
Note: You can enter expressions and variables for elements. 4. Press Í, }, or † to update the list. If you entered an expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element. When you edit a list element in the stat list editor, the list is updated in memory immediately.
1. Press … Í to display the stat list editor. 2. Press } to move the cursor to the top line. 3. Press | or ~, if necessary, to move the cursor onto the list name to which you want to attach the formula. Note: If a formula in quotation marks is displayed on the entry line, then a formula is already attached to the list name. To edit the formula, press Í, and then edit the formula. 4. Press ƒ ããä, enter the formula, and press ƒ ããä.
lock symbol Using the Stat List Editor When Formula-Generated Lists Are Displayed When you edit an element of a list referenced in an attached formula, the TI-84 Plus updates the corresponding element in the list to which the formula is attached (Chapter 11).
Handling Errors Resulting from Attached Formulas On the home screen, you can attach to a list a formula that references another list with dimension 0 (Chapter 11). However, you cannot display the formula-generated list in the stat list editor or on the home screen until you enter at least one element to the list that the formula references. All elements of a list referenced by an attached formula must be valid for the attached formula.
For example: • In the stat list editor, move the cursor onto the name of the list to which a formula is attached. Press Í ‘ Í. All list elements remain, but the formula is detached and the lock symbol disappears. • In the stat list editor, move the cursor onto an element of the list to which a formula is attached. Press Í, edit the element, and then press Í. The element changes, the formula is detached, and the lock symbol disappears. All other list elements remain. • Use ClrList.
Switching Stat List Editor Contexts Stat List Editor Contexts The stat list editor has four contexts. • View-elements context • View-names context • Edit-elements context • Enter-name context The stat list editor is first displayed in view-elements context. To switch through the four contexts, select 1:Edit from the STAT EDIT menu and follow these steps. 1. Press } to move the cursor onto a list name. You are now in view-names context.
4. Press Í again. You are now in edit-elements context. You may edit the current element in the entry line. 5. Press } until the cursor is on a list name, then press y 6. You are now in enter-name context. 6. Press ‘. You are now in view-names context. 7. Press †. You are now back in view-elements context.
To page down the list six elements, press ƒ †. To page up six elements, press ƒ }. To delete a list element, press {. Remaining elements shift up one row. To insert a new element, press y 6. 0 is the default value for a new element. Edit-Elements Context In edit-elements context, the data displayed in the entry line depends on the previous context. • When you switch to edit-elements context from view-elements context, the full value of the current element is displayed.
• When you switch to edit-elements context from view-names context, the full values of all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press ~ and | to edit any element in the list. Note: In edit-elements context, you can attach a formula to a list name only if you switched to it from view-names context. View-Names Context In view-names context, the entry line displays the list name and the list elements.
Enter-Name Context In enter-name context, the Name= prompt is displayed in the entry line, and alpha-lock is on. At the Name= prompt, you can create a new list name, paste a list name from L1 to L6 from the keyboard, or paste an existing list name from the LIST NAMES menu (Chapter 11). The Ù symbol is not required at the Name= prompt. To leave enter-name context without entering a list name, press ‘. The stat list editor switches to view-names context.
STAT EDIT Menu STAT EDIT Menu To display the STAT EDIT menu, press …. EDIT CALC TESTS 1: Edit... Displays the stat list editor. 2: SortA( Sorts a list in ascending order. 3: SortD( Sorts a list in descending order. 4: ClrList Deletes all elements of a list. 5: SetUpEditor Stores specified lists in the stat list editor. Note: Chapter 13: Inferential Statistics describes the STAT TESTS menu items. SortA(, SortD( SortA( (sort ascending) sorts list elements from low to high values.
keylistname. This lets you sort two-variable data on X and keep the data pairs together. All lists must have the same dimension. The sorted lists are updated in memory. SortA(listname) SortD(listname) SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[,dependlist2,...,dependlist n]) Note: SortA( and SortD( are the same as SortA( and SortD( on the LIST OPS menu. ClrList ClrList clears (deletes) from memory the elements of one or more listnames.
SetUpEditor With SetUpEditor you can set up the stat list editor to display one or more listnames in the order that you specify. You can specify zero to 20 listnames. Additionally, if you want to use listnames which happen to be archived, the SetUp Editor will automatically unarchive the listnames and place them in the stat list editor at the same time. SetUpEditor [listname1,listname2,...
Restoring L1 L1 through L6 L6 to the Stat List Editor SetUpEditor with no listnames removes all list names from the stat list editor and restores list names L1 through L6 in the stat list editor columns 1 through 6. Regression Model Features Regression Model Features STAT CALC menu items 3 through C are regression models. The automatic residual list and automatic regression equation features apply to all regression models. Diagnostics display mode applies to some regression models.
The TI-84 Plus uses the formula below to compute RESID list elements. The next section describes the variable RegEQ. RESID = Ylistname N RegEQ(Xlistname) Automatic Regression Equation Each regression model has an optional argument, regequ, for which you can specify a Y= variable such as Y1. Upon execution, the regression equation is stored automatically to the specified Y= variable and the Y= function is selected.
Note: For the regression equation, you can use the fixed-decimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit. Diagnostics Display Mode When you execute some regression models, the TI-84 Plus computes and stores diagnostics values for r (correlation coefficient) and r2 (coefficient of determination) or for R2 (coefficient of determination).
By default, these values are not displayed with the results of a regression model when you execute it. However, you can set the diagnostics display mode by executing the DiagnosticOn or DiagnosticOff instruction. Each instruction is in the CATALOG (Chapter 15). Note: To set DiagnosticOn or DiagnosticOff from the home screen, press y N, and then select the instruction for the mode you want. The instruction is pasted to the home screen. Press Í to set the mode.
STAT CALC Menu STAT CALC Menu To display the STAT CALC menu, press … ~. EDIT CALC TESTS 1: 1-Var Stats Calculates 1-variable statistics. 2: 2-Var Stats Calculates 2-variable statistics. 3: Med-Med Calculates a median-median line. 4: LinReg(ax+b) Fits a linear model to data. 5: QuadReg Fits a quadratic model to data. 6: CubicReg Fits a cubic model to data. 7: QuartReg Fits a quartic model to data. 8: LinReg(a+bx) Fits a linear model to data. 9: LnReg Fits a logarithmic model to data.
For each STAT CALC menu item, if neither Xlistname nor Ylistname is specified, then the default list names are L1 and L2. If you do not specify freqlist, then the default is 1 occurrence of each list element. Frequency of Occurrence for Data Points For most STAT CALC menu items, you can specify a list of data occurrences, or frequencies (freqlist). Each element in freqlist indicates how many times the corresponding data point or data pair occurs in the data set you are analyzing.
2-Var Stats 2-Var Stats (two-variable statistics) analyzes paired data. Xlistname is the independent variable. Ylistname is the dependent variable. Each element in freqlist is the frequency of occurrence for each data pair (Xlistname,Ylistname). 2-Var Stats [Xlistname,Ylistname,freqlist] Med-Med (ax+b) Med-Med (median-median) fits the model equation y=ax+b to the data using the median- median line (resistant line) technique, calculating the summary points x1, y1, x2, y2, x3, and y3.
LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ] QuadReg (ax2+bx+c) QuadReg (quadratic regression) fits the second-degree polynomial y=ax2+bx+c to the data. It displays values for a, b, and c; when DiagnosticOn is set, it also displays a value for R2. For three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points are required.
QuartReg [Xlistname,Ylistname,freqlist,regequ] LinReg—(a+bx) LinReg(a+bx) (linear regression) fits the model equation y=a+bx to the data using a leastsquares fit. It displays values for a (y-intercept) and b (slope); when DiagnosticOn is set, it also displays values for r2 and r. LinReg(a+bx) [Xlistname,Ylistname,freqlist,regequ] LnReg—(a+b ln(x)) LnReg (logarithmic regression) fits the model equation y=a+b ln(x) to the data using a least-squares fit and transformed values ln(x) and y.
PwrReg (power regression) fits the model equation y=axb to the data using a leastsquares fit and transformed values ln(x) and ln(y). It displays values for a and b; when DiagnosticOn is set, it also displays values for r2 and r. PwrReg [Xlistname,Ylistname,freqlist,regequ] Logistic—c/ Logistic—c/ (1+a…e (1+a e-bx) Logistic fits the model equation y=c/(1+a…eLbx) to the data using an iterative least-squares fit. It displays values for a, b, and c.
order. If you specify period, the algorithm may find a solution more quickly, or it may find a solution when it would not have found one if you had omitted a value for period. If you specify period, the differences between time values in Xlistname can be unequal. Note: The output of SinReg is always in radians, regardless of the Radian/Degree mode setting. SinReg Example: Daylight Hours in Alaska for One Year Compute the regression model for the number of hours of daylight in Alaska during one year.
With noisy data, you will achieve better convergence results when you specify an accurate estimate for period. You can obtain a period guess in either of two ways. • Plot the data and trace to determine the x-distance between the beginning and end of one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle. • Plot the data and trace to determine the x-distance between the beginning and end of N complete periods, or cycles.
2. Press the cursor navigation keys (} † | ~ ) to move the cursor to the desired location. Press Í to select the first point. 3. Press the cursor navigation keys (} † | ~ ) to move the cursor to the second location. Press Í. This displays a line containing the two points selected. The linear function is displayed. The Manual-Fit Line equation displays in the form of Y=mX+b. The current value of the first parameter (m) is highlighted in the symbolic expression.
Select y 5 to finish the Manual Fit function. The calculator stores the current mX+b expression into Y1 and makes that function active for graphing. You can also select Manual-Fit while on the Home screen. You can then enter a different Y-Var such as Y4 and then press Í. This takes you to the Graph screen and then pastes the ManualFit equation in the specified Y-Var. In this example, Y4. Statistical Variables The statistical variables are calculated and stored as indicated below.
Variables 1-Var Stats 2-Var Stats Other VARS menu population standard deviation of y sy XY sum of x … y Gxy G minimum of x values minX minX XY maximum of x values maxX maxX XY minimum of y values minY XY maximum of y values maxY XY 1st quartile median 3rd quartile regression/fit coefficients polynomial, Logistic, and SinReg coefficients correlation coefficient coefficient of determination regression equation summary points (Med-Med only) Q1 PTS Med PTS Q3 PTS a, b EQ a, b, c
Statistical Analysis in a Program Entering Stat Data You can enter statistical data, calculate statistical results, and fit models to data from a program. You can enter statistical data into lists directly within the program (Chapter 11). Statistical Calculations To perform a statistical calculation from a program, follow these steps. 1. On a blank line in the program editor, select the type of calculation from the STAT CALC menu. 2. Enter the names of the lists to use in the calculation.
Statistical Plotting Steps for Plotting Statistical Data in Lists You can plot statistical data that is stored in lists. The six types of plots available are scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal probability plot. You can define up to three plots. To plot statistical data in lists, follow these steps. 1. Store the stat data in one or more lists. 2. Select or deselect Y= functions as appropriate. 3. Define the stat plot. 4. Turn on the plots you want to display. 5.
Scatter Scatter (")plots plot the data points from Xlist and Ylist as coordinate pairs, showing each point as a box ( › ), cross ( + ), or dot ( ¦ ). Xlist and Ylist must be the same length. You can use the same list for Xlist and Ylist. xyLine xyLine (Ó)is a scatter plot in which the data points are plotted and connected in order of appearance in Xlist and Ylist. You may want to use SortA( or SortD( to sort the lists before you plot them.
Histogram Histogram (Ò) plots one-variable data. The Xscl window variable value determines the width of each bar, beginning at Xmin. ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to include all values, and also adjusts Xscl. The inequality (Xmax N Xmin) à Xscl 47 must be true. A value that occurs on the edge of a bar is counted in the bar to the right. ModBoxplot ModBoxplot (Õ) (modified box plot) plots one-variable data, like the regular box plot, except points that are 1.
in the middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom. Boxplot Boxplot (Ö)(regular box plot) plots one-variable data. The whiskers on the plot extend from the minimum data point in the set (minX) to the first quartile (Q1) and from the third quartile (Q3) to the maximum point (maxX). The box is defined by Q1, Med (median), and Q3. Box plots are plotted with respect to Xmin and Xmax, but ignore Ymin and Ymax.
NormProbPlot NormProbPlot (Ô) (normal probability plot) plots each observation X in Data List versus the corresponding quantile z of the standard normal distribution. If the plotted points lie close to a straight line, then the plot indicates that the data are normal. Enter a valid list name in the Data List field. Select X or Y for the Data Axis setting. • If you select X, the TI-84 Plus plots the data on the x-axis and the z-values on the y-axis.
1. Press y ,. The STAT PLOTS menu is displayed with the current plot definitions. 2. Select the plot you want to use. The stat plot editor is displayed for the plot you selected. 3. Press Í to select On if you want to plot the statistical data immediately. The definition is stored whether you select On or Off. 4. Select the type of plot. Each type prompts for the options checked in this table.
XList YList Mark Freq Data List Data Axis Õ ModBoxplot _ œ _ _ œ œ Ö Boxplot _ œ œ _ œ œ Ô NormProbPlot œ œ _ œ _ _ Plot Type 5. Enter list names or select options for the plot type.
Turning On and Turning Off Stat Plots PlotsOn and PlotsOff allow you to turn on or turn off stat plots from the home screen or a program. With no plot number, PlotsOn turns on all plots and PlotsOff turns off all plots. With one or more plot numbers (1, 2, and 3), PlotsOn turns on specified plots, and PlotsOff turns off specified plots. PlotsOff [1,2,3] PlotsOn [1,2,3] Note: You also can turn on and turn off stat plots in the top line of the Y= editor (Chapter 3).
Defining the Viewing Window Stat plots are displayed on the current graph. To define the viewing window, press p and enter values for the window variables. ZoomStat redefines the viewing window to display all statistical data points. Tracing a Stat Plot When you trace a scatter plot or xyLine, tracing begins at the first element in the lists. When you trace a histogram, the cursor moves from the top center of one column to the top center of the next, starting at the first column.
To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps. 1. Press y , to display the STAT PLOTS menu. 2. Select the plot to define, which pastes Plot1(, Plot2(, or Plot3( to the cursor location. 3. Press y , ~ to display the STAT TYPE menu. 4. Select the type of plot, which pastes the name of the plot type to the cursor location.
5. Press ¢. Enter the list names, separated by commas. 6. Press ¢ y , | to display the STAT PLOT MARK menu. (This step is not necessary if you selected 3:Histogram or 5:Boxplot in step 4.) Select the type of mark (› or + or ¦) for each data point. The selected mark symbol is pasted to the cursor location. 7. Press ¤ Í to complete the command line. Displaying a Stat Plot from a Program To display a plot from a program, use the DispGraph instruction (Chapter 16) or any of the ZOOM instructions (Chapter 3).
Chapter 12: Statistics 329
Chapter 13: Inferential Statistics and Distributions Getting Started: Mean Height of a Population Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to estimate the mean height of a population of women given the random sample below. Because heights among a biological population tend to be normally distributed, a t distribution confidence interval can be used when estimating the mean.
2. Enter [H] [G] [H] [T] at the Name= prompt, and then press Í. The list to which you will store the women’s height data is created. Press † to move the cursor onto the first row of the list. HGHT(1)= is displayed on the bottom line. 3. Press 169 Ë 43 to enter the first height value. As you enter it, it is displayed on the bottom line. Press Í. The value is displayed in the first row, and the rectangular cursor moves to the next row. Enter the other nine height values the same way. 4.
6. Press † to move the cursor onto Calculate, and then press Í. The confidence interval is calculated, and the TInterval results are displayed on the home screen. Interpret the results. The first line, (159.74,173.94), shows that the 99 percent confidence interval for the population mean is between about 159.74 centimeters and 173.94 centimeters. This is about a 14.2 centimeters spread. The .
of 7.1 calculated from the larger random sample. This time, use the Stats (summary statistics) input option. 7. Press … | 8 to display the inferential stat editor for TInterval. Press ~ Í to select Inpt:Stats. The editor changes so that you can enter summary statistics as input. 8. Press † 163 Ë 8 Í to store 163.8 to v. Press 7 Ë 1 Í to store 7.1 to Sx. Press 90 Í to store 90 to n. 9. Press † to move the cursor onto Calculate, and then press Í to calculate the new 99 percent confidence interval.
If the height distribution among a population of women is normally distributed with a mean m of 165.1 centimeters and a standard deviation s of 6.35 centimeters, what height is exceeded by only 5 percent of the women (the 95th percentile)? 10. Press ‘ to clear the home screen. Press y = to display the DISTR (distributions) menu. 11. Press 3 to paste invNorm( to the home screen. Press Ë 95 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤ Í. .95 is the area, 165.1 is m, and 6.35 is s.
13. Press y = ~ to display the DISTR DRAW menu. 14. Press Í to paste ShadeNorm( to the home screen. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. Ans (175.5448205 from step 11) is the lower bound. 1â99 is the upper bound. The normal curve is defined by a mean m of 165.1 and a standard deviation s of 6.35. 15. Press Í to plot and shade the normal curve. Area is the area above the 95th percentile. low is the lower bound. up is the upper bound.
according to each test or interval’s input requirements. Below is the inferential stat editor for T-Test. Note: When you select the ANOVA( instruction, it is pasted to the home screen. ANOVA( does not have an editor screen. Using an Inferential Stat Editor To use an inferential stat editor, follow these steps. 1. Select a hypothesis test or confidence interval from the STAT TESTS menu. The appropriate editor is displayed. 2. Select Data or Stats input, if the selection is available.
This chapter describes the selections in the above steps for each hypothesis test and confidence interval instruction. Select Data or Stats input Enter values for arguments Select an alternative hypothesis Select Calculate or Draw output Selecting Data or Stats Most inferential stat editors prompt you to select one of two types of input. (1-PropZInt and 2-PropZTest, 1-PropZInt and 2-PropZInt, c2-Test, c2GOF-Test, LinRegTInt, and LinRegTTest do not.) • Select Data to enter the data lists as input.
When you enter values in any inferential stat editor, the TI-84 Plus stores them in memory so that you can run many tests or intervals without having to reenter every value. Selecting an Alternative Hypothesis (ă ( < >) Most of the inferential stat editors for the hypothesis tests prompt you to select one of three alternative hypotheses. • The first is a ƒ alternative hypothesis, such as mƒm0 for the Z-Test. • The second is a < alternative hypothesis, such as m1
Selecting Calculate or Draw for a Hypothesis Test After you have entered all arguments in an inferential stat editor for a hypothesis test, you must select whether you want to see the calculated results on the home screen (Calculate) or on the graph screen (Draw). • Calculate calculates the test results and displays the outputs on the home screen. • Draw draws a graph of the test results and displays the test statistic and p-value with the graph.
Note: You can paste a hypothesis test or confidence interval instruction to a command line in a program. From within the program editor, select the instruction from either the CATALOG (Chapter 15) or the STAT TESTS menu. STAT TESTS Menu STAT TESTS Menu To display the STAT TESTS menu, press … |. When you select an inferential statistics instruction, the appropriate inferential stat editor is displayed. Most STAT TESTS instructions store some output variables to memory.
EDIT CALC TESTS 0: 2-SampTInt... Confidence interval for difference of 2 m’s, unknown s’s A: 1-PropZInt... Confidence interval for 1 proportion B: 2-PropZInt... Confidence interval for difference of 2 proportions C: c2-Test... Chi-square test for 2-way tables D: c2-GOF Test... Chi-square Goodness of Fit test E: 2-SampÛTest... Test comparing 2 s’s F: LinRegTTest... t test for regression slope and r G: LinRegTInt...
The description then shows the unique output screen for that instruction with the example results. • Descriptions of instructions that offer the Calculate/Draw output choice show both types of screens: calculated and graphic results. • Descriptions of instructions that offer only the Calculate output choice show the calculated results on the home screen.
L1={299.4 297.7 301 298.9 300.
Note: All STAT TESTS examples assume a fixed-decimal mode setting of 4 (Chapter 1). If you set the decimal mode to Float or a different fixed-decimal setting, your output may differ from the output in the examples. T-Test T-Test (one-sample t test; item 2) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown. It tests the null hypothesis H0: m=m0 against one of the alternatives below.
Data Stats Calculated results: Drawn results: 2-SampZTest 2-SampZTest (two-sample z test; item 3) tests the equality of the means of two populations (m1 and m2) based on independent samples when both population standard deviations (s1 and s2) are known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below.
In the example: LISTA={154 109 137 115 140} LISTB={108 115 126 92 146} Data Stats Input: Calculated results: Chapter 13: Inferential Statistics and Distributions 346
Data Stats Drawn results: 2-SampTTest 2-SampTTest (two-sample t test; item 4) tests the equality of the means of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is known. The null hypothesis H0: m1=m2 is tested against one of the alternatives below.
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.
Data Stats Drawn results: 1-PropZTest 1-PropZTest (one-proportion z test; item 5) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n. 1-PropZTest tests the null hypothesis H0: prop=p0 against one of the alternatives below.
Calculated results: Drawn results: 2-PropZTest 2-PropZTest (two-proportion z test; item 6) computes a test to compare the proportion of successes (p1 and p2) from two populations. It takes as input the count of successes in each sample (x1 and x2) and the count of observations in each sample (n1 and n2). 2-PropZTest tests the null hypothesis H0: p1=p2 (using the pooled sample proportion Ç) against one of the alternatives below.
• Ha: p1>p2 (p1:>p2) Input: Calculated results: Drawn results: Chapter 13: Inferential Statistics and Distributions 351
ZInterval ZInterval (one-sample z confidence interval; item 7) computes a confidence interval for an unknown population mean m when the population standard deviation s is known. The computed confidence interval depends on the user-specified confidence level. In the example: L1={299.4 297.7 301 298.9 300.
TInterval TInterval (one-sample t confidence interval; item 8) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level. In the example: L6={1.6 1.7 1.8 1.
2-SampZInt 2-SampZInt (two-sample z confidence interval; item 9) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are known. The computed confidence interval depends on the user-specified confidence level.
Data Stats Calculated results: 2-SampTInt 2-SampTInt (two-sample t confidence interval; item 0) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. The computed confidence interval depends on the user-specified confidence level.
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.
1-PropZInt 1-PropZInt (one-proportion z confidence interval; item A) computes a confidence interval for an unknown proportion of successes. It takes as input the count of successes in the sample x and the count of observations in the sample n. The computed confidence interval depends on the user-specified confidence level.
observations in each sample (n1 and n2). The computed confidence interval depends on the user-specified confidence level. Input: Calculated results: c2-Test c2-Test (chi-square test; item C) computes a chi-square test for association on the twoway table of counts in the specified Observed matrix. The null hypothesis H 0 for a two-way table is: no association exists between row variables and column variables. The alternative hypothesis is: the variables are related.
Expected: prompt, enter the matrix variable name to which you want the computed expected counts to be stored; default=[B]. Matrix editor: Note: Press y ú ~ ~ 1 to select 1:[A] from the MATRX EDIT menu. Input: Note: Press y ú †] Í to display matrix [B].
Drawn results: c2GOF-Test c2GOF-Test (Chi Square Goodness of Fit; item D) performs a test to confirm that sample data is from a population that conforms to a specified distribution. For example, c2 GOF can confirm that the sample data came from a normal distribution. In the example: list 1={16,25,22,8,10} list 2={16.2,21.6,16.2,14.4,12.6} The Chi-square Goodness of Fit input screen: Note: Press … ~ ~ to select TESTS. Press † several times to select D:X2GOF-Test... Press Í.
Calculated results: Drawn results: 2-SampFTest 2-SampÜTest (two-sample Ü-test; item E) computes an Ü-test to compare two normal population standard deviations (s1 and s2). The population means and standard deviations are all unknown. 2-SampÜTest, which uses the ratio of sample variances Sx12/Sx22, tests the null hypothesis H0: s1=s2 against one of the alternatives below.
In the example: SAMP4={ SAMP5={ 7 L1 L4 12 18 L1 17 L3 L3 3 L5 L5 Data 1 5 10 2 11 L11 L2} L1 L3} Stats Input: Calculated results: Chapter 13: Inferential Statistics and Distributions 362
Data Stats Drawn results: LinRegTTest LinRegTTest (linear regression t test; item F) computes a linear regression on the given data and a t test on the value of slope b and the correlation coefficient r for the equation y=a+bx. It tests the null hypothesis H0: b=0 (equivalently, r=0) against one of the alternatives below.
Input: Calculated results: When LinRegTTest is executed, the list of residuals is created and stored to the list name RESID automatically. RESID is placed on the LIST NAMES menu. Note: For the regression equation, you can use the fix-decimal mode setting to control the number of digits stored after the decimal point (Chapter 1). However, limiting the number of digits to a small number could affect the accuracy of the fit.
LinRegTInt LinRegTInt computes a linear regression T confidence interval for the slope coefficient b. If the confidence interval contains 0, this is insufficient evidence to indicate that the data exhibits a linear relationship. In the example: list 1={4, 5, 6, 7, 8} list 2={1, 2, 3, 3.5, 4.5} LinRegTInt input screen: Note: Press … ~ ~ to select TESTS. Press † several times to select G:LinRegTint... Press Í. Press † several times to select Calculate. Press Í.
Xlist, Ylist is the list of independent and dependent variables. The list containing the Freq (frequency) values for the data is stored in List. The default is 1. All elements must be real numbers. Each element in the Freq list is the frequency of occurence for each corresponding data point in the input list specified in the List fields. RegEQ (optional) is the designated Yn variable for storing the regression equation. StoreRegEqn (optional) is the designated variable for storing the regression equation.
Calculated results: Note: SS is sum of squares and MS is mean square. Inferential Statistics Input Descriptions The tables in this section describe the inferential statistics inputs discussed in this chapter. You enter values for these inputs in the inferential stat editors. The tables present the inputs in the same order that they appear in this chapter. Input Description m0 Hypothesized value of the population mean that you are testing.
Input Description List The name of the list containing the data you are testing. Freq The name of the list containing the frequency values for the data in List. Default=1. All elements must be integers | 0. Calculate/Draw Determines the type of output to generate for tests and intervals. Calculate displays the output on the home screen. In tests, Draw draws a graph of the results. v, Sx, n Summary statistics (mean, standard deviation, and sample size) for the one-sample tests and intervals.
Input Description p0 The expected sample proportion for 1-PropZTest. Must be a real number, such that 0 < p0 < 1. x The count of successes in the sample for the 1-PropZTest and 1-PropZInt. Must be an integer | 0. n The count of observations in the sample for the 1-PropZTest and 1-PropZInt. Must be an integer > 0. x1 The count of successes from sample one for the 2-PropZTest and 2-PropZInt. Must be an integer | 0. x2 The count of successes from sample two for the 2-PropZTest and 2-PropZInt.
Input Description df df (degree of freedom) represents (number of sample categories) - (number of estimated parameters for the selected distribution + 1). Xlist, Ylist The names of the lists containing the data for LinRegTTest and LinRegTInt. Defaults are L1 and L2, respectively. The dimensions of Xlist and Ylist must be the same. RegEQ The prompt for the name of the Y= variable where the calculated regression equation is to be stored.
LinRegTTest, ANOVA VARS Menu Variables Tests Intervals number of data points for sample 1 and sample 2 n1, n2 n1, n2 SxP SxP ‚Ç ‚Ç TEST ‚Ç1 ‚Ç1 TEST ‚Ç2 ‚Ç2 TEST pooled standard deviation estimated sample proportion estimated sample proportion for population 1 estimated sample proportion for population 2 confidence interval pair mean of x values sample standard deviation of x number of data points TEST SxP TEST lower, upper TEST v v XY Sx Sx XY n n XY standard error about th
Distribution Functions DISTR menu To display the DISTR menu, press y =.
DISTR DRAW B: binomcdf( Binomial cumulative density C: poissonpdf( Poisson probability D: poissoncdf( Poisson cumulative density E: geometpdf( Geometric probability F: geometcdf( Geometric cumulative density Note: L1â99 and 1â99 specify infinity. If you want to view the area left of upperbound, for example, specify lowerbound= L1â99. normalpdf( normalpdf( computes the probability density function (pdf) for the normal distribution at a specified x value.
normalpdf(x[,m,s]) Note: For this example, Xmin = 28 Xmax = 42 Ymin = 0 Ymax = .2 Xscl = 1 Yscl = .1 Note: For plotting the normal distribution, you can set window variables Xmin and Xmax so that the mean m falls between them, and then select 0:ZoomFit from the ZOOM menu. normalcdf( normalcdf( computes the normal distribution probability between lowerbound and upperbound for the specified mean m and standard deviation s. The defaults are m=0 and s=1.
invNorm( invNorm( computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean m and standard deviation s. It calculates the x value associated with an area to the left of the x value. 0 area 1 must be true. The defaults are m=0 and s=1. invNorm(area[,m,s]) invT( invT( computes the inverse cumulative Student-t probability function specified by Degree of Freedom, df for a given Area under the curve.
tpdf( tpdf( computes the probability density function (pdf) for the Student-t distribution at a specified x value. df (degrees of freedom) must be > 0. To plot the Student-t distribution, paste tpdf( to the Y= editor. The probability density function (pdf) is: Γ [ ( df + 1 )/2 ] f ( x ) = --------------------------------Γ ( df ⁄ 2 ) 2 – ( df + 1 )/2 ( 1 + x /df ) ------------------------------------------------πdf tpdf(x,df) Note: For this example, Xmin = L4.5 Xmax = 4.5 Ymin = 0 Ymax = .
c2pdf( c2pdf( computes the probability density function (pdf) for the c2 (chi-square) distribution at a specified x value. df (degrees of freedom) must be an integer > 0. To plot the c2 distribution, paste c2pdf( to the Y= editor. The probability density function (pdf) is: df/2 df ⁄ 2 – 1 – x/2 1 f ( x ) = -------------------- ( 1/2 ) x e ,x ≥ 0 Γ ( df ⁄ 2 ) c2pdf(x,df) Note: For this example, Xmin = 0 Xmax = 30 Ymin = L.02 Ymax = .
c2cdf( c2cdf( computes the c2 (chi-square) distribution probability between lowerbound and upperbound for the specified df (degrees of freedom), which must be an integer > 0. c2cdf(lowerbound,upperbound,df) Fpdf( Üpdf( computes the probability density function (pdf) for the Ü distribution at a specified x value. numerator df (degrees of freedom) and denominator df must be integers > 0. To plot the Ü distribution, paste Üpdf( to the Y= editor.
Üpdf(x,numerator df,denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = 0 Ymax = 1 Fcdf( Ücdf( computes the Ü distribution probability between lowerbound and upperbound for the specified numerator df (degrees of freedom) and denominator df. numerator df and denominator df must be integers > 0.
of integers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of probabilities from 0 to numtrials is returned. The probability density function (pdf) is: n–x n x f(x) = ⎛ ⎞ p (1 – p) ,x = 0,1,...,n ⎝x ⎠ where n = numtrials binompdf(numtrials,p[,x]) binomcdf( binomcdf( computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability of success (p) on each trial. x can be a real number or a list of real numbers.
poissonpdf( poissonpdf( computes a probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be an integer or a list of integers. The probability density function (pdf) is: –µ x f ( x ) = e µ ⁄ x! ,x = 0,1,2,... poissonpdf(m,x) poissoncdf( poissoncdf( computes a cumulative probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be a real number or a list of real numbers.
0p1 must be true. x can be an integer or a list of integers. The probability density function (pdf) is: f(x) = p(1 – p) x–1 ,x = 1,2,... geometpdf(p,x) geometcdf( geometcdf( computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p. 0p1 must be true. x can be a real number or a list of real numbers.
To clear the drawings, select 1:ClrDraw from the DRAW menu (Chapter 8). Note: Before you execute a DISTR DRAW instruction, you must set the window variables so that the desired distribution fits the screen. DISTR DRAW 1: ShadeNorm( Shades normal distribution. 2: Shade_t( Shades Student-t distribution. 3: Shadec2( Shades c2 distribution. 4: ShadeÜ( Shades Üdistribution. Note: L1â99 and 1â99 specify infinity. If you want to view the area left of upperbound, for example, specify lowerbound=L1â99.
ShadeNorm(lowerbound,upperbound[,m,s]) Note: For this example, Xmin = 55 Xmax = 72 Ymin = L.05 Ymax = .2 Shade_t( Shade_t( draws the density function for the Student-t distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. Shade_t(lowerbound,upperbound,df) Note: For this example, Xmin = L3 Xmax = 3 Ymin = L.15 Ymax = .
Shadec Shade 2( Shadec2( draws the density function for the c2 (chi-square) distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. Shadec2(lowerbound,upperbound,df) Note: For this example, Xmin = 0 Xmax = 35 Ymin = L.025 Ymax = .1 ShadeF( ShadeÜ( draws the density function for the Ü distribution specified by numerator df (degrees of freedom) and denominator df and shades the area between lowerbound and upperbound.
ShadeÜ(lowerbound,upperbound,numerator df,denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = L.25 Ymax = .
Chapter 14: Applications The Applications Menu The TI-84 Plus comes with Finance and EasyData App and several other applications already listed on the APPLICATIONS menu. Except for the Finance application, you can add and remove applications as space permits. The Finance application is built into the TI-84 Plus code and cannot be deleted. You can buy additional TI-84 Plus software applications that allow you to customize further your calculator’s functionality. The calculator reserves 1.
2. Select from list of functions. Getting Started: Financing a Car Getting Started is a fast-paced introduction. Read the chapter for details. You have found a car you would like to buy. The car costs 9,000. You can afford payments of 250 per month for four years. What annual percentage rate (APR) will make it possible for you to afford the car? 1. Press z † ~ ~ ~ Í to set the fixed-decimal mode setting to 2. The TI-84 Plus will display all numbers with two decimal places). 2.
3. Press Í to select 1:TVM Solver from the CALC VARS menu. The TVM Solver is displayed. Press 48 Í to store 48 months to Ú. Press † 9000 Í to store 9,000 to PV. Press Ì 250 Í to store L250 to PMT. (Negation indicates cash outflow.) Press 0 Í to store 0 to FV. Press 12 Í to store 12 payments per year to P/Y and 12 compounding periods per year to C/Y. Setting P/Y to 12 will compute an annual percentage rate (compounded monthly) for æ.
Note: Because there are no payments when you solve compound interest problems, PMT must be set to 0 and P/Y must be set to 1. 1. Press Œ Í to select 1:Finance from the APPLICATIONS menu. 2. Press Í to select 1:TVM Solver from the CALC VARS menu. The TVM Solver is displayed. Press 7 to enter the number of periods in years. Press † † Ì 1250 to enter the present value as a cash outflow (investment). Press † 0 to specify no payments. Press † 2000 to enter the future value as a cash inflow (return).
Using the TVM Solver Using the TVM Solver The TVM Solver displays the time-value-of-money (TVM) variables. Given four variable values, the TVM Solver solves for the fifth variable. The FINANCE VARS menu section describes the five TVM variables (Ú, æ, PV, PMT, and FV) and P/Y and C/Y. PMT: END BEGIN in the TVM Solver corresponds to the FINANCE CALC menu items Pmt_End (payment at the end of each period) and Pmt_Bgn (payment at the beginning of each period).
3. Enter a value for P/Y, which automatically enters the same value for C/Y; if P/Y ƒ C/Y, enter a unique value for C/Y. 4. Select END or BEGIN to specify the payment method. 5. Place the cursor on the TVM variable for which you want to solve. 6. Press ƒ \. The answer is computed, displayed in the TVM Solver, and stored to the appropriate TVM variable. An indicator square in the left column designates the solution variable.
FINANCE CALC Menu To display the FINANCE CALC menu, press ÎŒ Í. CALC VARS 1: TVM Solver... Displays the TVM Solver. 2: tvm_Pmt Computes the amount of each payment. 3: tvm_¾¾æ Computes the interest rate per year. 4: tvm_PV Computes the present value. 5: tvm_òòÚ Computes the number of payment periods. 6: tvm_FV Computes the future value. 7: npv( Computes the net present value. 8: irr( Computes the internal rate of return. 9: bal( Computes the amortization sched. balance.
TVM Solver TVM Solver displays the TVM Solver. Calculating Time Value of Money (TVM) Calculating Time Value of Money Use time-value-of-money (TVM) functions (menu items 2 through 6) to analyze financial instruments such as annuities, loans, mortgages, leases, and savings. Each TVM function takes zero to six arguments, which must be real numbers. The values that you specify as arguments for TVM functions are not stored to the TVM variables.
tvm_Pmt[(òÚ,¾æ,PV,FV,P/Y,C/Y)] Note: In the example above, the values are stored to the TVM variables in the TVM Solver. Then the payment (tvm_Pmt) is computed on the home screen using the values in the TVM Solver. Next, the interest rate is changed to 9.5 to illustrate the effect on the payment amount. tvm_I% tvm_æ computes the annual interest rate. tvm_¾æ [(Ú,PV,PMT,FV,P/Y,C/Y)] tvm_PV tvm_PV computes the present value.
tvm_PV[(Ú,¾æ,PMT,FV,P/Y,C/Y)] tvm_N tvm_Ú computes the number of payment periods. tvm_Ú[(æ¾,PV,PMT,FV,P/Y,C/Y)] tvm_FV tvm_FV computes the future value.
Calculating Cash Flows Calculating a Cash Flow Use the cash flow functions (menu items 7 and 8) to analyze the value of money over equal time periods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntax descriptions for npv( and irr( use these arguments. • interest rate is the rate by which to discount the cash flows (the cost of money) over one period. • CF0 is the initial cash flow at time 0; it must be a real number.
npv(, irr( npv( (net present value) is the sum of the present values for the cash inflows and outflows. A positive result for npv indicates a profitable investment. npv(interest rate,CF0,CFList[,CFFreq]) irr( (internal rate of return) is the interest rate at which the net present value of the cash flows is equal to zero.
Calculating Amortization Calculating an Amortization Schedule Use the amortization functions (menu items 9, 0, and A) to calculate balance, sum of principal, and sum of interest for an amortization schedule. bal( bal( computes the balance for an amortization schedule using stored values for æ, PV, and PMT. npmt is the number of the payment at which you want to calculate a balance. It must be a positive integer < 10,000.
Note: You must enter values for æ, PV, PMT, and before computing the principal. GPrn(pmt1,pmt2[,roundvalue]) GInt( computes the sum of the interest during a specified period for an amortization schedule using stored values for ¾æ, PV, and PMT. pmt1 is the starting payment. pmt2 is the ending payment in the range. pmt1 and pmt2 must be positive integers < 10,000.
2. Press Î Œ Í Í to display the TVM Solver. 3. Press 360 to enter number of payments. Press † 8 to enter the interest rate. Press † † Ì 800 to enter the payment amount. Press † 0 to enter the future value of the mortgage. Press † 12 to enter the payments per year, which also sets the compounding periods per year to 12. Press † † Í to select PMT:END. 4. Press } } } } } to place the cursor on the PV prompt. Press ƒ \ to solve for the present value. 5. Press o to display the parametric Y= editor.
8. Press y - and enter the values below. TblStart=0 @Tbl=12 9. Press y 0 to display the table of outstanding balances (Y1T). 10. Press z † † † † † † † ~ ~ Í to select G-T split-screen mode, in which the graph and table are displayed simultaneously. Press r to display X1T (time) and Y1T (balance) in the table.
4Nom( computes the nominal interest rate. effective rate and compounding periods must be real numbers. compounding periods must be >0. 4Nom(effective rate,compounding periods) 4Eff( Eff( 4Eff( computes the effective interest rate. nominal rate and compounding periods must be real numbers. compounding periods must be >0.
dbd(date1,date2) You can enter date1 and date2 in either of two formats. • MM.DDYY (United States) • DDMM.YY (Europe) The decimal placement differentiates the date formats. Defining the Payment Method Pmt_End and Pmt_Bgn (menu items E and F) specify a transaction as an ordinary annuity or an annuity due. When you execute either command, the TVM Solver is updated. Pmt_End Pmt_End (payment end) specifies an ordinary annuity, where payments occur at the end of each payment period.
Pmt_Bgn Pmt_Bgn (payment beginning) specifies an annuity due, where payments occur at the beginning of each payment period. Most leases are in this category. Pmt_Bgn On the TVM Solver’s PMT:END BEGIN line, select BEGIN to set PMT to annuity due. Using the TVM Variables FINANCE VARS Menu To display the FINANCE VARS menu, press Î Œ Í ~. You can use TVM variables in TVM functions and store values to them on the home screen.
N, I%, PV, PMT, FV Ú, æ, PV, PMT, and FV are the five TVM variables. They represent the elements of common financial transactions, as described in the table above. æ is an annual interest rate that is converted to a per-period rate based on the values of P/Y and C/Y. P/Y and C/Y P/Y is the number of payment periods per year in a financial transaction. C/Y is the number of compounding periods per year in the same transaction.
Steps for Running the EasyData App Follow these basic steps when using the EasyData App. Starting EasyData 1. Attach your data collection device to your TI-84 Plus. Make sure the cables are firmly connected. 2. If the EasyData app has not auto-launched, press Œ and the } or † to select the EasyData App. 3. Press Í. The EasyData information screen is displayed for about three seconds followed by the main screen. Quitting EasyData 1. To quit EasyData, select Quit (press s).
To change a predefined setting: 1. From the main screen in the EasyData App, choose Setup and select 2: Time Graph. The current settings are displayed on the calculator. Note: If using a motion detector, settings for 3: Distance Match and 4: Ball Bounce in the Setup menu are preset and cannot be changed. 2. Select Next (press q) to move to the setting you want to change. Press ‘ to clear a setting. 3. Repeat to cycle through the available options.
Starting and Stopping Data Collection Starting Data Collection To start sampling, select Start (press q). Sampling will automatically stop when the number of samples set in the Time Graph Settings menu is reached. The TI-84 Plus will then display a graph of the sampled data. Stopping Data Collection To stop sampling before it automatically stops, select Stop (press and hold q) at any time during the sampling process. When sampling stops, a graph of the sampled data is displayed.
Chapter 14: Applications 410
Chapter 15: CATALOG, Strings, Hyperbolic Functions Browsing the TI-84 Plus CATALOG What Is the CATALOG? The CATALOG is an alphabetical list of all functions and instructions on the TI-84 Plus.
The 4 in the first column is the selection cursor. 2. Press † or } to scroll the CATALOG until the selection cursor points to the item you want. • To jump to the first item beginning with a particular letter, press that letter; alphalock is on. • Items that begin with a number are in alphabetical order according to the first letter after the number. For example, 2-PropZTest( is among the items that begin with the letter P.
Entering and Using Strings What Is a String? A string is a sequence of characters that you enclose within quotation marks. On the TI-84 Plus, a string has two primary applications. • It defines text to be displayed in a program. • It accepts input from the keyboard in a program. Characters are the units that you combine to form a string. • Count each number, letter, and space as one character.
3. Press ƒ [ã] to indicate the end of the string. ãstringã 4. Press Í. On the home screen, the string is displayed on the next line without quotations. An ellipsis (...) indicates that the string continues beyond the screen. To scroll the entire string, press ~ and |. Note: Quotation marks do not count as string characters. Storing Strings to String Variables String Variables The TI-84 Plus has 10 variables to which you can store strings.
2. Press Í to display the STRING secondary menu. Storing a String to a String Variable To store a string to a string variable, follow these steps. 1. Press ƒ [ã], enter the string, and press ƒ [ã]. 2. Press ¿. 3. Press 7 to display the VARS STRING menu. 4. Select the string variable (from Str1 to Str9, or Str0) to which you want to store the string. The string variable is pasted to the current cursor location, next to the store symbol (!).
5. Press Í to store the string to the string variable. On the home screen, the stored string is displayed on the next line without quotation marks. Displaying the Contents of a String Variable To display the contents of a string variable on the home screen, select the string variable from the VARS STRING menu, and then press Í. The string is displayed.
other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... Equ4String( Converts an equation to a string. expr( Converts a string to an expression. ... inString( Returns a character’s place number. ... length( Returns a string’s character length. ... String4Equ( Converts a string to an equation. sub( Returns a string subset as a string. ... Concatenation To concatenate two or more strings, follow these steps. 1.
3. Enter string2, which can be a string or string name. If necessary, press à and enter string3, and so on. string1+string2+string3... 4. Press Í to display the strings as a single string. Selecting a String Function from the CATALOG To select a string function or instruction and paste it to the current screen, follow the steps for selecting an item from the CATALOG. Equ4String( Equ String( Equ4String( converts to a string an equation that is stored to any VARS Y-VARS variable. Yn contains the equation.
expr( expr( converts the character string contained in string to an expression and executes it. string can be a string or a string variable. expr(string) inString( inString( returns the character position in string of the first character of substring. string can be a string or a string variable. start is an optional character position at which to start the search; the default is 1.
length( length( returns the number of characters in string. string can be a string or string variable. Note: An instruction or function name, such as sin( or cos(, counts as one character. length(string) String4Equ( String Equ( String4Equ( converts string into an equation and stores the equation to Yn. string can be a string or string variable. String4Equ( is the inverse of Equ4String(.
sub( sub( returns a string that is a subset of an existing string. string can be a string or a string variable. begin is the position number of the first character of the subset. length is the number of characters in the subset. sub(string,begin,length) Entering a Function to Graph during Program Execution In a program, you can enter a function to graph during program execution using these commands.
Note: When you execute this program, enter a function to store to Y3 at the ENTRY= prompt. Hyperbolic Functions in the CATALOG Hyperbolic Functions The hyperbolic functions are available only from the CATALOG. The table below lists the hyperbolic functions in the order in which they appear among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... cosh( Hyperbolic cosine cosh-1( Hyperbolic arccosine ...
CATALOG sinh-1( Hyperbolic arcsine ... tanh( Hyperbolic tangent tanh-1( Hyperbolic arctangent ... sinh(, cosh(, tanh( sinh(, cosh(, and tanh( are the hyperbolic functions. Each is valid for real numbers, expressions, and lists. sinh(value) cosh(value) tanh(value) sinh-1(, cosh-1(, tanh-1( sinh-1( is the hyperbolic arcsine function. cosh-1( is the hyperbolic arccosine function. tanh-1( is the hyperbolic arctangent function. Each is valid for real numbers, expressions, and lists.
sinh-1(value) cosh-1(value) sinh-1(value) Chapter 15: CATALOG, Strings, Hyperbolic Functions 424
Chapter 16: Programming Getting Started: Volume of a Cylinder Getting Started is a fast-paced introduction. Read the chapter for details. A program is a set of commands that the TI-84 Plus executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume. 1. Press ~ ~ to display the PRGM NEW menu. 2. Press Í to select 1:Create New. The Name= prompt is displayed, and alpha-lock is on.
3. Press ~ 2 to select 2:Prompt from the PRGM I/O menu. Prompt is copied to the command line. Press ƒ [R] ¢ ƒ [H] to enter the variable names for radius and height. Press Í. 4. Press y B ƒ [R] ¡ ƒ [H] ¿ ƒ [V] Í to enter the expression pR 2H and store it to the variable V. 5. Press ~ 3 to select 3:Disp from the PRGM I/O menu. Disp is pasted to the command line.
8. Press Í to paste prgmCYLINDER to the current cursor location. (If CYLINDER is not item 1 on your PRGM EXEC menu, move the cursor to CYLINDER before you press Í.) 9. Press Í to execute the program. Enter 1.5 for the radius, and then press Í. Enter 3 for the height, and then press Í. The text VOLUME IS, the value of V, and Done are displayed. Repeat steps 7 through 9 and enter different values for R and H. Creating and Deleting Programs What Is a Program? A program is a set of one or more command lines.
2. Press Í to select 1:Create New. The Name= prompt is displayed, and alpha-lock is on. 3. Press a letter from A to Z or q to enter the first character of the new program name. Note: A program name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q. 4. Enter zero to seven letters, numbers, or q to complete the new program name. 5. Press Í. The program editor is displayed. 6.
The TI-84 Plus expresses memory quantities in bytes. You can increase available memory in one of two ways. You can delete one or more programs or you can archive some programs. To increase available memory by deleting a specific program: 1. Press y L and then select 2:Mem Mgmt/Del from the MEMORY menu. 2. Select 7:Prgm to display the PRGM editor (Chapter 18). 3. Press } and † to move the selection cursor (4) next to the program you want to delete, and then press {. The program is deleted from memory.
4. Press y L and then select 2:Mem Mgmt/Del from the MEMORY menu. 5. Select 2:Mem Mgmt/Del to display the MEM MGMT/DEL menu. 6. Select 7:Prgm... to display the PRGM menu. 7. Press Í to archive the program. An asterisk will appear to the left of the program to indicate it is an archived program. To unarchive a program in this screen, put the cursor next to the archived program and press Í. The asterisk will disappear. Note: Archive programs cannot be edited or executed.
While in the program editor, you can display and select from menus. You can return to the program editor from a menu in either of two ways. • Select a menu item, which pastes the item to the current command line. • Press ‘. When you complete a command line, press Í. The cursor moves to the next command line. Programs can access variables, lists, matrices, and strings saved in memory.
The TI-84 Plus checks for errors during program execution. It does not check for errors as you enter a program. Breaking a Program To stop program execution, press É. The ERR:BREAK menu is displayed. • To return to the home screen, select 1:Quit. • To go where the interruption occurred, select 2:Goto. Editing Programs Editing a Program To edit a stored program, follow these steps. 1. Press ~ to display the PRGM EDIT menu. 2. Select a program name from the PRGM EDIT menu.
Note: To move the cursor to the beginning of a command line, press y |; to move to the end, press y ~. To scroll the cursor down seven command lines, press ƒ †. To scroll the cursor up seven command lines, press ƒ }. Inserting and Deleting Command Lines To insert a new command line anywhere in the program, place the cursor where you want the new line, press y 6, and then press Í. A colon indicates a new line.
Copying programs has at least two convenient applications. • You can create a template for groups of instructions that you use frequently. • You can rename a program by copying its contents into a new program. Note: You also can copy all the command lines from one existing program to another existing program using RCL. Scrolling the PRGM EXEC and PRGM EDIT Menus The TI-84 Plus sorts PRGM EXEC and PRGM EDIT menu items automatically into alphanumerical order.
PRGM CTL (Control) Instructions PRGM CTL Menu To display the PRGM CTL (program control) menu, press from the program editor only. CTL I/O EXEC 1: If Creates a conditional test. 2: Then Executes commands when If is true. 3: Else Executes commands when If is false. 4: For( Creates an incrementing loop. 5: While Creates a conditional loop. 6: Repeat Creates a conditional loop. 7: End Signifies the end of a block. 8: Pause Pauses program execution. 9: Lbl Defines a label.
CTL I/O EXEC D: prgm Executes a program as a subroutine. E: Return Returns from a subroutine. F: Stop Stops execution. G: DelVar Deletes a variable from within program. H: GraphStyle( Designates the graph style to be drawn. These menu items direct the flow of an executing program. They make it easy to repeat or skip a group of commands during program execution. When you select an item from the menu, the name is pasted to the cursor location on a command line in the program.
If Use If for testing and branching. If condition is false (zero), then the command immediately following If is skipped. If condition is true (nonzero), then the next command is executed. If instructions can be nested. :If condition :command (if true) :command Program Output If-Then Then following an If executes a group of commands if condition is true (nonzero). End identifies the end of the group of commands.
:End :command Program Output If-Then-Else Else following If-Then executes a group of commands if condition is false (zero). End identifies the end of the group of commands.
For( For( loops and increments. It increments variable from begin to end by increment. increment is optional (default is 1) and can be negative (end
While While performs a group of commands while condition is true. condition is frequently a relational test (Chapter 2). condition is tested when While is encountered. If condition is true (nonzero), the program executes a group of commands. End signifies the end of the group. When condition is false (zero), the program executes each command following End. While instructions can be nested.
:command (until condition is true) :End :command Program Output End End identifies the end of a group of commands. You must include an End instruction at the end of each For(, While, or Repeat loop. Also, you must paste an End instruction at the end of each If-Then group and each If-Then-Else group. Pause Pause suspends execution of the program so that you can see answers or graphs. During the pause, the pause indicator is on in the top-right corner. Press Í to resume execution.
Pause [value] Program Output Lbl, Goto Lbl (label) and Goto (go to) are used together for branching. Lbl specifies the label for a command. label can be one or two characters (A through Z, 0 through 99, or q). Lbl label Goto causes the program to branch to label when Goto is encountered.
Goto label Program Output IS>( IS>( (increment and skip) adds 1 to variable. If the answer is > value (which can be an expression), the next command is skipped; if the answer is { value, the next command is executed. variable cannot be a system variable. :IS>(variable,value) :command (if answer value) :command (if answer > value) Program Output Note: IS>( is not a looping instruction.
DS<( DS<( (decrement and skip) subtracts 1 from variable. If the answer is < value (which can be an expression), the next command is skipped; if the answer is | value, the next command is executed. variable cannot be a system variable. :DS<(variable,value) :command (if answer ‚ value) :command (if answer < value) Program Output Note: DS<( is not a looping instruction. Menu( Menu( sets up branching within a program.
Menu("title","text1",label1,"text2",label2, . . .) Program Output The program above pauses until you select 1 or 2. If you select 2, for example, the menu disappears and the program continues execution at Lbl B. prgm Use prgm to execute other programs as subroutines. When you select prgm, it is pasted to the cursor location. Enter characters to spell a program name.
Stop Stop stops execution of a program and returns to the home screen. Stop is optional at the end of a program. DelVar DelVar deletes from memory the contents of variable. DelVar variable GraphStyle( GraphStyle( designates the style of the graph to be drawn. function# is the number of the Y= function name in the current graphing mode. graphstyle is a number from 1 to 7 that corresponds to the graph style, as shown below.
Not all graph styles are available in all graphing modes. For a detailed description of each graph style, see the Graph Styles table in Chapter 3. PRGM I/O (Input/Output) Instructions PRGM I/O Menu To display the PRGM I/O (program input/output) menu, press ~ from within the program editor only. CTL I/O EXEC 1: Input Enters a value or uses the cursor. 2: Prompt Prompts for entry of variable values. 3: Disp Displays text, value, or the home screen. 4: DispGraph Displays the current graph.
These instructions control input to and output from a program during execution. They allow you to enter values and display answers during program execution. To return to the program editor without selecting an item, press ‘. Displaying a Graph with Input Input without a variable displays the current graph. You can move the free-moving cursor, which updates X and Y (and R and q for PolarGC format). The pause indicator is on. Press Í to resume program execution.
Storing a Variable Value with Input Input with variable displays a ? (question mark) prompt during execution. variable may be a real number, complex number, list, matrix, string, or Y= function. During program execution, enter a value, which can be an expression, and then press Í. The value is evaluated and stored to variable, and the program resumes execution. Input [variable] You can display text or the contents of Strn (a string variable) of up to 16 characters as a prompt.
Prompt During program execution, Prompt displays each variable, one at a time, followed by =?. At each prompt, enter a value or expression for each variable, and then press Í. The values are stored, and the program resumes execution. Prompt variableA[,variableB,...,variable n] Program Output Note: Y= functions are not valid with Prompt. Displaying the Home Screen Disp (display) without a value displays the home screen.
• If value is a variable, the current value is displayed. • If value is an expression, it is evaluated and the result is displayed on the right side of the next line. • If value is text within quotation marks, it is displayed on the left side of the current display line. ! is not valid as text. Program Output If Pause is encountered after Disp, the program halts temporarily so you can examine the screen. To resume execution, press Í.
Output( Output( displays text or value on the current home screen beginning at row (1 through 8) and column (1 through 16), overwriting any existing characters. Note: You may want to precede Output( with ClrHome. Expressions are evaluated and values are displayed according to the current mode settings. Matrices are displayed in entry format and wrap to the next line. ! is not valid as text.
getKey getKey returns a number corresponding to the last key pressed, according to the key code diagram below. If no key has been pressed, getKey returns 0. Use getKey inside loops to transfer control, for example, when creating video games. Program Output Note: , Œ, , and Í were pressed during program execution. Note: You can press É at any time during execution to break the program.
TI-84 Plus Key Code Diagram ClrHome, ClrTable ClrHome (clear home screen) clears the home screen during program execution. ClrTable (clear table) clears the values in the table during program execution. GetCalc( GetCalc( gets the contents of variable on another TI-84 Plus and stores it to variable on the receiving TI-84 Plus. variable can be a real or complex number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture.
By default, the TI-84 Plus uses the USB port if it is connected. If the USB cable is not connected, it uses the I/O port. If you want to specify either the USB or I/O port, use the following portflag numbers: portflag=0 use USB port if connected; portflag=1 use USB port; portflag=2 use I/O port Note: GetCalc( does not work between TI.82 and TI-83 Plus or a TI.82 and TI-84 Plus calculators. Get(, Send( Get( gets data from the CBL 2™ or CBR™ and stores it to variable on the receiving TI-84 Plus.
Send(variable) Note: This program gets sound data and time in seconds from CBL 2™. Note: You can access Get(, Send(, and GetCalc( from the CATALOG to execute them from the home screen (Chapter 15). Calling Other Programs as Subroutines Calling a Program from Another Program On the TI-84 Plus, any stored program can be called from another program as a subroutine. Enter the name of the program to use as a subroutine on a line by itself. You can enter a program name on a command line in either of two ways.
command in the first program when it encounters either Return or the implied Return at the end of the second program. Program Output Subroutine ( ' Notes about Calling Programs Variables are global. label used with Goto and Lbl is local to the program where it is located. label in one program is not recognized by another program. You cannot use Goto to branch to a label in another program. Return exits a subroutine and returns to the calling program, even if it is encountered within nested loops.
Running an Assembly Language Program You can run programs written for the TI-84 Plus in assembly language. Typically, assembly language programs run much faster and provide greater control than than the keystroke programs that you write with the built-in program editor. Note: Because an assembly langauge program has greater control over the calculator, if your assembly language program has error(s), it may cause your calculator to reset and lose all data, programs, and applications stored in memory.
1. Follow the steps for writing a program (16-4) but be sure to include AsmPrgm as the first line of your program. 2. From the home screen, press y N and then select AsmComp( to paste it to the screen. 3. Press to display the PRGM EXEC menu. 4. Select the program you want to compile. It will be pasted to the home screen. 5. Press ¢ and then select prgm from the CATALOG. 6. Key in the name you have chosen for the output program. Note: This name must be unique — not a copy of an existing program name. 7.
Chapter 17: Activities The Quadratic Formula Entering a Calculation Use the quadratic formula to solve the quadratic equations 3x2 + 5x + 2 = 0 and 2x2 N x + 3 = 0. Begin with the equation 3x2 + 5x + 2 = 0. 1. Press 3 ¿ ƒ [A] (above ) to store the coefficient of the x2 term. 2. Press ƒ [:] (above Ë). The colon allows you to enter more than one instruction on a line. 3. Press 5 ¿ ƒ [B] (above Œ) to store the coefficient of the X term. Press ƒ [:] to enter a new instruction on the same line.
5. Press £ Ì ƒ [B] Ã y C ƒ [B] ¡ ¹ 4 ƒ [A] ƒ [C] ¤ ¤ ¥ £ 2 ƒ [A] ¤ to enter the expression for one of the solutions for the quadratic formula, 2 – b ± b – 4ac -------------------------------------2a 6. Press Í to find one solution for the equation 3x2 + 5x + 2 = 0. The answer is shown on the right side of the display. The cursor moves to the next line, ready for you to enter the next expression. Converting to a Fraction You can show the solution as a fraction. 1. Press to display the MATH menu.
2. Press 1 to select 1:4Frac from the MATH menu. When you press 1, Ans4Frac is displayed on the home screen. Ans is a variable that contains the last calculated answer. 3. Press Í to convert the result to a fraction. To save keystrokes, you can recall the last expression you entered, and then edit it for a new calculation. 4.
5. Press } to move the cursor onto the + sign in the formula. Press ¹ to edit the quadratic-formula expression to become: 2 – b – b – 4ac------------------------------------2a 6. Press Í to find the other solution for the quadratic equation 3x2 + 5x + 2 = 0. Displaying Complex Results Now solve the equation 2x2 N x + 3 = 0. When you set a+bi complex number mode, the TI-84 Plus displays complex results. 1. Press z † † † † † † (6 times), and then press ~ to position the cursor over a+bi.
2. Press y 5 (above z) to return to the home screen, and then press ‘ to clear it. 3. Press 2 ¿ ƒ [A] ƒ [:] Ì 1 ¿ ƒ [B] ƒ [:] 3 ¿ ƒ [C] Í. The coefficient of the x2 term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively. 4. Press y [ to recall the store instruction, and then press y [ again to recall the quadratic-formula expression, 2 – b – b – 4ac------------------------------------2a 5.
6. Press y [ repeatedly until this quadratic-formula expression is displayed: 2 – b + b – 4ac-------------------------------------2a 7. Press Í to find the other solution for the quadratic equation: 2x2 N x + 3 = 0. Note: An alternative for solving equations for real numbers is to use the built-in Equation Solver.
Box with Lid Defining a Function Take a 20 cm × 25 cm. sheet of paper and cut X × X squares from two corners. Cut X × 12½ cm rectangles from the other two corners as shown in the diagram below. Fold the paper into a box with a lid. What value of X would give your box the maximum volume V? Use the table and graphs to determine the solution. Begin by defining a function that describes the volume of the box. From the diagram: 2X + A = 20 2X + 2B = 25 V = A…B…X X 20 A X X B B 25 1.
2. Press £ 20 ¹ 2 „ ¤ £ 25 ¥ 2 ¹ „ ¤ „ Í to define the volume function as Y1 in terms of X. „ lets you enter X quickly, without having to press ƒ. The highlighted = sign indicates that Y1 is selected. Defining a Table of Values The table feature of the TI-84 Plus displays numeric information about a function. You can use a table of values from the function you just defined to estimate an answer to the problem. 1. Press y - (above p) to display the TABLE SETUP menu. 2. Press Í to accept TblStart=0. 3.
5. Press and hold † to scroll the table until a negative result for Y1 is displayed. Notice that the maximum length of X for this problem occurs where the sign of Y1 (box’s volume) changes from positive to negative, between 10 and 11. 6. Press y -. Notice that TblStart has changed to 6 to reflect the first line of the table as it was last displayed. (In step 5, the first value of X displayed in the table is 6.
2. Press y 0. 3. Press † and } to scroll the table. Notice that the maximum value for Y1 is 410.26, which occurs at X=3.7. Therefore, the maximum occurs where 3.6
7. Press † to display the other maximum. The value of Y1 at X=3.68 in full precision is 410.264064, at X=3.69 is 410.262318 and at X=3.7 is 410.256. The maximum volume of the box would occur at 3.68 if you could measure and cut the paper at .01-centimeter increments. Setting the Viewing Window You also can use the graphing features of the TI-84 Plus to find the maximum value of a previously defined function.
The standard window variables define the viewing window as shown. Xmin, Xmax, Ymin, and Ymax define the boundaries of the display. Xscl and Yscl define the distance between tick marks on the X and Y axes. Xres controls resolution. 2. Press 0 Í to define Xmin. 3. Press 20 ¥ 2 to define Xmax using an expression. 4. Press Í. The expression is evaluated, and 10 is stored in Xmax. Press Í to accept Xscl as 1. 5. Press 0 Í 500 Í 100 Í 1 Í to define the remaining window variables.
Displaying and Tracing the Graph Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph. You can trace along a function using the TRACE feature. 1. Press s to graph the selected function in the viewing window. The graph of Y1=(20N2X)(25à2NX)X is displayed. 2. Press ~ to activate the free-moving graph cursor. The X and Y coordinate values for the position of the graph cursor are displayed on the bottom line. 3.
4. Press r. The trace cursor is displayed on the Y1 function. The function that you are tracing is displayed in the top-left corner. 5. Press | and ~ to trace along Y1, one X dot at a time, evaluating Y1 at each X. You also can enter your estimate for the maximum value of X. 6. Press 3 Ë 8. When you press a number key while in TRACE, the X= prompt is displayed in the bottom-left corner. 7. Press Í. The trace cursor jumps to the point on the Y1 function evaluated at X=3.8. 8.
Zooming In on the Graph To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the ZOOM instructions. 1. Press q to display the ZOOM menu. This menu is a typical TI-84 Plus menu. To select an item, you can either press the number or letter next to the item, or you can press † until the item number or letter is highlighted, and then press Í. 2. Press 2 to select 2:Zoom In. The graph is displayed again.
4. Press p to display the new window settings. Finding the Calculated Maximum You can use a CALCULATE menu operation to calculate a local maximum of a function. 1. Press y / (above r) to display the CALCULATE menu. Press 4 to select 4:maximum. The graph is displayed again with a Left Bound? prompt. 2. Press | to trace along the curve to a point to the left of the maximum, and then press Í. A 4 at the top of the screen indicates the selected bound. A Right Bound? prompt is displayed.
3. Press ~ to trace along the curve to a point to the right of the maximum, and then press Í. A 3 at the top of the screen indicates the selected bound. A Guess? prompt is displayed. 4. Press | to trace to a point near the maximum, and then press Í. Or, press 3 Ë 8, and then press Í to enter a guess for the maximum. When you press a number key in TRACE, the X= prompt is displayed in the bottomleft corner.
Comparing Test Results Using Box Plots Problem An experiment found a significant difference between boys and girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains. The TI Graphics team conducted a similar test for adult men and women. The test involved 30 small objects, which participants were not allowed to see.
Correct Guesses Women Left Women Right Men Left Men Right 7 12 4 8 9 11 10 12 11 12 14 11 13 9 5 9 Procedure 1. Press … 5 to select 5:SetUpEditor. Enter list names WLEFT, WRGHT, MLEFT, and MRGHT, separated by commas. Press Í. The stat list editor now contains only these four lists. 2. Press … 1 to select 1:Edit. 3. Enter into WLEFT the number of correct guesses each woman made using her left hand (Women Left).
7. Press p. Set Xscl=1 and Yscl=0. Press q 9 to select 9:ZoomStat. This adjusts the viewing window and displays the box plots for the women’s results. 8. Press r. Women’s left-hand data Women’s right-hand data Use | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. Notice the outlier to the women’s right-hand data. What is the median for the left hand? For the right hand? With which hand were the women more accurate guessers, according to the box plots? 9. Examine the men’s results.
11. Compare the right-hand results. Define plot 1 to use WRGHT, define plot 2 to use MRGHT, and then press r to examine minX, Q1, Med, Q3, and maxX for each plot. Who were the better right-hand guessers? In the original experiment boys did not guess as well with right hands, while girls guessed equally well with either hand. This is not what our box plots show for adults.
Graphing Piecewise Functions Problem The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the cost of the ticket.
3. Press p and set Xmin=L2, Xscl=10, Ymin=L5, and Yscl=10. Ignore Xmax and Ymax; they are set by @X and @Y in step 4. 4. Press y 5 to return to the home screen. Store 1 to @X, and then store 5 to @Y. @X and @Y are on the VARS Window X/Y secondary menu. @X and @Y specify the horizontal and vertical distance between the centers of adjacent pixels. Integer values for @X and @Y produce nice values for tracing. 5. Press r to plot the function.
Graphing Inequalities Problem Graph the inequality 0.4x3 N 3x + 5 < 0.2x + 4. Use the TEST menu operations to explore the values of X where the inequality is true and where it is false. Procedure 1. Press z. Select Dot, Simul, and the default settings. Setting Dot mode changes all graph style icons to í (dot) in the Y= editor. 2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as Y4 and the right side as Y5. 3. Enter the statement of the inequality as Y6.
6. Press o. Turn off Y4, Y5, and Y6. Enter equations to graph only the inequality. 7. Press r. Notice that the values of Y7 and Y8 are zero where the inequality is false.
Solving a System of Nonlinear Equations Problem Using a graph, solve the equation x3N2x=2cos(x). Stated another way, solve the system of two equations and two unknowns: y = x 3N2x and y = 2cos(x). Use ZOOM factors to control the decimal places displayed on the graph. Procedure 1. Press z. Select the default mode settings. Press o. Turn off all functions and stat plots. Enter the functions. 2. Press q 4 to select 4:ZDecimal.
4. Press q 2 to select 2:Zoom In. Use |, ~, }, and † to move the free-moving cursor onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the X and Y values have one decimal place. 5. Press Í to zoom in. Move the cursor over the intersection. As you move the cursor, notice that now the X and Y values have two decimal places. 6. Press Í to zoom in again. Move the free-moving cursor onto a point exactly on the intersection.
Using a Program to Create the Sierpinski Triangle Setting up the Program This program creates a drawing of a famous fractal, the Sierpinski Triangle, and stores the drawing to a picture. To begin, press ~ ~ 1. Name the program SIERPINS, and then press Í. The program editor is displayed. Program PROGRAM:SIERPINS :FnOff :ClrDraw :PlotsOff :AxesOff :0!Xmin:1!Xmax :0!Ymin:1!Ymax Set viewing window. :rand!X:rand!Y :For(K,1,3000) :rand!N :If N1 à3 :Then :.5X!X :.
:If 1 à3
Graphing Cobweb Attractors Problem Using Web format, you can identify points with attracting and repelling behavior in sequence graphing. Procedure 1. Press z. Select Seq and the default mode settings. Press y .. Select Web format and the default format settings. 2. Press o. Clear all functions and turn off all stat plots. Enter the sequence that corresponds to the expression Y = K X(1NX). u(n)=Ku(nN1)(1Nu(nN1)) u(nMin)=.01 3. Press y 5 to return to the home screen, and then store 2.9 to K. 4. Press p.
6. Change K to 3.44 and trace the graph to show a cobweb with two attractors. 7. Change K to 3.54 and trace the graph to show a cobweb with four attractors.
Using a Program to Guess the Coefficients Setting Up the Program This program graphs the function A sin(BX) with random integer coefficients between 1 and 10. Try to guess the coefficients and graph your guess as C sin(DX). The program continues until your guess is correct. Program PROGRAM:GUESS :PlotsOff :Func :FnOff :Radian :ClrHome :"Asin(BX)"!Y1 :"Csin(DX)"!Y2 Define equations. :GraphStyle(1,1) :GraphStyle(2,5) Set line and path graph styles.
:L2p!Xmin :2p!Xmax :pà2!Xscl :L10!Ymin :10!Ymax :1!Yscl Set viewing window. :DispGraph :Pause Display graph. :FnOn 2 :Lbl Z :Prompt C,D Prompt for guess. :DispGraph :Pause Display graph. :If C=A :Text(1,1,"C IS OK") :If CƒA :Text(1,1,"C IS WRONG") :If D=B :Text(1,50,"D IS OK") :If DƒB :Text(1,50,"D IS WRONG") :DispGraph :Pause Chapter 17: Activities Display results. Display graph.
:If C=A and D=B :Stop :Goto Z Chapter 17: Activities Quit if guesses are correct.
Graphing the Unit Circle and Trigonometric Curves Problem Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them. Any function that can be plotted in Func mode can be plotted in Par mode by defining the X component as T and the Y component as F(T). Procedure 1. Press z. Select Par, Simul, and the default settings. 2. Press p. Set the viewing window. Tmin=0 Tmax=2p Tstep=.1 Xmin=L2 Xmax=7.4 Xscl=pà2 Ymin=L3 Ymax=3 Yscl=1 3. Press o.
5. Press r. As the graph is plotting, you may press Í to pause and Í again to resume graphing as you watch the sine function “unwrap” from the unit circle. Note: You can generalize the unwrapping. Replace sin(T) in Y2T with any other trig function to unwrap that function.
Finding the Area between Curves Problem Find the area of the region bounded by: f(x) g(x) x = = = 300x / (x2 + 625) 3cos(.1x) 75 Procedure 1. Press z. Select the default mode settings. 2. Press p. Set the viewing window. Xmin=0 Xmax=100 Xscl=10 Ymin=L5 Ymax=10 Yscl=1 Xres=1 3. Press o. Turn off all functions and stat plots. Enter the upper and lower functions. Y1=300Xà(X2+625) Y2=3cos(.1X) 4. Press y / 5 to select 5:Intersect. The graph is displayed.
5. Press y 5 to go to the home screen. Press y < 7 and use Shade( to see the area graphically. Shade(Y2,Y1,Ans,75) 6. Press y 5 to return to the home screen. Enter the expression to evaluate the integral for the shaded region. fnInt(Y1NY2,X,Ans,75) The area is 325.839962.
Using Parametric Equations: Ferris Wheel Problem Problem Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane. A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds.
Procedure 1. Press z. Select Par, Simul, and the default settings. Simul (simultaneous) mode simulates the two objects in motion over time. 2. Press p. Set the viewing window. Tmin=0 Tmax=12 Tstep=.1 Xmin=L13 Xmax=34 Xscl=10 Ymin=0 Ymax=31 Yscl=10 3. Press o. Turn off all functions and stat plots. Enter the expressions to define the path of the ferris wheel and the path of the ball. Set the graph style for X2T to ë (path).
5. Press p. Change the viewing window to concentrate on this portion of the graph. Tmin=1 Tmax=3 Tstep=.03 Xmin=0 Xmax=23.5 Xscl=10 Ymin=10 Ymax=25.5 Yscl=10 6. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross. Notice the values of X, Y, and T. 7. Press † to move to the path of the ball. Notice the values of X and Y (T is unchanged). Notice where the cursor is located.
You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion.
Demonstrating the Fundamental Theorem of Calculus Problem 1 Using the functions fnInt( and nDeriv( from the MATH menu to graph functions defined by integrals and derivatives demonstrates graphically that: F( x) = x Dx x ∫1 dt 1 ∫1 --t- dt = ln ( x ) , x > 0 and that = 1 --x Procedure 1 1. Press z. Select the default settings. 2. Press p. Set the viewing window. Xmin=.01 Xmax=10 Xscl=1 Ymin=L1.5 Ymax=2.5 Yscl=1 Xres=3 3. Press o. Turn off all functions and stat plots.
4. Press r. Press |, }, ~, and † to compare the values of Y1 and Y2. 5. Press o. Turn off Y1 and Y2, and then enter the numerical derivative of the integral of 1àX and the function 1àX. Set the graph style for Y3 to ç (line) and Y4 to è (thick). 6. Press r. Again, use the cursor keys to compare the values of the two graphed functions, Y3 and Y4.
Problem 2 Explore the functions defined by y = x 2 ∫2 t dt , x 2 ∫0 t dt , and x 2 ∫2 t dt Procedure 2 1. Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously. Store the function in Y5. 2. Press q 6 to select 6:ZStandard. 3. Press r. Notice that the functions appear identical, only shifted vertically by a constant. 4. Press o. Enter the numerical derivative of Y5 in Y6.
5. Press r. Notice that although the three graphs defined by Y5 are different, they share the same derivative.
Computing Areas of Regular N-Sided Polygons Problem Use the equation solver to store a formula for the area of a regular N-sided polygon, and then solve for each variable, given the other variables. Explore the fact that the limiting case is the area of a circle, pr2. Consider the formula A = NB 2 sin(pàN) cos(pàN) for the area of a regular polygon with N sides of equal length and B distance from the center to a vertex. N = 4 sides N = 8 sides N = 12 sides Procedure 1.
3. Enter N=4 and B=6 to find the area (A) of a square with a distance (B) from center to vertex of 6 centimeters. 4. Press } } to move the cursor onto A, and then press ă \. The solution for A is displayed on the interactive solver editor. 5. Now solve for B for a given area with various number of sides. Enter A=200 and N=6. To find the distance B, move the cursor onto B, and then press ƒ \. 6. Enter N=8. To find the distance B, move the cursor onto B, and then press ƒ \.
Now graph the equation to see visually how the area changes as the number of sides gets large. 8. Press z. Select the default mode settings. 9. Press p. Set the viewing window. Xmin=0 Xmax=200 Xscl=10 Ymin=0 Ymax=150 Yscl=10 Xres=1 10. Press o. Turn off all functions and stat plots. Enter the equation for the area. Use X in place of N. Set the graph styles as shown. 11. Press r. After the graph is plotted, press 100 Í to trace to X=100. Press 150 Í. Press 188 Í.
asymptote to Y1. The area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr 2) as N gets large.
Computing and Graphing Mortgage Payments Problem You are a loan officer at a mortgage company, and you recently closed on a 30-year home mortgage at 8 percent interest with monthly payments of 800. The new home owners want to know how much will be applied to the interest and how much will be applied to the principal when they make the 240th payment 20 years from now. Procedure 1. Press z and set the fixed-decimal mode to 2 decimal places. Set the other mode settings to the defaults. 2.
Now compare the graph of the amount of interest with the graph of the amount of principal for each payment. 4. Press z. Set Par and Simul. 5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown. Note: GPrn( and GInt( are located on the FINANCE menu (APPS 1:FINANCE). 6. Press p. Set these window variables. Tmin=1 Tmax=360 Tstep=12 Xmin=0 Xmax=360 Xscl=10 Ymin=0 Ymax=1000 Yscl=100 Note: To increase the graph speed, change Tstep to 24. 7. Press r.
The graph shows that for the 240th payment (X=240), 358.03 of the 800 payment is applied to principal (Y=358.03). Note: The sum of the payments (Y3T=Y1T+Y2T) is always 800. 8. Press † to move the cursor onto the function for interest defined by X2T and Y2T. Enter 240. The graph shows that for the 240th payment (X=240), 441.97 of the 800 payment is interest (Y=441.97). 9. Press y 5 Œ Í 9 to paste 9:bal( to the home screen. Check the figures from the graph.
At which monthly payment will the principal allocation surpass the interest allocation? Chapter 17: Activities 513
Chapter 18: Memory and Variable Management Checking Available Memory MEMORY Menu At any time you can check available memory or manage existing memory by selecting items from the MEMORY menu. To access this menu, press y L. MEMORY 1: About... Displays information about the graphing calculator including current OS version number. 2: Mem Mgmt/Del... Reports memory availability and variable usage. 3: Clear Entries Clears ENTRY (last-entry storage). 4: ClrAllLists Clears all lists in memory. 5: Archive...
RAM FREE displays the amount of available RAM. ARC FREE displays the amount of available Archive. Available RAM, Archive, and App Slots The TI-84 Plus / TI-84 Plus Silver Edition has Archive, RAM, and Application (App) slot memory for you to use and manage. The available RAM stores computations, lists, variables, and data. The available Archive lets you store programs, Apps, groups, and other variables. The App slots are actually individual sectors of Flash ROM where Apps are stored.
Displays the type of graphing calculator. Displays the OS version. As new software upgrades become available, you can electronically upgrade your unit. Displays the Product ID. Each Flash-based graphing calculator has a unique product ID, which you may need if you contact technical support. You can also use this 14 digit ID to register your calculator at education.ti.com, or identify your calculator in the event that it is lost or stolen.
1. Press y L to display the MEMORY menu. Note: The # and $ in the top or bottom of the left column indicate that you can scroll up or down to view more variable types. 2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu. The TI-84 Plus expresses memory quantities in bytes. 3. Select variable types from the list to display memory usage. Notes: Real, List, Y-Vars, and Prgm variable types never reset to zero, even after memory is cleared.
To leave the MEMORY MANAGEMENT/DELETE menu, press either y 5 or ‘. Both options display the home screen.
Deleting Items from Memory Deleting an Item To increase available memory by deleting the contents of any variable (real or complex number, list, matrix, Y= variable, program, Apps, AppVars, picture, graph database, or string), follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu. 3. Select the type of data you want to delete, or select 1:All for a list of all variables of all types.
4. Press } and † to move the selection cursor (4) next to the item you want to delete, and then press {. The variable is deleted from memory. You can delete individual variables one by one from this screen. No warning will be given to verify the deletion. Note: If you are deleting programs or Apps, you will receive a message asking you to confirm this delete action. Select 2:Yes to continue. To leave any variable screen without deleting anything, press y 5, which displays the home screen.
Clearing Entries and List Elements Clear Entries Clear Entries clears the contents of the ENTRY (last entry on home screen) storage area. To clear the ENTRY storage area, follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 3:Clear Entries to paste the instruction to the home screen. 3. Press Í to clear the ENTRY storage area. To cancel Clear Entries, press ‘.
3. Press Í to set the dimension of each list in memory to 0. To cancel ClrAllLists, press ‘. ClrAllLists does not delete list names from memory, from the LIST NAMES menu, or from the stat list editor. Note: If you select 4:ClrAllLists from within a program, the ClrAllLists instruction is pasted to the program editor. The lists are cleared when the program is executed.
Archiving and UnArchiving Variables Archiving and UnArchiving Variables Archiving lets you store data, programs, or other variables to the user data archive (ARC) where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory. Archived variables cannot be edited or executed. They can only be seen and unarchived.
Variable Type Names Archive? (yes/no) UnArchive? (yes/no) Functions Y1, Y2, . . . , Y9, Y0 no not applicable Parametric equations X1T and Y1T, ... , X6T and Y6T no not applicable Polar functions r1, r2, r3, r4, r5, r6 no not applicable Sequence functions u, v, w no not applicable Stat plots Plot1, Plot2, Plot3 no not applicable Graph databases GDB1, GDB2,... yes yes Graph pictures Pic1, Pic2, ... , Pic9, Pic0 yes yes Strings Str1, Str2, . . .
Variable Type Names Archive? (yes/no) UnArchive? (yes/no) System variables Xmin, Xmax, and others no not applicable Archiving and unarchiving can be done in two ways: • Use the 5:Archive or 6:UnArchive commands from the MEMORY menu or CATALOG. • Use a Memory Management editor screen. Before archiving or unarchiving variables, particularly those with a large byte size (such as large programs) use the MEMORY menu to: • Find the size of the variable. • See if there is enough free space.
To archive or unarchive a list variable (L1) using the Archive/UnArchive options from the MEMORY menu: 1. Press y L to display the MEMORY menu. 2. Select 5:Archive or 6:UnArchive to place the command in the Home screen. 3. Press y d to place the L1 variable in the Home screen. 4. Press Í to complete the archive process. Note: An asterisk will be displayed to the left of the Archived variable name to indicate it is archived.
2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu. 3. Select 4:List to display the LIST menu. 4. Press Í to archive L1. An asterisk will appear to the left of L1 to indicate it is an archived variable. To unarchive a variable in this screen, put the cursor next to the archived variable and press Í. The asterisk will disappear.
5. Press y 5 to leave the LIST menu. Note: You can access an archived variable for the purpose of linking, deleting, or unarchiving it, but you cannot edit it.
Resetting the TI-84 Plus RAM ARCHIVE ALL Menu Reset displays the RAM ARCHIVE ALL menu. This menu gives you the option of resetting all memory (including default settings) or resetting selected portions of memory while preserving other data stored in memory, such as programs and Y= functions. For instance, you can choose to reset all of RAM or just restore the default settings. Be aware that if you choose to reset RAM, all data and programs in RAM will be erased.
Displaying the RAM ARCHIVE ALL Menu To display the RAM ARCHIVE ALL menu on the TI-84 Plus, follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 7:Reset to display the RAM ARCHIVE ALL menu. Resetting RAM Memory Resetting all RAM restores RAM system variables to factory settings and deletes all nonsystem variables and all programs. Resetting RAM defaults restores all system variables to default settings without deleting variables and programs in RAM.
1. From the RAM ARCHIVE ALL menu, select 1:All RAM to display the RESET RAM menu or 2:Defaults to display the RESET DEFAULTS menu. 2. If you are resetting RAM, read the message below the RESET RAM menu. • To cancel the reset and return to the HOME screen, press Í. • To erase RAM memory or reset defaults, select 2:Reset. Depending on your choice, the message RAM cleared or Defaults set is displayed on the home screen.
2. Select one of the following: 1:Vars to display the RESET ARC VARS menu. 2:Apps to display the RESET ARC APPS menu. 3:Both to display the RESET ARC BOTH menu. 3. Read the message below the menu. • To cancel the reset and return to the HOME screen, press Í.
• To continue with the reset, select 2:Reset. A message indicating the type of archive memory cleared will be displayed on the HOME screen. Resetting All Memory When resetting all memory on the TI-84 Plus, RAM and user data archive memory is restored to factory settings. All nonsystem variables, applications, and programs are deleted. All system variables are reset to default settings. Before you reset all memory, consider restoring sufficient available memory by deleting only selected data.
• To continue with the reset, select 2:Reset. The message MEM cleared is displayed on the HOME screen. When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast by pressing y } or †.
Grouping and Ungrouping Variables Grouping Variables Grouping allows you to make a copy of two or more variables residing in RAM and then store them as a group in user data archive. The variables in RAM are not erased. The variables must exist in RAM before they can be grouped. In other words, archived data cannot be included in a group. Once grouped, the variables can be deleted from RAM to open memory. When the variables are needed later, they can be ungrouped for use. To create a group of variables: 1.
4. Enter a name for the new group and press Í. Note: A group name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q. 5. Select the type of data you want to group. You can select 1:All+ which shows all variables of all types available and selected. You can also select 2:All- which shows all variables of all types available but not selected.
6. Press } and † to move the selection cursor (4) next to the first item you want to copy into a group, and then press Í. A small square will remain to the left of all variables selected for grouping. Repeat the selection process until all variables for the new group are selected and then press ~ to display the DONE menu. 7. Press Í to complete the grouping process.
Note: You can only group variables in RAM. You cannot group some system variables, such as the last-answer variable Ans and the statistical variable RegEQ. Ungrouping Variables Ungrouping allows you to make a copy of variables in a group stored in user data archive and place them ungrouped in RAM. DuplicateName Menu During the ungrouping action, if a duplicate variable name is detected in RAM, the DUPLICATE NAME menu is displayed. DuplicateName 1: Rename Prompts to rename receiving variable.
• When you select 2:Overwrite, the unit overwrites the data of the duplicate variable name found in RAM. Ungrouping resumes. • When you select 3: Overwrite All, the unit overwrites the data of all duplicate variable names found in RAM. Ungrouping resumes. • When you select 4:Omit, the unit does not ungroup the variable in conflict with the duplicated variable name found in RAM. Ungrouping resumes with the next item. • When you select 5:Quit, ungrouping stops, and no further changes are made.
4. Press } and † to move the selection cursor (4) next to the group variable you want to ungroup, and then press Í. The ungroup action is completed. Note: Ungrouping does not remove the group from user data archive. You must delete the group in user data archive to remove it.
Garbage Collection Garbage Collection Message If you use the user data archive extensively, you may see a Garbage Collect? message. This occurs if you try to archive a variable when there is not enough free contiguous archive memory. The Garbage Collect? message lets you know an archive will take longer than usual. It also alerts you that the archive will fail if there is not enough memory. The message can also alert you when a program is caught in a loop that repetitively fills the user data archive.
Note: The process message Defragmenting... is displayed whenever an application marked for deletion is encountered. Garbage collection may take up to 20 minutes, depending on how much of archive memory has been used to store variables. After garbage collection, depending on how much additional space is freed, the variable may or may not be archived. If not, you can unarchive some variables and try again. Why Is Garbage Collection Necessary? The user data archive is divided into sectors.
Each variable that you archive is stored in the first empty block large enough to hold it. This process continues to the end of the last sector. Depending on the size of individual variables, the empty blocks may account for a significant amount of space. Garbage collection occurs when the variable you are archiving is larger than any empty block. How Unarchiving a Variable Affects the Process When you unarchive a variable, it is copied to RAM but it is not actually deleted from user data archive memory.
When you unarchive a variable, the Archive free amount increases immediately, but the space is not actually available until after the next garbage collection. If the Archive free amount shows enough available space for your variable, there probably will be enough space to archive it after garbage collection (depending on the usability of any empty blocks). The Garbage Collection Process The garbage collection process: • • Deletes unarchived variables from the user data archive.
1. From the HOME screen, press y N to display the CATALOG. 2. Press † or } to scroll the CATALOG until the selection cursor points to the GarbageCollect command or press G to skip to the commands starting with the letter G. 3. Press Í to paste the command to the HOME screen. 4. Press Í to display the Garbage Collect? message. 5. Select 2:Yes to begin garbage collection.
ERR:ARCHIVE FULL Message Even if the MEMORY screen shows enough free space to archive a variable or store an application, you may still get an ERR: ARCHIVE FULL message. An ERR:ARCHIVE FULL message may be displayed: • When there is insufficient space to archive a variable within a continuous block and within a single sector. • When there is insufficient space to store an application within a continuous block of memory.
Chapter 19: Communication Link Getting Started: Sending Variables Getting Started is a fast-paced introduction. Read the chapter for details. Create and store a variable and a matrix, and then transfer them to another TI-84 Plus. 1. On the home screen of the sending unit, press 5 Ë 5 ¿ ƒ Q. Press Í to store 5.5 to Q. 2. Press y H y H 1 ¢ 2 y I y H 3 ¢ 4 y I y I ¿ y > 1. Press Í to store the matrix to [A]. 3. On the sending unit, press y L to display the MEMORY menu. 4.
5. On the sending unit, press 5 to select 5:Matrix. The MATRIX editor screen is displayed. 6. On the sending unit, press Í to archive [A]. An asterisk (ä) will appear, signifying that [A] is now archived. 7. Connect the graphing calculators with the USB unit-to-unit cable. Push both ends in firmly. 8. On the receiving unit, press y 8 ~ to display the RECEIVE menu. Press 1 to select 1:Receive. The message Waiting... is displayed and the busy indicator is on. 9.
13. On the sending unit, press ~ to display the TRANSMIT menu. 14. On the sending unit, press 1 to select 1:Transmit and begin transmission. The receiving unit displays the message Receiving....When the items are transmitted, both units display the name and type of each transmitted variable.
TI-84 Plus LINK This chapter describes how to communicate with compatible TI units. The TI-84 Plus has a USB port to connect and communicate with another TI-84 Plus or TI-84 Plus Silver Edition. A USB unit-to-unit cable is included with the TI-84 Plus.
I/O Unit-to-Unit Cable The TI-84 Plus I/O link port is located at the top left edge of the graphing calculator. 1. Firmly insert either end of the I/O unit-to-unit cable into the port. 2. Insert the other end of the cable into the other graphing calculator’s I/O port. TI-84 Plus to a TI-83 Plus using I/O Unit-to-Unit Cable The TI-84 Plus I/O link port is located at the top left edge of the graphing calculator. The TI-83 Plus I/O link port is located at the bottom edge of the graphing calculator. 3.
Linking to a Computer With TI Connect™ software and the USB computer cable that is included with your TI-84 Plus, you can link the graphing calculator to a personal computer.
Selecting Items to Send LINK SEND Menu To display the LINK SEND menu, press y 8. SEND RECEIVE 1: All+... Displays all items as selected, including RAM and Flash applications. 2: AllN... Displays all items as deselected. 3: Prgm... Displays all program names. 4: List... Displays all list names. 5: Lists to TI82... Displays list names L1 through L6. 6: GDB... Displays all graph databases. 7: Pic... Displays all picture data types. 8: Matrix... Displays all matrix data types. 9: Real...
SEND RECEIVE D: AppVars... Displays all software application variables. E: Group... Displays all grouped variables. F: SendId Sends the Calculator ID number immediately. (You do not need to select SEND.) G: SendOS Sends operating system updates to another TI-84 Plus Silver Edition or TI-84 Plus. You can not send the operating system to the TI-83 Plus product family. H: Back Up...
Note: An asterisk (ä) to the left of an item indicates the item is archived. 5. Repeat steps 3 and 4 to select or deselect additional items. Sending the Selected Items After you have selected items to send on the sending unit and set the receiving unit to receive, follow these steps to transmit the items. To set the receiving unit, see Receiving Items. 1. Press ~ on the sending unit to display the TRANSMIT menu. 2. Confirm that Waiting...
3. Press Í to select 1:Transmit. The name and type of each item are displayed line-by-line on the sending unit as the item is queued for transmission, and then on the receiving unit as each item is accepted. Note: Items sent from the RAM of the sending unit are transmitted to the RAM of the receiving unit. Items sent from user data archive (flash) of the sending unit are transmitted to user data archive (flash) of the receiving unit.
• Variables and applications stored in the user data archive of the sending TI-84 Plus Silver Edition will be sent to the user data archive of the receiving TI-84 Plus Silver Edition or TI-84 Plus. After sending or receiving data, you can repeat the same transmission to additional TI-84 Plus Silver Edition or TI-84 Plus units—from either the sending unit or the receiving unit—without having to reselect data to send. The current items remain selected.
12. Press Í on the receiving unit. 13. Press Í on the sending unit. A copy of the selected item(s) is sent to the receiving unit. 14. Repeat steps 7 through 13 until the items are sent to all additional units. Sending to a TI-83 Plus or TI-83 Plus Silver Edition You can send all variables from a TI-84 Plus to a TI-83 Plus or TI-83 Plus Silver Edition except Flash applications with new features, or programs with new features in them.
Receiving Items LINK RECEIVE Menu To display the LINK RECEIVE menu, press y 8 ~. SEND RECEIVE 1: Receive Sets unit to receive data transmission. Receiving Unit When you select 1:Receive from the LINK RECEIVE menu on the receiving unit, the message Waiting... and the busy indicator are displayed. The receiving unit is ready to receive transmitted items. To exit the receive mode without receiving items, press É, and then select 1:Quit from the Error in Xmit menu.
DuplicateName Menu During transmission, if a variable name is duplicated, the DuplicateName menu is displayed on the receiving unit. DuplicateName 1: Rename Prompts to rename receiving variable. 2: Overwrite Overwrites data in receiving variable. 3: Omit Skips transmission of sending variable. 4: Quit Stops transmission at duplicate variable. When you select 1:Rename, the Name= prompt is displayed, and alpha-lock is on. Enter a new variable name, and then press Í. Transmission resumes.
You cannot send memory backups between the TI-84 Plus product family and the TI-83 Plus product family. Receiving from a TI-83 Plus Silver Edition or TI-83 Plus The TI-84 Plus product family and the TI-83 Plus product family are compatible with a few exceptions. Receiving from a TI-83 You can transfer all variables and programs from a TI-83 to a TI-84 Plus if they fit in the RAM of the TI-84 Plus. The RAM of the TI-84 Plus is slightly less than the RAM of the TI-83.
Backing Up RAM Memory Warning: H:Back Up overwrites the RAM memory and mode settings in the receiving unit. All information in the RAM memory of the receiving unit is lost. Note: Archived items on the receiving unit are not overwritten. You can backup the contents of RAM memory and mode settings (no Flash applications or archived items) to another TI-84 Plus Silver Edition. You can also backup RAM memory and mode settings to a TI-84 Plus. To perform a RAM memory backup: 1.
6. Press Í on the receiving unit to continue the backup. — or — Press 2:Quit on the receiving unit to cancel the backup and return to the LINK SEND menu Note: If a transmission error is returned during a backup, the receiving unit is reset. Memory Backup Complete When the backup is complete, both the sending graphing calculator and receiving graphing calculator display a confirmation screen.
Error Conditions A transmission error occurs after one or two seconds if: • A cable is not attached to the sending unit. • A cable is not attached to the receiving unit. Note: If the cable is attached, push it in firmly and try again. • The receiving unit is not set to receive transmission. • You attempt a backup between a TI-73, TI-82, TI-83, TI-83 Plus, or TI-83 Plus Silver Edition.
• You try to use GetCalc( with a TI-83 instead of a TI-84 Plus or TI-84 Plus Silver Edition. Insufficient Memory in Receiving Unit • During transmission, if the receiving unit does not have sufficient memory to receive an item, the Memory Full menu is displayed on the receiving unit. • To skip this item for the current transmission, select 1:Omit. Transmission resumes with the next item. • To cancel the transmission and exit receive mode, select 2:Quit.
Appendix A: Functions and Instructions Functions return a value, list, or matrix. You can use functions in an expression. Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table.
Function or Instruction/Arguments valueA and valueB angle(value) Result Returns 1 if both valueA and valueB are ƒ 0. valueA and valueB can be real numbers, expressions, or lists. Performs a one-way analysis of variance for comparing the means of two to 20 populations. Ans Returns the last answer. Archive Moves the specified variables from RAM to the user data archive memory.
Function or Instruction/Arguments augment(matrixA, matrixB) augment(listA,listB) Result Returns a matrix, which is matrixB appended to matrixA as new columns. Key or Keys/Menu or Screen/Item y> MATH 7:augment( Returns a list, which is listB y 9 concatenated to the end of OPS listA. 9:augment( AxesOff Turns off the graph axes. †y. AxesOff AxesOn Turns on the graph axes. †y. AxesOn a+bi Sets the mode to rectangular complex number mode (a+bi).
Function or Instruction/Arguments binompdf(numtrials,p [,x]) c2cdf(lowerbound, upperbound,df) c2pdf(x,df) Result Computes a probability at x y = for the discrete binomial DISTR distribution with the A:binompdf( specified numtrials and probability p of success on each trial. y= Computes the c2 DISTR distribution probability between lowerbound and 8:c2cdf( upperbound for the specified degrees of freedom df.
Function or Instruction/Arguments checkTmr(starttime) Circle(X,Y,radius) Clear Entries ClockOff ClockOn ClrAllLists ClrDraw ClrHome Result Returns the number of seconds since you used startTmr to start the timer. The starttime is the value displayed by startTmr. Draws a circle with center (X,Y) and radius. Clears the contents of the Last Entry storage area. Turns off the clock display in the mode screen. Turns on the clock display in the mode screen. Sets to 0 the dimension of all lists in memory.
Function or Instruction/Arguments Result ClrList listname1 [,listname2, ..., listname n] Sets to 0 the dimension of one or more listnames. ClrTable Clears all values from the table. conj(value) Returns the complex conjugate of a complex number or list of complex numbers. Connected Sets connected plotting mode; resets all Y= editor graph-style settings to ç . CoordOff Turns off cursor coordinate value display.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item coshL1 (value) Returns hyperbolic yN arccosine of a real number, coshL1( expression, or list. CubicReg [Xlistname, Ylistname,freqlist, regequ] Fits a cubic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. cumSum(list) Returns a list of the cumulative sums of the elements in list, starting with the first element.
Function or Instruction/Arguments dbd(date1,date2) Result Calculates the number of days between date1 and date2 using the actual-daycount method. Key or Keys/Menu or Screen/Item Œ 1:Finance CALC D:dbd( value4Dec Displays a real or complex number, expression, list, or MATH matrix in decimal format. 2:4Dec Degree Sets degree angle mode. †z Degree DelVar variable Deletes from memory the contents of variable. † CTL G:DelVar DependAsk Sets table to ask for †ydependent-variable values.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item DiagnosticOn Sets diagnostics-on mode; yN r, r2, and R2 are displayed as regression model results. dim(listname) dim(matrixname) Returns the dimension of listname. Returns the dimension of matrixname as a list. DiagnosticOn y9 OPS 3:dim( y> MATH 3:dim( length!dim(listname) Assigns a new dimension y9 (length) to a new or existing OPS listname.
Function or Instruction/Arguments Result DispTable Displays the table. value4DMS Displays value in DMS format. Dot Sets dot plotting mode; resets all Y= editor graphstyle settings to í . DrawF expression Draws expression (in terms of X) on the graph. DrawInv expression Key or Keys/Menu or Screen/Item † I/O 5:DispTable y; ANGLE 4:4DMS †z Dot y< DRAW 6:DrawF y< Draws the inverse of expression by plotting X values on the y-axis and Y values on the x-axis.
Function or Instruction/Arguments Result Exponent: listâexponent Returns list elements times 10 to the exponent. Exponent: matrixâexponent Returns matrix elements times 10 to the exponent. 4Eff(nominal rate, compounding periods) Computes the effective interest rate. Key or Keys/Menu or Screen/Item yD yD Œ 1:Finance CALC C:4Eff( Else See If:Then:Else End Identifies end of For(, If-Then-Else, Repeat, or While loop. † CTL 7:End Eng Sets engineering display mode.
Result Key or Keys/Menu or Screen/Item ExprOff Turns off the expression display during TRACE. †y. ExprOff ExprOn Turns on the expression display during TRACE. †y. ExprOn Ücdf(lowerbound, upperbound, numerator df, denominator df) Computes the Û y= distribution probability DISTR between lowerbound and 0:Ücdf( upperbound for the specified numerator df (degrees of freedom) and denominator df. Fill(value,matrixname) Stores value to each element in matrixname.
Function or Instruction/Arguments Result fMax(expression, variable,lower,upper [,tolerance]) Returns the value of variable where the local maximum of expression occurs, between lower and upper, with specified tolerance. fMin(expression,variable, lower,upper[,tolerance]) Returns the value of variable where the local minimum of expression occurs, between lower and upper, with specified tolerance.
Key or Keys/Menu or Screen/Item Function or Instruction/Arguments Result :For(variable,begin,end [,increment]) :commands :End :commands Executes commands † through End, incrementing CTL variable from begin by 4:For( increment until variable>end. fPart(value) Returns the fractional part or parts of a real or complex number, expression, list, or matrix.
Function or Instruction/Arguments GarbageCollect gcd(valueA,valueB) geometcdf(p,x) geometpdf(p,x) Get(variable) Result Displays the garbage collection menu to allow cleanup of unused archive memory. Returns the greatest common divisor of valueA and valueB, which can be real numbers or lists.
Function or Instruction/Arguments GetCalc(variable [,portflag]) getDate getDtFmt Result Key or Keys/Menu or Screen/Item Gets contents of variable on † another TI-84 Plus and I/O stores it to variable on the 0:GetCalc( receiving TI-84 Plus. By default, the TI-84 Plus uses the USB port if it is connected. If the USB cable is not connected, it uses the I/O port. portflag=0 use USB port if connected; portflag=1 use USB port; portflag=2 use I/O port.
Function or Instruction/Arguments getDtStr(integer) getKey getTime getTmFmt getTmStr(integer) Result Key or Keys/Menu or Screen/Item Returns a string of the yN current date in the format getDtStr( specified by integer, where: 1 = M/D/Y 2 = D/M/Y 3 = Y/M/D Returns the key code for † the current keystroke, or 0, I/O if no key is pressed. 7:getKey Returns a list giving the yN time according to the getTime current value of the clock. The list is in {hour,minute,second} format.
Key or Keys/Menu or Screen/Item Function or Instruction/Arguments Result Goto label Transfers control to label. GraphStyle(function#, graphstyle#) Sets a graphstyle for function#. † CTL H:GraphStyle( GridOff Turns off grid format. †y. GridOff GridOn Turns on grid format. †y. GridOn G-T Sets graph-table vertical split-screen mode. †z G-T Horiz Horizontal y identity(dimension) :If condition :commandA :commands † CTL 0:Goto Sets horizontal split-screen † z mode.
Function or Instruction/Arguments :If condition :Then :commands :End :commands :If condition :Then :commands :Else :commands :End :commands imag(value) Result Key or Keys/Menu or Screen/Item Executes commands from † Then to End if condition = 1 CTL (true). 2:Then Executes commands from † Then to Else if CTL condition = 1 (true); from 3:Else Else to End if condition = 0 (false). Returns the imaginary (nonreal) part of a complex CPX number or list of complex 3:imag( numbers.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item Input [variable] Input ["text",variable] Prompts for value to store to variable. † I/O 1:Input Input [Strn,variable] Displays Strn and stores entered value to variable. † I/O 1:Input inString(string,substring [,start]) Returns the character position in string of the first character of substring beginning at start.
Function or Instruction/Arguments invT(area,df) iPart(value) irr(CF0,CFList[,CFFreq]) Result Computes the inverse y= cumulative student-t DISTR probability function 4:invT( specified by degree of freedom, df for a given area under the curve. Returns the integer part of a real or complex number, expression, list, or matrix. Increments variable by 1; skips commandA if variable>value. isClockOn Identifies if clock is ON or OFF. Returns 1 if the clock is ON. Returns 0 if the clock is OFF.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item LabelOn Turns on axes labels. †y. LabelOn Lbl label Creates a label of one or two characters. † CTL 9:Lbl lcm(valueA,valueB) Returns the least common multiple of valueA and valueB, which can be real numbers or lists. length(string) Line(X1,Y1,X2,Y2) Line(X1,Y1,X2,Y2,0) Returns the number of characters in string. NUM 8:lcm( yN length( Draws a line from (X1,Y1) to y < (X2,Y2).
Function or Instruction/Arguments Result LinReg(ax+b) [Xlistname, Fits a linear regression Ylistname,freqlist, model to Xlistname and regequ] Ylistname with frequency freqlist, and stores the regression equation to regequ. LinRegTTest [Xlistname, Ylistname,freqlist, alternative,regequ] LinRegTInt [Xlistname, Ylistname,freqlist, confidence level, regequ] @List(list) Performs a linear regression and a t-test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >.
Function or Instruction/Arguments LnReg [Xlistname, Ylistname,freqlist, regequ] Result Key or Keys/Menu or Screen/Item Fits a logarithmic … regression model to CALC Xlistname and Ylistname with 9:LnReg frequency freqlist, and stores the regression equation to regequ. log(value) Returns logarithm of a real or complex number, expression, or list.
Function or Instruction/Arguments max(valueA,valueB) max(list) max(listA,listB) max(value,list) mean(list[,freqlist]) median(list[,freqlist]) Med-Med [Xlistname, Ylistname,freqlist, regequ] Result Key or Keys/Menu or Screen/Item Returns the larger of valueA and valueB. NUM 7:max( Returns largest real or complex element in list. y9 MATH 2:max( Returns a real or complex y9 list of the larger of each pair MATH of elements in listA and 2:max( listB.
Function or Instruction/Arguments Menu("title","text1", label1[,...,"text7",label7]) min(valueA,valueB) min(list) min(listA,listB) min(value,list) valueA nCr valueB value nCr list Result Key or Keys/Menu or Screen/Item Generates a menu of up to † seven items during CTL program execution. C:Menu( Returns smaller of valueA and valueB. Returns smallest real or complex element in list.
Function or Instruction/Arguments list nCr value listA nCr listB Result Returns a list of the combinations of each element in list taken value at a time. PRB 3:nCr Returns a list of the combinations of each PRB element in listA taken each 3:nCr element in listB at a time. nDeriv(expression, variable,value[,H]) Returns approximate numerical derivative of expression with respect to variable at value, with specified H. 4Nom(effective rate, compounding periods) Computes the nominal interest rate.
Function or Instruction/Arguments normalpdf(x[,m,s]) not(value) valueA nPr valueB value nPr list list nPr value listA nPr listB npv(interest rate,CF0, CFList[,CFFreq]) Result Computes the probability density function for the normal distribution at a specified x value for the specified m and s. Key or Keys/Menu or Screen/Item y= DISTR 1:normalpdf( Returns 0 if value is ƒ 0. y: value can be a real number, LOGIC expression, or list.
Function or Instruction/Arguments valueA or valueB Result Returns 1 if valueA or valueB is ƒ 0. valueA and valueB can be real numbers, expressions, or lists. Key or Keys/Menu or Screen/Item y: LOGIC 2:or † I/O 6:Output( Output(row,column, "text") Displays text beginning at specified row and column. Output(row,column, value) Displays value beginning at † specified row and column. I/O 6:Output( Param Sets parametric graphing mode. †z Par Pause Suspends program execution until you press Í.
Result Key or Keys/Menu or Screen/Item Plot#(type,Xlistname, freqlist) Defines Plot# (1, 2, or 3) of type Histogram or Boxplot for Xlistname with frequency freqlist. †y, STAT PLOTS 1:Plot12:Plot23:Plot3- Plot#(type,Xlistname, freqlist,mark) Defines Plot# (1, 2, or 3) of type ModBoxplot for Xlistname with frequency freqlist using mark.
Function or Instruction/Arguments Pmt_End poissoncdf(m,x) poissonpdf(m,x) Result Specifies an ordinary annuity, where payments occur at the end of each payment period. Computes a cumulative probability at x for the discrete Poisson distribution with specified mean m. Computes a probability at x for the discrete Poisson distribution with the specified mean m. Polar Sets polar graphing mode. complex value 4Polar Displays complex value in polar format.
Function or Instruction/Arguments GPrn(pmt1,pmt2 [,roundvalue]) prod(list[,start,end]) Prompt variableA [,variableB,...,variable n] Result Computes the sum, rounded to roundvalue, of the principal amount between pmt1 and pmt2 for an amortization schedule. Key or Keys/Menu or Screen/Item Π1:Finance CALC 0:GPrn( Returns product of list y9 elements between start and MATH end. 6:prod( Prompts for value for variableA, then variableB, and so on.
Function or Instruction/Arguments 2-PropZTest(x1,n1,x2,n2 [,alternative,drawflag]) Pt-Change(x,y) Result Key or Keys/Menu or Screen/Item Computes a two-proportion † … z test. alternative=L1 is <; TESTS 6:2-PropZTest( alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Reverses a point at (x,y). y< POINTS 3:Pt-Change( Pt-Off(x,y[,mark]) Pt-On(x,y[,mark]) Erases a point at (x,y) using y < mark. POINTS 2:Pt-Off( Draws a point at (x,y) using y < mark.
Function or Instruction/Arguments Pxl-Off(row,column) Pxl-On(row,column) pxl-Test(row,column) Result Erases pixel at (row,column); 0 row 62 and 0 column 94. Key or Keys/Menu or Screen/Item y< POINTS 5:Pxl-Off( Draws pixel at (row,column); y < 0 row 62 and POINTS 4:Pxl-On( 0 column 94. Returns 1 if pixel (row, column) is on, 0 if it is off; 0 row 62 and 0 column 94.
Function or Instruction/Arguments Result QuartReg [Xlistname, Ylistname,freqlist, regequ] Fits a quartic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. Radian Sets radian angle mode. rand[(numtrials)] Returns a random number between 0 and 1 for a specified number of trials numtrials.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item randNorm(m,s [,numtrials]) Generates and displays a random real number from a PRB specified Normal 6:randNorm( distribution specified by m and s for a specified number of trials numtrials. re^qi Sets the mode to polar complex number mode (re^qi). Real Sets mode to display complex results only when you enter complex numbers. real(value) Returns the real part of a complex number or list of complex numbers.
Result Key or Keys/Menu or Screen/Item RectGC Sets rectangular graphing coordinates format. †y. RectGC ref(matrix) Returns the row-echelon form of a matrix. Function or Instruction/Arguments y> MATH A:ref( :Repeat condition :commands :End :commands Executes commands until condition is true. † CTL 6:Repeat Return Returns to the calling program. † CTL E:Return round(value[,#decimals]) Returns a number, expression, list, or matrix rounded to #decimals ( 9).
Function or Instruction/Arguments Result rowSwap(matrix,rowA, rowB) Returns a matrix with rowA of matrix swapped with rowB. rref(matrix) Returns the reduced rowechelon form of a matrix. Key or Keys/Menu or Screen/Item y> MATH C:rowSwap( y> MATH B:rref( R4Pr(x,y) Returns R, given y; rectangular coordinates x ANGLE and y or a list of rectangular 5:R4Pr( coordinates. R4Pq(x,y) Returns q, given y; rectangular coordinates x ANGLE and y or a list of rectangular 6:R4Pq( coordinates.
Function or Instruction/Arguments 2-SampÜTest Sx1,n1, Sx2,n2[,alternative, drawflag] (Summary stats input) Result Performs a two-sample Û test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. 2-SampTInt [listname1, listname2, freqlist1,freqlist2, confidence level,pooled] (Data list input) Computes a two-sample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances.
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item †… TESTS 4:2-SampTTest 2-SampTTest v1,Sx1,n1, v2,Sx2,n2[,alternative, pooled,drawflag] (Summary stats input) Computes a two-sample t test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results.
Function or Instruction/Arguments 2-SampZTest(s1,s2, v1,n1,v2,n2 [,alternative,drawflag]) (Summary stats input) Sci Select(Xlistname, Ylistname) Result Computes a two-sample z test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. Sets scientific notation display mode.
Function or Instruction/Arguments Sequential setDate(year,month,day) setDtFmt(integer) setTime(hour,minute, second) setTmFmt(integer) SetUpEditor Result Key or Keys/Menu or Screen/Item Sets mode to graph functions sequentially. †z Sequential Sets the date using a year, y N month, day format. The setDate( year must be 4 digits; month and day can be 1 or 2 digit. Sets the date format. 1 = M/D/Y 2 = D/M/Y 3 = Y/M/D yN setDtFmt( Sets the time using an yN hour, minute, second setTime( format.
Function or Instruction/Arguments SetUpEditor listname1 [,listname2,..., listname20] Shade(lowerfunc, upperfunc[,Xleft,Xright, pattern,patres]) Key or Keys/Menu or Screen/Item Result Removes all list names … from the stat list editor, then EDIT sets it up to display one or 5:SetUpEditor more listnames in the specified order, starting with column 1.
Function or Instruction/Arguments ShadeNorm(lowerbound, upperbound[,m,s]) Shade_t(lowerbound, upperbound,df) Simul sin(value) sinL1(value) sinh(value) sinhL1 (value) Result Key or Keys/Menu or Screen/Item Draws the normal density y= function specified by m and DRAW 1:ShadeNorm( s and shades the area between lowerbound and upperbound. Draws the density function y = for the Student-t DRAW distribution specified by 2:Shade_t( degrees of freedom df, and shades the area between lowerbound and upperbound.
Function or Instruction/Arguments Result SinReg [iterations, Xlistname,Ylistname, period,regequ] Attempts iterations times to fit a sinusoidal regression model to Xlistname and Ylistname using a period guess, and stores the regression equation to regequ. solve(expression, variable,guess, {lower,upper}) Solves expression for variable, given an initial guess and lower and upper bounds within which the solution is sought. SortA(listname) Sorts elements of listname in ascending order.
Function or Instruction/Arguments Result SortD(keylistname,dependl Sorts elements of ist1[,dependlist2, keylistname in descending ..., dependlist n]) order, then sorts each dependlist as a dependent list. startTmr stdDev(list[,freqlist]) Stop Store: value!variable StoreGDB n StorePic n Key or Keys/Menu or Screen/Item y9 OPS 2:SortD( Starts the clock timer. Store y N or note the displayed value, startTmr and use it as the argument for checkTmr( ) to check the elapsed time.
Function or Instruction/Arguments sub(string,begin,length) sum(list[,start,end]) tan(value) Result Key or Keys/Menu or Screen/Item Returns a string that is a subset of another string, from begin to length. sub( yN Returns the sum of y9 elements of list from start to MATH end. 5:sum( Returns the tangent of a š real number, expression, or list. tanL1(value) Returns the arctangent of a y A real number, expression, or list. Tangent(expression, value) Draws a line tangent to expression at X=value.
Function or Instruction/Arguments Text(row,column,text1, text2,...,text n) Result Writes text on graph beginning at pixel (row,column), where 0 row 57 and 0 column 94. Key or Keys/Menu or Screen/Item y< DRAW 0:Text( Then See If:Then Time timeCnv(seconds) Sets sequence graphs to plot with respect to time. †y. Time Converts seconds to units y N of time that can be more timeCnv easily understood for evaluation. The list is in {days,hours,minutes,seconds} format.
Function or Instruction/Arguments tpdf(x,df) Result Key or Keys/Menu or Screen/Item Computes the probability y= density function (pdf) for DISTR the Student-t distribution at 5:tpdf( a specified x value with specified degrees of freedom df. r Trace Displays the graph and enters TRACE mode. T-Test m0[,listname, freqlist,alternative, drawflag] (Data list input) Performs a t test with frequency freqlist. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >.
Function or Instruction/Arguments Result tvm_æ[(Ú,PV,PMT,FV, P/Y,C/Y)] Computes the annual interest rate. tvm_Ú[(æ,PV,PMT,FV, P/Y,C/Y)] Computes the number of payment periods. tvm_Pmt[(Ú,æ,PV,FV, P/Y,C/Y)] Computes the amount of each payment. tvm_PV[(Ú,æ,PMT,FV, P/Y,C/Y)] Computes the present value. UnArchive Moves the specified variables from the user data archive memory to RAM. To archive variables, use Archive. uvAxes Sets sequence graphs to plot u(n) on the x-axis and v(n) on the y-axis.
Function or Instruction/Arguments 1-Var Stats [Xlistname, freqlist] 2-Var Stats [Xlistname, Ylistname,freqlist] variance(list[,freqlist]) Vertical x Result Performs one-variable analysis on the data in Xlistname with frequency freqlist. Key or Keys/Menu or Screen/Item … CALC 1:1-Var Stats Performs two-variable … analysis on the data in CALC Xlistname and Ylistname with 2:2-Var Stats frequency freqlist. Returns the variance of the y 9 elements in list with MATH frequency freqlist.
Function or Instruction/Arguments valueA xor valueB ZBox ZDecimal Result Returns 1 if only valueA or valueB = 0. valueA and valueB can be real numbers, expressions, or lists. Displays a graph, lets you draw a box that defines a new viewing window, and updates the window. Key or Keys/Menu or Screen/Item y: LOGIC 3:xor †q ZOOM 1:ZBox Adjusts the viewing window † q so that @X=0.1 and ZOOM 4:ZDecimal @Y=0.1, and displays the graph screen with the origin centered on the screen.
Result Key or Keys/Menu or Screen/Item Zoom In Magnifies the part of the graph that surrounds the cursor location. †q ZOOM 2:Zoom In Zoom Out Displays a greater portion of the graph, centered on the cursor location. †q ZOOM 3:Zoom Out Function or Instruction/Arguments ZoomFit Recalculates Ymin and †q Ymax to include the ZOOM minimum and maximum Y 0:ZoomFit values, between Xmin and Xmax, of the selected functions and replots the functions.
Function or Instruction/Arguments ZPrevious Result Key or Keys/Menu or Screen/Item Replots the graph using the † q window variables of the MEMORY graph that was displayed 1:ZPrevious before you executed the last ZOOM instruction. ZSquare Adjusts the X or Y window settings so that each pixel represents an equal width and height in the coordinate system, and updates the viewing window. ZStandard Replots the functions immediately, updating the window variables to the default values.
Function or Instruction/Arguments Result Z-Test(m0,s,v,n [,alternative,drawflag]) (Summary stats input) Performs a z test. alternative=L1 is <; alternative=0 is ƒ; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results. ZTrig Replots the functions immediately, updating the window variables to preset values for plotting trig functions. Factorial: value! Returns factorial of value.
Function or Instruction/Arguments Transpose: matrixT xthrootx‡value Result Key or Keys/Menu or Screen/Item Returns a matrix in which y> each element (row, column) MATH is swapped with the 2:T corresponding element (column, row) of matrix. Returns xthroot of value. MATH 5:x‡ xthrootx‡list Returns xthroot of list elements. MATH 5:x‡ listx‡value Returns list roots of value. MATH 5:x‡ listAx‡listB Returns listA roots of listB.
Function or Instruction/Arguments Equal: valueA=valueB Result Returns 1 if valueA = valueB. Returns 0 if valueA ƒ valueB. valueA and valueB can be real or complex numbers, expressions, lists, or matrices. Not equal: valueAƒvalueB Returns 1 if valueA ƒ valueB. Returns 0 if valueA = valueB. valueA and valueB can be real or complex numbers, expressions, lists, or matrices. Less than: valueA
Function or Instruction/Arguments Less than or equal: valueAvalueB Greater than or equal: valueA‚valueB Result Returns 1 if valueA valueB. Returns 0 if valueA > valueB. valueA and valueB can be real or complex numbers, expressions, or lists. Key or Keys/Menu or Screen/Item y: TEST 6: Returns 1 if valueA ‚ y: valueB. Returns 0 if TEST valueA < valueB. valueA and 4:‚ valueB can be real or complex numbers, expressions, or lists.
Function or Instruction/Arguments Result Powers: value^power Returns value raised to power. value can be a real or complex number or expression. Powers: list^power Returns list elements raised to power. Powers: value^list Returns value raised to list elements. Powers: matrix^power Returns matrix elements raised to power. Negation: Lvalue Returns the negative of a real or complex number, expression, list, or matrix.
Function or Instruction/Arguments Result Multiplication: valueälist Returns value times each list element. Multiplication: listävalue Returns each list element times value. Multiplication: listAälistB Returns listA elements times listB elements. Multiplication: valueämatrix Returns value times matrix elements. Multiplication: matrixAämatrixB Returns matrixA times matrixB. Division: valueAàvalueB Returns valueA divided by valueB. Division: listàvalue Returns list elements divided by value.
Function or Instruction/Arguments Result Addition: matrixA+matrixB Returns matrixA elements plus matrixB elements. Concatenation: string1+string2 Concatenates two or more strings. Subtraction: valueANvalueB Subtracts valueB from valueA. Subtraction: valueNlist Subtracts list elements from value. Subtraction: listNvalue Subtracts value from list elements. Subtraction: listANlistB Subtracts listB elements from listA elements.
Appendix B: Reference Information Variables User Variables The TI-84 Plus uses the variables listed below in various ways. Some variables are restricted to specific data types. The variables A through Z and q are defined as real or complex numbers. You may store to them. The TI-84 Plus can update X, Y, R, q, and T during graphing, so you may want to avoid using these variables to store nongraphing data.
Except for system variables, you can store any string of characters, functions, instructions, or variables to the functions Yn, (1 through 9, and 0), XnT/YnT (1 through 6), rn (1 through 6), u(n), v(n), and w(n) directly or through the Y= editor. The validity of the string is determined when the function is evaluated. Archive Variables You can store data, programs or any variable from RAM to user data archive memory where they cannot be edited or deleted inadvertantly.
Statistics Formulas This section contains statistics formulas for the Logistic and SinReg regressions, ANOVA, 2-SampÜTest, and 2-SampTTest.
SinReg The sine regression algorithm applies nonlinear recursive least-squares techniques to optimize the following cost function: N ∑ [a sin ( bxi + c ) + d – yi ] J = 2 i=1 which is the sum of the squares of the residual errors, where: x = the independent variable list y = the dependent variable list N = the dimension of the lists This technique attempts to recursively estimate the constants a, b, c, and d to make J as small as possible.
The mean squares (MS) that make up Ü are: FactorSS FactorMS = -----------------------Factordf ErrorMS = ErrorSS --------------------Errordf The sum of squares (SS) that make up the mean squares are: I FactorSS = ∑ ni ( xi –x ) 2 i=1 I ErrorSS = ∑ ( ni –1 )Sxi2 i=1 The degrees of freedom df that make up the mean squares are: Factordf = I – 1 = numeratordf for Ü I Errordf = ∑ ( ni – 1 ) = denominatordf for Ü i=1 where: I xi Sxi ni x = = = = = number of populations the mean of each list the stan
2-SampFTest Below is the definition for the 2-SampÜTest. Sx1, Sx2 = Sample standard deviations having n – 1 1 and n 2 – 1 degrees of freedom df, respectively. ⎛ Sx1-⎞ = Û-statistic = ⎝ -------Sx2⎠ Ü df(x, n 1 – 1 , n 2 – 1 ) p 2 = Ûpdf( ) with degrees of freedom df, n – 1 , 1 and n 2 – 1 = reported p value 2-SampÜTest for the alternative hypothesis σ 1 > σ 2 . α p = ∫ f ( x ,n 1 – 1 ,n 2 – 1 )dx F 2-SampÜTest for the alternative hypothesis σ 1 < σ 2 .
2-SampÜTest for the alternative hypothesis s1 ƒ s2. Limits must satisfy the following: p = --2 where: ∞ L bnd ∫ f ( x ,n 1 – 1 ,n 2 – 1 ) dx = 0 ∫ f ( x ,n 1 – 1 ,n 2 – 1 ) dx U bnd [Lbnd,Ubnd] = lower and upper limits The Ü-statistic is used as the bound producing the smallest integral. The remaining bound is selected to achieve the preceding integral’s equality relationship. 2-SampTTest The following is the definition for the 2-SampTTest.
where the computation of S and df are dependent on whether the variances are pooled.
Financial Formulas This section contains financial formulas for computing time value of money, amortization, cash flow, interest-rate conversions, and days between dates. Time Value of Money i = [e ( y × ln ( x + 1 ) ) where PMT y : x C/Y P/Y I% ƒ = = = = = ] –1 0 C/Y ÷ P/Y (.
The iteration used to compute i: –N –N 1 – (1 + i) 0 = PV + PMT × G i ------------------------------ + FV × ( 1 + i ) i I% = 100 × C ⁄ Y × [ e where: x y ( y × ln ( x + 1 ) ) – 1] = i = P/Y ÷ C/Y Gi = 1 + i × k where: k k = 0 for end-of-period payments = 1 for beginning-of-period payments PMT × G i – FV × i ln ⎛ ----------------------------------------------⎞ ⎝ PMT × G i + PV × i⎠ N = ---------------------------------------------------------ln ( 1 + i ) where: i ƒ 0 N = – ( PV + FV ) ÷ PMT Append
where: i = 0 –i PV + FV PMT = ----- × PV + ---------------------------N Gi (1 + i) – 1 where: i ƒ 0 PMT = – ( PV + FV ) ÷ N where: i = 0 PMT × G 1 - PMT × G i PV = ------------------------i – FV × -----------------– -----------------------N i i (1 + i) where: i ƒ 0 PV = – ( FV + PMT × N ) where: i = 0 PMT × G PMT × G N FV = ------------------------i – ( 1 + i ) × ⎛ PV + ------------------------i⎞ ⎝ ⎠ i i where: i ƒ 0 FV = – ( PV + PMT × N ) where: i = 0 Appendix B: Reference Information 637
Amortization If computing bal(), pmt2 = npmt Let bal(0) = RND(PV) Iterate from m = 1 to pmt2 ⎧ I m = RND [ RND12 ( – i × bal ( m – 1 ) ) ] ⎨ ⎩ bal ( m ) = bal ( m – 1 ) – I m + RND ( PMT ) then: bal( ) = bal ( pmt2 ) ΣPrn( ) = bal ( pmt2 ) – bal ( pmt1 ) ΣInt( ) = ( pmt2 – pmt1 + 1 ) × RND ( PMT ) – ΣPrn( ) where: RND RND12 = round the display to the number of decimal places selected = round to 12 decimal places Balance, principal, and interest are dependent on the values of PMT, PV, æ, and pmt1 and pmt2.
Cash Flow N ∑ CFj ( 1 + i ) npv( ) = CF 0 + -S – 1(1 j j=1 ⎧ j ⎪ n ⎪ Sj = ⎨ ∑ i i = 1 ⎪ ⎪ 0 ⎩ where: - nj – (1 + i) ) ----------------------------------i j≥1 j = 0 Net present value is dependent on the values of the initial cash flow (CF0), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i). irr() = 100 × i, where i satisfies npv() = 0 Internal rate of return is dependent on the values of the initial cash flow (CF0) and subsequent cash flows (CFj).
4Nom = where: x 100 × CP × [ e 1 ÷ CP × ln ( x + 1 ) – 1] = .01 × Eff Eff = effective rate CP = compounding periods Nom = nominal rate Days between Dates With the dbd( function, you can enter or compute a date within the range Jan. 1, 1950, through Dec. 31, 2049.
+ (number of days MB to M2) + DT2 + ( Y2 – YB ) -----------------------4 where: M1 DT1 Y1 M2 DT2 Y2 MB DB YB = = = = = = = = = month of first date day of first date year of first date month of second date day of second date year of second date base month (January) base day (1) base year (first year after leap year) Appendix B: Reference Information 641
Important Things You Need to Know About Your TI-84 Plus TI-84 Plus Results There may be a number of reasons that your TI-84 Plus is not displaying the expected results; however, the most common solutions involve order of operations or mode settings. Your calculator uses an Equation Operating System (EOS) which evaluates the functions in an expression in the following order: 1. Functions that precede the argument, such as square root, sin(, or log( 2.
If you are using trigonometric functions or performing polar and rectangular conversions, the unexpected results may be caused by an angle mode setting. The Radian and Degree angle mode settings control how the TI-84 Plus interprets angle values. To change the angle mode settings, follow these steps: 1. Press z to display the Mode settings. 2. Select Degree or Radian. 3. Press Í to save the angle mode setting.
TI-84 Plus Identification Code Your graphing calculator has a unique identification (ID) code that you should record and keep. You can use this 14 digit ID to register your calculator at education.ti.com or identify your calculator in the event that it is lost or stolen. A valid ID includes numbers 0 through 9 and the letters A through F. You can view the calculator’s Operating System, Product Number, ID, and Certificate Revision Number from the About screen.
Apps TI-84 Plus Software Applications (Apps) is software that you can add to your calculator in the same way you would add software to your computer. Apps let you customize your calculator for peak performance in specific areas of study. You can find apps for the TI-84 Plus at the TI Online Store at education.ti.com. TI-Cares KnowledgeBase The TI-Cares KnowledgeBase provides 24-hour access through the Web to find answers to frequently asked questions.
Error Conditions When the TI-84 Plus detects an error, it returns an error message as a menu title, such as ERR:SYNTAX or ERR:DOMAIN. This table contains each error type, possible causes, and suggestions for correction. The error types listed in this table are each preceded by ERR: on your graphing calculator display. For example, you will see ERR:ARCHIVED as a menu title when your graphing calculator detects an ARCHIVED error type.
Error Type Possible Causes and Suggested Remedies BAD GUESS • In a CALC operation, you specified a Guess that is not between Left Bound and Right Bound. • For the solve( function or the equation solver, you specified a guess that is not between lower and upper. • Your guess and several points around it are undefined. Examine a graph of the function. If the equation has a solution, change the bounds and/or the initial guess.
Error Type Possible Causes and Suggested Remedies DIM MISMATCH Your calculator displays the ERR:DIM MISMATCH error if you are trying to perform an operation that references one or more lists or matrices whose dimensions do not match. For example, multiplying L1*L2, where L1={1,2,3,4,5} and L2={1,2} produces an ERR:DIM MISMATCH error because the number of elements in L1 and L2 do not match. DIVIDE BY 0 • You attempted to divide by zero. This error is not returned during graphing.
Error Type Possible Causes and Suggested Remedies Error in Xmit • • The TI-84 Plus was unable to transmit an item. Check to see that the cable is firmly connected to both units and that the receiving unit is in receive mode. You pressed É to break during transmission. • You attempted to perform a backup from a TI.82 to a TI-84 Plus. • You attempted to transfer data (other than L1 through L6) from a TI-84 Plus to a TI.82. • You attempted to transfer L1 through L6 from a TI-84 Plus to a TI.
Error Type Possible Causes and Suggested Remedies INVALID • You attempted to reference a variable or use a function where it is not valid. For example, Yn cannot reference Y, Xmin, @X, or TblStart. • You attempted to reference a variable or function that was transferred from the TI.82 and is not valid for the TI-84 Plus For example, you may have transferred UnN1 to the TI-84 Plus from the TI.82 and then tried to reference it.
Error Type Possible Causes and Suggested Remedies ITERATIONS • The solve( function or the equation solver has exceeded the maximum number of permitted iterations. Examine a graph of the function. If the equation has a solution, change the bounds, or the initial guess, or both. • irr( has exceeded the maximum number of permitted iterations. • When computing æ, the maximum number of iterations was exceeded. LABEL The label in the Goto instruction is not defined with a Lbl instruction in the program.
Error Type Possible Causes and Suggested Remedies MODE You attempted to store to a window variable in another graphing mode or to perform an instruction while in the wrong mode; for example, DrawInv in a graphing mode other than Func. NO SIGN CHNG • • • The solve( function or the equation solver did not detect a sign change. You attempted to compute æ when FV, (Ú…PMT), and PV are all ‚ 0, or when FV, (Ú…PMT), and PV are all _ 0.
Error Type Possible Causes and Suggested Remedies SINGULAR MAT • A singular matrix (determinant = 0) is not valid as the argument for L1. • The SinReg instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph.
Error Type Possible Causes and Suggested Remedies SYNTAX The command contains a syntax error. Look for misplaced functions, arguments, parentheses, or commas. Appendix A displays the arguments and punctuation needed to execute the function or instruction. For example, stdDev(list[,freqlist]) is a function of the TI-84 Plus. The arguments are shown in italics. The arguments in brackets are optional and you need not type them. You must also be sure to separate multiple arguments with a comma (,).
Error Type Possible Causes and Suggested Remedies VARIABLE You have tried to archive a variable that cannot be archived or you have tried to unarchive an application or group. Examples of variables that cannot be archived include: • Real numbers LRESID, R, T, X, Y, Theta, Statistic variables under Vars, STATISTICS menu, Yvars, and the AppIdList. VERSION You have attempted to receive an incompatible variable version from another graphing calculator.
Accuracy Information Computational Accuracy To maximize accuracy, the TI-84 Plus carries more digits internally than it displays. Values are stored in memory using up to 14 digits with a two-digit exponent. • You can store a value in the window variables using up to 10 digits (12 for Xscl, Yscl, Tstep, and qstep). • Displayed values are rounded as specified by the mode setting with a maximum of 10 digits and a two-digit exponent. • RegEQ displays up to 14 digits in Float mode.
• In Full screen mode, @Y is calculated as (Ymax N Ymin) à 62. In Horiz split-screen mode, @Y is calculated as (Ymax N Ymin) à 30. In G-T split-screen mode, @Y is calculated as (Ymax N Ymin) à 50. • If you enter a value for @Y from the home screen or a program in Full screen mode, Ymax is calculated as Ymin + @Y É… 62. In Horiz split-screen mode, Ymax is calculated as Ymin + @Y … 30. In G-T split-screen mode, Ymax is calculated as Ymin + @Y É … 50.
Function Range of Input Values sinh x, cosh x |x| 230.25850929940 tanh x |x| < 10 100 sinhL1 x |x| < 5 × 10 99 coshL1 x 1 x < 5 × 10 99 tanhL1 x L1 < x < 1 ‡x (real mode) 0 x < 10 100 ‡x (complex mode) |x| < 10 100 x! L.5 _x 69, where x is a multiple of .
Appendix C: Service and Warranty Information Texas Instruments Support and Service For general information Home Page: education.ti.com KnowledgeBase and e-mail inquiries: education.ti.com/support Phone: (800) TI-CARES / (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands only International information: education.ti.com/international For technical support KnowledgeBase and support by e-mail: education.ti.
Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin Islands: Always contact Texas Instruments Customer Support before returning a product for service. All other customers: Refer to the leaflet enclosed with this product (hardware) or contact your local Texas Instruments retailer/distributor.
Texas Instruments (TI) Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments ("TI") electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage.
Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction.
All Other Customers For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor.
Battery Information When to Replace the Batteries The TI-84 Plus uses five batteries: four AAA alkaline batteries and one SR44SW or 303 silver oxide backup battery. The silver oxide battery provides auxiliary power to retain memory while you replace the AAA batteries. When the battery voltage level drops below a usable level, the TI-84 Plus: Displays this message when you turn on the unit. Displays this message when you attempt to download an application.
Effects of Replacing the Batteries Do not remove both types of batteries (AAA and silver oxide) at the same time. Do not allow the batteries to lose power completely. If you follow these guidelines and the steps for replacing batteries, you can replace either type of battery without losing any information in memory. Battery Precautions Take these precautions when replacing batteries. • Do not leave batteries within reach of children • Do not mix new and used batteries.
1. Turn off the graphing calculator. Replace the slide cover over the keyboard to avoid inadvertently turning on the graphing calculator. Turn the back of the unit toward you. 2. Hold the graphing calculator upright, push downward on the latch on the top of the battery cover, and then pull the cover toward you. Note: To avoid loss of information stored in memory, you must turn off the graphing calculator. Do not remove the AAA batteries and the silver oxide battery simultaneously. 3.
In Case of Difficulty Handling a Difficulty To handle a difficulty, follow these steps. 1. If you cannot see anything on the screen, you may need to adjust the graphing calculator contrast. To darken the screen, press and release y, and then press and hold } until the display is sufficiently dark. To lighten the screen, press and release y, and then press and hold † until the display is sufficiently light. 2. If an error menu is displayed, follow these steps: • Note the error type (ERR:error type).
• Select the type of data you want to delete, or select 1:All for a list of all variables of all types. A screen is displayed listing each variable of the type you selected and the number of bytes each variable is using. • Press } and † to move the selection cursor (4) next to the item you want to delete, and then press {. 5. If the graphing calculator does not seem to work at all, be sure the alkaline batteries are fresh and that they are installed properly. 6.
Appendix C: Service and Warranty Information 669
Index Symbols !dim( (assign dimension) . . . . . . . . . 261 (- (degrees notation) . . . . . . . . . . . . . 620 (- (negation) . . . . . . . . . . . . . . 42, 55, 624 (– (subtraction) . . . . . . . . . . . . . . . 53, 626 (! (factorial) . . . . . . . . . . . . . . . . . . . . . 620 (! Store . . . . . . . . . . . . . . . . . . . . 27, 611 (!dim( (assign dimension) . . . . . 238, 574 (# (not equal to) . . . . . . . . . . . . . . . . . 622 ($( (square root) . . . . . . . . . . . . .
{ } (list indicator) . . . . . . . . . . . . . . . . 249 Numerics 10^( (power of ten) . . . . . . . . . . . . . . 624 1-PropZInt (one-proportion z confidence interval) . . . . . . . . . . . . . . . 357, 597 1-PropZTest (one-proportion z test) . 349, 597 1-Var Stats (one-variable statistics) . 307, 616 2-PropZInt (two-proportion z confidence interval) . . . . . . . . . . . . . . . 357, 597 2-PropZTest (two-proportion z test) . 350, 598 2-SampFTest (two-sample F-Test) . .
archive full error . . . . . . . . . 546, 646 garbage collection . . . . . . . . . . . 542 memory error . . . . . . . . . . . . . . . 542 archived variables . . . . . . . . . . . . . . . 628 arcsine (sin/( ) . . . . . . . . . . . . . . . . . . 53 arctangent (tan/( ) . . . . . . . . . . . . . . . 53 Asm( . . . . . . . . . . . . . . . . . . . . . 458, 567 AsmComp( . . . . . . . . . . . . . . . . 458, 567 AsmPrgm( . . . . . . . . . . . . . . . . . 458, 567 assembly language programs . . . . . 458 augment( . .
home screen (ClrHome) . . . 454, 570 list (ClrList) . . . . . . . . . . . . . 300, 571 table (ClrTable) . . . . . . . . . 454, 571 Clock . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Clock Off . . . . . . . . . . . . . . . . . . . . . . . 14 Clock On . . . . . . . . . . . . . . . . . . . . . . . 13 ClockOff, turn clock off . . . . . . . . . . . 570 ClockOn, turn clock on . . . . . . . . . . . 570 ClrAllLists (clear all lists) . . . . . . 514, 570 ClrDraw (clear drawing) . . . . . .
cosh/( (hyperbolic arccosine) . . 423, 572 cosine (cos( ) . . . . . . . . . . . . . . . . . . . 53 cosine (cos( ) . . . . . . . . . . . . . . . . . . 571 cross pixel mark (+) . . . . . . . . . 203, 322 cube (³) . . . . . . . . . . . . . . . . . . . . 58, 621 cube root (³$( ) . . . . . . . . . . . . . . . . . . 58 cube root (³$( ) . . . . . . . . . . . . . . . . . 621 cubic regression (CubicReg) . . 309, 572 CubicReg (cubic regression) . .
invNorm( . . . . . . . . . . . . . . . 375, 585 normalcdf( . . . . . . . . . . . . . 374, 592 normalpdf( . . . . . . . . . . . . . 373, 593 poissoncdf( . . . . . . . . . . . . . 381, 596 poissonpdf( . . . . . . . . . . . . . 381, 596 distribution shading instructions Shade_t( . . . . . . . . . . . . . . . 384, 609 Shadeχ²( . . . . . . . . . . . . . . 385, 608 ShadeF( . . . . . . . . . . . . . . . 385, 608 ShadeNorm( . . . . . . . . . . . . 383, 609 division (/) . . . . . . . . . . . . . . . . . .
areas of regular n-sided polygons . . 506 box plots . . . . . . . . . . . . . . . . . . . 477 box with lid . . . . . . . . . . . . . . . . . 466 defining a 466 defining a table of values 467 setting the viewing window 470 tracing the graph 472 zooming in on the graph 474 zooming in on the table 468 cobweb attractors . . . . . . . . . . . . 489 fundamental theorem of calculus 502 guess the coefficients . . . . . . . . . 491 inequalities . . . . . . . . . . . . . . . . . 483 mortgage payments . . . . . . . .
F Faceplates . . . . . . . . . . . . . . . . . . . . . 10 factorial (!) . . . . . . . . . . . . . . . . . . . . . 620 family of curves . . . . . . . . . . . . . . . . . 112 FCC statement . . . . . . . . . . . . . . . . . . . iii Fill( . . . . . . . . . . . . . . . . . . . . . . 239, 577 FINANCE CALC menu . . . . . . . . . . . 393 FINANCE VARS menu . . . . . . . . . . . 405 financial functions amortization schedules . . . . . . . 399 cash flows . . . . . . . . . . . . . . . . . 397 days between dates . . . .
moving the cursor to a value . . . 116 overlaying functions on a graph . 112 panning . . . . . . . . . . . . . . . . . . . 117 pausing or stopping a graph . . . . 111 Quick Zoom . . . . . . . . . . . . . . . . 117 selecting . . . . . . . . . . . . 99, 100, 578 shading . . . . . . . . . . . . . . . . . . . . 103 Smart Graph . . . . . . . . . . . . . . . . 111 tracing . . . . . . . . . . . . . . . . . . . . 115 viewing window . . . . . . . . . . . . . 105 window variables . . . . . . . . 105, 106 Y= editor .
greatest common divisor (gcd( ) . . . . . 71 greatest common divisor (gcd( ) . . . . 580 greatest integer (int( ) . . . . . . . . . 70, 235 greatest integer (int( ) . . . . . . . . . . . . 585 GridOff . . . . . . . . . . . . . . . . . . . 109, 583 GridOn . . . . . . . . . . . . . . . . . . . 109, 583 grouping . . . . . . . . . . . . . . . . . . . . . . 535 G-T (graph-table split-screen mode) . 24, 216, . . . . . . . . . . . . . . . . . . . . . . 583 H Histogram plot type (&) . . . . . . . . .
interest rate conversions 4Eff( (compute effective interest rate) 402, . . . . . . . . . . . . . . . . . . . 403 4Nom( (compute nominal interest rate) . . . . . . . . . . . . . . . . . . . . . . . 402 calculating . . . . . . . . . . . . . . . . . 402 formula . . . . . . . . . . . . . . . . . . . . 639 internal rate of return (irr( ) . . . . . . . . 398 internal rate of return (irr( ) . . . . . . . . 586 intersect operation on a graph . . . . . 129 inverse (/) . . . . . . . . . . . . . .
LinRegTTest (linear regression t test) . . 363, . . . . . . . . . . . . . . . . . . . . . . 588 LinReqTInt (confidence interval for slope) 365 LIST MATH menu . . . . . . . . . . . . . . . 269 LIST NAMES menu . . . . . . . . . . . . . 251 LIST OPS menu . . . . . . . . . . . . . . . . 258 List4matr( (lists-to-matrix conversion) 241, . . . . . . . . . . . . . . . . . . . . . . 267, 588 lists accessing an element . . . . . . . . 250 attaching formulas . . . 253, 255, 289 clearing all elements . . . . . . . . .
selecting . . . . . . . . . . . . . . . . . . . 223 viewing . . . . . . . . . . . . . . . . . . . . 225 MATRX EDIT menu . . . . . . . . . . . . . 223 MATRX MATH menu . . . . . . . . . . . . 236 MATRX NAMES menu . . . . . . . . . . . 228 max( (maximum) . . . . . . . . . 70, 270, 590 maximum of a function (fMax( ) . . . . . 59 maximum of a function (fMax( ) . . . . 578 maximum operation on a graph . . . . 129 mean( . . . . . . . . . . . . . . . . . . . . 270, 590 Med(Med (median-median) . . . . . . .
multiplication (*) . . . . . . . . . . . . . 53, 624 multiplicative inverse . . . . . . . . . . . . . 54 N N (number of payment periods variable) . 391, . . . . . . . . . . . . . . . . . . . . . . 406 nCr (number of combinations) . . 80, 591 nDeriv( (numerical derivative) . . . 60, 592 negation (-) . . . . . . . . . . . . . . 42, 55, 624 nonrecursive sequences . . . . . . . . . . 157 normal distribution probability (normalcdf( ) . . . . . . . . . . . . 374, 592 Normal notation mode . . . . . . . .
tracing . . . . . . . . . . . . . . . . . . . . 141 window variables . . . . . . . . . . . . 139 Y= editor . . . . . . . . . . . . . . . . . . . 137 zoom operations . . . . . . . . . . . . . 143 parentheses . . . . . . . . . . . . . . . . . . . . 41 path graph style . . . . . . . . . . . . . . . . 101 Pause . . . . . . . . . . . . . . . . . . . . 441, 594 pausing a graph . . . . . . . . . . . . . . . . 111 Pen . . . . . . . . . . . . . . . . . . . . . . . . . . 200 permutations (nPr) . . . . . . . . . . .
probability density function (normalpdf( ) 373 probability density function (normalpdf( ) 593 prod( (product) . . . . . . . . . . . . . 271, 597 programming copying and renaming . . . . . . . . 433 creating new . . . . . . . . . . . . . . . . 427 defined . . . . . . . . . . . . . . . . . . . . 427 deleting . . . . . . . . . . . . . . . . . . . . 428 deleting command lines . . . . . . . 433 editing . . . . . . . . . . . . . . . . . . . . . 432 entering command lines . . . . . . . 430 executing . . . . . . .
RecallGDB . . . . . . . . . . . . . . . . 209, 601 RecallPic . . . . . . . . . . . . . . . . . . 206, 601 rectangular form, complex numbers . . 74 RectGC (rectangular graphing coordinates) . . . . . . . . . . . . 109, 602 recursive sequences . . . . . . . . . . . . . 158 ref( (row-echelon form) . . . . . . . 243, 602 RegEQ (regression equation variable) . . 303, . . . . . . . . . . . . . . . . . . . . . . 519 regression model automatic regression equation . . 303 automatic residual list feature . .
graph styles . . . . . . . . . . . . . . . . 156 moving the cursor to a value . . . 163 nonrecursive sequences . . . . . . 157 recursive sequences . . . . . . . . . 158 selecting and deselecting . . . . . . 156 TI-84 Plus versus TI-82 table . . . 173 tracing . . . . . . . . . . . . . . . . . . . . 162 web plots . . . . . . . . . . . . . . . . . . 165 window variables . . . . . . . . . . . . 159 Y= editor . . . . . . . . . . . . . . . . . . . 155 ZOOM (zoom menu) . . . . . . . . .
STAT CALC menu . . . . . . . . . . . . . . 306 STAT EDIT menu . . . . . . . . . . . . . . . 299 stat list editor attaching formulas to list names . 289 clearing elements from lists . . . . 287 creating list names . . . . . . . . . . . 286 detaching formulas from list names . 292 displaying . . . . . . . . . . . . . . . . . . 283 edit-elements context . . . . . . . . . 296 editing elements of formula-generated lists . . . . . . . . . . . . . . . . . . . 293 editing list elements . . . . . . . . . .
tracing . . . . . . . . . . . . . . . . . . . . 326 turning on/off stat plots . . . . 100, 325 viewing window . . . . . . . . . . . . . 326 xyLine . . . . . . . . . . . . . . . . . . . . . 319 statistical variables table . . . . . . . . . . 315 Stats input option . . . . . . . . . . . 336, 337 stdDev( (standard deviation) . . 272, 611 Stop . . . . . . . . . . . . . . . . . . . . . 446, 611 Store (!) . . . . . . . . . . . . . . . . . . . 27, 611 StoreGDB . . . . . . . . . . . . . . . . . 208, 611 StorePic .
TEST LOGIC (Boolean menu) . . . . . . 90 Text( instruction . . . . . . . . . . 198, 219, 613 placing on a graph . . . . . . . 198, 219 Then . . . . . . . . . . . . . . . . . . . . . 437, 584 thick graph style . . . . . . . . . . . . . . . . 101 TI Connect™ . . . . . . . . . . . . . . . . . . 552 TI-84 Plus key code diagram . . . . . . . . . . . . 454 keyboard . . . . . . . . . . . . . . . . . . . . 1 Time axes format . . . . . . . . . . .
axes . . . . . . . . . . . . . . . . . . . . . . 110 calculator . . . . . . . . . . . . . . . . . . . . 4 coordinates . . . . . . . . . . . . . . . . . 109 expressions . . . . . . . . . . . . . . . . 110 functions . . . . . . . . . . . . . . . . . . . 100 grid . . . . . . . . . . . . . . . . . . . . . . . 109 labels . . . . . . . . . . . . . . . . . . . . . 110 points . . . . . . . . . . . . . . . . . . . . . 201 stat plots . . . . . . . . . . . . . . . 100, 325 tvm_FV (future value) . . . . . . . .
Zoom . . . . . . . . . . . . . . . . . . . . . . 38 Vertical (draw line) . . . . . . . . . . 191, 616 viewing window . . . . . . . . . . . . . . . . . 105 vw/uvAxes (axes format) . . . . . 161, 616 W w sequence function . . . . . . . . . . . . . warranty . . . . . . . . . . . . . . . . . . . . . . Web (axes format) . . . . . . . . . . 161, web plots . . . . . . . . . . . . . . . . . . . . . While . . . . . . . . . . . . . . . . . . . . . 440, window variables function graphing . . . . . . . . . . . .
ZPrevious (use previous window) . . . 619 ZSquare (set square pixels) . . . 121, 619 ZStandard (use standard window) . . 122, 619 Z-Test (one-sample z test) . . . . 342, 619 ZTrig (trigonometric window) . .
