TI-80 GRAPHING CALCULATOR GUIDEBOOK TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments Incorporated. Windows is a registered trademark of Microsoft Corporation. Macintosh is a registered trademark of Apple Computer, Inc. © 1995–1997, 2001 by Texas Instruments Incorporated. $TITLEPG.
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Table of Contents This manual describes how to use the TI.80 Graphing Calculator. Getting Started gives a quick overview of its features. The first chapter gives general instructions on operating the TI.80. Other chapters describe its interactive features. The applications in Chapter 11 show how to use these features together. Using this Guidebook Effectively.................... Glossary ......................................... viii xii Getting Started: Do This First! TI-80 Keyboard ...................
Chapter 2: Math, Angle, and Test Operations Getting Started: Lottery Chances .................... Using the TI-80 Functions .......................... Keyboard Math Operations ......................... MATH MATH Operations ........................... MATH NUM (Number) Operations ................... MATH PRB (Probability) Operations................. ANGLE Operations ................................ TEST (Relational) Operations.......................
Chapter 6: Tables Getting Started: Roots of a Function ................. Defining the Independent Variable .................. Defining the Dependent Variable .................... Displaying the Table ............................... 6-2 6-3 6-4 6-5 Chapter 7: Draw Operations Getting Started: Shading a Graph .................... DRAW DRAW Menu ............................... Drawing Lines .................................... Drawing Horizontal and Vertical Lines ............... Drawing a Function ........
Chapter 10: Programming Getting Started: Rolling a Die ....................... 10-2 About TI-80 Programs ............................. 10-4 Creating and Executing Programs ................... 10-5 Editing Programs ................................. 10-6 PRGM CTL (Control) Instructions ................... 10-7 PRGM I/O (Input/Output) Instructions ............... 10-11 Calling Other Programs ............................ 10-14 Chapter 11: Applications Probability Experiments: Coins, Dice, and Spinners ...
Appendix A: Tables and Reference Information Table of TI-80 Functions and Instructions ............ Menu Map........................................ TI-80 Variables ................................... A-2 A-20 A-26 Appendix B: Service and Warranty Information Battery Information ............................... Accuracy Information ............................. In Case of Difficulty ............................... Service and Support Information ................... Warranty Information...................
Using this Guidebook Effectively The structure of the TI-80 guidebook and the design of its pages can help you find the information you need quickly. Consistent presentation techniques are used throughout to make the guidebook easy to use. Structure of the Guidebook Page-Design Conventions viii Introduction The guidebook is designed to teach you how to use the calculator. ¦ Getting Started is a fast-paced, keystroke-by-keystroke introduction.
InformationMapping Conventions ¦ Specific text—The text to the right of a subheading presents detailed information about that specific topic or task. The information may be presented as paragraphs, numbered procedures, bulleted lists, or illustrations. ¦ Page “footers”—The bottom of each page shows the chapter name, chapter number, and page number. Several conventions are used to present information concisely and in an easily referenced format.
Reference Aids x Introduction Several techniques have been used to help you look up specific information when you need it. These include: ¦ A chapter table of contents on the first page of each chapter, as well as the full table of contents at the front of the guidebook. ¦ A glossary at the end of this section, defining important terms used throughout the guidebook.
Glossary This glossary provides definitions for important terms that are used throughout this guidebook. Argument An argument is an input upon which the value of a function depends. Command A command is any entry submitted to the calculator using ¸. There are two types of TI-80 commands: instructions and expressions. Expression An expression is a complete sequence of numbers, variables, functions, and their arguments that can be evaluated to a single answer.
Pixel A pixel (picture element) is a square dot on the TI-80 display. The TI-80 display is 64 pixels wide and 48 pixels high. Real Number On the TI-80, real numbers are individual decimal or fraction values. Value A value is a single decimal or fraction number or a list of decimals or fractions. Variable A variable is the name given to a location in memory in which a value, an expression, a list, or another named item is stored.
Getting Started: Do This First! Getting Started contains two keystroke-by-keystroke examplesan interest rate problem and a volume problemwhich introduce you to some principal operating and graphing features of the TI.80. You will learn to use the TI.80 more quickly by completing both of these examples first. Contents TI-80 Keyboard ................................... First Steps ....................................... TI-80 Menus ......................................
TI-80 Keyboard The keys on the TI.80 are grouped by color and physical layout to allow easy location of the key you need. The keys are divided into zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys. The Zones of the Keyboard Graphing Editing Advanced Functions Scientific Calculator & & & & Graphing Keys These keys are most frequently used to access the interactive graphing features of the TI-80.
First Steps Before beginning the two sample problems, follow the steps on this page to reset the TI-80 to its factory settings. (Resetting the TI-80 erases all previously entered data.) This ensures that following the keystrokes in this section produces the same actions. 1. Press ´ to turn the calculator on. If the screen is very dark or blank, adjust the display contrast. Press and release 2, and then press and hold 8 (to make the display lighter) or press and hold 7 (to make the display darker).
TI-80 Menus To leave the keyboard uncluttered, the TI.80 uses full-screen menus to display many additional operations. The use of specific menus is described in the appropriate chapters. Displaying a Menu When you press a key that displays a menu, such as I, that menu screen temporarily replaces the screen where you are working. After you make a selection from a menu, you usually are returned to the screen where you were. Moving from One Menu to Another A menu key may display more than one menu name.
Entering a Calculation: Compound Interest The TI.80 displays up to 8 16-characters lines so that you see an expression and its solution together. You can store values to variables, enter multiple instructions on one line, and recall previous entries. Using trial and error, determine when an amount invested at 6% annual compounded interest will double in value. 1. For the first guess, compute the amount available at the end of 10 years. Enter the expression just as you would write it.
Continuing a Calculation To save keystrokes, you can use the Last Entry feature to recall the last expression entered and then edit it for a new calculation. In addition, the next expression can be continued from the previous result. 1. The next guess should be less than, but close to, 12 years. Compute the amount available at the end of 11.9 years, using the Last Entry feature. Press 2, followed by ² (the second function of ¸). The last calculated expression is shown on the next line of the display.
Defining a Function: Box with Lid Take an 8½"×11" sheet of paper and cut X by X squares from two corners and X by (X+B) rectangles from the other two corners. Now fold the paper into a box with lid. What X would give the maximum volume V of a box made in this way? Use tables and graphs to determine the solution. Begin by defining a function that describes the volume of the box.
Defining a Table of Values The table feature of the TI.80 provides numeric information about a function. Use a table of values from the previously defined function to estimate an answer to the problem. 1. Press y # (above p) to display the TABLE SETUP screen. 2. Press Í to accept TBLMIN=0. 3. Press .5 Í to define the table increment @TBL=.5. 4. Press y & (above s) to display the table. Note that the maximum value is around 1.5, between 1 and 2. 5.
Zooming In on the Table You can adjust the way a table is displayed to get more detailed information about any defined function. By varying the value of @TBL, you can “zoom in” on the table. 1. Adjust the table setup to get a more accurate estimate of the maximum size of the cutout. Press 1 Í to set TBLMIN. Press .1 to set @Tbl. 2. Press y &. 3. Use † and } to scroll the table. Note that the maximum value displayed is 33.072, which occurs at X=1.6. The maximum occurs at 1.5
4. Press y #. Press 1.5 Í to set TBLMIN. Press .01 Í to set @TBL. 5. Press y & and use † and } to scroll the table. Two “equal” maximum values are shown, 33.074 at X=1.58 and X=1.59. 6. Press † or } to move the cursor to 1.58. Press ~ to move the cursor into the Y1 column. The bottom line of the display shows the value of Y1 at 1.58 in full precision, 33.073824. 7. Press † to display the “other” maximum. The value of Y1 at 1.59 in full precision is 33.073908.
Changing the Viewing Window The viewing window defines the portion of the coordinate plane that appears in the display. The values of the Window variables determine the size of the viewing window. You can view and change these values. 1. Press p to display the Window variables edit screen. You can view and edit the values of the Window variables here. The standard Window variables define the viewing window as shown. XMIN, XMAX, YMIN, and YMAX define the boundaries of the display.
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 with TRACE. 1. Press s to graph the selected function in the viewing window. The graph of Y1=(W–2X)(Là2–X)X is shown in the display. 2. Press ~ once to display the free-moving cursor just to the right of the center of the screen.
Zooming In on the Graph You can magnify the viewing window around a specific location using the Zoom instructions to help identify maximums, minimums, roots, and intersections of functions. 1. Press q to display the ZOOM menu. This menu is typical of TI-80 menus. To select an item, you may either press the number to the left of the item, or you may press † until the item number is highlighted and then press Í. 2. To ZOOM IN, press 2. The graph is displayed again.
Other TI.80 Features Getting Started has introduced you to basic calculator operation and the table and function graphing features of the TI-80. The remainder of this Guidebook describes these features in more detail and also covers other capabilities of the TI-80. Fractions You can enter fractions directly from the keyboard and perform calculations with fractions. You can convert between fractions and their decimal equivalents. In MANSIMP mode, you can simplify fractions step-by-step.
Chapter 1: Operating the TI-80 This chapter describes the TI.80 and provides general information about its operation. Chapter Contents Turning the TI.80 On and Off ....................... Setting the Display Contrast ........................ The Display ...................................... Entering Expressions and Instructions ............... The Edit Keys .................................... Setting Modes .................................... TI.80 Modes ......................................
Turning the TI-80 On and Off To turn the TI.80 on, press the ´ key. To turn it off, press and release y, and then press ®. After about five minutes without any activity, the APD™ (Automatic Power Down™) feature turns the TI.80 off automatically. Turning the Calculator On Turning the Calculator Off APD™ (Automatic Power Down™) Press ´ to turn the TI-80 on. ¦ If you pressed y ® to turn the calculator off, the display shows the Home screen as it was when you last used it, and errors are cleared.
Setting the Display Contrast The brightness and contrast of the display depend on room lighting, battery freshness, viewing angle, and the adjustment of the display contrast. The contrast setting is retained in memory when the TI.80 is turned off. Adjusting the Display Contrast You can adjust the display contrast to suit your viewing angle and lighting conditions. As you adjust the contrast setting, the display becomes lighter or darker.
The Display The TI.80 displays both text and graphs. Graphs are described in Chapters 4 and 5. Home Screen The primary screen of the TI-80 is the Home screen. You enter instructions to be executed, expressions to be evaluated, and see the results on the Home screen. Displaying Entries and Answers When text is displayed, the TI-80 screen can show a maximum of eight lines with 16 characters each. ¦ If all lines of the display are filled, text “scrolls” off the top of the display.
Display Cursors In most cases, the appearance of the cursor indicates what will happen when you press the next key. Cursor Appearance Meaning Entry Blinking 0 The next keystroke is entered at the cursor; it types over any character. INS (insert) Blinking _ The next keystroke is inserted at the cursor. 2nd Blinking The next keystroke is a 2nd operation. ALPHA Blinking The next keystroke is an alphabetic character.
Entering Expressions and Instructions In most places where a value is required, you can use an expression to enter the value. You can enter instructions, which initiate an action, on the Home screen or in the program editor (Chapter 10). An expression is a complete sequence of numbers, variables, functions, and their arguments that evaluate to a single answer. For example, prñ is an expression. On the TI-80, you enter an expression in the same order as you would write it.
Entering a Number in Scientific Notation To enter a number in scientific notation: 1. Type the part of the number that precedes the exponent. This value can be an expression. 2. Press 2 ^. í is displayed. 3. If the exponent is negative, press ·, and then type the exponent, which can be one or two digits. Entering a number in scientific notation does not cause the answers to be displayed in scientific notation.
The Edit Keys The arrow keys near the upper right of the keyboard control the movement of the cursor. In normal entry, a keystroke types over the character or characters at the position of the cursor. The 4 and y / keys delete or insert characters. Key(s) Action(s) 9 or 6 Moves the cursor within an expression. These keys repeat when you hold them down. 7 or 8 Moves the cursor between lines within an expression. These keys repeat when you hold them down.
Setting Modes Modes control how numbers and graphs are displayed and interpreted by the calculator. Mode settings are retained by the Constant Memory feature when the TI.80 is turned off. Checking MODE Settings Press 3 to display the MODE screen. The current settings are highlighted. The settings are described on the following pages. NORMAL SCI FLOAT 0123456789 RADIAN DEGREE aÀbºc bºc AUTOSIMP MANSIMP FUNC PARAM CONNECTED DOT SEQUENTIAL SIMUL Changing MODE Settings Numeric display format.
TI-80 Modes The TI.80 has eight mode settings. They control how numeric entries are interpreted, how answers are calculated or displayed, and how graphs appear in the display. Modes are set on the MODE screen (page 1.9). NORMAL SCI Notation formats affect only how an answer is displayed on the Home screen. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. You can enter a number in any format.
RADIAN DEGREE The angle mode controls: How the calculator interprets angle arguments in SIN, COS, TAN, and polar-to-rectangular conversions. ¦ How the calculator returns angle answers to SINê, COSê, TANê, and rectangular-to-polar conversions. ¦ RADIAN mode interprets angle arguments as radians and returns angle answers in radians. DEGREE mode interprets angle arguments as degrees and returns angle answers in degrees.
Variable Names On the TI.80 you can enter, name, and use several types of data: numeric values (including fractions), lists, functions, and statistical plots. Variables and Defined Items The TI-80 uses both user-assigned and pre-assigned names for variables and other items saved in memory. Variable Type Names Numeric values (including fractions) A, B, ..., Z, q (single character only). Lists L1, L2, L3, L4, L5, L6 (on the keyboard). Functions Y1, Y2, Y3, Y4 (on the Y= editor in FUNC mode).
Storing and Recalling Variable Values Values are stored to and recalled from memory using variable names. When an expression containing the name of a variable is evaluated, the value of the variable at that time is used. Storing Values in a Variable You can store a value to a variable from the Home screen or a program using the § key. Begin on a blank line. 1. Enter the value that you want to store (this can be an expression). 2. Press §. The symbol ! is copied to the cursor location. 3.
Last Entry When you press ¸ on the Home screen to evaluate an expression or execute an instruction, the expression or instruction is stored in an area called Last Entry, which you can recall. When you turn the TI.80 off, Last Entry is retained in memory. Using Last Entry Displaying a Previous Entry You can recall Last Entry and edit it from the Home screen. Press y ². The current line is cleared, and the Last Entry is copied to the line. The cursor is positioned at the end of the entry.
Re.executing the Previous Entry Multiple Entries on a Line To execute Last Entry, press ¸ on a blank line on the Home screen. The entry is executed, but it does not display again. 0§?N ¸ ?N«1§?N ¸ ¸ ¸ To enter more than one expression or instruction on a line, separate them with a colon (:). They are all stored together in Last Entry. If the previous entry contained more than one expression or instruction, separated with a colon (page 1-6), they all are recalled.
Last Answer When an expression is evaluated successfully from the Home screen or from a program, the TI.80 stores the answer to a variable, ANS (Last Answer). ANS may be a decimal number, a fraction, or a list. When you turn the TI.80 off, the value in ANS is retained in memory. Using Last Answer (ANS) in an Expression You can use the variable ANS to represent the last answer in most places. When you press y ±, the variable name ANS is copied to the cursor location.
TI-80 Menus To leave the keyboard uncluttered, the TI.80 uses full.screen menus to give you access to many additional operations. The use of specific menus is described in the appropriate chapters. Moving from One Menu to Another Some menu keys, such as I, display more than one menu. The names of the menus appear on the top line. The current menu is highlighted and the items in that menu are displayed. Press 9 or 6 to move the cursor to a different menu.
Leaving a Menu without Making a Selection There are several ways to leave a menu without making a selection from the menu. ¦ To return to the Home screen, press 2 .. ¦ To return to the screen where you were, press M. ¦ To display a different menu, press the appropriate key, such as *. ¦ To select another screen, press the appropriate key, such as ).
The VARS and Y.VARS Menus You may want to use the names of system variables (such as XMIN) and functions (such as Y1) in an expression. You may also want to store values directly to those variables. Use the VARS or Y.VARS menus to access the names. VARS Menu The VARS menu displays the names of window variables such as XMIN and TSTEP, statistics variables such as v and Q1, and table variables such as TBLMIN. Press L to display the VARS menu. Some of the items display more than one menu of variable names.
EOS (Equation Operating System) The Equation Operating System (EOS™) defines the order of operations for the calculatorthat is, the order in which the TI.80 evaluates functions in expressions. EOS lets you enter numbers and functions in a simple, straightforward sequence. Order of Evaluation A function returns a value. EOS evaluates the functions in an expression in the following order. 1 Functions that are entered after the argument, such as Añ, 2ê, 22!, 45¡, 2pô, and úSIMP.
Implied Multiplication The TI-80 recognizes implied multiplication. For example, it understands 2p, 4SIN 45, 5(1+2), and (2×5)7 as implied multiplication. Parentheses All calculations inside a pair of parentheses are completed first. For example, in the expression 4(1+2), EOS first evaluates the portion inside the parentheses, 1+2, and then multiplies the answer, 3, by 4. You can omit any right (closing) parenthesis at the end of an expression.
Error Conditions The TI.80 detects any errors at the time it evaluates an expression, executes an instruction, plots a graph, or stores a value. Calculations stop and an error message with a menu is displayed immediately. Error codes and conditions are described in detail in Appendix B. Diagnosing an Error If the TI-80 detects an error, it displays the error screen. The top line indicates the general type of error, such as SYNTAX or DOMAIN.
Chapter 2: Math, Angle, and Test Operations This chapter describes the math, angle, and relational operations that are available on the TI.80. The most commonly used functions are accessed from the keyboard; others are accessed through menus. Chapter Contents Getting Started: Lottery Chances .................... Using the TI-80 Functions .......................... Keyboard Math Operations ......................... MATH MATH Operations ........................... MATH NUM (Number) Operations ...............
Getting Started: Lottery Chances Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to enter a lottery where six numbers will be drawn out of 50. To win, you must pick all six numbers (in any order). What is the probability of winning if you buy one ticket? What is the probability of winning if you buy five tickets? 1. Determine the number of combinations possible. On the Home screen, press 50 to enter the total number of items.
Using the TI-80 Functions This page contains some general information you should know about the TI.80 functions described in Chapter 1. Using Lists with Functions Functions that are valid for lists return a list calculated on an element-by-element basis. If two lists are used in the same expression, they must be the same length. For more information about lists, see Chapter 8. Using Fractions with Functions Some math functions (+, –, ×, à, xñ, úbºc, úaÀbºc, úDEC) accept fractions as input values.
Keyboard Math Operations The most commonly used math functions are on the keyboard. The keyboard math operations can be used with decimal numbers, fractions (except as noted), expressions, and lists. + (Add) – (Subtract) × (Multiply) à (Divide) Trig Functions The basic arithmetic functions are: addition «, subtraction |, multiplication p, and division e. Each argument for these functions can be a list.
^ (Power) 2 (Square) ‡ (Square Root) ^ (power, Z), 2 (square, a), and ‡ (square root, 2 ]) may be used with decimal numbers, fractions, expressions, or lists. When used with a fraction, ‡ returns a decimal number. value^power, value2, ‡value Note: Raising a negative number to a noninteger power can result in a complex number, which returns an error. LOG 10^ LN e^ These functions find the logarithm l, power of ten 2 h, and natural log x of the specified value or list of values.
L (Negation) L (negation, ·) returns the negative of a number, expression, or list. The narrow negation symbol (L) distinguishes negation from the subtraction or minus (–). Lvalue EOS rules (Chapter 1) determine when negation is evaluated. For example, LA 2 returns a negative number because squaring is evaluated before negation. Use parentheses to square a negated number, (LA) 2. ABS ABS (absolute value, 2 P) returns the absolute value of a number, expression, or list.
MATH MATH Operations To display the MATH MATH menu, press I. When you select a menu item, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis. MATH MATH Menu MATH NUM PRB 1: INT÷ Displays quotient and remainder. 2: 8DEC Displays answer in decimal form. 3: 3 Cube. 4: 3‡ Cube root. 5: x‡ n th root. 6: NDERIV( Numerical derivative.
8DEC 8DEC (convert to decimal, MATH MATH, item 2) displays an answer in decimal form. 8DEC can only be used after a value and at the end of an expression. value can be a list. value8DEC expression8DEC 3 (Cube) 3 (cube, MATH MATH, item 3) returns the cube of a number, expression, or list. value3 3‡ (Cube Root) 3‡ (cube root, MATH MATH, item 4) returns the cube root of a number, expression, or list.
NDERIV( NDERIV( (numerical derivative, MATH MATH, item 6) returns an approximate derivative of an expression with respect to a specified variable, given the value at which to calculate the derivative, and H (optional; if none is specified, 1í-3 is used).
MATH NUM (Number) Operations To display the MATH NUM menu, press I 9. When you select a menu item, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis. MATH NUM Menu MATH NUM PRB 1: ROUND( 2: IPART 3: FPART 4: INT 5: MIN( 6: MAX( 7: REMAINDER( ROUND( ROUND( (MATH NUM, item 1) returns a number, expression, or list rounded to a specified number of decimals (9).
MIN( MAX( MIN( (minimum value, MATH NUM, item 5) returns the smaller of two values or the smallest element in a list. If two lists are compared, it returns a list of the smaller of each pair of elements. If a list and a value are compared, it compares each element in the list to the value. MAX( (maximum value, MATH NUM, item 6) returns the larger of two values or the largest element in a list. If two lists are compared, it returns a list of the larger of each pair of elements.
MATH PRB (Probability) Operations To display the MATH PRB menu, press I 6. When you select a menu item, the name is copied to the cursor location. Functions that are valid for lists return a list calculated on an element-by-element basis. MATH PRB Menu MATH NUM PRB 1: RAND 2: nPr 3: nCr 4: ! 5: RANDINT( RAND RAND (random number, MATH PRB, item 1) generates and Random number generator. Number of permutations. Number of combinations. Factorial. Random integer generator.
nPr nCr nPr (number of permutations, MATH PRB, item 2) returns the number of permutations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists. nCr (number of combinations, MATH PRB, item 3) returns the number of combinations of items taken number at a time. items and number must be nonnegative integers. Both items and number can be lists.
ANGLE Operations To display the ANGLE menu, press 2 E. The ANGLE menu displays angle indicators and instructions. When you select an item from the menu, the name is copied to the cursor location. ANGLE Menu ANGLE 1: ¡ 2: r 3: R8Pr( 4: R8Pq( 5: P8Rx( 6: P8Ry( °(Degree) ¡ (degree, ANGLE, item 1) lets you designate an angle or list of Degree notation. Radian notation. Returns r, given X and Y. Returns q, given X and Y. Returns x, given R and q. Returns y, given R and q.
R8Pr ( R8Pq( P8Rx( P8Ry( Note: When converting from one coordinate system to the other, be sure that the angle mode setting, DEGREE or RADIAN, is appropriate for your angle measurements. (Press 3 to check the current setting.) R8Pr( (ANGLE, item 3) converts the given rectangular coordinates to polar coordinates and returns r. R8Pq( (ANGLE, item 4) converts the given rectangular coordinates to polar coordinates and returns q. Both X and Y can be lists.
TEST (Relational) Operations To display the TEST menu, press 2 D. When you select from the menu, the name is copied to the cursor location. These functions are valid for lists; they return a list calculated on an element-by-element basis. TEST Menu TEST 1:= 2:ƒ 3:> 4:‚ 5:< 6: = ƒ > ‚ < Relational operators compare valueA and valueB and return 1 if the test is true or 0 if the test is false. valueA and valueB can be numbers, expressions, or lists. True if: Equal. Not equal to. Greater than.
Chapter 3: Fractions This chapter describes how to use the fraction operations on the TI.80. Chapter Contents Getting Started: Working with Fractions ............. Setting Modes for Fraction Results .................. Entering and Using Fractions in Calculations ......... The FRACTION Menu .............................. 3-2 3-4 3-6 3-8 Fractions 3-1 8003ENG.
Getting Started: Working with Fractions Getting Started is a fast-paced introduction. Read the chapter for details. Enter the expression 1 6/27 + 1 1/9. Evaluate the expression, simplify the result, and then use the conversion options on the FRACTION menu to convert the result. This example is performed in MANSIMP (manual simplification) mode. MANSIMP mode is especially useful for students when they are learning fraction concepts.
The TI.80 uses the lowest common factor for simplification. If you want to choose the simplification factor yourself, you can enter it as part of the expression. 6. Press M to clear the screen. Reenter the expression, or press 2 ² until you see the expression 1À6º27 + 1À1º9. 7. Press 2 6 2 / c 2 9 b 9 d. This adds the simplification factor 9 and places the expression in parentheses. 8. Press J 1 to copy úSIMP to the cursor location. 9. Press ¸ to simplify the fraction result.
Setting Modes for Fraction Results From the MODE screen, you can select simplification and display format options for fraction results. AUTOSIMP Mode with bºc and aÀbºc Modes AUTOSIMP mode simplifies fractions automatically. Simplification takes place before the expression is evaluated. Then the result is simplified to its lowest terms. For example, 12à16 is simplified to 3à4 when you press ¸. There are two formats for displaying fractions results.
MANSIMP Mode with aÀbºc Mode MANSIMP mode lets you simplify fractions manually. MANSIMP was designed for teaching and learning fractions concepts. In MANSIMP mode, you can simplify fractions and the results of expressions using fractions, step-by-step. When a fraction result is not expressed in its lowest terms, a down arrow (ï) is displayed to remind you that you can simplify the result. Use úSIMP from the FRACTION menu to simplify the fraction.
Entering and Using Fractions in Calculations The TI.80 lets you enter fractions directly from the keyboard. Entering Simple Fractions A simple fraction is a fraction with no whole-number part; for example, 3à4 or 4à3. To enter a simple fraction: 1. Enter the numerator (up to six digits), and then press 2 _. 2. Enter the denominator (up to and including 1000). For example, press 2 2 _ 3 to enter 2à3.
In general, you can use fractions in expressions just as you would use other numbers. The results of the expressions, however, may or may not be fractions. Using Fractions in Expressions The absolute value of a fraction on the TI-80 cannot be ≥1000. «, |, p, e, V, a, ·, and 2 P accept fraction entries and return fraction results.
The FRACTION Menu To display the FRACTION menu, press J. The menu items let you simplify and convert fractions. When you select a menu item, the name is copied to the cursor location. FRACTION Menu Simplifying Fractions úSIMP FRACTION 1: 8SIMP 2: 8bºc 3: 8aÀbºc 4: 8FRAC 5: 8DEC Simplifies the fraction. Converts to a simple fraction. Converts to a mixed fraction. Converts a decimal to a fraction based on mode. Converts a fraction to a decimal.
Converting Simple and Mixed Fractions úbºc 8aÀbºc 8bºc (convert to simple fraction, FRACTION, item 2) converts value to a simple fraction. 8aÀbºc (convert to mixed fraction, item 3) converts value to a mixed fraction. value8bºc value8aÀbºc Both 8bºc and 8aÀbºc can be used only at the end of an expression. A ! (§) instruction, however, can follow them. Fractions 3-9 8003ENG.
Converting Decimals and Fractions úFRAC 8DEC 8FRAC (convert to fraction, FRACTION, item 4) converts a decimal value to its fraction equivalent and displays it. The decimal may be a number, expression, or list. In MANSIMP mode, 8FRAC first attempts to return a fraction in terms of 10ths, 100ths, or 1000ths. If this is not possible, 8FRAC converts the decimal to its fraction equivalent as it would in AUTOSIMP mode.
Chapter 4: Function Graphing This chapter describes function graphing on the TI.80 in detail. It also lays the foundation for using the parametric graphing features described in Chapter 5. Chapter Contents Getting Started: Graphing a Circle ................... Defining a Graph .................................. Setting Graph Modes .............................. Defining Functions in the Y= List .................... Evaluating Y= Functions in Expressions ............. Selecting Functions ...................
Getting Started: Graphing a Circle Getting Started is a fast-paced introduction. Read the chapter for details. Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph a circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSQUARE to adjust the display to make the functions appear as a circle. Make sure that your TI-80 is in FUNC mode and all STAT PLOTS are turned off. 1. Press ( to display the Y= edit screen.
Defining a Graph To define a graph, you set the modes, enter and select the functions to graph, and define the viewing window and the graphing format. Once you have defined a graph, you can plot it, display it, and explore it. Steps in Defining a Graph There are six basic steps to defining a graph, although you may not need to do all of the steps each time you define a graph. The procedures are described in detail on the following pages. 1. Set the mode to FUNC graphing (Chapter 1). 2.
Setting Graph Modes Pressing 3 displays the current mode settings, as described in Chapter 1. For function graphing, the graphing mode must be set to FUNC. Before you graph a function, check to be sure that the mode settings are appropriate. Checking and Changing Graphing Modes Press 3 to display the mode settings. The current settings are highlighted. The TI-80 has two graphing modes.
Defining Functions in the Y= List Pressing ( displays the Y= edit screen. This is where you enter the functions to graph. You can store up to four functions in memory at one time. You can graph one or more of these functions at a time. Displaying the Functions in the Y= List Press ( to display the Y= edit screen. In the example below, the Y1 and Y2 functions are defined. Defining a New Function To define a new function in the Y= list: 1. Press ( to display the Y= edit screen. 2.
Editing a Function To edit a function in the Y= list: 1. Press ( to display the Y= list, and move the cursor to the function you want to change. 2. Make the changes. You can also press M to erase the expression, and then enter a new expression. The expression is stored in the Y= list and selected (turned on) as you edit it. Clearing a Function To clear or erase a function on the Y= edit screen, position the cursor anywhere on the function, and then press M.
Evaluating Y= Functions in Expressions You can the calculate the value of a Y= function at a specified value of X. Entering the Functions in the Y= List Evaluating Functions To display the Y= list, press (. Enter these functions for Y1, Y2, and Y3: X 2, X+2, and Y1(Y2(X)). @a¸ @«2¸ 2G1c2G2 c@dd To evaluate the functions, first specify the value of X. Note that X may be a list. 2.
Selecting Functions Only functions that are selected (turned on) are graphed. All four functions may be selected at one time. Turning a Function “On” or “Off” You can select and deselect (“turn on” and “turn off”) functions on the Y= edit screen. The = sign on a selected function is highlighted. To change the selection status of a function: 1. Display the Y= list, and move the cursor to the function whose status you want to change. 2. Press 6 to place the cursor over the = sign of the function. 3.
Defining the Viewing Window The Window variables determine the boundaries and other attributes of the viewing window. The Window variables are shared by all graphing modes. The Viewing Window The viewing window of the TI-80 is the portion of the coordinate plane defined by XMIN, XMAX, YMIN, and YMAX. The distance between tick marks is defined by XSCL for the X axis and YSCL for the Y axis. YMAX XSCL XMIN XMAX YSCL YMIN Checking the Viewing Window Press ) to display the current Window variable values.
Leaving the Window Screen To leave the Window screen: ¦ ¦ Storing to a Window Variable from the Home Screen or a Program Select another screen by pressing the appropriate key, such as , or (. Press 2 . to return to the Home screen. To store to a Window variable from the Home screen or from a program, begin on a blank line. 1. Enter the value (which can be an expression) that you want to store. 2. Press §. 3. Press L to display the VARS menu. 4. Select WINDOW... to display the Window variables. 5.
Displaying a Graph Pressing , graphs any functions selected on the Y= edit screen. The current mode settings apply, and the current values of the Window variables define the viewing window. Turning the Grid Points On and Off Grid points correspond to the axis tick marks. To turn the grid points on and off use GRIDON and GRIDOFF. The default for the TI-80 is GRIDOFF. 1. From the Home screen, press 2 F to display the DRAW menu. 2. Press 9 to select GRIDON, or press 0 to select GRIDOFF. 3. Press ¸.
Exploring a Graph with the Free-Moving Cursor While a graph is displayed, you can move the free-moving cursor anywhere on the graph and display the coordinates of any location on the graph. Free-Moving Cursor You can press 6, 9, 7, or 8 to move the cursor around the graph. When you first display the graph, no cursor is visible. As soon as you press 6, 9, 7, or 8, the cursor moves from the center of the viewing window.
Exploring a Graph with TRACE TRACE moves the cursor from one plotted point to the next along a function. The cursor coordinates are displayed at the bottom of the screen. Beginning a Trace Press + to begin a trace. If the graph is not displayed already, the TI-80 displays it. The cursor is on the first selected function in the Y= list at the middle X value on the screen. The number of the function appears at the upper right of the display.
Moving from Function to Function To trace another selected function on the graph, press 8 or 7 to move the cursor to that function. The cursor moves to the new function at the same X value. The function number in the upper right corner of the display changes. The cursor movement is based on the order of the selected functions in the Y= list, not the appearance of the functions as graphed on the screen.
Exploring a Graph with ZOOM Pressing * displays a menu that allows you to adjust the viewing window of the graph quickly in a variety of ways. All of the Zoom instructions are accessible from programs. ZOOM Menu ZOOM 1: ZBOX 2: ZOOM IN 3: ZOOM OUT 4: ZDECIMAL 5: ZSQUARE 6: ZSTANDARD 7: ZTRIG ZBOX ZBOX lets you use the cursor to select opposite corners of a Draws box to define viewing window. Magnifies graph around cursor. Views more of graph around cursor. Sets .1 as dot size.
ZOOM IN ZOOM OUT ZOOM IN magnifies the graph around the cursor location. The XFACT and YFACT settings determine the extent of the zoom (page 4-18). The default value for both XFACT and YFACT is 4. 1. After checking or changing XFACT and YFACT, select ZOOM IN from the ZOOM menu. Notice the different cursor. It indicates that you are using a Zoom instruction. 2. Move the cursor to the point that you want as the center of the new viewing window, and then press ¸.
ZDECIMAL ZDECIMAL replots the functions immediately, updates the Window variables to preset values that set @X and @Y equal to .1, and defines the X and Y value of each pixel as one decimal. XMIN = L3 . 1 XMAX = 3.1 XSCL = 1 YMIN = L2 . 3 YMAX = 2.3 YSCL = 1 ZSQUARE ZSQUARE replots the functions immediately, redefining the window based on the current Window variables, but adjusted in only one direction so that @X=@Y. This makes the graph of a circle look like a circle. XSCL and YSCL remain unchanged.
Setting the Zoom Factors The Zoom factors, XFACT and YFACT, determine the extent of the change for the viewing window created by ZOOM IN or ZOOM OUT on a graph. Zoom Factors Zoom factors are positive numbers (not necessarily integers) greater than or equal to 1. They define the magnification or reduction factor used to ZOOM IN or ZOOM OUT around a point. Checking Zoom Factors To review the current values of the Zoom factors (XFACT and YFACT): 1. Press L, and then press 1 to select WINDOW.... 2.
Chapter 5: Parametric Graphing This chapter describes how to graph parametric equations on the TI.80. Before doing parametric graphing, you should be familiar with Chapter 4, Function Graphing. Chapter Contents Getting Started: Path of a Ball ...................... Defining and Displaying a Parametric Graph .......... Exploring a Parametric Graph ......................
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 kicked at an angle of 60¡ with an initial velocity of 15 meters per second. (Ignore air resistance.) What is the maximum height? When does the ball strike the ground? 1. Press 3, and then press 8 8 8 8 8 9 ¸ to select PARAM mode.
Defining and Displaying a Parametric Graph Parametric equations consist of an X component and a Y component, each expressed in terms of the same independent variable T. They are often used to graph equations over time. Up to three pairs of parametric equations can be defined and graphed at a time. Defining a Parametric Graph The steps for defining a parametric graph are the same as those for defining a function graph (page 4-3). Differences are noted below.
Selecting Parametric Equations The TI-80 graphs only the parametric equations you select. The highlighted = sign on both components of an equation indicates that the equation is selected. You may select any or all of the equations on the parametric Y= edit screen. To change the selection status of a parametric equation, press 6 to move the cursor onto the = sign of either the X or Y component and press ¸. The status on both the X and Y components changes.
Displaying a Graph When you press ,, the TI-80 plots the selected parametric equations. It evaluates both the X and the Y component for each value of T (from TMIN to TMAX in intervals of TSTEP) and then plots each point defined by X and Y. The Window variables define the viewing window. As a graph is plotted, the TI-80 updates X, Y, and T. Note: Smart Graph applies to parametric graphs also (page 4-11). VARS WINDOW and Y-VARS Menus By means of the VARS WINDOW...
Exploring a Parametric Graph As in function graphing, three tools are available for exploring a graph: the freemoving cursor, tracing, and zooming. Free-Moving Cursor The free-moving cursor works the same in parametric graphing as in function graphing (page 4-12). Tracing a Parametric Graph Pressing + puts the Trace cursor on the first selected equation, at TMIN. You can then trace along the equation. 6 or 9 Moves the cursor one TSTEP at a time. 2 6 or 9 ~ Moves the cursor five TSTEPs at a time.
Chapter 6: Tables This chapter describes how to use tables on the TI.80. A table evaluates the selected functions from the Y= list and displays each value for the independent variable along with the evaluated value for each corresponding dependent variable. Chapter Contents Getting Started: Roots of a Function ................. Defining the Independent Variable .................. Defining the Dependent Variable .................... Displaying the Table ...............................
Getting Started: Roots of a Function Getting Started is a fast-paced introduction. Read the chapter for details. Evaluate the function Y=X 2 – 4X+3 at each integer between L10 and 10. How many sign changes are there, and where do they occur? 1. If necessary, select FUNC from the MODE menu. Press 2 # to display the TABLE SETUP screen. Press · 10 to set TBLMIN=L10. Leave @TBL=1. 2. Press ( @ a | 4 @ « 3 to enter the function Y1=X 2 – 4X+3. 3. Press 2 & to display the table screen. 4.
Defining the Independent Variable The independent variable for a table is the independent variable in the current graphing mode (X for FUNC mode and T for PARAM mode). You define the minimum value and the incremental value for the independent variable on the TABLE SETUP screen. TABLE SETUP Screen To display the TABLE SETUP screen, press 2 #. The default values are shown below. TBLMIN and @TBL TBLMIN (table minimum) defines the initial value for the independent variable: X (FUNC mode) or T (PARAM mode).
Defining the Dependent Variable The selected functions from the Y= list define the dependent variables. You can have as many dependent variables as there are functions in the current graphing mode (four for FUNC mode and six for PARAM mode). From the Y= Editor Enter the functions to define the dependent variables in the Y= editor. FUNC Mode PARAM Mode In PARAM mode, you must define both components of the parametric equation (Chapter 5). Only functions that are selected are displayed in the table.
Displaying the Table The table displays up to six values for the independent variable, along with the six corresponding values of one dependent variable, at a time. Once the table is displayed, you can press 6, 7, 9, and 8 to move around and scroll the table, displaying other independent and dependent values. The Table Press 2 & to display the table screen.
Displaying Other Dependent Variables 6-6 Tables If you have more than one function defined and selected, press 9 to display other dependent variables. In the example below, TBLMIN=0, @TBL=1, Y1=X 2+2 and Y2=X 3–2. You can press 9 9 to see the values for Y2.
Chapter 7: Draw Operations This chapter describes how to use the DRAW operations of the TI.80. Before using the DRAW operations, you should be familiar with Chapter 4, Function Graphing. Chapter Contents Getting Started: Shading a Graph .................... DRAW DRAW Menu ............................... Drawing Lines .................................... Drawing Horizontal and Vertical Lines ............... Drawing a Function ............................... Shading Areas on a Graph .........................
Getting Started: Shading a Graph Getting Started is a fast-paced introduction. Read the chapter for details. Shade the area below the function Y=XäN2 and above the functions Y=X+1 and Y=-X. 1. If necessary, select FUNC mode. Press ( and enter the functions: Y1= @ a | 2 ¸ Y2= @ « 1 ¸ Y3= · @ ¸ (Be sure that Y4 is cleared or turned off.) 2. Press * 4 to select the ZDECIMAL viewing window, clear any existing drawings, and display the viewing window and graph. 3. Press 2 . to return to the Home screen. 4.
DRAW DRAW Menu To display the DRAW DRAW menu, press 2 F. What happens when you select an item from this menu depends on whether or not a graph is displayed when you access the menu, as described under each operation. DRAW DRAW Menu DRAW POINTS 1: CLRDRAW 2: LINE( 3: HORIZONTAL 4: VERTICAL 5: DRAWF 6: SHADE_Y> 7: SHADE_Y< 8: SHADE( 9: GRIDON 0: GRIDOFF Clears all drawn elements. Draws a line between two points. Draws a horizontal line. Draws a vertical line. Draws a function. Shades an area.
Drawing Lines While a graph is displayed, LINE( lets you use the cursor to define a line on the graph. If a graph is not displayed, the instruction is copied to the Home screen. Directly on a Graph To define a line directly on a graph: 1. When a graph is displayed, select LINE( from the DRAW DRAW menu (item 2). 2. Position the cursor at the beginning point of the line you want to draw. Press ¸. 3. Move the cursor to the end point of the line you want to draw. The line is displayed as you move the cursor.
Drawing Horizontal and Vertical Lines While a graph is displayed, HORIZONTAL and VERTICAL let you define lines on the graph using the cursor. If a graph is not displayed, the instruction is copied to the Home screen. Directly on a Graph To draw horizontal and vertical lines directly on a graph: 1. When a graph is displayed, select HORIZONTAL (item 3) or VERTICAL (item 4) from the DRAW DRAW menu. 2. A line is displayed that moves as you move the cursor. Position the cursor where you want to draw the line.
Drawing a Function DRAWF (draw function) draws a function on the current graph. DRAWF must be entered on the Home screen or in the program editor. Drawing a Function DRAWF (draw function, DRAW DRAW, item 5) is not an interactive operation. It draws the specified expression as a function in terms of X on the current graph. DRAWF expression For example, if Y1=.2Xò–2X+6 is the only selected function, DRAWF Y1–5 plots Y1 and then draws the function Y1–5 when you press ¸.
Shading Areas on a Graph There are three shading instructions on the DRAW DRAW menu: SHADE_Y>, SHADE_Y<, and SHADE(. These instructions are not interactive; they must be entered on the Home screen or in the program editor. Shading Areas above a Function SHADE_Y> (DRAW DRAW, item 6) takes up to four arguments (functions of X). SHADE_Y>function SHADE_Y>function1, . . . ,function4 When executed, SHADE_Y> plots the specified function(s) on the graph and shades the area above the function with a pattern.
Shading Areas below a Function SHADE_Y< (DRAW DRAW, item 7) takes up to four arguments (functions of X). SHADE_Y
Shading a Graph SHADE( (DRAW DRAW, item 8) shades the area on a graph that is below one specified function and above another, between two X values. SHADE( is not an interactive operation. It draws lowerfunc and upperfunc in terms of X on the current graph and shades the area that is specifically above lowerfunc and below upperfunc. Only the areas where lowerfunc < upperfunc are shaded. You can specify the shading resolution (an integer between 1 and 9). If none is specified, 1 is used.
Drawing Points To display the DRAW POINTS menu, press 2 F 9. What happens when you select an item from this menu depends on whether or not a graph is displayed when you access the menu, as described under each operation. DRAW POINTS Menu DRAW POINTS 1: PT-ON( Turn on a point. 2: PT-OFF( Turn off a point. 3: PT-CHANGE( Toggle a point on or off. Drawing a Point Directly on a Graph To draw points directly on a graph: 1. When a graph is displayed, select PT.ON( from the DRAW POINTS menu (item 1). 2.
PT.OFF( PT.CHANGE( Procedures for using PT.OFF( (point off, DRAW POINTS, item 2) to turn off (erase) a point and PT.CHANGE( (point change, DRAW POINTS, item 3) to toggle (reverse) a point on and off are the same as for PT.ON(. From the Home Screen or a Program When you use these instructions from the Home screen or a program, you must specify the X-coordinate and the Y-coordinate of the point as arguments for the instructions. PT.ON( turns on the point at (X=X,Y=Y). PT.OFF( turns the point off, and PT.
Clearing a Drawing All points, lines, and shading drawn on a graph with DRAW operations are temporary. They remain only until you execute a CLRDRAW (clear drawing) instruction or a change prompts Smart Graph to replot the graph, at which time all drawn elements are erased. When a Graph Is Displayed To clear drawings from the currently displayed graph, select CLRDRAW from the DRAW DRAW menu (item 1). The current graph is plotted and displayed immediately with no drawn elements.
Chapter 8: Lists This chapter describes the list features of the TI-80. The TI.80 can store up to six lists. A list, depending on available memory, can have up to 99 elements. Chapter Contents Getting Started: Generating a Sequence .............. About Lists ....................................... LIST OPS Operations .............................. LIST MATH Operations ............................
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 1àA ñ and display them in fraction form. The SEQ( function returns a list of values based on five arguments: an expression, a variable to be incremented, a beginning value, an ending value, and an increment. For this example, the beginning value is 1, the ending value is 8, and the increment is 1. 1. Begin on a blank line on the Home screen.
About Lists The TI-80 has six list variables: L1, L2, L3, L4, L5, and L6. On the Home screen or in a program, you can use, enter, store, and display lists. The list names are on the keyboard. A list may have a maximum of 99 elements. Using a List in an Expression Entering a List in an Expression To use a list in an expression, you may: ¦ Use the name of the list (L1, L2, L3, L4, L5, or L6) in the expression. ¦ Enter the list directly in the expression. 1.
Displaying a List on the Home Screen To display the contents of a list on the Home screen, enter the name of the list, and press ¸. Storing to or Recalling a List Element You can store a value to or recall a value from a specific list element. Enter the name of the list, followed by the number of the element in parentheses. You can store to any element within the currently defined list dimensions or one beyond.
Notes about Using Math Functions with Lists A list can be used to input several values for certain functions. (Other chapters and Appendix A state when a list is valid.) The function is evaluated for each element in the list, and a list is returned. ¦ If a list is used with a function, the function must be valid for every element in the list. ) This returns an error because 1 is divided by 0. ¦ If two lists are used with a two-argument function, the lengths of the lists must be the same.
LIST OPS Operations Press 2 = to display the list operations on the LIST OPS menu. LIST OPS Menu OPS MATH 1: SORTA( 2: SORTD( 3: DIM 4: SEQ( Sorts lists in ascending order. Sorts lists in descending order. Accesses the list dimension. Creates a sequence. Note: SORTA( and SORTD( are the same as SORTA( and SORTD( on the STAT EDIT menu. SORTA( SORTD( SORTA( (sort ascending, LIST OPS, item 1) and SORTD( (sort descending, LIST OPS, item 2) have two uses.
Accessing List Dimensions with DIM DIM (dimension, LIST OPS, item 3) returns the length (number Creating a List with DIM DIM is used with § to create a new list with a specified of elements) of the specified list. DIM list number of elements. The elements of the new list are zeros. length!DIM listname Redimensioning a List with DIM DIM is also used with § to redimension an existing list. ¦ The elements in the old list that are within the new dimension are not changed.
SEQ( SEQ( (sequence, LIST OPS, item 4) requires five arguments: an expression, a variable to be incremented, a beginning value, an ending value, and an increment. SEQ( returns a list in which each element is the result of the evaluation of expression with regard to variable for values ranging from begin to end at steps of increment. SEQ(expression,variable,begin,end,increment) The variable need not be defined in memory. The increment can be negative. SEQ( can be used to generate a list of index numbers.
LIST MATH Operations Pressing 2 = 9 accesses the list math operations on the LIST MATH menu. LIST MATH Menu OPS MATH 1: MIN( 2: MAX( 3: MEAN( 4: MEDIAN( 5: SUM 6: PROD Returns minimum element of a list. Returns maximum element of a list. Returns mean of a list. Returns median of a list. Returns sum of all elements in a list. Returns product of all elements in a list. Note: MIN( and MAX( are the same as MIN( and MAX( on the MATH NUM menu.
SUM SUM (summation, LIST MATH, item 5) returns the sum of the elements in the specified list. SUM list PROD PROD (product, LIST MATH, item 6) returns the product of the elements of the list.
Chapter 9: Statistics This chapter describes the tools for analyzing statistical data on the TI-80. These include entering lists of data, calculating statistical results, fitting data to a model, and plotting data. Chapter Contents Getting Started: Building Height and City Size......... Setting Up a Statistical Analysis ..................... The STAT List Editor .............................. Viewing, Entering, and Editing Lists ................. Sorting and Clearing Lists ..........................
Getting Started: Building Height and City Size Getting Started is a fast-paced introduction. Read the chapter for details. Determine a linear equation to fit the data below. Enter the data, and perform a linear regression. Then plot the data. Predict how many buildings of more than 12 stories you would expect to find in a city of 300 thousand people. Population in Thousands 150 500 800 250 550 750 Buildings > 12 Stories 4 31 42 9 20 55 1.
5. Enter the remaining elements of L1. Press: 500 ¸. 800 ¸. 250 ¸. 550 ¸. 750 ¸. 6. Press 9 to move to the first element of list L2. 7. Enter the elements (number of buildings with more than 12 stories) of L2. Press: 4 ¸. 31 ¸. 42 ¸. 9 ¸. 20 ¸. 55 ¸. 8. You can sort the data by size of city. Press 2 . M to return to a clear Home screen. Press A 2 to select SORTA(, which is copied to the Home screen. Press 2 ¢ to select the independent list and then press b 2 £ to select the dependent list. Press d ¸.
After entering and sorting the data, define the STAT PLOTS and Window variables; then perform a linear regression (aX + b). 10. Press y ¸ to display the STAT PLOTS screen. 11. Press 1 to display the PLOT1 screen. Move the cursor to ON, if necessary, and press Í to turn PLOT1 on. Leave TYPE as scatter plot (¼), XL (independent list) as L1, YL (dependent list) as L2, and Mark as ›. 12. Press ) to display the Window variables. Enter the following values.
Store the regression equation into the Y= list and graph it. 15. In FUNC mode, press ( to display the Y= editor. Press M to clear Y1, if necessary. Turn off all other functions, if necessary. 16. Press L to display the VARS menu. 17. Press 2 to select STATISTICS..., and press 9 9 to display the VARS EQ menu. 18. Press 5 to select REGEQ, which copies the linear regression to the Y= editor screen. Note: Each time you calculate a regression, the regression equation (REGEQ) is updated. 19. Press ,.
You can enter expressions to define lists in the STAT list editor. For example, you can now define predicted values and residuals (the differences between the observed values and the predicted values) for this problem. 21. Press … 1 to display the STAT list editor. Press ~ ~ } to move the cursor onto the name L3. 22. Press y ãY-VARSä 1 to select Y1, and then press £ y ¢ ¤. This defines Lå as the values predicted by the LINREG line. 23. Press Í to store the values in L3. 24.
Plot the residuals, and predict how many buildings of 12 or more stories there are in a city with a population of 300 thousand. 27. Press ( 6 ¸ to turn off Y1. 28. Press ), and change the Window variable values to best show the residuals. Use the minimum and maximum values of L4 (M10.31862745 and 10.74019608) as guidelines for setting YMIN and YMAX. 29. Press , to plot the residuals. + marks each residual value. 30. Press y ãQUITä M to return to a clear Home screen. Press y ãY-VARSä 1 to select Y1.
Setting Up a Statistical Analysis The data for statistical analyses is stored in lists. The TI.80 has six list variables (Lã through Lè) that you can use in STAT calculations. Several types of statistical analyses are available. Steps Follow these basic steps to perform statistical analyses. 1. Enter the statistical data in lists (pages 9-9 through 9-13). 2. Select the type of statistical calculations you want to do (pages 9-14 through 9-16), and specify the list names for the data. 3.
The STAT List Editor Pressing A accesses the STAT list editor and several instructions for use with lists (Lã through Lè). The instructions are discussed on page 9-13. STAT EDIT Menu EDIT CALC 1: EDIT... 2: SORTA( 3: SORTD( 4: CLRLIST Displaying the STAT List Editor The STAT list editor gives you an easy environment in which to enter or edit lists. You can also create lists directly from the keyboard (Chapter 8), if you prefer. Displays list editor. Sorts list in ascending order.
Viewing, Entering, and Editing Lists The STAT list editor has two “contexts,” viewing and editing. The current context determines the result of a key press. In both contexts, the full value of the highlighted element is displayed on the bottom line. Viewing Context In the viewing context, you can move quickly from one list element to the next. 6 or 9 8 or 7 ¸ M Any entry character 2/ 4 Editing Context 9-10 Statistics Moves the rectangular cursor to the previous or next list.
Deleting a List Editing a List Element You can delete the contents of a list in several ways: ¦ With the CLRLIST instruction (page 9-13). ¦ Through the MEMORY menu (Chapter 12). ¦ In the STAT list editor, by pressing 7 to move onto the list name and then pressing M ¸. ¦ In the STAT list editor, by deleting each element. ¦ On a command line, by entering 0!DIM listname. To edit a list element: 1. Display the STAT list editor. 2. Move the rectangular cursor to the element you want to change. 3.
You can enter or edit an entire list by moving the cursor to a list name on the top line of the STAT list editor and then pressing ¸. The bottom line displays Ln =Ln ×1, if there is data already in the list. Type any expression that returns a list, and press ¸. The new list is displayed. Entering an Entire List To enter an entire list: 1. Press A ¸. Enter several elements in L1. 2. Press 7 and 9 as many times as necessary to move the cursor to the list name L2. 3. Press 2 ¢ p 2.
Sorting and Clearing Lists Items 2 through 4 on the STAT EDIT menuSORTA(, SORTD(, and CLRLISTlet you sort or clear list data. Pressing A displays these instructions, and selecting an item copies the name of the instruction to the Home screen. Note that SORTA( and SORTD( are the same as SORTA( and SORTD( on the LIST OPS menu (Chapter 8). SORTA( SORTD( SORTA( (sort ascending, STAT EDIT, item 2) and SORTA( (sort descending, STAT EDIT, item 3) have two uses.
Statistical Analysis Pressing A 9 accesses the STAT CALC menu, where you select and perform statistical calculations. The TI-80 can analyze one-variable or two-variable statistics. Both can have associated frequency lists. STAT CALC Menu EDIT CALC 1: 1-VAR STATS 2: 2-VAR STATS 3: LINREG(aX+b) 4: QUADREG 5: LINREG(a+bX) 6: LNREG 7: EXPREG 8: PWRREG Selecting and Performing a Statistical Calculation To select and perform statistical calculations: Calculates 1-variable statistics.
Types of Statistical Analysis These calculations return statistical results based on the list(s) you reference. If you reference a third list name as an argument for 2-VAR STATS or any of the regression models, the list is interpreted as the frequencies of occurrence for the data pairs in the first two lists. 1-VAR STATS 1-VAR STATS (one-variable statistics, STAT CALC, item 1) analyzes data with one measured variable and calculates statistical results as indicated on page 9-17.
QUADREG QUADREG (quadratic regression, STAT CALC, item 4) fits the data to the second-order polynomial y=ax 2+bx+c. It displays a, b, and c. For three data points the equation is a polynomial fit; for four or more, it is a polynomial regression. At least three data points are required. QUADREG Xlistname,Ylistname QUADREG Xlistname,Ylistname,freqlistname LINREG (a+bX) LINREG (a+bX) (linear regression, STAT CALC, item 5) fits the data to the model equation y=a+bx using a least-squares fit and x and y.
Statistical Variables The statistical variables are calculated as indicated below. Some are displayed when 1-VAR STATS or 2-VAR STATS are calculated. You can access these variables for use in expressions through the VARS STATISTICS... menus. If you edit a list, all statistical variables are cleared.
Statistical Plotting You can plot statistical data that you have entered in lists. The types of plots available include scatter plots, x-y lines, box and whisker plots, and histograms. You can define up to three plots at a time. Steps To plot statistical data: 1. Enter the statistical data as lists (page 9-9 and Chapter 8). 2. Select the statistical calculations (pages 9-14 through 9-16 ), and calculate the statistical variables (page 9-17) or fit the data to a model, if desired. 3.
Box Plot ¾ ¾ (box plot) plots one-variable data. The whiskers on the plot extend from the minimum data point in the set (MINX) to the first quartile (Q1) and from the third quartile (Q3) to the maximum point (MAXX). The box is defined by Q1, the median (MED), and Q3 (page 9-17). Box plots are plotted with respect to XMIN and XMAX, but ignore YMIN and YMAX. When two box plots are plotted, the first plots at the top of the screen and the second plots in the middle.
Defining the Plots To define plots: 1. Press 2 ". The STAT PLOTS screen shows the current plot definitions. 2. Select the plot to define (PLOT1, PLOT2, or PLOT3). 3. If you wish to plot the statistical data immediately, select ON. You can define a plot at any time and leave it OFF. The definition will be available in the future. 4. Select the type of plot. The options change appropriately.
Turning Plots Off or On PLOTSOFF and PLOTSON allow you to turn statistical plots off or on from the Home screen or a program. Used without plot#, they turn all plots off or all plots on. Used with plot#, they turn specific plots off or on. PLOTSOFF or PLOTSON PLOTSOFF plot#,plot#, . . . PLOTSON plot#,plot#, . . . For example, PLOTSOFF followed by PLOTSON 3 turns all plots off and then turns PLOT3 on. Defining the Viewing Window Statistical plots are displayed on the current graph.
Statistical Analysis in a Program You can enter statistical data, calculate statistical results, and fit data to models from a program. Entering Stat Data Enter the statistical data directly into lists (Chapter 8) in the program. Statistical Calculations To calculate statistical results or fit data to a model from a program: 1. On a blank line in the program editor, select the type of calculation from the STAT CALC menu. 2. Enter the names of the lists, separated by commas, to use in the calculation.
Statistical Plotting in a Program To display a statistical plot, you may define the plot(s), then turn the plot(s) on, and then display the graph. If you do not define the plot, the current definitions are used. Defining a Stat Plot in a Program To define a statistical plot in a program: 1. Enter the data into list(s). On a blank line in the program editor, press 2 " to display the PLOTS menu. 2. Select the plot to define. PLOT1(, PLOT2(, or PLOT3( is copied to the cursor location. 3.
Displaying a Stat Plot from a Program 9-24 Statistics To display a plot, use any of the Zoom instructions (Chapter 4), or use the DISPGRAPH instruction (Chapter 10).
Chapter 10: Programming This chapter describes specific programming instructions and explains how to enter and execute programs on the TI.80. Chapter Contents Getting Started: Rolling a Die ....................... 10-2 About TI-80 Programs ............................. 10-4 Creating and Executing Programs .................. 10-5 Editing Programs ................................. 10-6 PRGM CTL (Control) Instructions .................. 10-7 PRGM I/O (Input/Output) Instructions ...............
Getting Started: Rolling a Die Getting Started is a fast-paced introduction. Read the chapter for details. A program is a set of commands that can be executed sequentially, as if they had been entered from the keyboard. Write a simple program to simulate the rolling of a single die. It should prompt for the number of rolls and then store the results of the rolls in a list. 1. Press K 9 9 to display the PRGM NEW menu. 2. Press ¸ to select CREATE NEW. (The keyboard is now in ALPHA-LOCK.
7. Press I 6 to access the MATH PRB menu. Press 5 (to copy RANDINT( to the cursor location) 1 b 6 d § 2 ¢ c ? I d to generate random integers from 1 to 6 and store them into element I of L1. Press ¸ to complete the instruction. 8. Press K 9 2 to select DISP (display), which is copied to the cursor location. Press 2 ¢ c ? I d. This instruction displays the value of element I (the result of the last roll) in L1. Press ¸ to complete the instruction. 9.
About TI-80 Programs Most features of the TI.80 are accessible from programs. Programs can access all variables and named items. The number of programs that the TI.80 can store is limited only by available memory. Notes about Programs Programs are identified by names of up to seven characters, beginning with a letter. A program consists of a series of program commands, which begin with a : (colon).
Creating and Executing Programs Access the program editor by pressing K. Then either choose to create a new program or edit an existing program. In general, anything that can be executed from the Home screen can be included in a program. A program command always begins with a colon (:). Creating a New Program To create a new program: 1. Press K 9 9 to display the PRGM NEW menu. Press ¸ to select CREATE NEW. 2. The keyboard is in ALPHA-LOCK. Enter the name you want for the program, followed by ¸.
Editing Programs The program editor also lets you edit an existing program. As you edit, you can enter commands just as you did when you created the program. Editing a Program To edit a program: 1. Press K 9 to display the PRGM EDIT menu. 2. Select the name of an existing program. The program editor and the commands in that program are displayed. 3. Edit the program by changing, inserting, or deleting commands, as needed. Changing Instructions Move the cursor to the command you want to change.
PRGM CTL (Control) Instructions PRGM CTL (program control) instructions are accessed only from within the program editor. They direct the flow within an executing program, making it easy to repeat or skip commands during program execution. While the program editor is displayed, press K. The selected menu item is copied to the cursor location.
IF-THEN END THEN (PRGM CTL, item 2) following an IF executes a group of commands if the condition is true (nonzero). END (PRGM CTL, item 5) identifies the end of the group. :IF condition :THEN :command if true :... :END :command IF-THEN-ELSE END ELSE (PRGM CTL, item 3) following IF-THEN executes a group of commands if the condition is false (zero). END (PRGM CTL, item 5) identifies the end of the group. :IF condition :THEN :command if true :... :ELSE :command if false :...
FOR( END FOR( (PRGM CTL, item 4) is used for looping and incrementing. It increments the variable from the beginning value to the ending value, by the specified increment. The ending value is a maximum or minimum value that is not to be exceeded. The increment is optional (if not specified, 1 is used) and can be negative (ending value < beginning value). END identifies the end of the loop. FOR( loops can be nested. :FOR(variable,begin,end,increment) :command while end not exceeded :...
LBL GOTO LBL (label) and GOTO (go to) are used together for branching. LBL (PRGM CTL, item 7) gives a label to a command line in a program. The label is one character (A–Z, 0–9, or q). LBL label GOTO (PRGM CTL, item 8) causes the program to branch to the command line with the same label. GOTO label PRGM_ PRGM_ (PRGM CTL, item 9) calls (executes) other programs as subroutines (pages 10-14). When you select PRGM_, it is copied to the cursor location. You may type the letters of an existing program name.
PRGM I/O (Input/Output) Instructions The PRGM I/O (program input/output) instructions are accessed only from the program editor. They control input to and output from a program, allowing you to enter values and display answers during program execution. While the program editor is displayed, press K. The selected menu item is copied to the cursor location. PRGM I/O Menu CTL I/O EXEC 1: INPUT Enters a value or displays the current graph. 2: DISP Displays text, value, or the Home screen.
Storing a Variable Value with INPUT INPUT with a variable displays a ? prompt during program execution. The value for the variable may be a real number, a list, or Y= function. During program execution, enter a value (a real number, an expression, or a list), and press ¸. The value is evaluated and stored to the variable, listname, or Y= function, and the program resumes execution.
Displaying the Home Screen DISP (display, PRGM I/O, item 2) with no value displays the Home screen. To view the Home screen during program execution, follow the DISP instruction with a PAUSE. Displaying Values and Messages DISP (display, PRGM I/O, item 2) with one or more values displays the value of each. DISP value DISP valueA,valueB... ¦ If value is a variable, the current value is displayed.
Calling Other Programs On the TI.80, any 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. Calling a Program from Another Program To call one program from another, begin on a blank line in the program editor and do one of the following. ¦ Press K 6 to display the PRGM EXEC menu, and select the name of the program. PRGM_ and the name are copied to the cursor location.
Chapter 11: Applications This chapter contains application examples that incorporate the TI.80 features described in the preceding chapters. Several of the examples use programs. Chapter Contents Probability Experiments: Coins, Dice, and Spinners ... The Unit Circle and Trigonometric Curves............ Program: Newton’s Numerical Solve Routine ......... Program: Numerical Integration ..................... Program: Window Variables Store and Recall ......... Graphing the Inverse of a Function ..............
Probability Experiments: Coins, Dice, and Spinners The RANDINT( (random integer) function can be used for probability experiments. RANDINT( takes two arguments that define a set of integers from which to draw for the probability experiments below. Problem Using RANDINT( from the MATH PRB menu, devise probability experiments that employ the toss of a coin, the roll of two dice, and the spin of a wheel. Procedure For the coin tossing experiment, enter RANDINT(0,1) from the Home screen.
The Unit Circle and Trigonometric Curves You can use the parametric graphing feature of the TI.80 to show the relationship between the unit circle and any trigonometric curve. Problem Graph the unit circle and the sine curve to demonstrate graphically the relationship between them. Any function that can be plotted in function graphing can be plotted in parametric graphing by defining the X component as T and the Y component as F(T). Procedure Following this procedure to solve the problem. 1.
Program: Newton’s Numerical Solve Routine This program uses the Newton-Raphson method to find the roots (zeros) of a function numerically. Problem Find the roots of ex ì3X. Program This program uses the Newton-Raphson method to find a root of Y1 based on an initial guess. The program prompts for the initial guess. One way to make this initial guess is to graph and trace the function, and then enter X as the guess.
5. Press + and move the cursor close to the left root. The variables X and Y are updated as you move the cursor. 6. From a blank line on the Home screen, execute the program NEWTON. 7. Enter X as the initial guess, and press ¸ repeatedly. The program stops when the relative difference between the new root estimate and the previous root estimate is less than XíL10. 8. When program execution is complete, evaluate the function at the estimated root. Repeat the steps in this procedure to find the other root.
Program: Numerical Integration This program uses Simpson’s method to estimate the definite integral of a function. Problem Estimate the definite integral of ‰ 1.5(6ì6x )dx 5 0 and graph the area of the integral. Program The program estimates the definite integral for Y1 using Simpson’s method. It prompts for the lower and upper limits of integration and the number of divisions.
3. Set the Window variables. 4. Execute the program SIMPSON from a clear Home screen, entering the limits and divisions as you are prompted. 5. You can display the calculated area graphically, using SHADE( from a clear Home screen.
Program: Window Variables Store and Recall The program below lets you store the values for the current Window variables, and it lets you display a graph using previously stored values. It also demonstrates a method for including menus in a program.
Procedure Follow this procedure to see how the program works. 1. Execute the program WINMEM from a blank Home screen. The program prompts with three options. ¦ Store the Window variables you are currently using. ¦ View a graph using a previously stored set of Window variables. ¦ Quit the program. 2. Press 1, 2, or 3 and then ¸ to respond to the prompts. The Window values are stored in variables A, B, C, D, E, and F.
Graphing the Inverse of a Function You can use the parametric graphing feature of the TI.80 to graph the inverse relation of any function by defining the function in XãT and YãT and its inverse in XäT and YäT. Problem The function Y=.2X3ì2X+6 can be expressed in parametric form as XT=T and YT=.2T3ì2T+6. The inverse relation of the function can be expressed in parametric form as XT=F(T) and YT=T. For example, Y=.2X3ì2X+6 would be expressed as XT=.2T3ì2T+6 and YT=T. Graph the function Y=.
5. Enter the expressions to define the line Y=X, about which the graph of the function and the graph of its inverse are symmetric. That is, the reflection of the graph of the function through the line Y=X produces the graph of its inverse. X3î=T Y3î=T 6. Press , to plot the graph. Press +, and then press 9 several times (until the cursor appears). Next, press 8 and 7 several times to move the cursor from a point on the relation to the reflected point and back again.
Graphing a Piecewise Function The test functions of the TI.80 can be used to build piecewise defined functions. Problem Define and graph this piecewise defined function. f(x)= xñ, 1.5x+1, 6ìx, for x≤3 for 3
4. Add the third piece of the function to Y1. This piece is f(x)=6ìx for x≥5. It is entered as (6ìx) (x≥5). When x is greater than or equal to 5, the test (x≥5) returns 1. The third piece of the function is then equivalent to (6ìx)×1. When X is less than 5, the test (x≥5) returns 0. The third piece of the function is then equivalent to (6ìx)×0. 5. Enter these Window variable values. Xmin=ë2 Xmax=8 Xscl=2 Ymin=ë2 Ymax=10 Yscl=1 6. Graph the piecewise function first in CONNECTED and then DOT mode.
Graphing Inequalities Examine the inequality .4Xòì3X+5<.2X+4 graphically. Use the TEST functions to explore the values of X where the inequality is true and where it is false. Procedure 1. Press 3. Select DOT, SIMUL, and the default mode settings. Press 2 ", and turn off all stat plots. 2. Press (, and turn off all functions. Enter the left side of the inequality as Y1, the right side as Y2, and the statement of the inequality as Y3. Y3 evaluates to 1 if true and 0 if false. 3.
Graphing a Polar Equation The parametric graphing feature of the TI.80 can be used to graph polar equations. Graph the Spiral of Archimedes, the name given to the curve defined by the polar equation r=aq. Problem A polar equation r=f(q) can be graphed by applying the conversion formulas, x=f(q) cos(q) and y=f(q) sin(q). Thus, the Spiral of Archimedes can be expressed parametrically as: x = .5 q cos(q) y = .5 q sin(q) Procedure Follow this procedure to solve the problem. 1. Select PARAM mode.
Program: Guess the Coefficients This program generates a function in the form A×SIN(BX) with random integer coefficients between 1 and 10. Seven data points from the function are plotted. You are prompted to guess the coefficients, which are plotted as C×SIN(DX). The program continues until your guess is correct. It can be modified for other functions.
Chapter 12: Memory Management This chapter describes how to manage memory on the TI.80. To increase the amount of memory available for use, occasionally you may want to delete stored items that you are no longer using. You can also reset the calculator, erasing all data and programs. Chapter Contents Checking Available Memory ........................ Deleting Items from Memory ....................... Resetting the TI-80 ................................
Checking Available Memory The MEMORY CHECK RAM screen displays the total amount of available memory and the amount of memory used by each variable type. This allows you to determine the amount of memory available for new items such as programs and the amount used by old items that you no longer need. Displaying the MEM FREE Screen To check the amounts of available and used memory: 1. Press 2 ¯ to display the MEMORY menu. 2. Press 1 or ¸ to select CHECK RAM....
Deleting Items from Memory You can delete the contents of any variable (real number, list, or Y= function) or program from memory to increase available memory. Deleting an Item To delete an item: 1. Press 2 ¯ to display the MEMORY menu. 2. Press 2 to select DELETE... A screen showing all variables currently in use and the amount of memory used by each is displayed. The file names are listed in the following order: ¦ ¦ ¦ ¦ Program names List names Y= equation names Numeric variable names 3.
Resetting the TI-80 Resetting the TI.80 restores memory to the factory settings, including deleting the contents of all variables and programs and resetting all system variables to the original settings. Because you can increase available memory by deleting individual items, you should rarely need to reset the TI.80. Resetting To reset the TI-80: 1. Press 2 ¯ to display the MEMORY menu. 2. Press 3 to select RESET.... 3.
Appendix A: Tables and Reference Information This appendix provides a list of all TI-80 functions that you can use in expressions and instructions that you can use on the Home screen and in programs. It also includes other reference information that can help you. Appendix Contents Table of TI-80 Functions and Instructions .......... A-2 Menu Map ....................................... A-20 TI-80 Variables...................................
Table of TI-80 Functions and Instructions A function (F) returns a value or a list and can be used in expressions; an instruction (I) initiates an action. Some, but not all, have arguments. † indicates that the instruction is available for copying only from the program editor. aÀbºc Sets the display format for † 3 áaÀbºcâ fraction results to aÀbºc (mixed fraction) mode. (I) valueaÀbºc Returns value as a mixed fraction. (F) ABS value Returns the absolute value 2 P of value.
Sets connected line graphing format. (I) †3 áCONNECTEDâ COS value Returns the cosine of value. (F) X COS list Returns a list of the cosine for each list element. (F) X Returns the arccosine of value. (F) 2R COSê list Returns a list of the arccosine for each list element. (F) 2R Cube: value ò Returns the cube of value. I MATH áòâ (F) 2-8 CONNECTED COSê value 1-11 2-4 2-4 2-4 2-4 Cube: list ò Returns a list of the cube for each list element.
DISPGRAPH Displays the current graph. (I) † K I/O áDISPGRAPHâ Division: valueAàvalueB Returns valueA divided by e valueB. (F) Division: listàvalue Returns list elements divided by value. (F) e Division: valueàlist Returns value divided by list elements. (F) e Division: listAàlistB e Returns listA elements divided by listB elements. (F) DOT Sets dot graphing format. (I) †3 áDOTâ DRAWF expression Draws expression (in X) on the current graph.
EXPREG Xlistname,Ylistname EXPREG Xlistname,Ylistname, freqlistname Factorial: value! Factorial: list! Fits Xlistname and Ylistname to the exponential model. (I) A CALC áEXPREGâ Fits Xlistname and Ylistname to the exponential model with frequency freqlistname. (I) A CALC áEXPREGâ Returns the factorial of value (0 integer 69). (F) I PRB á!â Returns a list containing the factorial for each list element (0 ≤ integers ≤ 69).
FPART value Returns the fractional part I NUM áFPARTâ of value. (F) FPART list Returns a list of the fractional parts for each list element. (F) I NUM áFPARTâ value8FRAC Returns value in fraction form, according to the current fraction display format. (I) J á4FRACâ Displays list in fraction form, according to the current fraction display format. (I) J á4FRACâ FUNC Sets function graphing mode. (I) †3 áFUNCâ GOTO label Branches the program to label.
HORIZONTAL Y Draws a horizontal line at 2 F DRAW áHORIZONTALâ value Y. (I) 7-5 IF condition:commandA :commands If condition = 0 (false), skips commandA. (I) † K CTL áIFâ 10-7 IF condition :THEN:commands :END Executes commands from † K CTL áTHENâ THEN to END if condition = 1 (true). (I) 10-8 IF condition :THEN:commands :ELSE:commands :END Executes commands from † K CTL áELSEâ THEN to ELSE if condition = 1 (true); from ELSE to END if condition = 0 (false).
IPART value Returns the integer part of I NUM áIPARTâ value. (F) 2-10 IPART list Returns a list of the integer part for each list element. (F) I NUM áIPARTâ LBL label Assigns label to the command. (I) † K CTL áLBLâ Less Than: valueA
Fits Xlistname and Ylistname to the logarithmic model. (I) A CALC áLNREGâ Fits Xlistname and Ylistname to the logarithmic model with frequency freqlistname. (I) A CALC áLNREGâ LOG value Returns the logarithm of value. (F) l LOG list Returns a list of the logarithm for each list element. (F) l MANSIMP Selects manual simplification mode for fractions. (I) †3 áMANSIMPâ MAX(valueA,valueB) Returns the larger of valueA and valueB.
Returns a list of the smaller of each pair of elements in listA and listB. (F) 2 = MATH áMIN(â MIN(list,value) or MIN(value,list) Returns a list of the smaller of each list element compared to value. (F) 2 = MATH áMIN(â Multiplication: valueA×valueB Returns valueA times valueB. (F) p Multiplication: value×list or list×value p Returns a list containing each value times each list element.
Returns the negative of value. (F) · Negation: ëlist Returns a list with each list element negated. (F) · NORMAL Sets normal display mode. † 3 áNORMALâ (I) Not Equal: valueAƒvalueB Returns 1 if valueA ƒ valueB. Returns 0 if valueA = valueB. (F) Negation: ëvalue 2-6 2-6 2-16 Not Equal: listAƒlistB Applies the ƒ test to each 2 D áƒâ element of listA and listB and returns a list. (F) Not Equal: listƒvalue or valueƒlist Applies the ƒ test to each element of list and value and returns a list.
PAUSE Suspends execution of the † K CTL áPAUSEâ program until ¸ is pressed. (I) Pi Returns the value of π rounded to 13 digits. (F) PLOTn(type,Xlist,Ylist) Plots stat plot n (1-3) of †2" type (¼ or ½) for Xlist áPLOTnâ and Ylist coordinate pairs. 9-20 PLOTn(type,Xlist,Ylist, mark) Plots stat plot n (1-3) of †2" type (¼ or ½) for Xlist áPLOTnâ and Ylist coordinate pairs with the specified type of mark.
Executes the program programname. (I) † K CTRL áPRGM_(â PROD list Returns the product of elements in list. (F) 2 = MATH áPRODâ P8Rx(R,q) 2E Returns the rectangular áP4Ry(â coordinate x, given the polar coordinates R and q. (F) 2-15 P8Rx(Rlist,q) 2E Returns a list of x áP4Ry(â coordinates, given the R coordinates in Rlist and a single q. (F) 2-15 P8Rx(R,qlist) Returns a list of x coordinates, given the single R coordinate and the q coordinates in qlist.
Fits Xlistname and Ylistname to the power model. (I) A CALC áPWRREGâ PWRREG Xlistname, Ylistname,freqlistname Fits Xlistname and Ylistname to the power model with frequency freqlistname. (I) A CALC áPWRREGâ QUADREG Xlistname, Fits Xlistname and Ylistname to the quadratic model. (I) A CALC Fits Xlistname and Ylistname to the quadratic model with frequency freqlistname. (I) A CALC RADIAN Sets radian mode. (I) †3 áRADIANâ 1-11 Radian Notation: valuer Interprets value as an angle in radians.
Returns a list of remainders from the division of each element in list by value. I NUM áREMAINDER(â REMAINDER(listA, listB) Returns a list of remainders from the division of each element in listA by the each element in listB. I NUM áREMAINDER(â Return Returns to the calling program. (I) † K CTL áRETURNâ 10-10 Returns nthroot of value. (F) I MATH áx‡â 2-8 nthrootx‡list Returns a list of nthroot for each list element. (F) I MATH áx‡â 2-8 listx‡value Returns list roots of value.
R8Pr(Xlist,Ylist) 2E Returns a list of r áR4Pq(â coordinates, given the X coordinates in Xlist and the Y coordinates in Ylist. (F) 2-15 R8Pq(X,Y) 2E Returns the polar áR4Pq(â coordinate q, given the rectangular coordinates X and Y. (F) 2-15 R8Pq(Xlist,Y) 2E Returns a list of q áR4Pq(â coordinates, given the X coordinates in Xlist and a single Y coordinate. (F) 2-15 R8Pq(X,Ylist) 2E Returns a list of q coordinates, given a single áR4Pq(â X coordinate and the Y coordinates in Ylist.
2 F DRAW áSHADE(â SHADE(lowerfunc, upperfunc,resolution, Xleft,Xright) Shades the area above lowerfunc, below upperfunc, to right of X=Xleft, to left of X=Xright, and with resolution (1 through 9). (I) SHADE_Y>func1,func2, . . . 2 F DRAW Shades the area above func1 with vertical áSHADE_Y>â pattern and above func2 with diagonal pattern (lower left to upper right), etc. (I) 7-7 SHADE_Y
SORTD(listname) Sorts the elements of listname in descending order. (I) 2 = OPS áSORTD(â SORTD(keylistname, dependlist1, dependlist2, . . .) Sorts the elements of keylistname in descending order with dependlist1, dependlist2 . . . as dependent lists. (I) 2 = OPS áSORTD(â Square: valueñ Returns value multiplied by itself. (F) a Returns a list of each list element squared. (F) a Square: listñ 8-6 8-6 2-5 2-5 Square Root: ‡value Returns the square root of 2 ] value.
TAN list Returns a list of the tangent for each list element. (F) Y TANê value Returns the arctangent of value. (F) 2S TANê list Returns a list of the arctangent for each list element. (F) 2S TRACE Displays a graph and enters Trace mode. (I) †+ 2-VAR STATS Xlistname,Ylistname Performs two-variable analysis using Xlistname and Ylistname. (I) A CALC á2-VAR STATSâ 2-VAR STATS Xlistname,Ylistname, Performs two-variable analysis using Xlistname and Ylistname with frequency freqlistname.
TI-80 Menu Map Menus begin in the upper left of the keyboard. Default values are shown.
2" ÚÄÄÄÄÄÙ STAT PLOTS 1:PLOT1... OFF ¼ L1 L2 Â 2:PLOT2... OFF ¼ L1 L2 Â 3:PLOT3...
2= ÚÄÄÁÄÄÄÄÄÄÄÄÄ¿ MATH OPS 1:MIN( 1:SORTA( 2:MAX( 2:SORTD( 3:MEAN( 3:DIM 4:MEDIAN( 4:SEQ( 5:SUM 6:PROD I ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ PRB NUM MATH 1:RAND 1:ROUND( 1:INT÷ 2:nPr 2:IPART 2:4DEC 3: 3 3:nCr 3:FPART 4:! 4:INT 4:3 ‡ 5:RANDINT( 5:MIN( 5: X ‡ 6:NDERIV( 6:MAX( 7:REMAINDER( J ÚÙ FRACTION 1:4SIMP 2:4bºc 3:4aÀbºc 4:4FRAC 5:4DEC 2D ÚÄÄÄÄÙ TEST 1:= 2:ƒ 3:> 4:‚ 5:< 6: A-22 Tables and Reference Information 2E ÚÄÄÄÄÙ ANGLE 1:¡ 2: r 3:R4Pr( 4:R4Pq( 5:P4Rx( 6:P4Ry(
K ÚÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄ¿ NEW EDIT EXEC 1:CREATE NEW 1:name 1:name 2:name 2:name 3:name 3:name © © K (in program editor) ÚÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿ EXEC I/O CTL 1:name 1:INPUT 1:IF 2:name 2:DISP 2:THEN 3:DISPGRAPH 3:name 3:ELSE © 4:CLRHOME 4:FOR( 5:END 6:PAUSE 7:LBL 8:GOTO 9:PRGM_ 0:RETURN A:STOP 2 F ÚÄÄÄÄÁÄÄÄÄÄÄÄÄÄÄ¿ POINTS DRAW 1:PT-ON( 1:CLRDRAW 2:PT-OFF( 2:LINE( 3:HORIZONTAL 3:PT-CHANGE( 4:VERTICAL 5:DRAWF 6:SHADE_Y> 7:SHADE_Y< 8:SHADE( 9:GRIDON 0:GRIDOFF Tables and Reference Information A-23
L ÚÄÙ VARS 1:WINDOW...
2¯ ÚÄÙ MEMORY 1:CHECK RAM… 2:DELETE… 3:RESET… 2 ¯ áCHECK RAM…â ÚÄÄÄÄÙ MEM FREE 7014 REAL 14 LIST 0 Y-VARS 80 PRGM 14 2 ¯ áDELETE…â ÚÄÄÄÄÄÄÙ DELETE: úname memory name memory name memory © © 2 ¯ áRESET…â ÚÄÄÄÄÄÄÙ 1:NO 2:RESET Resetting memory erases all data and programs. (names include defined programs, lists, Y= equations, and user variables, in that order.
TI-80 Variables The variables listed below are used by the TI-80 in various ways. Some have restrictions on their use. User Variables The variables A through Z and q can hold only numbers— either decimals or fractions. You may store to these variables. The TI-80 can update X, Y, and T during graphing; therefore, you may wish to reserve those variables for graphing activities. The variables Lã through L6 are defined as lists. You cannot store another type of data to them.
Appendix B: Service and Warranty Information This appendix provides supplemental information that may be helpful as you use the TI.80. It includes procedures that may help you correct problems with the calculator. Appendix Contents Battery Information ............................... Accuracy Information ............................. In Case of Difficulty ............................... Error Conditions .................................. Service and Support Information ...................
Battery Information The TI.80 uses two CR2032 lithium 3-volt batteries. When to Replace the Batteries As you use the TI.80, the battery voltage will gradually drop, and the display will dim. You can adjust the contrast to darken the display when this happens. If the display is dim and adjusting the contrast to level 9 does not make it dark enough, you should replace the batteries. Refer to pages B-3 through B-7 for instructions on how to change the batteries.
Changing the Batteries (Continued) To change the batteries, first: a. Turn the calculator off. b. Replace the plastic slide cover over the keys. c. Turn the calculator so that the back is facing you. Placing your thumb on the ridged area of the plastic battery compartment cover, push down slightly and slide the cover to the right until you can lift off the cover. Push the red switch up to free the metal battery cover over the lower battery.
Changing the Batteries (Continued) Slide the metal battery cover away from the battery. The battery pops up. Remove the old battery. Insert a new battery, positive side (+) up. Hold the new battery in place and slide the metal battery cover back into position over the battery.
Changing the Batteries (Continued) Push the red switch all the way down to free the metal battery cover over the upper battery. Slide the metal battery cover away from the battery. Remove the old battery. Insert a new battery, positive side (+) up.
Changing the Batteries (Continued) Hold the new battery in place and slide the metal battery cover back into position over the battery. Push the red switch to its center position to lock the metal covers and batteries into place. Note: The calculator will not turn on unless the red switch is in the center position.
Changing the Batteries (Continued) Replace the plastic battery compartment cover. Turn the calculator on and adjust the contrast display. To adjust the display contrast, press and release the 2 key. To increase the contrast (darken the screen), press and hold 7. To decrease the contrast (lighten the screen), press and hold 8.
Accuracy Information To maximize accuracy, the TI.80 carries more digits internally than it displays. Computational Accuracy Graphing Accuracy Values in memory are stored using up to 13 digits with a two-digit exponent. ¦ You can store values in the Window variables using up to 10 digits (13 digits for XSCL, YSCL, and TSTEP). ¦ When a value is displayed, the displayed value is rounded as specified by the MODE setting (Chapter 1), with a maximum of 10 digits and a two-digit exponent.
Function Limits Following is a table of functions and the range of input values for each. Function Input Values SIN x, COS x, TAN x SIN -1 x, COS-1 x LN x, LOG x 0 | x | < 10 10 (degree) -1 x 1 10 -100 < x < 10 100 -10 100 < x 230.2585092993 -10 100 < x < 100 0 x < 10 100 0 x 69, where x is an integer ex 10x ‡x x! Function Results Following is a table of functions and the range of the result for each.
In Case of Difficulty If you have difficulty operating the calculator, the following suggestions may help you to correct the problem. Handling a Difficulty Follow these procedures if you have difficulties. 1. If you cannot see anything on the display, perhaps the display contrast needs adjusting. Press and release the 2 key. To increase the contrast (darken the screen), press and hold 7. To decrease the contrast (lighten the screen), press and hold 8.
Error Conditions When the TI.80 detects an error, it displays ERR:message and the error menu. The general procedure for correcting errors is described on page 1.22. The error messages, their possible causes, and suggestions for correction are shown below. ARGUMENT A function or instruction does not have the correct number of arguments. See Appendix A and the appropriate chapter.
INCREMENT ¦ INVALID You are attempting to reference a variable or use a function in a place where it is not valid. For example, Yn cannot reference Y, XMIN, @X, or TBLMIN. INVALID DIM ¦ ¦ ¦ The increment in SEQ( is 0 or has the wrong sign. This error does not occur during graphing. The TI-80 allows for undefined values on a graph. The increment in FOR( is 0 or has the wrong sign. The dimension of the argument is not appropriate for the operation.
STAT ¦ ¦ ¦ ¦ ¦ You are attempting a linear regression with a vertical line. Statistical analyses must have at least two data points; QUADREG must have at least three data points. The list of s (frequency) elements must be ≥ 0, and at least one F value must be ≥ 0. The frequency list, when used for “sorting” statistics (median, Qã, Qå, or boxplot), must be an integer ≥ 0 and 99. (XMAX.XMIN)àXSCL must be 31 for a histogram.
Support and Service Information Product Support Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands For general questions, contact Texas Instruments Customer Support: phone: e-mail: 1.800.TI.CARES (1.800.842.2737) ti-cares@ti.com For technical questions, call the Programming Assistance Group of Customer Support: phone: 1.972.917.8324 Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands Contact TI by e-mail or visit the TI calculator home page on the World Wide Web.
Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Electronic Product This Texas Instruments (“TI”) electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This TI electronic product is warranted against defective materials and construction.
Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction.
Index A a variable, 9-15 to 9-17, A-26 aÀbºc MODE, 1-9, 1-11, 3-4, A-2 8aÀbºc, 3-8, 3-9, A-2 ABS, 2-6, A-2 Absolute value, 2-6, A-2 Accuracy, 4-12, B-8, B-9 Addition: +, 2-4, A-2 ALPHA, ALPHA-LOCK, 1-8 Angle entry indicators (¡, r), 2-14, A-2, A-14 ANGLE menu, 2-14, 2-15 Angle MODE, 1-11 ANS, 6, 1-16, 8-2, 10-4 APD, 1-2 Applications Box with lid, 7 to 13 Building height and city size, 9-2 to 9-7 Compound interest, 5 , 6 Generating a sequence, 8-2 Graphing a circle, 4-2 Graphing inequalities, 11-14 Graphing
C (Cont.) D (Cont.) Conversions decimals, 2-7, 2-8, 3-8, 3-10, 82, A-3 fractions, 3-8, 3-10, A-6 polar to rectangular, 2-14, 2-15, A-13 rectangular to polar, 2-14, 2-15, A-15, A-16 Coordinates, 4-12 Correlation coefficient r, 9-15 to 9-17 COS, COS –1, 2-4, A-3, B-9 Cosine, 2-4, A-3, B-9 CTL (PRGM) menu, 10-7 to 10-10 Cube:3, 2-7, 2-8, A-3 Cube root: 3‡, 2-7, 2-8, A-3 Cursor coordinates, 4-12, B-8 Cursor keys, 1-8 Cursors, 1-5, 1-8 Curve fitting, 9-18 to 9-21 Display (Cont.
E (Cont.) Equation Operating System, 1-20, 1-21 Equations, parametric, 5-2 to 5-6 Erasing a program, 10-4, 12-3 Errors, 1-22, 8-5, 10-4, B-11 to B-13 Evaluating expressions, 1-6, 3-4 Evaluating functions, 4-7 Executing programs, 10-5 Exponent: E, 1-7, A-4 Exponential regression, 9-14, 9-16, A-5 EXPREG, 9-14, 9-16, A-5 Expressions, x, 1-6 G Getting Started.
K keyboard, 2 L Ln (lists), 8-2 to 8-5, A-26 LABEL error, B-12 Labels (program), 10-10 Last Answer, 1-16, 10-4 Last Entry, 1-14, 1-15, 10-4 LBL, 10-7, 10-10, A-8, B-12 Less than: <, 2-16, A-8 Less than or equal: , 2-16, A-8 LINE(, 7-3, 7-4, A-8 Line (stat), 9-18, 9-20 to 9-21 Linear regression, 9-15, 9-16, A-8 LINREG, 9-14 to 9-16, A-8 LIST MATH menu, 8-9, 8-10 LIST OPS menu, 8-6 to 8-8 Lists, x, 8-2 to 8-10 arguments, 2-3, 8-5 copying, 8-3 deleting, 9-11, 9-13 dimension, 8-6, 8-7, A-3 displaying, 8-4 ed
N n (statistics), 9-17, A-26 Natural log, 2-5, A-8 nCr, 2-12, 2-13, A-10 NDERIV(, 2-7, 2-9, A-10 Negation: -, 1-21, 2-6, A-11 NEST LEVEL error, B-12 NORMAL MODE, 1-9, 1-10, A-11 Not equal: ƒ, 2-16, A-11 nPr, 2-12, A-11 NUM (MATH) menu, 2-10, 2-11 Numerical derivative, 2-7, 2-9, A-10 O OFF, ON, 3, 1-2 1-VAR STATS, 9-14, 9-15, A-11 One-variable statistics, 9-14, 9-15, A-11 OVERFLOW error, B-12 P (Cont.
R (Cont.
T (Cont.) Turning functions on and off, 1-19, 4-8, 5-4 Turning the TI-80 on and off, 3, 1-2 2-VAR STATS, 9-14, 9-15, A-19 Two-variable statistics, 9-14, 9-15, A-19 U UNDEFINED error, B-13 Y (Cont.) Y-VARS menu, 1-19 Yn, 1-19, 4-5 to 4-7, 10-12, A-26 Y1, Y2, Y3, 9-14, 9-15, A-26 YnT functions, 1-19, 5-3, A-26 Y= editor, 1-19, 4-5 to 4-7, 5-3, 6-4, A-26 Y= functions.
TI-80 STAT PLOT X,T FRAC x { x x x E } b c