Summary of Contents for Texas Instruments TI-84 Plus
Page 1
TI-84 Plus TI-84 Plus Silver Edition Guidebook...
Page 2
Important Information Important Information Important Information Important Information Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is"...
Page 3
Interference Interference Interference Interference This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications.
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. The two graphing calculators differ only in available RAM memory, interchangeable faceplates, and Flash application ROM memory.
Page 5
— Scientific calculator keys access the capabilities of a standard scientific Scientific calculator. TI-84 Plus TI-84 Plus TI-84 Plus TI-84 Plus Graphing Keys Editing Keys Advanced Function Keys Scientific Calculator Keys Chapter 1: Operating the TI-84 Plus Silver Edition...
Coded Keyboard 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.
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. Chapter 1: Operating the TI-84 Plus Silver Edition...
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.
Page 9
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. The TI-84 Plus has 40 contrast settings, so each number 0 through 9 represents Note: four settings.
Page 10
Types of Displays Types of Displays The TI-84 Plus displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI-84 Plus can display a horizontally or vertically split screen to show graphs and text simultaneously. Home Screen...
Page 11
Displaying Entries and Answers 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.
Page 12
Busy Indicator 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.
Page 13
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 Removing a Faceplate Removing a Faceplate Removing a Faceplate 1.
Page 14
Use the Clock to set the time and date, select the clock display format, and turn the clock on and off. The clock is turned on by default and is accessed from the mode screen. Chapter 1: Operating the TI-84 Plus Silver Edition...
Page 15
Press Í. 6. Press † to highlight HOUR the hour. A number from 1–12 or 0–23. Chapter 1: Operating the TI-84 Plus Silver Edition SET CLOCK . Press ‘ and type YEAR . Press ‘ and MONTH .
Page 16
Turning the Clock On There are two options to turn the clock on. One option is through the other is through the Catalog. Chapter 1: Operating the TI-84 Plus Silver Edition . Press ‘ and MINUTE . Press ~ or | to AM/PM .
Page 17
1. Press y N. 2. Press † or } to scroll the selection cursor points to 3. Press Í. will turn off the Clock display. ClockOff Chapter 1: Operating the TI-84 Plus Silver Edition until the CATALOG ClockOn. until the CATALOG...
Page 18
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, pR is an expression.
Page 19
2. Press y D. â is pasted to the cursor location. 3. If the exponent is negative, press Ì, and then enter the exponent, which can be one or two digits. Chapter 1: Operating the TI-84 Plus Silver Edition ¤...
Page 20
A function returns a value. For example, example on the previous page. In general, the first letter of each function is lowercase on the TI-84 Plus. Most functions take at least one argument, as indicated by an open parenthesis ( ) following the name.
Page 21
Deletes a character at the cursor; this key repeats. Changes the cursor to an underline (__); inserts characters in front of the underline cursor; to end insertion, press † Chapter 1: Operating the TI-84 Plus Silver Edition moves the † moves the...
Page 22
Mode settings control how the TI-84 Plus displays and interprets numbers and graphs. Mode settings are retained by the Constant Memory feature when the TI-84 Plus is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings.
Page 23
1. Press † or } to move the cursor to the line of the setting that you want to change. 2. Press ~ or | to move the cursor to the setting you want. 3. Press Í. Chapter 1: Operating the TI-84 Plus Silver Edition...
Page 24
12.34567 If you select Note: Normal absolute value is less than .001), the TI-84 Plus expresses the answer in scientific notation. Chapter 1: Operating the TI-84 Plus Silver Edition . From a blank program command line, select the mode setting 12345.67...
Page 25
Radian, Degree Radian, Degree Radian, Degree Radian, Degree Angle modes control how the TI-84 Plus interprets angle values in trigonometric functions and polar/rectangular conversions. mode interprets angle values as radians. Answers display in radians. Radian mode interprets angle values as degrees. Answers display in degrees.
Page 26
(simultaneous) graphing-order mode evaluates and plots all selected functions for Simul a single value of X and then evaluates and plots them for the next value of X. Chapter 1: Operating the TI-84 Plus Silver Edition is a function of q (Chapter 5).
Page 27
Regardless of which graphing mode is selected, the TI-84 Plus will sequentially Note: graph all stat plots before it graphs any functions. Real, a+b Real, a+b , re^ re^q Real, a+b Real, a+b , re^ , re^ mode does not display complex results unless complex numbers are entered as Real input.
Page 28
Variables and Defined Items Variables and Defined Items 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.
Page 29
Flash ROM. Apps variable holder used to store variables created by independent applications. You cannot edit or change variables in which created them. Chapter 1: Operating the TI-84 Plus Silver Edition Names Applications Application variables Grouped variables Xmin, Xmax, and others functions (Chapters 3, 4, 5, and 6).
Page 30
Displaying a Variable Value Displaying a Variable Value Displaying a Variable Value To display the value of a variable, enter the name on a blank line on the home screen, and then press Í. Chapter 1: Operating the TI-84 Plus Silver Edition...
Page 31
• menu; then select the type and then the name of the variable or function. Chapter 1: Operating the TI-84 Plus Silver Edition and the edit cursor are displayed on the bottom line of the menu or ~ to display the...
Page 32
When you press Í on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI-84 Plus, ENTRY is retained in memory. Chapter 1: Operating the TI-84 Plus Silver Edition...
Page 33
Accessing a Previous Entry Accessing a Previous Entry The TI-84 Plus retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes. To scroll those entries, press y [ repeatedly. If a single entry is more than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage area.
Page 34
To store to ENTRY two or more expressions or instructions, separate each expression or instruction with a colon, then press Í. All expressions and instructions separated by colons are stored in ENTRY. Chapter 1: Operating the TI-84 Plus Silver Edition...
Page 35
When an expression is evaluated successfully from the home screen or from a program, the TI-84 Plus stores the answer to a storage area called a real or complex number, a list, a matrix, or a string. When you turn off the TI-84 Plus, the value in is retained in memory.
Page 36
Continuing an Expression You can use as the first entry in the next expression without entering the value again or pressing y Z. On a blank line on the home screen, enter the function. The TI-84 Plus pastes the variable name ¥...
Page 37
Using a TI-84 Plus Menu 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.
Page 38
Displaying a Menu Displaying a Menu Displaying a Menu While using your TI-84 Plus, you often will need to access items from its menus. When you press a key that displays a menu, that menu temporarily replaces the screen where you are working.
Page 39
To page down six menu items at a time, press ƒ †. To page up six menu items at a time, press ƒ }. The green arrows on the graphing calculator, between † and }, are the page-down and page-up symbols.
Page 40
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. On the Note: LIST NAMES and 0 are labeled in such a way that you can select them by pressing the appropriate number key.
Page 41
VARS Y-VARS 1: Window... 2: Zoom... Chapter 1: Operating the TI-84 Plus Silver Edition menu items display secondary menus, VARS 1:Window X/Y, T/ , and U/V/W variables...
Page 42
¬, −, and ®. To select a variable from the 1. Display the VARS Press to display the • Chapter 1: Operating the TI-84 Plus Silver Edition Graph database variables Picture variables , EQ, TEST, and PTS variables TABLE variables String variables menu, press ...
Page 43
Order of Evaluation The Equation Operating System (EOS) defines the order in which functions in expressions are entered and evaluated on the TI-84 Plus. EOS lets you enter numbers and functions in a simple, straightforward sequence. EOS evaluates the functions in an expression in this order.
Page 44
Implied Multiplication Implied Multiplication Implied Multiplication 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 … as implied multiplication. TI-84 Plus implied multiplication rules, although like the TI-83, differ from those of Note: the TI-82.
Page 45
To enter a negative number, use the negation key. Press Ì and then enter the number. On the TI-84 Plus, negation is in the third level in the EOS hierarchy. Functions in the first level, such as squaring, are evaluated before negation.
Page 46
1.5 Megabytes (M) of Available Memory 1.5 Megabytes (M) of Available Memory 1.5 M of available memory are built into the TI-84 Plus Silver Edition, and .5 M for the TI-84 Plus. About 24 kilobytes (K) of RAM (random access memory) are available for you to compute and store functions, programs, and data.
Page 47
Archiving Archiving Archiving You can store variables in the TI-84 Plus user data archive, a protected area of memory separate from RAM. The user data archive lets you: • Store data, programs, applications or any other variables to a safe location where they cannot be edited or deleted inadvertently.
Page 48
You can split the screen horizontally to display both a graph and a related editor (such as the Y= editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously. Chapter 1: Operating the TI-84 Plus Silver Edition...
Page 49
You can plot the data as a histogram, xyLine, scatter plot, modified or regular box-and-whisker plot, or normal probability plot. You can define and store up to three stat plot definitions. For details, refer to: Chapter 12 Chapter 1: Operating the TI-84 Plus Silver Edition...
Page 50
CATALOG CATALOG The CATALOG is a convenient, alphabetical list of all functions and instructions on the TI-84 Plus. You can paste any function or instruction from the CATALOG to the current cursor location. For details, refer to: Chapter 15 Programming...
Page 51
I/O port using an I/O unit-to-unit cable to communicate with a TI-84 Plus Silver Edition, a TI-84 Plus, a TI-83 Plus Silver Edition, a TI-83 Plus, a TI-83, a TI-82, a TI-73, CBL 2™, or a CBR™ System.
Page 52
• Plotting a graph • Storing a value When the TI-84 Plus detects an error, it returns an error message as a menu title, such ERR:SYNTAX ERR:DOMAIN reasons for the error. (or press y 5 or ‘), then the home screen is displayed.
Page 53
, if it is available. The previous screen is displayed with the cursor at or 2:Goto near the error location. 3. Determine the error. If you cannot recognize the error, refer to Appendix B. 4. Correct the expression. Chapter 1: Operating the TI-84 Plus Silver Edition...
Page 54
Math, Angle, and Test Operations Math, Angle, and Test Operations Math, Angle, and Test Operations Math, Angle, and Test Operations Getting Started: Coin Flip Getting Started: Coin Flip Getting Started: Coin Flip 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.
Page 55
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 . You then can use the data for another activity, such as plotting a histogram (Chapter 12).
Page 56
Addition, Subtraction, Multiplication, Addition, Subtraction, Addition, Subtraction, Addition, Subtraction, 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 valueB …...
Page 57
Power, Square, Square Root Power, Square, Square Root Power, Square, Square Root Power, Square, Square Root (power, ›), You can use complex numbers, expressions, lists, and matrices. You cannot use ‡ È value^power Inverse Inverse Inverse Inverse (inverse, œ) with real and complex numbers, expressions, lists, and You can use matrices.
Page 58
Constant Constant Constant Constant (constant, y ) is stored as a constant on the TI-84 Plus. Press y the cursor location. In calculations, the TI-84 Plus uses 2.718281828459 for Negation Negation Negation Negation M (negation, Ì) returns the negative of numbers, expressions, lists, and matrices.
Page 59
(N), which is displayed when you press ¹. Pi 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. Chapter 2: Math, Angle, and Test Operations...
Page 60
MATH Menu MATH Menu MATH Menu MATH Menu menu, press . To display the MATH MATH NUM CPX PRB 4Frac Displays the answer as a fraction. 4Dec Displays the answer as a decimal. Calculates the cube. Calculates the cube root. ‡( ‡...
Page 61
cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use 4 Frac value (display as a decimal) displays an answer in decimal form. You can use 4 real or complex numbers, expressions, lists, and matrices. You can only use 4 following value value...
Page 62
(Root) (Root) (Root) (Root) ‡ ‡ ( root) returns the expressions, and lists. ‡ root value fMin(, fMax( fMin(, fMax( fMin(, fMax( fMin(, fMax( (function minimum) and fMin( local minimum or local maximum value of between values for lower upper accuracy is controlled by fMin(expression,variable,lower,upper fMax(expression,variable,lower,upper...
Page 63
You can use once in nDeriv( the TI-84 Plus can return a false derivative value at a nondifferentiable point. Chapter 2: Math, Angle, and Test Operations at which to calculate the derivative and H (if not specified, the . Because of the method used to calculate...
Page 64
fnInt( fnInt( fnInt( fnInt( (function integral) returns the numerical integral (Gauss-Kronrod method) of fnInt( with respect to expression variable specified, the default is 1âL5). fnInt(expression,variable,lower,upper To speed the drawing of integration graphs (when Note: increase the value of the Using the Equation Solver Using the Equation Solver Using the Equation Solver Using the Equation Solver...
Page 65
Entering an Expression in the Equation Solver Entering an Expression in the Equation Solver Entering an Expression in the Equation Solver Entering an Expression in the Equation Solver To enter an expression in the equation solver, assuming that the variable follow these steps.
Page 66
• 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 â...
Page 67
3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-84 Plus will attempt to display the solution that is closest to your guess. Chapter 2: Math, Angle, and Test Operations...
Page 68
A solid square in the first column next to Chapter 2: Math, Angle, and Test Operations upper lower ---------------------------------------- - are the bounds between which the TI-84 Plus lower upper â â...
Page 69
Controlling the Solution for Solver or solve( Controlling the Solution for Solver or solve( The TI-84 Plus solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds.
Page 70
Using solve( on the Home Screen or from a Program Using solve( on the Home Screen or from a Program Using solve( on the Home Screen or from a Program Using solve( on the Home Screen or from a Program The function is available only from solve(...
Page 71
MATH NUM Menu MATH NUM Menu MATH NUM Menu MATH NUM Menu To display the MATH NUM MATH NUM CPX PRB Absolute value abs( Round round( Integer part iPart( Fractional part fPart( Greatest integer int( Minimum value min( Maximum value max( Least common multiple lcm(...
Page 72
is also available on the Note: abs( round( round( round( round( returns a number, expression, list, or matrix rounded to round( is omitted, is rounded to the digits that are displayed, up to 10 digits. value round(value[,#decimals]) iPart(, fPart( iPart(, fPart( iPart(, fPart( iPart(, fPart( (integer part) returns the integer part or parts of real or complex numbers,...
Page 73
fPart(value) int( int( int( int( (greatest integer) returns the largest integer real or complex numbers, int( expressions, lists, and matrices. int(value) For a given , the result of Note: value numbers and negative integers, but one integer less than the result of noninteger numbers.
Page 74
(maximum value) returns the larger of max( are compared, listA listB are compared, list value min(valueA,valueB) min(list) min(listA,listB) min(list,value) also are available on the Note: min( max( lcm(, gcd( lcm(, gcd( lcm(, gcd( lcm(, gcd( returns the least common multiple of lcm( nonnegative integers.
Page 75
Entering and Using Complex Numbers Complex-Number Modes Complex-Number Modes Complex-Number Modes 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. • (rectangular-complex mode) a+bi •...
Page 76
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 returns an answer.
Page 77
In degree mode, complex identities such as true because the values for cos and sin are converted to radians, while those for e^() are not. For example, 45) = cos(45) + 45) = cos(p/4) + sin(p/4). Complex identities are always true in radian mode. Interpreting Complex Results Interpreting Complex Results Interpreting Complex Results...
Page 78
Polar-Complex Mode Polar-Complex Mode Polar-Complex Mode Polar-Complex Mode Polar-complex mode recognizes and displays a complex number in the form is the base of the natural log, q is the angle, and is the magnitude, 1 – To enter a complex number in polar form, enter the value of (exponential function), enter the value of q ( press ¤.
Page 79
MATH CPX Menu MATH CPX Menu MATH CPX Menu MATH CPX Menu To display the MATH CPX MATH NUM CPX PRB Returns the complex conjugate. conj( Returns the real part. real( Returns the imaginary part. imag( Returns the polar angle. angle( Returns the magnitude (modulus).
Page 80
real( real( real( real( (real part) returns the real part of a complex number or list of complex numbers. real( real(a+bi) returns a. † real(re^( i)) returns r cos( imag( imag( imag( imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of imag( complex numbers.
Page 81
angle(a+bi) returns tan (b/a). angle(re^( i)) returns , where abs( abs( abs( abs( (absolute value) returns the magnitude (modulus), abs( number or list of complex numbers. abs(a+bi) returns abs(re^( i)) returns r (magnitude). Rect Rect Rect 4Rect (display as rectangular) displays a complex result in rectangular form. It is valid Rect only at the end of an expression.
Page 82
Polar Polar Polar 4Polar (display as polar) displays a complex result in polar form. It is valid only at the end Polar of an expression. It is not valid if the result is real. Polar returns re^( complex result MATH PRB (Probability) Operations MATH PRB (Probability) Operations MATH PRB (Probability) Operations MATH PRB (Probability) Operations...
Page 83
With each execution, the TI-84 Plus generates the same random-number sequence rand for a given seed value. The TI-84 Plus factory-set seed value for different random-number sequence, store any nonzero seed value to the factory-set seed value, store 0 to...
Page 84
(number of combinations) returns the number of combinations of at a time. items number lists. items nCr number Factorial Factorial Factorial 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.
Page 85
(The variable n equals value randInt( randInt( randInt( randInt( (random integer) generates and displays a random integer within a range randInt( specified by lower upper specify an integer > 1 for randInt(lower,upper[,numtrials]) randNorm( randNorm( randNorm( randNorm( (random Normal) generates and displays a random real number from a randNorm( specified Normal distribution.
Page 86
randBin( randBin( randBin( randBin( (random Binomial) generates and displays a random integer from a specified randBin( Binomial distribution. numtrials must be ‚ 0 and 1. To generate a list of random numbers, specify an integer > 1 for (number of simulations); if not specified, the default is 1. numsimulations randBin(numtrials,prob[,numsimulations]) The seed value stored to...
Page 87
ANGLE Menu ANGLE Menu ANGLE Menu ANGLE Menu menu, press y ;. The To display the ANGLE indicators and instructions. The Radian/Degree mode setting affects the TI-84 Plus’s interpretation of menu entries. ANGLE ANGLE ¡ Degree notation DMS minute notation...
Page 88
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 Degree...
Page 89
value Degree mode 8DMS (degree/minute/second) displays to be interpreted as degrees, minutes, and seconds. 8 Degree for answer only at the end of a line. answer R R R R 8P P P P r r r r (, R (, R (, R8P P P P q( ( ( ( , P (, R...
Page 90
Pr(x,y), R (x,y) converts polar coordinates to rectangular coordinates and returns converts polar coordinates to rectangular coordinates and returns Rx(r, ), P Ry(r, Chapter 2: Math, Angle, and Test Operations Radian mode is set. Note: Radian mode is set. Note: and q can be lists.
Page 91
TEST Menu TEST Menu TEST Menu TEST Menu menu, press y :. To display the TEST This operator... Returns 1 (true) if... TEST LOGIC Equal 1: = 2: ƒ Not equal to Greater than 3: > 4: ‚ Greater than or equal to Less than 5: <...
Page 92
2, 1, and 3. Chapter 2: Math, Angle, and Test Operations ƒ valueA valueB ‚ valueA valueB valueA valueB returns . The TI-84 Plus performs the addition first returns . The TI-84 Plus performs the relational test first...
Page 93
TEST LOGIC Menu TEST LOGIC Menu TEST LOGIC Menu TEST LOGIC Menu To display the TEST LOGIC This operator... Returns a 1 (true) if... TEST LOGIC Both values are nonzero (true). 1: and At least one value is nonzero (true). 2: or Only one value is zero (false).
Page 94
valueA and valueB valueA or valueB valueA xor valueB valueA valueB ƒ ƒ ƒ ƒ not( not( not( not( returns 1 if (which can be an expression) is 0. not( value not(value) Using Boolean Operations Using Boolean Operations Using Boolean Operations Using Boolean Operations Boolean logic is often used with relational tests.
Page 95
Y=‡(100NX top half of the circle. The expression Y=L‡(100NX half of the circle. On the TI-84 Plus, you can define one function in terms of another. To define press Ì to enter the negation sign. Press ~...
Page 96
TI-84 Plus—Graphing Mode Similarities Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-84 Plus graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametric graphing, polar graphing, and sequence graphing.
Page 97
Displaying and Exploring a Graph After you have defined a graph, press s to display it. Explore the behavior of the function or functions using the TI-84 Plus tools described in this chapter. Saving a Graph for Later Use Saving a Graph for Later Use...
Page 98
Checking and Changing the Graphing Mode To display the mode screen, press z. The default settings are highlighted below. To graph functions, you must select variables and before you enter the functions. The TI-84 Plus has four graphing modes. • (function graphing) Func •...
Page 99
Other mode settings affect graphing results. Chapter 1 describes each mode setting. • (fixed) decimal mode affects displayed graph coordinates. Float 0123456789 • angle mode affects interpretation of some functions. Radian Degree • plotting mode affects plotting of selected functions. Connected •...
Page 100
Defining or Editing a Function Defining or Editing a Function Defining or Editing a Function 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 ‘.
Page 101
5. Press Í to complete the instruction. "expression" When the instruction is executed, the TI-84 Plus stores the expression to the designated variable , selects the function, and displays the message Evaluating Y= Functions in Expressions...
Page 102
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.
Page 103
Turning On or Turning Off a Stat Plot in the Y= Editor Turning On or Turning Off a Stat Plot in the Y= Editor Turning On or Turning Off a Stat Plot in the Y= Editor 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 (the top line of the Y= editor).
Page 104
• To turn on or turn off all functions, do not enter a number after 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 For example, in mode,...
Page 105
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...
Page 106
Shading Above and Below 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.
Page 107
When é or ê is selected for a Y= function that graphs a family of curves, such as Note: , the four shading patterns rotate for each member of the family of curves. Y1={1,2,3}X Setting a Graph Style from a Program Setting a Graph Style from a Program Setting a Graph Style from a Program Setting a Graph Style from a Program...
Page 108
The TI-84 Plus Viewing Window The TI-84 Plus Viewing Window The TI-84 Plus Viewing Window The TI-84 Plus Viewing Window The viewing window is the portion of the coordinate plane defined by (X scale) defines the distance between tick marks on the x-axis.
Page 109
Enter a new value, which clears the original value. • Move the cursor to a specific digit, and then edit it. 3. Press Í, †, or }. If you entered an expression, the TI-84 Plus evaluates it. The new value is stored. Note: Xmin<Xmax Ymin<Ymax...
Page 110
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. @X and...
Page 111
Displaying the Format Settings Displaying the Format Settings Displaying the Format Settings Displaying the Format Settings To display the format settings, press y .. The default settings are highlighted below. RectGC PolarGC CoordOn CoordOff GridOff GridOn AxesOn AxesOff LabelOff LabelOn ExprOn ExprOff Format settings define a graph’s appearance on the display.
Page 112
RectGC, PolarGC RectGC, PolarGC RectGC, PolarGC RectGC, PolarGC (rectangular graphing coordinates) displays the cursor location as rectangular RectGC coordinates X and Y. (polar graphing coordinates) displays the cursor location as polar coordinates R PolarGC and q. setting determines which variables are updated when you plot the RectGC PolarGC graph, move the free-moving cursor, or trace.
Page 113
displays grid points. GridOn AxesOn, AxesOff AxesOn, AxesOff AxesOn, AxesOff AxesOn, AxesOff displays the axes. AxesOn does not display the axes. AxesOff This overrides the LabelOff LabelOff, LabelOn LabelOff, LabelOn LabelOff, LabelOn LabelOff, LabelOn determine whether to display labels for the axes (X and Y), if LabelOff LabelOn format is also selected.
Page 114
If you performed any of these actions since the graph was last displayed, the TI-84 Plus will replot the graph based on new values when you press s.
Page 115
Graphing a Family of Curves Graphing a Family of Curves If you enter a list (Chapter 11) as an element in an expression, the TI-84 Plus plots the function for each value in the list, thereby graphing a family of curves. In Simul graphing- order mode, it graphs all functions sequentially for the first element in each list, and then for the second, and so on.
Page 116
graphs three functions: {2,4,6}sin(X) graphs {2,4,6}sin({1,2,3}X) When using more than one list, the lists must have the same dimensions. Note: Exploring Graphs with the Free-Moving Cursor Exploring Graphs with the Free-Moving Cursor Exploring Graphs with the Free-Moving Cursor Exploring Graphs with the Free-Moving Cursor Free-Moving Cursor Free-Moving Cursor Free-Moving Cursor...
Page 117
As you move the cursor around the graph, the coordinate values of the cursor location are displayed at the bottom of the screen if 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.
Page 118
Beginning a Trace Beginning a Trace Beginning a 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.
Page 119
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 Moving the Trace Cursor from Function to Function Moving the Trace Cursor from Function to Function Moving the Trace Cursor from Function to Function To move the trace cursor from function to function, press †...
Page 120
value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor. This feature does not apply to stat plots. Note: Panning to the Left or Right Panning to the Left or Right Panning to the Left or Right Panning to the Left or Right If you trace a function beyond the left or right side of the screen, the viewing window...
Page 121
Using TRACE in a Program Using TRACE in a Program Using TRACE in a Program Using TRACE in a Program On a blank line in the program editor, press r. The instruction cursor location. When the instruction is encountered during program execution, the graph is displayed with the trace cursor on the first selected function.
Page 122
ZOOM MEMORY Sets the standard window variables. 6: ZStandard Sets the built-in trig window variables. 7: ZTrig Sets integer values on the X and Y axes. 8: ZInteger Sets the values for current stat lists. 9: ZoomStat Fits YMin and YMax between XMin and XMax. 0: ZoomFit Zoom Cursor Zoom Cursor...
Page 123
3. Move the zoom cursor to the point that is to be the center of the new viewing window. 4. Press Í. The TI-83 Plus adjusts the viewing window by updates the window variables; and replots the selected functions, centered on the cursor location.
Page 124
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 To cancel Zoom In Zoom Out...
Page 125
ZStandard ZStandard ZStandard ZStandard replots the functions immediately. It updates the window variables to the ZStandard standard values shown below. Xmin= Xmax=10 Xscl=1 ZTrig ZTrig ZTrig ZTrig replots the functions immediately. It updates the window variables to preset values ZTrig that are appropriate for plotting trig functions.
Page 126
ZoomStat ZoomStat ZoomStat ZoomStat redefines the viewing window so that all statistical data points are displayed. ZoomStat For regular and modified box plots, only ZoomFit ZoomFit ZoomFit ZoomFit replots the functions immediately. ZoomFit include the minimum and maximum Y values of the selected functions between the current XMin XMax...
Page 127
ZPrevious ZPrevious ZPrevious ZPrevious replots the graph using the window variables of the graph that was displayed ZPrevious before you executed the last ZOOM instruction. ZoomSto ZoomSto ZoomSto ZoomSto immediately stores the current viewing window. The graph is displayed, and the ZoomSto values of the current window variables are stored in the user-defined ZXmin...
Page 128
Checking XFact and YFact Checking XFact and YFact Checking XFact and YFact Checking XFact and YFact To display the ZOOM FACTORS screen, where you can review the current values for , select XFact YFact 4:SetFactors are the defaults. Changing XFact and YFact Changing XFact and YFact Changing XFact and YFact Changing XFact and YFact...
Page 129
CALCULATE Menu CALCULATE Menu CALCULATE Menu CALCULATE Menu To display the CALCULATE analyze the current graph functions. CALCULATE Calculates a function Y value for a given X. value Finds a zero (x-intercept) of a function. zero Finds a minimum of a function. minimum Finds a maximum of a function.
Page 130
1. Select from the 1:value bottom-left corner. 2. Enter a real value, which can be an expression, for 3. Press Í. The cursor is on the first selected function in the Y= editor at the and the coordinates are displayed, even if To move the cursor from function to function at the entered restore the free-moving cursor, press | or ~.
Page 131
1. Select from the 2:zero in the bottom-left corner. Bound? 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.
Page 132
minimum, maximum minimum, maximum minimum, maximum minimum, maximum find a minimum or maximum of a function within a specified minimum maximum interval to a tolerance of 1âL5. To find a minimum or maximum, follow these steps. 1. Select 3:minimum displayed. 2.
Page 133
2. Press † or }, if necessary, to move the cursor to the first function, and then press Í. Second curve? 3. Press † or }, if necessary, to move the cursor to the second function, and then press Í. 4.
Page 134
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 ~.
Page 135
3. Set lower and upper limits as you would set left and right bounds for integral value is displayed, and the integrated area is shaded. The shaded area is a drawing. Use Note: invokes Smart Graph to clear the shaded area. Chapter 3: Function Graphing (Chapter 8) or any action that ClrDraw...
Page 136
Parametric Graphing Parametric Graphing Parametric Graphing Parametric Graphing Getting Started: Path of a Ball Getting Started: Path of a Ball Getting Started: Path of a Ball 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.
Page 137
1. Press z. Press † † † ~ Í to select mode. Press † † ~ Í to select simultaneous graphing of all three parametric equations in this example. 2. Press o. Press „ ™ select ¡) ¤ Í to define „...
Page 138
The horizontal component vector is defined by 6. Press ~ , and then press Í to define . Press 7. Press | | } Í to change the graph style to è for . Press } Í Í to change the graph style to ë...
Page 139
Defining and Displaying Parametric Graphs Defining and Displaying Parametric Graphs Defining and Displaying Parametric Graphs Defining and Displaying Parametric Graphs TI-84 Plus Graphing Mode Similarities TI-84 Plus Graphing Mode Similarities TI-84 Plus Graphing Mode Similarities TI-84 Plus Graphing Mode Similarities The steps for defining a parametric graph are similar to the steps for defining a function graph.
Page 140
Setting Parametric Graphing Mode Setting Parametric Graphing Mode Setting Parametric Graphing Mode 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.
Page 141
Selecting and Deselecting Parametric Equations Selecting and Deselecting Parametric Equations The TI-84 Plus graphs only the selected parametric equations. In the Y= editor, a parametric equation is selected when the highlighted. You may select any or all of the equations To change the selection status, move the cursor onto the component and press Í.
Page 142
Setting Window Variables Setting Window Variables Setting Window Variables 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 Tmax=6.2831853... Tstep=.1308996...
Page 143
Displaying a Graph 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 ), and then plots each point defined by X and Y. The window variables define the Tstep viewing window.
Page 144
• Select or deselect parametric equations. • Store values directly to window variables. Exploring Parametric Graphs Exploring Parametric Graphs Exploring Parametric Graphs Exploring Parametric Graphs Free-Moving Cursor Free-Moving Cursor Free-Moving Cursor Free-Moving Cursor The free-moving cursor in Par graphing works the same as in Func graphing. format, moving the cursor updates the values of X and Y;...
Page 145
cursor is on the first selected function at displayed. format, TRACE updates and displays the values of X, Y, and T if RectGC format is on. format, X, Y, R, q and T are updated; if PolarGC 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 ~.
Page 146
ZOOM ZOOM ZOOM ZOOM operations in Par graphing work the same as in Func graphing. Only the ZOOM , and ) and Xmax Xscl Ymin window variables ( . The ZStandard VARS ZOOM are the zoom memory variables for Par graphing. 3:ZTstep CALC CALC...
Page 147
Polar Graphing Polar Graphing Polar Graphing Polar Graphing Getting Started: Polar Rose Getting Started: Polar Rose Getting Started: Polar Rose 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.
Page 148
Defining and Displaying Polar Graphs Defining and Displaying Polar Graphs Defining and Displaying Polar Graphs Defining and Displaying Polar Graphs TI-84 Plus Graphing Mode Similarities TI-84 Plus Graphing Mode Similarities TI-84 Plus Graphing Mode Similarities TI-84 Plus Graphing Mode Similarities The steps for defining a polar graph are similar to the steps for defining a function graph.
Page 149
Setting Polar Graphing Mode Setting Polar Graphing Mode Setting Polar Graphing Mode 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.
Page 150
Selecting and Deselecting Polar Equations Selecting and Deselecting Polar Equations 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 equations. To change the selection status, move the cursor onto the...
Page 151
Displaying a Graph Displaying a Graph Displaying a Graph When you press s, the TI-84 Plus plots the selected polar equations. It evaluates R for each value of q (from q The window variables define the viewing window. As the graph is plotted, X, Y, R, and q are updated.
Page 152
Window Variables and Y Y Y Y ..VARS Window Variables and Window Variables and Window Variables and You can perform these actions from the home screen or a program. • Access functions by using the name of the equation as a variable. •...
Page 153
Free-Moving Cursor Free-Moving Cursor Free-Moving Cursor Free-Moving Cursor The free-moving cursor in Pol graphing works the same as in Func graphing. In format, moving the cursor updates the values of X and Y; if X and Y are displayed. In is selected, R and q are displayed.
Page 154
Moving the Trace Cursor to Any Valid Theta Value Moving the Trace Cursor to Any Valid Theta Value Moving the Trace Cursor to Any Valid Theta Value 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 the bottom-left corner of the screen.
Page 155
Sequence Graphing Sequence Graphing Sequence Graphing Sequence Graphing Getting Started: Forest and Trees Getting Started: Forest and Trees Getting Started: Forest and Trees Getting Started: Forest and Trees Getting Started is a fast-paced introduction. Read the chapter for details. Note: A small forest of 4,000 trees is under a new forestry plan.
Page 156
3. Press o. If the graph-style icon is not ç (dot), press | |, press Í until ç is displayed, and then press ~ ~. 4. Press ~ to select because only whole trees are harvested. After each annual harvest, 80 percent (.80) of the trees remain.
Page 157
TI-84 Plus Sequence Functions u, v, and w TI-84 Plus Sequence Functions u, v, and w The TI-84 Plus has three sequence functions that you can enter from the keyboard: u, v, and w. They are above the ¬, −, and ® keys.
Page 158
• The previous term or the term that precedes the previous term in another sequence function, such as Statements in this chapter about Note: about are also true for Displaying the Sequence Y= Editor Displaying the Sequence Y= Editor Displaying the Sequence Y= Editor Displaying the Sequence Y= Editor After selecting Seq mode, press o to display the sequence Y= editor.
Page 159
Selecting and Deselecting Sequence Functions Selecting and Deselecting Sequence Functions Selecting and Deselecting Sequence Functions The TI-84 Plus graphs only the selected sequence functions. In the Y= editor, a sequence function is selected when the highlighted. To change the selection status of a sequence function, move the cursor onto the of the function name, and then press Í.
Page 160
• To enter the function name • To enter the function name • To enter the function name Generally, sequences are either nonrecursive or recursive. Sequences are evaluated only at consecutive integer values. at zero or any positive integer. Nonrecursive Sequences Nonrecursive Sequences Nonrecursive Sequences Nonrecursive Sequences...
Page 161
Using an initial value u(nMin) = 1 On the TI-84 Plus, you must type each character of the terms. For example, to Note: , press y enter Recursive sequences require an initial value or values, since they reference undefined terms.
Page 162
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 Setting Window Variables Setting Window Variables Setting Window Variables...
Page 163
Largest X value to be displayed Xmax=10 Spacing between the X tick marks Xscl=1 Smallest Y value to be displayed Ymin=L10 Largest Y value to be displayed Ymax=10 Spacing between the Y tick marks Yscl=1 must be an integer | 0. nMin is the smallest value to evaluate.
Page 164
Setting the Graph Format Setting the Graph Format Setting the Graph Format 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.
Page 165
Displaying a Sequence Graph Displaying a Sequence Graph 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 Smart Graph applies to sequence graphs (Chapter 3).
Page 166
When , or Time sequence one increment at a time. To move five plotted points at once, press PlotStep y ~ or y |. • When you begin a trace, the trace cursor is on the first selected sequence at the term number specified by •...
Page 167
value must be valid for the current viewing window. When you have completed the entry, press Í to move the cursor. ZOOM ZOOM ZOOM ZOOM operations in Seq graphing work the same as in Func graphing. Only the ZOOM , and ) and Xmax Xscl...
Page 168
• When , or axes format is selected, axes format setting. For example, for represents v(n) Evaluating u, v, and w Evaluating u, v, and w Evaluating u, v, and w Evaluating u, v, and w To enter the sequence names names in any of three ways.
Page 169
It cannot reference any defined sequence except itself. Displaying the Graph Screen Displaying the Graph Screen Displaying the Graph Screen Displaying the Graph Screen In Web format, press s to display the graph screen. The TI-84 Plus: • Draws a reference line in •...
Page 170
2. It moves vertically (up or down) to the sequence. 3. It moves horizontally to the 4. It repeats this vertical and horizontal movement as you continue to press ~. Using Web Plots to Illustrate Convergence Using Web Plots to Illustrate Convergence Using Web Plots to Illustrate Convergence Using Web Plots to Illustrate Convergence Example: Convergence...
Page 171
5. Press y . and select the 6. Press p and change the variables below. Xmin= 7. Press s to graph the sequence. 8. Press r, and then press ~ to draw the web. The displayed cursor coordinates ), and u(n) displayed, and the trace cursor is on the sequence.
Page 172
Graphing with uv, vw, and uw Graphing with uv, vw, and uw Graphing with uv, vw, and uw Graphing with uv, vw, and uw The phase-plot axes settings sequences. To select a phase-plot axes setting, press y ., press ~ until the cursor is on , or Axes Setting...
Page 173
number of foxes fox population growth rate with rabbits fox population death rate without rabbits time (in months) (1+M (1+GR 1. Press o in mode to display the sequence Y= editor. Define the sequences and initial values for R and W the sequence W 2.
Page 174
3. Press p and set the variables as shown below. nMin=0 nMax=400 PlotStart=1 PlotStep=1 4. Press s to graph the sequence. 5. Press r ~ to individually trace the number of rabbits ( time ( Press a number, and then press Í to jump to a specific Note: while in TRACE.
Page 175
Sequences and Window Variables Sequences and Window Variables Sequences and Window Variables Refer to the table if you are familiar with the TI-82. It shows TI-84 Plus sequences and sequence window variables, as well as their TI-82 counterparts. TI-84 Plus...
Page 176
Sequence Keystroke Changes Sequence Keystroke Changes Sequence Keystroke Changes Refer to the table if you are familiar with the TI-82. It compares TI-84 Plus sequence- name syntax and variable syntax with TI-82 sequence-name syntax and variable syntax. TI-84 Plus / TI-82...
Page 177
TI-84 Plus / TI-82 v(n) / Vn w(n) 1) / Un 1) / Vn Chapter 6: Sequence Graphing On TI-84 Plus, press: £ „ ¤ £ „ ¤ £ „ ¹ À ¤ £ „ ¹ À ¤ £ „ ¹ À ¤...
Page 178
Tables Tables Tables Tables Getting Started: Roots of a Function Getting Started: Roots of a Function Getting Started: Roots of a Function Getting Started: Roots of a Function Getting Started is a fast-paced introduction. Read the chapter for details. Evaluate the function Y = X changes occur, and at what X values? 1.
Page 179
Press Í to select generated independent values). Press † Í to select (automatically generated Depend: Auto dependent values). 4. Press y 0 to display the table screen. 5. Press † until you see the sign changes in the value of . How many sign changes occur, and at what X values? Setting Up the Table Setting Up the Table...
Page 180
TblStart, TblStart, @Tbl TblStart, TblStart, (table start) defines the initial value for the independent variable. TblStart only when the independent variable is generated automatically (when selected). (table step) defines the increment for the independent variable. In Seq mode, both Note: Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask Indpnt: Auto, Indpnt: Ask, Depend: Auto, Depend: Ask...
Page 181
Setting Up the Table from the Home Screen or a Program Setting Up the Table from the Home Screen or a Program Setting Up the Table from the Home Screen or a Program Setting Up the Table from the Home Screen or a Program To store a value to TblStart the variable name from the...
Page 182
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. You also can use this feature to view the function that defines a dependent Note: variable without having to leave the table.
Page 183
The Table The Table The Table The Table To display the table, press y 0. The table abbreviates the values, if necessary. Note: Independent-variable values in the first column Current cell’s full value Independent and Dependent Variables Independent and Dependent Variables Independent and Dependent Variables Independent and Dependent Variables The current graphing mode determines which independent and dependent variables are...
Page 184
variable X and the dependent variables mode is set. Independent Variable Graphing Mode Func (function) Par (parametric) Pol (polar) Seq (sequence) Clearing the Table from the Home Screen or a Program Clearing the Table from the Home Screen or a Program Clearing the Table from the Home Screen or a Program Clearing the Table from the Home Screen or a Program From the home screen, select the...
Page 185
values also are displayed. All dependent-variable values may not be displayed if is selected. Depend: Ask You can scroll back from the value entered for Note: updated automatically to the value shown on the top line of the table. In the example and @ above, TblStart=0...
Page 186
To simultaneously display two dependent variables on the table that are not defined Note: 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.
Page 187
Draw Instructions Draw Instructions Draw Instructions Draw Instructions Getting Started: Drawing a Tangent Line Getting Started: Drawing a Tangent Line Getting Started: Drawing a Tangent Line Getting Started: Drawing a Tangent Line Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to find the equation of the tangent line at X = Y=sin(X).
Page 188
3. Press y < to select tangent instruction is initiated. 4. Press y C ¤ ¥ 5. Press Í. The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph. Chapter 8: Draw Instructions .
Page 189
DRAW Menu DRAW Menu DRAW Menu DRAW Menu menu, press y <. The TI-84 Plus’s interpretation of these To display the DRAW instructions depends on whether you accessed the menu from the home screen or the program editor or directly from a graph.
Page 190
Before Drawing on a Graph Before Drawing on a Graph Before Drawing on a Graph 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. •...
Page 191
Clearing Drawings When a Graph Is Displayed Clearing Drawings When a Graph Is Displayed Clearing Drawings When a Graph Is Displayed 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 menu.
Page 192
Drawing a Line Segment Directly on a Graph Drawing a Line Segment Directly on a Graph Drawing a Line Segment Directly on a Graph Drawing a Line Segment Directly on a Graph To draw a line segment when a graph is displayed, follow these steps. 1.
Page 193
Line(X1,Y1,X2,Y2) To erase a line segment, enter Drawing Horizontal and Vertical Lines Drawing Horizontal and Vertical Lines Drawing Horizontal and Vertical Lines Drawing Horizontal and Vertical Lines Drawing a Line Directly on a Graph Drawing a Line Directly on a Graph Drawing a Line Directly on a Graph Drawing a Line Directly on a Graph To draw a horizontal or vertical line when a graph is displayed, follow these steps.
Page 194
Horizontal y (vertical line) draws a vertical line at Vertical Vertical x To instruct the TI-84 Plus to draw more than one horizontal or vertical line, separate each instruction with a colon ( Chapter 8: Draw Instructions , press ‘.
Page 195
Drawing Tangent Lines Drawing Tangent Lines Drawing Tangent Lines Drawing Tangent Lines Drawing a Tangent Line Directly on a Graph Drawing a Tangent Line Directly on a Graph Drawing a Tangent Line Directly on a Graph Drawing a Tangent Line Directly on a Graph To draw a tangent line when a graph is displayed, follow these steps.
Page 196
Change the fixed decimal setting on the mode screen if you want to see fewer Note: digits displayed for X and the equation for Y. Drawing a Tangent Line from the Home Screen or a Program Drawing a Tangent Line from the Home Screen or a Program Drawing a Tangent Line from the Home Screen or a Program Drawing a Tangent Line from the Home Screen or a Program (tangent line) draws a line tangent to...
Page 197
Func mode only. DrawInv Chapter 8: Draw Instructions as a function in terms of X on the current graph. expression from the menu, the TI-84 Plus returns to the home DRAW is not interactive. DrawF to draw a family of curves. expression...
Page 198
DrawInv expression You cannot use a list in Note: Shading Areas on a Graph Shading Areas on a Graph Shading Areas on a Graph Shading Areas on a Graph Shading a Graph Shading a Graph Shading a Graph Shading a Graph To shade an area on a graph, select pasted to the home screen or to the program editor.
Page 199
specifies one of four shading patterns. pattern vertical (default) pattern=1 horizontal pattern=2 pattern=3 negative—slope 45 pattern=4 positive—slope 45 specifies one of eight shading resolutions. patres patres=1 shades every pixel (default) patres=2 shades every second pixel shades every third pixel patres=3 shades every fourth pixel patres=4 shades every fifth pixel...
Page 200
Drawing a Circle Directly on a Graph Drawing a Circle Directly on a Graph Drawing a Circle Directly on a Graph Drawing a Circle Directly on a Graph To draw a circle directly on a displayed graph using the cursor, follow these steps. 1.
Page 201
3. Enter the characters. Press ƒ or y 7 to enter letters and q. You may enter TI-84 Plus functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the graph.
Page 202
94. Both column Text(row,column,value,value…) can be text enclosed in quotation marks ( " ), or it can be an expression. The TI-84 value Plus will evaluate an expression and display the result with up to 10 characters. Split Screen...
Page 203
Using Pen to Draw on a Graph Using Pen to Draw on a Graph Using Pen to Draw on a Graph Using Pen to Draw on a Graph draws directly on a graph only. You cannot execute program. To draw on a displayed graph, follow these steps. 1.
Page 204
2. Move the cursor to the position where you want to draw the point. 3. Press Í to draw the point. Chapter 8: Draw Instructions menu, press y < ~. The TI-84 Plus’s interpretation of Turns on a point. Turns off a point.
Page 205
To continue drawing points, repeat steps 2 and 3. To cancel Erasing Points with Erasing Points with Pt Erasing Points with Erasing Points with To erase (turn off) a drawn point on a graph, follow these steps. 1. Select (point off) from the 2:Pt-Off( 2.
Page 206
TI-84 Plus Pixels TI-84 Plus Pixels A pixel is a square dot on the TI-84 Plus display. The on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from the or the program editor.
Page 207
Turning On and Off Pixels with Pxl Turning On and Off Pixels with Turning On and Off Pixels with Turning On and Off Pixels with (pixel on) turns on the pixel at ( Pxl-On( 62 and is an integer between 0 and 94. column turns the pixel off.
Page 208
DRAW STO Menu Menu To display the DRAW STO from the menu, the TI-84 Plus returns to the home screen or the program DRAW STO editor. The picture and graph database instructions are not interactive. DRAW POINTS 1: StorePic 2: RecallPic...
Page 209
2. Enter the number (from 1 to 9, or 0) of the picture variable to which you want to store the picture. For example, if you enter 3, the TI-84 Plus will store the picture to You also can select a variable from the...
Page 210
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...
Page 211
3:StoreGDB cursor location. 2. Enter the number (from 1 to 9, or 0) of the the graph database. For example, if you enter 7, the TI-84 Plus will store the GDB7 You also can select a variable from the Note: variable is pasted next to 3.
Page 212
4:RecallGDB cursor location. 2. Enter the number (from 1 to 9, or 0) of the recall a . For example, if you enter 7, the TI-84 Plus will recall the GDB7 You also can select a variable from the Note: variable is pasted next to 3.
Page 214
Split Screen Split Screen Split Screen Split Screen Getting Started: Exploring the Unit Circle Getting Started: Exploring the Unit Circle Getting Started: Exploring the Unit Circle Getting Started: Exploring the Unit Circle Getting Started is a fast-paced introduction. Read the chapter for details. (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¡...
Page 215
3. Press o to display the Y= editor for mode. Press ™ „ ¤ Í to store . Press ÷ ˜ „ ¤ Í to store 4. Press p to display the window editor. Enter these values for the window variables. Tmin=0 Xmin= Tmax=360 Xmax=2.3...
Page 216
Setting a Split-Screen Mode Setting a Split-Screen Mode Setting a Split-Screen Mode 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 (horizontal) to display the graph screen and another screen split Horiz horizontally.
Page 217
If you press y 0, the cursor is placed in the half in which the table is displayed. The TI-84 Plus will remain in split-screen mode until you change back to screen Full mode.
Page 218
Horiz Mode Horiz Mode Horiz Mode Horiz Mode (horizontal) split-screen mode, a horizontal line splits the screen into top and Horiz bottom halves. The top half displays the graph. The bottom half displays any of these editors. • Home screen (four lines) •...
Page 219
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). •...
Page 220
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 Moving from Half to Half in G-T Mode Moving from Half to Half in G-T Mode Moving from Half to Half in G-T Mode...
Page 221
TI-84 Plus Pixels in Horiz and G-T Modes TI-84 Plus Pixels in Horiz and G-T Modes TI-84 Plus Pixels in Horiz and G-T Modes...
Page 222
Each set of numbers in parentheses above represents the row and column of a Note: corner pixel, which is turned on. DRAW POINTS Menu Pixel Instructions DRAW POINTS Menu Pixel Instructions DRAW POINTS Menu Pixel Instructions DRAW POINTS Menu Pixel Instructions Pxl-On( Pxl-Off( Pxl-Change(...
Page 223
Output(row,column,"text") instruction can only be used within a program. Note: Output( Setting a Split-Screen Mode from the Home Screen or a Program Setting a Split-Screen Mode from the Home Screen or a Program Setting a Split-Screen Mode from the Home Screen or a Program Setting a Split-Screen Mode from the Home Screen or a Program To set from a program, follow these steps.
Page 224
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 to obtain the reduced row-echelon form.
Page 225
The TI-84 Plus has 10 matrix variables, directly in an expression. A matrix, depending on available memory, may have up to 99 rows or columns. You can store only real numbers in TI-84 Plus matrices. Chapter 10: Matrices Í to complete the first Í...
Page 226
Selecting a Matrix Selecting a Matrix Selecting a Matrix 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 previously defined matrices are displayed.
Page 227
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 Viewing and Editing Matrix Elements Viewing and Editing Matrix Elements Viewing and Editing Matrix Elements...
Page 228
Deleting a Matrix Deleting a Matrix Deleting a Matrix Deleting a Matrix To delete matrices from memory, use the menu (Chapter 18). Viewing a Matrix Viewing a Matrix Viewing a Matrix 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.
Page 229
Function Í Switches to editing context; activates the edit cursor on the bottom line ‘ Switches to editing context; clears the value on the bottom line Any entry character Switches to editing context; clears the value on the bottom line; copies the character to the bottom line Nothing Nothing...
Page 230
5. Press Í, }, or † to move to another element. Editing-Context Keys Editing-Context Keys Editing-Context Keys Editing-Context Keys Function Moves the edit cursor within the value † Stores the value displayed on the bottom line to the matrix element; switches to viewing context and moves the rectangular cursor within the column Í...
Page 231
Using a Matrix in an Expression Using a Matrix in an Expression Using a Matrix in an Expression 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 Recall the contents of the matrix into the expression with y K (Chapter 1).
Page 232
6. Press y [ ] to indicate the end of the matrix. are not necessary at the end of an expression or preceding !. The closing Note: The resulting matrix is displayed in the form: [[element1,1, ,element1,n], Any expressions are evaluated when the entry is executed. The commas that you must enter to separate elements are not displayed on Note: output.
Page 233
Copying One Matrix to Another Copying One Matrix to Another Copying One Matrix to Another Copying One Matrix to Another To copy a matrix, follow these steps. 1. Press y > to display the 2. Select the name of the matrix you want to copy. 3.
Page 234
Using Math Functions with Matrices 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 menu, and the MATH NUM must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same.
Page 235
… matrixA matrixB Multiplying a by a matrix value is multiplied by matrix value … matrix value … value matrix Negation Negation Negation Negation Negating a matrix (Ì) returns a matrix in which the sign of every element is changed (reversed).
Page 236
abs( abs( abs( abs( (absolute value, abs( MATH NUM each element of matrix abs(matrix) round( round( round( round( menu) returns a matrix. It rounds every element in round( MATH NUM ( 9). If is omitted, the elements are rounded to 10 digits. #decimals round(matrix #decimals...
Page 237
matrix Powers Powers Powers Powers To raise a matrix to a power, (›) for integer ^power matrix matrix matrix^power Relational Operations Relational Operations Relational Operations Relational Operations To compare two matrices using the relational operations have the same dimensions. element basis. The other relational operations are not valid with matrices. Chapter 10: Matrices must be square.
returns 1 if every comparison is true; it returns 0 if any comparison is matrixA=matrixB false. ƒ returns if at least one comparison is false; it returns matrixA matrixB is false. iPart(, fPart(, int( iPart(, fPart(, int( iPart(, fPart(, int( iPart(, fPart(, int( (integer part), iPart(...
iPart(matrix) fPart(matrix) int(matrix) Using the Using the MATRX MATH Using the Using the MATRX MATH Operations MATRX MATH MATRX MATH MATRX MATH Menu MATRX MATH Menu MATRX MATH Menu MATRX MATH Menu To display the MATRX MATH NAMES MATH EDIT Calculates the determinant.
Page 240
NAMES MATH EDIT Stores a list to a matrix. 9: List4matr( Returns the cumulative sums of a matrix. 0: cumSum( Returns the row-echelon form of a matrix. A: ref( Returns the reduced row-echelon form. B: rref( Swaps two rows of a matrix. C: rowSwap( Adds two rows;...
Page 241
matrix Accessing Matrix Dimensions with Accessing Matrix Dimensions with dim( Accessing Matrix Dimensions with Accessing Matrix Dimensions with (dimension) returns a list containing the dimensions ( dim( dim(matrix) " Note: dim(matrix) Ln:Ln(1) number of columns. Creating a Matrix with dim( Creating a Matrix with Creating a Matrix with Creating a Matrix with...
Page 242
Redimensioning a Matrix with Redimensioning a Matrix with dim( Redimensioning Redimensioning a Matrix with a Matrix with with ¿ to redimension an existing dim( The elements in the old matrixname Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted.
Page 243
identity(dimension) randM( randM( randM( randM( (create random matrix) returns a randM( and 9. The seed value stored to the randM(rows,columns) augment( augment( augment( augment( appends augment( matrixA the same number of rows. augment(matrixA,matrixB) Matr4list( Matr list( Matr Matr list( list( Chapter 10: Matrices ×...
Page 244
(matrix stored to list) fills each Matr list( ignores extra Matr list( listname columns. Matr list(matrix,listnameA, also fills a Matr list( listname a specific column from matrix Matr list(matrix,column#,listname) List List4matr( List List matr( matr( matr( (lists stored to matrix) fills List matr( each...
Page 245
List matr(listA, ,list n,matrixname) cumSum( cumSum( cumSum( cumSum( returns cumulative sums of the elements in cumSum( element. Each element is the cumulative sum of the column from top to bottom. cumSum(matrix) Row Operations Row Operations Row Operations Row Operations menu items MATRX MATH in an expression.
Page 246
ref(, rref( ref(, rref( ref(, rref( ref(, rref( (row-echelon form) returns the row-echelon form of a real ref( columns must be greater than or equal to the number of rows. ref(matrix) (reduced row-echelon form) returns the reduced row-echelon form of a real rref( The number of columns must be greater than or equal to the number of rows.
Page 247
row+( row+( row+( row+( (row addition) returns a matrix. It adds row+( results in rowB row+(matrix,rowA,rowB) row( row( row( …row( … (row multiplication) returns a matrix. It multiplies row( results in … row(value,matrix,row) row+( row+( row+( …row+( … (row multiplication and addition) returns a matrix. It multiplies row+( , adds it to , and stores the results in...
Page 249
Lists Lists Lists Lists Getting Started: Generating a Sequence Getting Started: Generating a Sequence Getting Started: Generating a Sequence 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/A list.
Page 250
Naming Lists Naming Lists Naming Lists Naming Lists Using TI-84 Plus List Names L1 1 1 1 through L Using TI-84 Plus List Names L Using TI-84 Plus List Names L Using TI-84 Plus List Names L The TI-84 Plus has six list names in memory: are on the keyboard above the numeric keys À...
Page 251
Creating a List Name on the Home Screen Creating a List Name on the Home Screen Creating a List Name on the Home Screen Creating a List Name on the Home Screen To create a list name on the home screen, follow these steps. 1.
Page 252
List1:, List2: stat editors • On the home screen using You can create as many list names as your TI-84 Plus memory has space to store. Storing and Displaying Lists Storing and Displaying Lists Storing and Displaying Lists Storing and Displaying Lists...
Page 253
Displaying a List on the Home Screen Displaying a List on the Home Screen Displaying a List on the Home Screen 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.
Page 254
Deleting a List from Memory Deleting a List from Memory Deleting a List from Memory Deleting a List from Memory To delete lists from memory, including MEMORY MANAGEMENT/DELETE restores through . Removing a list from the stat list editor does not delete it from memory.
Page 255
From the top of a menu, press } to move to the bottom. From the bottom, press † Note: to move to the top. When you select a list name from the current cursor location. The list name symbol Ù precedes a list name when the name is pasted where non- •...
Page 256
Ù, which pastes Ù to the current cursor location. Ù is not always necessary. 2. Select 3. Enter the characters that comprise the list name. Attaching Formulas to List Names Attaching Formulas to List Names Attaching Formulas to List Names Attaching Formulas to List Names Attaching a Formula to a List Name Attaching a Formula to a List Name...
Page 257
For example, the first screen below shows that elements are stored to , and the is attached to the list name Ù formula . The quotation marks designate the L3+10 ADD10 formula to be attached to Ù . Each element of Ù is the sum of an element in ADD10 ADD10...
Page 258
2. Press ¿. 3. Enter the name of the list to which you want to attach the formula. Press y, and then enter a TI-84 Plus list name • Press y 9 and select a user.created list name from the •...
Page 259
Detaching a Formula from a List Detaching a Formula from a List Detaching a Formula from a List Detaching a Formula from a List You can detach (clear) an attached formula from a list in several ways. For example: Enter ã ã ! •...
Page 260
Use y K to recall the contents of the list into an expression at the cursor location • (Chapter 1). You must paste user-created list names to the Note: menu. You cannot enter them directly using Ù. LIST NAMES Using Lists with Math Functions Using Lists with Math Functions Using Lists with Math Functions Using Lists with Math Functions...
Page 261
• 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 LIST OPS Menu LIST OPS Menu LIST OPS Menu LIST OPS Menu LIST OPS Menu LIST OPS Menu menu, press y 9 ~.
Page 262
NAMES OPS MATH Selects specific data points. Select( Concatenates two lists. augment( Stores a list to a matrix. List4matr( Stores a matrix to a list. Matr4list( Ù Designates the list-name data type. SortA(, SortD( SortA(, SortD( SortA(, SortD( SortA(, SortD( (sort ascending) sorts list elements from low to high values.
Page 263
SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[,dependlist2,...,dependlist n]) Note: • In the example, 5 is the first element in , 5 becomes the second element of SortA(L4,L5) second element of • are the same as SortA( SortD( (Chapter 12). Using dim( to Find List Dimensions Using dim( to Find List Dimensions Using dim( to Find List Dimensions Using dim( to Find List Dimensions...
Page 264
Using dim( to Create a List Using dim( to Create a List Using dim( to Create a List Using dim( to Create a List with ¿ to create a new You can use dim( The elements are zeros. dim(listname) length Using dim( to Redimension a List Using dim( to Redimension a List Using dim( to Redimension a List...
Page 265
Fill( Fill( Fill( Fill( replaces each element in Fill( Fill(value,listname) are the same as Note: dim( Fill( (Chapter 10). seq( seq( seq( seq( (sequence) returns a list in which each element is the result of the evaluation of seq( with regard to expression variable need not be defined in memory.
Page 266
cumSum( cumSum( cumSum( cumSum( (cumulative sum) returns the cumulative sums of the elements in cumSum( with the first element. list cumSum(list) List( List( List( @List( returns a list containing the differences between consecutive elements in List( subtracts the first element in from the third, and so on.
Page 267
example, you can use Select( CBL 2™/CBL™ or CBR™ data. Select(xlistname,ylistname) Before you use Note: Select( plot. Also, the plot must be displayed in the current viewing window. Before Using Select( Before Using Select( Before Using Select( Before Using Select( Before using , follow these steps.
Page 268
, press ¢, enter 2. Enter xlistname into which you want the selected data to be stored. 3. Press Í. The graph screen is displayed with 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.
Page 269
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 A new stat plot of xlistname selected data points.
Page 270
augment( augment( augment( augment( concatenates the elements of augment( complex numbers. augment(listA,listB) List4matr( List matr( List List matr( matr( (lists stored to matrix) fills List matr( each list. If the dimensions of all lists are not equal, then row with 0. Complex lists are not valid. matrixname List matr(list1,list2, ...
Page 271
(matrix stored to lists) fills each Matr list( . If the number of matrix listname ignores extra Matr list( listname exceeds the number of listname Matr list(matrix,listname1,listname2, . . . ,listname n) also fills a Matr list( listname with a specific column from Matr list(matrix,column#,listname) Ù...
Page 272
Ù need not precede a user-created list name where a list name is the only valid input, for example, at the prompt in the stat list editor or the Name= stat plot editor. If you enter Ù where it is not necessary, the TI-84 Plus will ignore the entry. LIST MATH Menu LIST MATH Menu...
Page 273
min(, max( min(, max( min(, max( min(, max( (minimum) and min( max( lists are compared, it returns a list of the smaller or larger of each pair of elements in . For a complex list, the element with smallest or largest magnitude (modulus) is listB returned.
Page 274
sum(, prod( sum(, prod( sum(, prod( sum(, prod( (summation) returns the sum of the elements in sum( specify a range of elements. returns the product of all elements of prod( specify a range of list elements. sum(list[,start,end]) Sums and Products of Numeric Sequences Sums and Products of Numeric Sequences Sums and Products of Numeric Sequences Sums and Products of Numeric Sequences...
Page 275
stdDev(, variance( stdDev(, variance( stdDev(, variance( stdDev(, variance( returns the standard deviation of the elements in stdDev( 1. Each element counts the number of consecutive occurrences of the freqlist corresponding element in • returns the variance of the elements in variance( Each element counts the number of consecutive occurrences of the...
Page 276
Statistics Statistics Statistics Statistics Getting Started: Pendulum Lengths and Periods Getting Started: Pendulum Lengths and Periods Getting Started: Pendulum Lengths and Periods 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).
Page 277
2. Press … to select is pasted to the home screen. Press Í. This removes lists from stat list editor columns 1 through 20, and then stores lists through in columns 1 through 6. Removing lists from the stat list editor does Note: not delete them from memory.
Page 278
6. Press o to display the Y= editor. If necessary, press ‘ to clear the function As necessary, press }, Í, and ~ to turn off , and Plot1 Plot2 Plot3 Y= editor (Chapter 3). As necessary, press †, |, and Í...
Page 279
Since the scatter plot of time-versus-length data appears to be approximately linear, fit a line to the data. 10. Press … ~ to select regression model) from the is pasted to the home screen. LinReg(ax+b) 11. Press y d ¢ y e ¢. Press ~ display the VARS Y-VARS FUNCTION menu, and then press...
Page 280
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 … to select displayed. Press ~ and } to move the cursor onto Press y 6.
Page 281
Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in four are negative. The latter correspond to the longer string lengths in residuals will show this pattern more clearly. 18. Press y , menu.
Page 282
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.
Page 283
25. Press Í to calculate the power regression. Values for are displayed on the home screen. The power regression equation is stored . Residuals are calculated and stored automatically in the list name 26. Press s. The regression line and the scatter plot are displayed.
Page 284
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.
Page 285
Using Lists to Store Data Using Lists to Store Data Data for statistical analyses is stored in lists, which you can create and edit using the stat list editor. The TI-84 Plus has six list variables in memory, Chapter 12: Statistics settings...
Page 286
can store data for statistical calculations. Also, you can store data to list names that you create (Chapter 11). Setting Up a Statistical Analysis Setting Up a Statistical Analysis Setting Up a Statistical Analysis Setting Up a Statistical Analysis To set up a statistical analysis, follow these steps. Read the chapter for details. 1.
Page 287
The top line displays list names. 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;...
Page 288
2. Enter a valid list name in any of four ways. • Select a name from the • Enter • 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.
Page 289
To begin entering, scrolling, or editing list elements, press †. The rectangular cursor is displayed. If the list name you entered in step 2 already was stored in another stat list Note: editor column, then the list and its elements, if any, move to the current column from the previous column.
Page 290
Removing a List from the Stat List Editor Removing a List from the Stat List Editor Removing a List from the Stat List Editor 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 {.
Page 291
• On the home screen or in the program editor, enter dimension of listname • to clear all lists in memory (Chapter 18). ClrAllLists Editing a List Element Editing a List Element Editing a List Element Editing a List Element To edit a list element, follow these steps.
Page 292
You can enter expressions and variables for elements. Note: 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.
Page 293
Note: symbol (Chapter 11). 5. Press Í. The TI-84 Plus calculates each list element and stores it to the list name to which the formula is attached. A lock symbol is displayed in the stat list editor, next to the list name to which the formula is attached.
Page 294
Using the Stat List Editor When Formula-Generated Lists Are Displayed 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).
Page 295
Handling Errors Resulting from Attached Formulas Handling Errors Resulting from Attached Formulas Handling Errors Resulting from Attached Formulas 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).
Page 296
As described above, one way to detach a formula from a list name is to edit an element of the list to which the formula is attached. The TI-84 Plus protects against inadvertently detaching the formula from the list name by editing an element of the formula-generated list.
Page 297
Stat List Editor Contexts Stat List Editor Contexts 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 from the 1:Edit...
Page 298
4. Press Í again. You are now in edit-elements 5. Press } until the cursor is on a list name, then press 6. Press ‘. You are now in view-names context. 7. Press †. You are now back in view-elements context. Stat List Editor Contexts Stat List Editor Contexts Stat List Editor Contexts...
Page 299
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. Edit-Elements Context Edit-Elements Context Edit-Elements Context Edit-Elements Context...
Page 300
• 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. In edit-elements context, you can attach a formula to a list name only if you Note: switched to it from view-names context.
Page 301
Enter-Name Context Enter-Name Context Enter-Name Context Enter-Name Context In enter-name context, the At the prompt, you can create a new list name, paste a list name from Name= from the keyboard, or paste an existing list name from the (Chapter 11). The Ù symbol is not required at the To leave enter-name context without entering a list name, press ‘.
Page 302
STAT EDIT Menu STAT EDIT Menu STAT EDIT Menu STAT EDIT Menu To display the STAT EDIT EDIT CALC TESTS 1: Edit... 2: SortA( 3: SortD( 4: ClrList 5: SetUpEditor Chapter 13: Inferential Statistics describes the Note: SortA(, SortD( SortA(, SortD( SortA(, SortD( SortA(, SortD( (sort ascending) sorts list elements from low to high values.
Page 303
. This lets you sort two-variable data on X and keep the data pairs together. keylistname All lists must have the same dimension. The sorted lists are updated in memory. SortA(listname) SortD(listname) SortA(keylistname,dependlist1 SortD(keylistname,dependlist1 are the same as Note: SortA( SortD( ClrList ClrList...
Page 304
SetUpEditor SetUpEditor SetUpEditor SetUpEditor With you can set up the stat list editor to display one or more SetUpEditor order that you specify. You can specify zero to 20 Additionally, if you want to use will automatically unarchive the time. SetUpEditor listname1,listname2, with one to 20...
Page 305
Restoring L Restoring L1 1 1 1 through L Restoring L Restoring L through L6 6 6 6 to the Stat List Editor through L through L with no SetUpEditor listnames list names through Regression Model Features Regression Model Features Regression Model Features Regression Model Features Regression Model Features...
Page 306
The TI-84 Plus uses the formula below to compute RESID list elements. The next section describes the variable RESID = Ylistname RegEQ(Xlistname) Automatic Regression Equation Automatic Regression Equation Automatic Regression Equation Automatic Regression Equation Each regression model has an optional argument, variable such as .
Page 307
Diagnostics Display Mode Diagnostics Display Mode Diagnostics Display Mode Diagnostics Display Mode When you execute some regression models, the TI-84 Plus computes and stores diagnostics values for (correlation coefficient) and (coefficient of determination). are computed and stored for these regression models.
Page 308
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 instruction. Each instruction is in the CATALOG DiagnosticOn DiagnosticOff (Chapter 15). from the home screen, press y N, To set Note:...
Page 309
STAT CALC Menu STAT CALC Menu STAT CALC Menu STAT CALC Menu To display the STAT CALC EDIT CALC 1: 1-Var Stats 2: 2-Var Stats 3: Med-Med 4: LinReg(ax+b) 5: QuadReg 6: CubicReg 7: QuartReg 8: LinReg(a+bx) 9: LnReg 0: ExpReg A: PwrReg B: Logistic C: SinReg...
Page 310
15 occurs once, 12 occurs four times, 9 FREQ are undefined; values are not displayed for is specified, then the Ylistname , then the default is 1 freqlist , then the TI-84 Plus interprets the contains freqlist...
Page 311
2-Var Stats 2-Var Stats 2-Var Stats 2-Var Stats (two-variable statistics) analyzes paired data. 2-Var Stats variable. is the dependent variable. Each element in Ylistname occurrence for each data pair ( 2-Var Stats Xlistname,Ylistname,freqlist Med-Med (ax+b) Med-Med (ax+b) Med-Med (ax+b) Med-Med (ax+b) (median-median) fits the model equation y=ax+b to the data using the median- Med-Med median line (resistant line) technique, calculating the summary points x1, y1, x2, y2, x3,...
Page 312
LinReg(ax+b) Xlistname,Ylistname,freqlist,regequ QuadReg (ax QuadReg (ax QuadReg (ax QuadReg (ax +bx+c) +bx+c) +bx+c) +bx+c) (quadratic regression) fits the second-degree polynomial y=ax QuadReg data. It displays values for . For three data points, the equation is a polynomial fit; for four or more, it is a polynomial regression.
Page 313
QuartReg Xlistname,Ylistname,freqlist,regequ LinReg—(a+bx) LinReg—(a+bx) LinReg—(a+bx) LinReg—(a+bx) (linear regression) fits the model equation y=a+bx to the data using a least- LinReg(a+bx) squares fit. It displays values for also displays values for LinReg(a+bx) Xlistname,Ylistname,freqlist,regequ LnReg—(a+b ln(x)) LnReg—(a+b ln(x)) LnReg—(a+b ln(x)) LnReg—(a+b ln(x)) (logarithmic regression) fits the model equation y=a+b ln(x) to the data using a LnReg least-squares fit and transformed values ln(x) and y.
Page 314
(power regression) fits the model equation y=ax PwrReg squares fit and transformed values ln(x) and ln(y). It displays values for is set, it also displays values for DiagnosticOn PwrReg Xlistname,Ylistname,freqlist,regequ Logistic—c/ Logistic— c/ (1+a (1+a…e e e e Logistic— Logistic— c/ c/ (1+a (1+a...
Page 315
order. If you specify period solution when it would not have found one if you had omitted a value for specify , the differences between time values in period The output of Note: SinReg setting. SinReg Example: SinReg Example: Daylight Hours in Alaska for One Year Daylight Hours in Alaska for One Year SinReg SinReg...
Page 316
With noisy data, you will achieve better convergence results when you specify an accurate estimate for period • 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.
Page 317
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.
Page 318
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 and then press Í. This takes you to the Graph screen and then pastes the Manual-...
Page 319
Variables population standard deviation of y … sum of x minimum of x values maximum of x values minimum of y values maximum of y values 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)
Page 320
Entering Stat Data Entering Stat Data Entering Stat Data 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 Statistical Calculations Statistical Calculations...
Page 321
Steps for Plotting Statistical Data in Lists Steps for Plotting Statistical Data in Lists Steps for Plotting Statistical Data in Lists 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.
Page 322
Scatter Scatter Scatter Scatter (")plots plot the data points from Scatter each point as a box ( › ), cross ( You can use the same list for xyLine xyLine xyLine xyLine (Ó)is a scatter plot in which the data points are plotted and connected in order xyLine of appearance in Xlist...
Page 323
Histogram Histogram Histogram Histogram (Ò) plots one-variable data. The Histogram width of each bar, beginning at include all values, and also adjusts true. A value that occurs on the edge of a bar is counted in the bar to the right. ModBoxplot ModBoxplot ModBoxplot...
Page 324
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 Boxplot Boxplot (Ö)(regular box plot) plots one-variable data. The whiskers on the plot extend Boxplot from the minimum data point in the set ( quartile (...
Page 325
Enter a valid list name in the • If you select X, the TI-84 Plus plots the data on the x-axis and the z-values on the y-axis. •...
Page 326
1. Press y ,. The 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 definition is stored whether you select 4. Select the type of plot. Each type prompts for the options checked in this table. Plot Type "...
Page 327
Plot Type Õ ModBoxplot Ö Boxplot Ô NormProbPlot 5. Enter list names or select options for the plot type. • (list name containing independent data) Xlist • (list name containing dependent data) Ylist or ¦) • (› or Mark • (frequency list for Freq •...
Page 328
Turning On and Turning Off Stat Plots Turning On and Turning Off Stat Plots Turning On and Turning Off Stat Plots Turning On and Turning Off Stat Plots allow you to turn on or turn off stat plots from the home screen or a PlotsOn PlotsOff program.
Page 329
Defining the Viewing Window Defining the Viewing Window Defining the Viewing Window 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. window to display all statistical data points. Tracing a Stat Plot Tracing a Stat Plot Tracing a Stat Plot...
Page 330
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 menu. STAT PLOTS 2. Select the plot to define, which pastes , or to the cursor location.
Page 331
5. Press ¢. Enter the list names, separated by commas. 6. Press ¢ y , | to display the necessary if you selected Select the type of mark (› or pasted to the cursor location. 7. Press ¤ Í to complete the command line. Displaying a Stat Plot from a Program Displaying a Stat Plot from a Program Displaying a Stat Plot from a Program...
Page 333
Inferential Statistics and Distributions Inferential Statistics and Distributions Inferential Statistics and Distributions Inferential Statistics and Distributions Getting Started: Mean Height of a Population Getting Started: Mean Height of a Population Getting Started: Mean Height of a Population Getting Started: Mean Height of a Population Getting Started is a fast-paced introduction.
Page 334
2. Enter at the [H] [G] [H] [T] 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. is displayed on the bottom line. HGHT(1)= Ë...
Page 335
6. Press † to move the cursor onto then press Í. The confidence interval is calculated, and the TInterval on the home screen. Interpret the results. The first line, ( 159.74,173.94 population mean is between about 159.74 centimeters and 173.94 centimeters. This is about a 14.2 centimeters spread.
Page 336
of 7.1 calculated from the larger random sample. This time, use the statistics) input option. 7. Press … | to display the inferential stat editor for TInterval Press ~ Í to select changes so that you can enter summary statistics as input.
Page 337
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.
Page 338
13. Press y = ~ to display the menu. 14. Press Í to paste screen. Press y Z ¢ ¤. (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.
Page 339
according to each test or interval’s input requirements. Below is the inferential stat editor T-Test When you select the Note: does not have an editor screen. Using an Inferential Stat Editor Using an Inferential Stat Editor Using an Inferential Stat Editor Using an Inferential Stat Editor To use an inferential stat editor, follow these steps.
Page 340
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 Selecting Data or Stats Selecting Data or Stats Selecting Data or Stats Selecting Data or Stats Most inferential stat editors prompt you to select one of two types of input.
Page 341
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 ( Selecting an Alternative Hypothesis...
Page 342
Selecting Calculate or Draw for a Hypothesis Test Selecting Calculate or Draw for a Hypothesis Test Selecting Calculate or Draw for a Hypothesis Test 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 ) or on the graph screen ( Calculate...
Page 343
You can paste a hypothesis test or confidence interval instruction to a command Note: line in a program. From within the program editor, select the instruction from either the (Chapter 15) or the CATALOG STAT TESTS Menu STAT TESTS Menu STAT TESTS Menu STAT TESTS Menu STAT TESTS Menu...
Page 344
EDIT CALC TESTS 0: 2-SampTInt... A: 1-PropZInt... B: 2-PropZInt... C: c -Test... D: c -GOF Test... E: 2-SampÛTest... F: LinRegTTest... G: LinRegTInt... H: ANOVA( When a new test or interval is computed, all previous output variables are Note: invalidated. Inferential Stat Editors for the STAT TESTS Instructions Inferential Stat Editors for the STAT TESTS Instructions Inferential Stat Editors for the STAT TESTS Instructions Inferential Stat Editors for the STAT TESTS Instructions...
Page 345
The description then shows the unique output screen for that instruction with the example results. • Descriptions of instructions that offer the types of screens: calculated and graphic results. • Descriptions of instructions that offer only the calculated results on the home screen. Z-Test Z-Test Z-Test...
Page 347
examples assume a fixed-decimal mode setting of 4 (Chapter 1). If Note: STAT TESTS you set the decimal mode to differ from the output in the examples. T-Test T-Test T-Test T-Test (one-sample test; item T-Test population mean m when the population standard deviation s is unknown. It tests the null : m=m hypothesis H against one of the alternatives below.
Page 348
Data Calculated results: Drawn results: 2-SampZTest 2-SampZTest 2-SampZTest 2-SampZTest (two-sample 2-SampZTest and m populations (m ) based on independent samples when both population standard and s deviations (s ) are known. The null hypothesis H the alternatives below. ƒm ƒm •...
Page 349
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...
Page 350
Data Drawn results: 2-SampTTest 2-SampTTest 2-SampTTest 2-SampTTest (two-sample 2-SampTTest and m populations (m ) based on independent samples when neither population or s standard deviation (s one of the alternatives below. ƒm ƒm • • <m 1:< • >m 1:> In the example: Chapter 13: Inferential Statistics and Distributions test;...
Page 352
Data Drawn results: 1-PropZTest 1-PropZTest 1-PropZTest 1-PropZTest (one-proportion 1-PropZTest successes (prop). It takes as input the count of successes in the sample of observations in the sample against one of the alternatives below. ƒ • : propƒp prop: • : prop<p prop:<p0 •...
Page 353
Calculated results: Drawn results: 2-PropZTest 2-PropZTest 2-PropZTest 2-PropZTest (two-proportion 2-PropZTest successes (p and p ) from two populations. It takes as input the count of successes in each sample ( ) and the count of observations in each sample ( tests the null hypothesis H 2-PropZTest against one of the alternatives below.
Page 355
ZInterval ZInterval ZInterval ZInterval (one-sample confidence interval; item ZInterval 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={299.4 297.7 301 298.9 300.2 297} Data Input: Calculated...
Page 356
TInterval TInterval TInterval TInterval (one-sample confidence interval; item TInterval 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 1.9} Data Input: Calculated results: Chapter 13: Inferential Statistics and Distributions...
Page 357
2-SampZInt 2-SampZInt 2-SampZInt 2-SampZInt (two-sample 2-SampZInt the difference between two population means (m and s deviations (s ) are known. The computed confidence interval depends on the user-specified confidence level. In the example: LISTC={154 109 137 115 140} LISTD={108 115 126 92 146} Data Input: Chapter 13: Inferential Statistics and Distributions...
Page 358
Data Calculated results: 2-SampTInt 2-SampTInt 2-SampTInt 2-SampTInt (two-sample 2-SampTInt the difference between two population means (m and s deviations (s ) are unknown. The computed confidence interval depends on the user-specified confidence level. In the example: Chapter 13: Inferential Statistics and Distributions confidence interval;...
Page 360
1-PropZInt 1-PropZInt 1-PropZInt 1-PropZInt (one-proportion 1-PropZInt for an unknown proportion of successes. It takes as input the count of successes in the sample and the count of observations in the sample interval depends on the user-specified confidence level. Input: Calculated results: 2-PropZInt 2-PropZInt...
Page 361
observations in each sample ( the user-specified confidence level. Input: Calculated results: -Test -Test -Test -Test (chi-square test; item -Test way table of counts in the specified table is: no association exists between row variables and column variables. The alternative hypothesis is: the variables are related. Before computing a c -Test, enter the observed counts in a matrix.
Page 362
prompt, enter the matrix variable name to which you want the computed Expected: expected counts to be stored; default= Matrix editor: Input: Calculated results: Chapter 13: Inferential Statistics and Distributions y ú ~ ~ Note: Press select 1:[A] from the MATRX EDIT menu.
Page 363
Drawn results: GOF-Test GOF-Test GOF-Test GOF-Test (Chi Square Goodness of Fit; item D) performs a test to confirm that sample -Test data is from a population that conforms to a specified distribution. For example, c 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}...
Page 364
Calculated results: Drawn results: 2-SampFTest 2-SampFTest 2-SampFTest 2-SampFTest Ü (two-sample Ü-test; item 2-Samp Test population standard deviations (s deviations are all unknown. /Sx2 , tests the null hypothesis H ƒ s ƒs • • <s 1:< • >s 1:> Chapter 13: Inferential Statistics and Distributions ) computes an Ü-test to compare two normal and s ).
Page 365
In the example: SAMP4={ SAMP5={ Data Input: Calculated results: Chapter 13: Inferential Statistics and Distributions Stats...
Page 366
Data Drawn results: LinRegTTest LinRegTTest LinRegTTest LinRegTTest (linear regression LinRegTTest test on the value of slope b and the correlation coefficient r for the equation data and a =a+bx. It tests the null hypothesis H alternatives below. : bƒ0 and rƒ0 (b •...
Page 367
Input: Calculated results: When is executed, the list of residuals is created and stored to the list name LinRegTTest automatically. is placed on the menu. RESID RESID LIST NAMES For the regression equation, you can use the fix-decimal mode setting to control Note: the number of digits stored after the decimal point (Chapter 1).
Page 368
LinRegTInt LinRegTInt LinRegTInt 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:...
Page 369
Xlist, Ylist is the list of independent and dependent variables. The list containing the (frequency) values for the data is stored in real numbers. Each element in the corresponding data point in the input list specified in the the designated Yn variable for storing the regression equation. StoreRegEqn (optional) is the designated variable for storing the regression equation.
Page 370
Calculated results: is sum of squares and Note: SS Inferential Statistics Input Descriptions Inferential Statistics Input Descriptions Inferential Statistics Input Descriptions 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.
Page 371
Pooled Specifies whether variances are to be pooled for 2-SampTTest and 2-SampTInt. No instructs the TI-84 Plus not to pool the variances. Yes instructs the TI-84 Plus to pool the variances. Chapter 13: Inferential Statistics and Distributions...
Page 372
Input Description The expected sample proportion for 1-PropZTest. Must be a real number, such that 0 < p The count of successes in the sample for the 1-PropZTest and 1-PropZInt. Must be an integer The count of observations in the sample for the 1-PropZTest and 1-PropZInt.
Page 373
Input Description df (degree of freedom) represents (number of sample categories) - (number of estimated parameters for the selected distribution + 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.
Page 374
Variables number of data points for sample 1 and sample 2 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 standard error about the line regression/fit coefficients...
Page 375
DISTR menu DISTR menu DISTR menu DISTR menu To display the DISTR menu, press y =. DISTR DRAW 1: normalpdf( 2: normalcdf( 3: invNorm( 4: invT( 5: tpdf( 6: tcdf( 7: c pdf( 8: c 9: Üpdf( 0: Ücdf( A: binompdf( Chapter 13: Inferential Statistics and Distributions nn probability density function nn cumulative distribution function...
Page 376
DISTR DRAW B: binomcdf( C: poissonpdf( D: poissoncdf( E: geometpdf( F: geometcdf( L1â99 and 1â99 specify infinity. If you want to view the area left of Note: example, specify lowerbound normalpdf( normalpdf( normalpdf( normalpdf( computes the probability density function ( normalpdf( value.
Page 377
normalpdf(x For plotting the normal distribution, you can set window variables Note: so that the mean m falls between them, and then select normalcdf( normalcdf( normalcdf( normalcdf( computes the normal distribution probability between normalcdf( for the specified mean m and standard deviation s. The defaults are m=0 and upperbound s=1.
Page 378
invNorm( invNorm( invNorm( invNorm( computes the inverse cumulative normal distribution function for a given invNorm( under the normal distribution curve specified by mean m and standard deviation s. It calculates the value associated with an be true. The defaults are m=0 and s=1. invNorm(area[, invT( invT(...
Page 379
tpdf( tpdf( tpdf( tpdf( computes the probability density function ( tpdf( specified value. (degrees of freedom) must be > 0. To plot the Student- paste to the Y= editor. The probability density function ( tpdf( Γ df f x ( ) ------------------------------------------------ - -------------------------------- - Γ...
Page 380
pdf( pdf( pdf( pdf( computes the probability density function ( pdf( (degrees of freedom) must be an integer > 0. To plot the c at a specified value. distribution, paste c pdf( df/2 f x ( ) -------------------- 1/2 Γ df 2 ⁄ pdf(x,df) Chapter 13: Inferential Statistics and Distributions to the Y= editor.
Page 381
cdf( cdf( cdf( cdf( computes the c (chi-square) distribution probability between cdf( for the specified upperbound cdf(lowerbound,upperbound,df) Fpdf( Fpdf( Fpdf( Fpdf( Ü computes the probability density function ( pdf( value. (degrees of freedom) and numerator df the Ü distribution, paste Ü Γ...
Page 382
Ü pdf(x,numerator df,denominator df) Fcdf( Fcdf( Fcdf( Fcdf( Ü computes the Ü distribution probability between cdf( specified (degrees of freedom) and numerator df must be integers > 0. Ü cdf(lowerbound,upperbound,numerator df,denominator df) binompdf binompdf binompdf binompdf computes a probability at binompdf( specified and probability of success (...
Page 383
1 must be true. of integers. 0 list of probabilities from 0 to ⎛ ⎞ p – f x ( ) – x ⎝ ⎠ where n = numtrials binompdf(numtrials,p[,x]) binomcdf( binomcdf( binomcdf( binomcdf( computes a cumulative probability at binomcdf( with the specified numtrials number or a list of real numbers.
Page 384
poissonpdf( poissonpdf( poissonpdf( poissonpdf( computes a probability at poissonpdf( specified mean m, which must be a real number > 0. integers. The probability density function ( µ – f x ( ) µ ⁄ 0,1,2,... poissonpdf( poissoncdf( poissoncdf( poissoncdf( poissoncdf( computes a cumulative probability at poissoncdf( with the specified mean m, which must be a real number >...
Page 385
1 must be true. 0 can be an integer or a list of integers. The probability density function (pdf) is: – f x ( ) p 1 p – geometpdf(p,x) geometcdf( geometcdf( geometcdf( geometcdf( computes a cumulative probability at geometcdf( first success occurs, for the discrete geometric distribution with the specified probability 1 must be true.
Page 386
To clear the drawings, select Before you execute a Note: so that the desired distribution fits the screen. DISTR DRAW Shades normal distribution. 1: ShadeNorm( Shades Student-t distribution. 2: Shade_t( 3: Shadec Shades 4: ShadeÜ( Shades L1â99 and 1â99 specify infinity. If you want to view the area left of Note: example, specify lowerbound...
Page 387
ShadeNorm(lowerbound,upperbound[, Shade_t( Shade_t( Shade_t( Shade_t( draws the density function for the Student- Shade_t( of freedom) and shades the area between Shade_t(lowerbound,upperbound,df) Chapter 13: Inferential Statistics and Distributions Note: For this example, Xmin = 55 Xmax = 72 Ymin = Ymax = .2 distribution specified by lowerbound upperbound...
Page 388
Shade Shadec Shade Shade ( ( ( ( draws the density function for the c Shade (degrees of freedom) and shades the area between Shade (lowerbound,upperbound,df) ShadeF( ShadeF( ShadeF( ShadeF( Ü draws the density function for the Ü distribution specified by Shade (degrees of freedom) and upperbound...
Page 389
Ü Shade (lowerbound,upperbound,numerator df,denominator df) Chapter 13: Inferential Statistics and Distributions Note: For this example, Xmin = 0 Xmax = 5 Ymin = Ymax = .9...
Page 390
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 1.54 M of space within ROM memory specifically for applications.
Page 391
1. Press z † ~ ~ ~ Í to set the fixed-decimal mode setting to . The TI-84 Plus will display all numbers with two decimal places). 2. Press Œ Í to select menu.
Page 392
3. Press Í to select menu. The TVM Solver is displayed. CALC VARS Í to store 48 months to Ú. Press † Press Í to store 9,000 to L250 to . (Negation indicates cash outflow.) Press Í to store 0 to Í...
Page 393
Because there are no payments when you solve compound interest problems, Note: must be set to 1. Press Œ Í to select menu. APPLICATIONS 2. Press Í to select menu. The TVM Solver is displayed. Press VARS enter the number of periods in years. Press † † Ì...
Page 394
Using the TVM Solver Using the TVM Solver 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. menu section describes the five TVM variables (Ú, æ, FINANCE VARS ) and in the TVM Solver corresponds to the...
Page 395
Entering Cash Inflows and Cash Outflows Entering Cash Inflows and Cash Outflows When using the TI-84 Plus financial functions, you must enter cash inflows (cash received) as positive numbers and cash outflows (cash paid) as negative numbers. The TI-84 Plus follows this convention when computing and displaying answers.
Page 396
FINANCE CALC Menu FINANCE CALC Menu FINANCE CALC Menu FINANCE CALC Menu To display the FINANCE CALC CALC VARS Displays the TVM Solver. 1: TVM Solver... Computes the amount of each payment. 2: tvm_Pmt 3: tvm_¾ ¾ ¾ ¾ æ Computes the interest rate per year.
Page 397
To store a value to a Note: variable on the FINANCE VARS If you enter less than six arguments, the TI-84 Plus substitutes a previously stored variable value for each unspecified argument. If you enter any arguments with a arguments in parentheses.
Page 398
òÚ ¾æ tvm_Pmt ,PV,FV,P/Y,C/Y) In the example above, the values are stored to the Note: TVM Solver. Then the payment ( 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_I% tvm_I%...
Page 399
Ú ¾æ tvm_PV ,PMT,FV,P/Y,C/Y) tvm_N tvm_N tvm_N tvm_N Ú computes the number of payment periods. tvm_ Ú[ æ¾ tvm_ ,PV,PMT,FV,P/Y,C/Y) tvm_FV tvm_FV tvm_FV tvm_FV computes the future value. tvm_FV Ú ¾æ tvm_FV ,PV,PMT,P/Y,C/Y) Chapter 14: Applications...
Page 400
Calculating a Cash Flow Calculating a Cash Flow Calculating a Cash Flow Calculating a Cash Flow Use the cash flow functions (menu items equal time periods. You can enter unequal cash flows, which can be cash inflows or outflows. The syntax descriptions for •...
Page 401
npv(, irr( npv(, irr( npv(, irr( npv(, irr( (net present value) is the sum of the present values for the cash inflows and npv( outflows. A positive result for npv(interest rate,CF0,CFList (internal rate of return) is the interest rate at which the net present value of the cash irr( flows is equal to zero.
Page 402
Prn( schedule using stored values for ¾æ, ending payment in the range. specifies the internal precision the calculator uses to calculate the principal; if you do not specify , the TI-84 Plus uses the current roundvalue...
Page 403
Chapter 14: Applications , and before computing the principal. , and must be positive integers < 10,000. pmt1 pmt2 , the TI-84 Plus uses the current . Press † † ~ Í to is the starting payment. pmt1 decimal-mode Float/Fix...
Page 404
2. Press Î Œ Í Í to display the TVM Solver. to enter number of payments. Press † 8 to 3. Press enter the interest rate. Press † † Ì payment amount. Press † of the mortgage. Press † year, which also sets the compounding periods per year to 12.
Page 405
8. Press y - and enter the values below. TblStart=0 Tbl=12 9. Press y 0 to display the table of outstanding balances ( 10. Press z † † † † † † † ~ ~ Í to select split-screen mode, in which the graph and table are displayed simultaneously.
Page 406
computes the nominal interest rate. Nom( real numbers. compounding periods Nom(effective rate,compounding periods) Eff( Eff( Eff( 4Eff( computes the effective interest rate. Eff( numbers. compounding periods Eff(nominal rate,compounding periods) Finding Days between Dates/Defining Payment Finding Days between Dates/Defining Payment Finding Days between Dates/Defining Payment Finding Days between Dates/Defining Payment Method Method...
Page 407
dbd(date1,date2) You can enter date1 date2 • MM.DDYY (United States) • DDMM.YY (Europe) The decimal placement differentiates the date formats. Defining the Payment Method Defining the Payment Method Defining the Payment Method Defining the Payment Method (menu items Pmt_End Pmt_Bgn annuity or an annuity due.
Page 408
Pmt_Bgn Pmt_Bgn Pmt_Bgn Pmt_Bgn (payment beginning) specifies an annuity due, where payments occur at the Pmt_Bgn beginning of each payment period. Most leases are in this category. Pmt_Bgn On the TVM Solver’s PMT:END BEGIN Using the TVM Variables Using the TVM Variables Using the TVM Variables Using the TVM Variables FINANCE VARS Menu...
Page 409
The App will only work with Vernier auto-ID sensors when using CBL 2é and Note: Vernier LabProê. The EasyData app will autolaunch on your TI-84 Plus if you plug in a USB sensor such as the CBR 2é or Vernier USB Temperature sensor. Chapter 14: Applications variables.
Page 410
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...
Page 411
To restore the default settings in EasyData while a data collection device is connected to the TI-84 Plus, choose File Chapter 14: Applications...
Page 412
Saving Collected Data Saving Collected Data Collected data is automatically transferred to the TI-84 Plus and stored in lists when data collection is complete. When you exit the EasyData App, a prompt reminds you of the lists in which time, distance, velocity, and acceleration are stored.
Page 414
What Is the CATALOG? What Is the CATALOG? What Is the CATALOG? The CATALOG is an alphabetical list of all functions and instructions on the TI-84 Plus. You also can access each CATALOG item from a menu or the keyboard, except: •...
Page 415
The 4 in the first column is the selection cursor. 2. Press † or } to scroll the want. • To jump to the first item beginning with a particular letter, press that letter; alpha- lock is on. • Items that begin with a number are in alphabetical order according to the first letter after the number.
Page 416
• Count each number, letter, and space as one character. • Count each instruction or function name, such as TI-84 Plus interprets each instruction or function name as one character. Entering a String Entering a String Entering a String Entering a String To enter a string on a blank line on the home screen or in a program, follow these steps.
Page 417
String Variables String Variables String Variables String Variables The TI-84 Plus has 10 variables to which you can store strings. You can use string variables with string functions and instructions. To display the VARS STRING 1. Press to display the Chapter 15: CATALOG, Strings, Hyperbolic Functions ) indicates that the string continues beyond the screen.
Page 418
2. Press Í to display the Storing a String to a String Variable Storing a String to a String Variable Storing a String to a String Variable Storing a String to a String Variable To store a string to a string variable, follow these steps. 1.
Page 419
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 Displaying the Contents of a String Variable Displaying the Contents of a String Variable Displaying the Contents of a String Variable To display the contents of a string variable on the home screen, select the string variable...
Page 420
other menu items. The ellipses in the table indicate the presence of additional CATALOG CATALOG items. CATALOG Equ4String( expr( inString( length( String4Equ( sub( Concatenation Concatenation Concatenation Concatenation To concatenate two or more strings, follow these steps. 1. Enter , which can be a string or string name. string1 2.
Page 421
, which can be a string or string name. If necessary, press Ã and enter 3. Enter string2 , and so on. string3 string1+string2+string3... 4. Press Í to display the strings as a single string. Selecting a String Function from the CATALOG Selecting a String Function from the CATALOG Selecting a String Function from the CATALOG Selecting a String Function from the CATALOG...
Page 422
expr( expr( expr( expr( converts the character string contained in expr( can be a string or a string variable. string expr(string) inString( inString( inString( inString( returns the character position in inString( be a string or a string variable. search; the default is 1. inString(string,substring[,start]) does not contain Note:...
Page 423
length( length( length( length( returns the number of characters in length( An instruction or function name, such as Note: length(string) String4Equ( String Equ( String String Equ( Equ( converts String Equ( string string or string variable. String String Equ(string,Yn) Chapter 15: CATALOG, Strings, Hyperbolic Functions string string sin(...
Page 424
sub( sub( sub( sub( returns a string that is a subset of an existing sub( variable. is the position number of the first character of the subset. begin number of characters in the subset. sub(string,begin,length) Entering a Function to Graph during Program Execution Entering a Function to Graph during Program Execution Entering a Function to Graph during Program Execution Entering a Function to Graph during Program Execution...
Page 425
When you execute this program, enter a function to store to Note: prompt. Hyperbolic Functions in the CATALOG Hyperbolic Functions in the CATALOG Hyperbolic Functions in the CATALOG Hyperbolic Functions in the CATALOG Hyperbolic Functions Hyperbolic Functions Hyperbolic Functions Hyperbolic Functions The hyperbolic functions are available only from the CATALOG.
Page 426
CATALOG sinh tanh( tanh sinh(, cosh(, tanh( sinh(, cosh(, tanh( sinh(, cosh(, tanh( sinh(, cosh(, tanh( , and are the hyperbolic functions. Each is valid for real numbers, sinh( cosh( tanh( expressions, and lists. sinh(value) cosh(value) tanh(value) sinh sinh (, cosh (, cosh (, tanh (, tanh...
Page 427
sinh (value) cosh (value) sinh (value) Chapter 15: CATALOG, Strings, Hyperbolic Functions...
Page 428
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.
Page 429
3. Press ~ to select menu. PRGM I/O Prompt line. Press ƒ variable names for radius and height. Press Í. 4. Press y B ƒ Í to enter the expression pR it to the variable 5. Press ~ to select menu.
Page 430
When you execute a program, the TI-84 Plus performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI-84 Plus can store is limited only by available memory. Creating a New Program...
Page 431
2. Press Í to select is on. 3. Press a letter from A to Z or q to enter the first character of the new program name. A program name can be one to eight characters long. The first character must Note: be a letter from A to Z or q.
Page 432
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.
Page 433
4. Press y L and then select 5. Select 2:Mem Mgmt/Del 6. Select to display the 7:Prgm... 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.
Page 434
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 ‘.
Page 435
The TI-84 Plus checks for errors during program execution. It does not check for errors as you enter a program. Breaking a Program Breaking a Program Breaking a Program Breaking a Program To stop program execution, press É. The •...
Page 436
To move the cursor to the beginning of a command line, press y |; to move to Note: 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 Inserting and Deleting Command Lines Inserting and Deleting Command Lines...
Page 437
Scrolling the PRGM EXEC and PRGM EDIT Menus Scrolling the PRGM EXEC and PRGM EDIT Menus Scrolling the PRGM EXEC and PRGM EDIT Menus The TI-84 Plus sorts PRGM EXEC alphanumerical order. Each menu only labels the first 10 items using 1 through 9, then 0.
Page 438
PRGM CTL Menu PRGM CTL Menu PRGM CTL Menu PRGM CTL Menu To display the PRGM CTL only. I/O EXEC 1: If 2: Then 3: Else 4: For( 5: While 6: Repeat 7: End 8: Pause 9: Lbl 0: Goto A: IS>( B: DS<( C: Menu(...
Page 439
To return to the program editor without selecting an item, press ‘. Controlling Program Flow Controlling Program Flow Controlling Program Flow Controlling Program Flow Program control instructions tell the TI-84 Plus which command to execute next in a program. , and While Repeat to execute next.
Page 440
If If If If for testing and branching. If following is skipped. If condition instructions can be nested. :If condition :command (if true) :command Program If-Then If-Then If-Then If-Then following an executes a group of Then identifies the end of the group of :If condition :Then :command (if true)
Page 441
:End :command Program If-Then-Else If-Then-Else If-Then-Else If-Then-Else following executes a group of Else If-Then identifies the end of the group of :If condition :Then :command (if true) :command (if true) :Else :command (if false) :command (if false) :End :command Program Chapter 16: Programming Output commands...
Page 442
For( For( For( For( loops and increments. It increments For( optional (default is 1) and can be negative ( value not to be exceeded. :For(variable,begin,end[,increment]) :command (while end not exceeded) :command (while end not exceeded) :End :command Program Chapter 16: Programming from variable <...
Page 443
While While While While performs a group of While relational test (Chapter 2). (nonzero), the program executes a group of When is false (zero), the program executes each condition instructions can be nested. :While condition :command (while condition is true) :command (while condition is true) :End :command...
Page 444
:command (until condition is true) :End :command Program identifies the end of a group of end of each , or For( While end of each group and each If-Then Pause Pause Pause Pause suspends execution of the program so that you can see answers or graphs. Pause During the pause, the pause indicator is on in the top-right corner.
Page 445
Pause [value] Program Lbl, Goto Lbl, Goto Lbl, Goto Lbl, Goto (label) and (go to) are used together for branching. Goto specifies the for a command. label through 99, or q). Lbl label causes the program to branch to Goto Chapter 16: Programming Output can be one or two characters (A through Z, 0...
Page 446
Goto label Program IS>( IS>( IS>( IS>( (increment and skip) adds 1 to IS>( expression), the next command executed. cannot be a system variable. variable :IS>(variable,value) :command (if answer value) :command (if answer > value) Program is not a looping instruction. Note: IS>( Chapter 16: Programming Output...
Page 447
DS<( DS<( DS<( DS<( (decrement and skip) subtracts 1 from DS<( an expression), the next executed. cannot be a system variable. variable :DS<(variable,value) ‚ :command (if answer value) :command (if answer < value) Program is not a looping instruction. Note: DS<( Menu( Menu( Menu(...
Page 448
Menu("title","text1",label1,"text2",label2, . . .) Program The program above pauses until you select disappears and the program continues execution at prgm prgm prgm prgm to execute other programs as subroutines. When you select prgm to the cursor location. Enter characters to spell a program to selecting existing programs from the enter the name of a program that you have not yet created.
Page 449
Stop Stop Stop Stop stops execution of a program and returns to the home screen. Stop the end of a program. DelVar DelVar DelVar DelVar deletes from memory the contents of DelVar DelVar variable GraphStyle( GraphStyle( GraphStyle( GraphStyle( designates the style of the graph to be drawn. GraphStyle( Y= function name in the current graphing mode.
Page 450
7: getKey Clears the display. 8: ClrHome Clears the current table. 9: ClrTable Gets a variable from another TI-84 Plus. 0: GetCalc( Gets a variable from CBL 2™ or CBR™. A: Get( Sends a variable to CBL 2 or CBR.
Page 451
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 Displaying a Graph with Input Displaying a Graph with Input Displaying a Graph with Input...
Page 452
Storing a Variable Value with Input Storing a Variable Value with Input Storing a Variable Value with Input Storing a Variable Value with Input with displays a Input variable 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.
Page 453
Prompt Prompt Prompt Prompt During program execution, At each prompt, enter a value or expression for each values are stored, and the program resumes execution. Prompt variableA[,variableB,...,variable n] Program Y= functions are not valid with Note: Displaying the Home Screen Displaying the Home Screen Displaying the Home Screen Displaying the Home Screen...
Page 454
• is a variable, the current value is displayed. value • is an expression, it is evaluated and the result is displayed on the right side of value the next line. • is text within quotation marks, it is displayed on the left side of the current value display line.
Page 455
Output( Output( Output( Output( displays Output( text value (1 through 16), overwriting any existing characters. column You may want to precede Note: 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.
Page 456
getKey getKey getKey getKey returns a number corresponding to the last key pressed, according to the key getKey code diagram below. If no key has been pressed, loops to transfer control, for example, when creating video games. Program You can press É at any time during execution to break the program. Note: Chapter 16: Programming returns 0.
Page 457
Y= variable, graph database, or picture. GetCalc(variable portflag Chapter 16: Programming on another TI-84 Plus and stores it to variable can be a real or complex number, list element, list name, on the variable...
Page 458
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: =0 use USB port if connected;...
Page 459
Calling a Program from Another Program 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.
Page 460
command in the first program when it encounters either the end of the second program. Program Subroutine Notes about Calling Programs Notes about Calling Programs Notes about Calling Programs Notes about Calling Programs Variables are global. used with label Goto program is not recognized by another program.
Page 461
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. Because an assembly langauge program has greater control over the calculator, if...
Page 462
1. Follow the steps for writing a program (16-4) but be sure to include first line of your program. 2. From the home screen, press y N and then select the screen. 3. Press to display the 4. Select the program you want to compile. It will be pasted to the home screen. 5.
Page 463
Activities Activities Activities Activities The Quadratic Formula The Quadratic Formula The Quadratic Formula The Quadratic Formula Entering a Calculation Entering a Calculation Entering a Calculation Entering a Calculation Use the quadratic formula to solve the quadratic equations 3x N x + 3 = 0. Begin with the equation 3x ¿...
Page 464
5. Press £ Ì ƒ [B] Ã y C ƒ [B] ¡ ¹ ƒ [A] ƒ [C] ¤ ¤ ¥ £ ƒ [A] ¤ to enter the expression for one of the solutions for the quadratic formula, ± – – -------------------------------------- 6.
Page 465
2. Press to select Frac menu. When you press on the home screen. 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.
Page 466
Displaying Complex Results Displaying Complex Results Now solve the equation 2x TI-84 Plus displays complex results. 1. Press z † † † † † † (6 times), and then press ~ to position the cursor . Press Í to select...
Page 467
2. Press y 5 (above z) to return to the home screen, and then press ‘ to clear it. ¿ ƒ [A] ƒ [:] Ì 3. Press ¿ ƒ [B] ƒ [:] [C] Í. The coefficient of the x coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively.
Page 468
6. Press y [ repeatedly until this quadratic-formula expression is displayed: – – -------------------------------------- - 7. Press Í to find the other solution for the quadratic equation: 2x An alternative for solving equations for real numbers is to use the built-in Equation Note: Solver.
Page 469
Defining a Function Defining a Function Defining a Function 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.
Page 470
Defining a Table of Values 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.
Page 471
5. Press and hold † to scroll the table until a negative result for Notice that the maximum length of this problem occurs where the sign of (box’s volume) changes from positive to negative, between 6. Press y -. Notice that has changed to TblStart reflect the first line of the table as it was...
Page 472
2. Press y 0. 3. Press † and } to scroll the table. Notice that the maximum value for , which occurs at 410.26 the maximum occurs where 4. Press y -. Press . Press Ë TblStart 5. Press y 0, and then press † and } to scroll the table.
Page 473
Setting the Viewing Window 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. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values of the window variables determine the size of the viewing window.
Page 474
The standard window variables define the viewing window as shown. , and Xmax Ymin Ymax boundaries of the display. define the distance between tick marks on the axes. resolution. Í to define 2. Press ¥ 3. Press to define expression. 4.
Page 475
Displaying and Tracing the Graph Displaying and Tracing the Graph Displaying and Tracing the Graph 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 feature.
Page 476
4. Press r. The trace cursor is displayed on the function. The function that you are tracing is displayed in the top-left corner. 5. Press | and ~ to trace along dot at a time, evaluating You also can enter your estimate for the maximum value of Ë...
Page 477
1. Press q to display the 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 †...
Page 478
4. Press p to display the new window settings. Finding the Calculated Maximum Finding the Calculated Maximum Finding the Calculated Maximum Finding the Calculated Maximum You can use a CALCULATE 1. Press y / (above r) to display menu. Press CALCULATE 4:maximum The graph is displayed again with a...
Page 479
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. prompt is displayed. Guess? 4. Press | to trace to a point near the maximum, and then press Í.
Page 480
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. First, they held 15 of the objects one by one in their left hands and guessed what they were.
Page 481
Women Women Left Right Procedure Procedure Procedure Procedure 1. Press … to select , separated by commas. Press Í. The stat list editor now contains only MRGHT these four lists. 2. Press … to select 3. Enter into the number of correct guesses each woman made using her left WLEFT ).
7. Press p. Set Xscl=1 adjusts the viewing window and displays the box plots for the women’s results. 8. Press r. Use | and ~ to examine 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.
Page 483
11. Compare the right-hand results. Define plot 1 to use , and then press r to examine MRGHT 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. Do you think that this is because adults have learned to adapt or because our sample was not large enough? Chapter 17: Activities...
Page 484
Problem Problem Problem 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.
Page 485
3. Press p and set ; they are set by @ Ymax 4. Press y 5 to return to the home screen. Store and @ are on the horizontal and vertical distance between the centers of adjacent pixels. Integer values for @ and @ 5.
Page 486
Problem Problem Problem Problem Graph the inequality 0.4x the values of X where the inequality is true and where it is false. Procedure Procedure Procedure Procedure 1. Press z. Select all graph style icons to í (dot) in the 2. Press o. Turn off all functions and stat plots. Enter the left side of the inequality as and the right side as 3.
Page 487
6. Press o. Turn off , and . Enter equations to graph only the inequality. 7. Press r. Notice that the values of are zero where the inequality is false. Chapter 17: Activities...
Page 488
Problem Problem Problem Problem Using a graph, solve the equation x of two equations and two unknowns: y = x control the decimal places displayed on the graph. Procedure Procedure Procedure Procedure 1. Press z. Select the default mode settings. Press o. Turn off all functions and stat plots.
Page 489
4. Press q to select cursor onto the apparent intersection of the functions on the right side of the display. As you move the cursor, notice that the 5. Press Í to zoom in. Move the cursor over the intersection. As you move the cursor, notice that now the 6.
Page 490
Setting up the Program Setting up the Program Setting up the Program 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 ~ ~ then press Í.
Page 491
:If 1 à3 <N and N2 à3 :Then :.5(.5+X)!X :.5(1+Y)!Y :End :If 2 à3 <N :Then :.5(1+X)!X :.5Y!Y :End :Pt-On(X,Y) :End :StorePic 6 After you execute the program above, you can recall and display the picture with the instruction RecallPic 6 Chapter 17: Activities If/Then group.
Page 492
Problem Problem Problem Problem Using format, you can identify points with attracting and repelling behavior in sequence graphing. Procedure Procedure Procedure Procedure 1. Press z. Select 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).
Page 493
6. Change and trace the graph to show a cobweb with two attractors. 3.44 7. Change and trace the graph to show a cobweb with four attractors. 3.54 Chapter 17: Activities...
Page 494
Setting Up the Program Setting Up the Program Setting Up the Program Setting Up the Program This program graphs the function A sin(BX) with random integer coefficients between 1 and 1