Texas Instruments TI-80 - Manuals

Introduction v Getting Started: Roots of a Function ................. 6 - 2 Defining the Independent Variable .................. 6 - 3 Defining the Dependent Variable .................... 6 - 4 Displaying the Table ............................... 6 - 5 Getting Started: Shading a Graph .................

vi Introduction 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 ................

Introduction vii Table of TI - 80 Functions and Instructions ............ A - 2 Menu Map ........................................ A - 20 TI - 80 Variables ................................... A - 26 Battery Information ............................... B - 2 Accuracy Information ..........................

viii Introduction 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 areused throughout to make the guidebook easy to use. The guidebook is designed to teach you how to use thecalculator. ¦ Getting...

x Introduction Several techniques have been used to help you look upspecific information when you need it. These include: ¦ A chapter table of contents on the first page of eachchapter, as well as the full table of contents at the front ofthe guidebook. ¦ A glossary at the end of this section, defin...

Introduction xi This glossary provides definitions for important terms that are used throughoutthis guidebook. An argument is an input upon which the value of a functiondepends. A command is any entry submitted to the calculator using ¸ . There are two types of TI - 80 commands: instructions and exp...

xii Introduction 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. On the TI - 80, real numbers are individual decimal or fraction values. A value is a single decimal or fraction number or a list ofdecimals or fractions. A var...

Getting Started 1 Getting Started contains two keystroke-by-keystroke examples  an interest rate problem and a volume problem  which 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 f...

2 Getting Started 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. Graphing & Editing & Advanced & FunctionsSci...

Getting Started 3 Before beginning the two sample problems, follow the steps on this page toreset the TI - 80 to its factory settings. (Resetting the TI - 80 erases all previously entered data.) This ensures that following the keystrokes in this sectionproduces the same actions. 1. Press ´ to turn t...

4 Getting Started 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 theappropriate chapters. Displaying a Menu When you press a key that displays a menu, such as I , that menu screen temporarily repl...

Getting Started 5 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 multipleinstructions on one line, and recall previous entries. Using trial and error, determine when an amount invested at 6% annualcom...

6 Getting Started To save keystrokes, you can use the Last Entry feature to recall the lastexpression entered and then edit it for a new calculation. In addition, the nextexpression can be continued from the previous result. 1. The next guess should be less than, but close to, 12 years. Compute the ...

Getting Started 7 Take an 8½"×11" sheet of paper and cut X by X squares from two corners and Xby (X+B) rectangles from the other two corners. Now fold the paper into a boxwith lid. What X would give the maximum volume V of a box made in this way?Use tables and graphs to determine the solutio...

8 Getting Started 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 answerto the problem. 1. Press y # (above p ) to display the TABLE SETUP screen. 2. Press Í to accept TBLMIN=0 . 3. Press .5 Í t...

Getting Started 9 You can adjust the way a table is displayed to get more detailed informationabout 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 TBLMI...

10 Getting Started 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 colum...

Getting Started 11 The viewing window defines the portion of the coordinate plane that appears inthe display. The values of the Window variables determine the size of theviewing window. You can view and change these values. 1. Press p to display the Window variables edit screen. You can view and edi...

12 Getting Started Now that you have defined the function to be graphed and the window in whichto graph it, you can display and explore the graph. You can trace along afunction with TRACE. 1. Press s to graph the selected function in the viewing window. The graph of Y1=(W–2X)(L à 2–X)X is shown in t...

Getting Started 13 You can magnify the viewing window around a specific location using the Zoominstructions to help identify maximums, minimums, roots, and intersections offunctions. 1. Press q to display the ZOOM menu. This menu is typical of TI - 80 menus. To select an item, you may either press t...

14 Getting Started Getting Started has introduced you to basic calculator operation and the tableand function graphing features of the TI - 80. The remainder of this Guidebook describes these features in more detail and also covers other capabilities of theTI - 80. You can enter fractions directly f...

1-2 Operating the TI-80 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. Press ´ to turn the TI - 80 on. ¦ If you pressed y ...

Operating the TI-80 1-3 The brightness and contrast of the display depend on room lighting, batteryfreshness, viewing angle, and the adjustment of the display contrast. Thecontrast setting is retained in memory when the TI . 80 is turned off. You can adjust the display contrast to suit your viewing ...

1-4 Operating the TI-80 The TI . 80 displays both text and graphs. Graphs are described in Chapters 4 and 5. The primary screen of the TI - 80 is the Home screen. You enter instructions to be executed, expressions to be evaluated, andsee the results on the Home screen. When text is displayed, the TI...

1-6 Operating the TI-80 In most places where a value is required, you can use an expression to enter thevalue. You can enter instructions, which initiate an action, on the Home screenor in the program editor (Chapter 10). An expression is a complete sequence of numbers, variables,functions, and thei...

1-8 Operating the TI-80 The arrow keys near the upper right of the keyboard control the movement ofthe cursor. In normal entry, a keystroke types over the character or charactersat the position of the cursor. The 4 and y / keys delete or insert characters. Key(s) Action(s) 9 or 6 Moves the cursor wi...

Operating the TI-80 1-9 Modes control how numbers and graphs are displayed and interpreted by thecalculator. Mode settings are retained by the Constant Memory feature when theTI . 80 is turned off. Press 3 to display the MODE screen. The current settings are highlighted. The settings are described o...

1-10 Operating the TI-80 The TI . 80 has eight mode settings. They control how numeric entries are interpreted, how answers are calculated or displayed, and how graphs appear inthe display. Modes are set on the MODE screen (page 1 . 9). Notation formats affect only how an answer is displayed onthe H...

1-12 Operating the TI-80 On the TI . 80 you can enter, name, and use several types of data: numeric values (including fractions), lists, functions, and statistical plots. The TI - 80 uses both user-assigned and pre-assigned names for variables and other items saved in memory. Variable Type Names Num...

Operating the TI-80 1-13 Values are stored to and recalled from memory using variable names. When anexpression containing the name of a variable is evaluated, the value of thevariable at that time is used. You can store a value to a variable from the Home screen or aprogram using the § key. Begin on...

1-14 Operating the TI-80 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 LastEntry, which you can recall. When you turn the TI . 80 off, Last Entry is retained in memory. You can recall Last Entry and ...

1-16 Operating the TI-80 When an expression is evaluated successfully from the Home screen or from aprogram, 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. You ...

Operating the TI-80 1-19 You may want to use the names of system variables (such as XMIN) andfunctions (such as Y1) in an expression. You may also want to store valuesdirectly to those variables. Use the VARS or Y . VARS menus to access the names. The VARS menu displays the names of window variables...

1-22 Operating the TI-80 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 errormessage with a menu is displayed immediately. Error codes and conditions aredescribed in detail in Appendix B. If t...

2-2 Math, Angle, and Test Operations 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 ofwinning if you buy one ticket...

Math, Angle, and Test Operations 2-3 This page contains some general information you should know about the TI . 80 functions described in Chapter 1. Functions that are valid for lists return a list calculated on anelement-by-element basis. If two lists are used in the sameexpression, they must be th...

2-4 Math, Angle, and Test Operations The most commonly used math functions are on the keyboard. The keyboardmath operations can be used with decimal numbers, fractions (except as noted),expressions, and lists. The basic arithmetic functions are: addition « , subtraction | , multiplication p , and di...

Math, Angle, and Test Operations 2-7 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 alist calculated on an element-by-element basis. MATH NUM PRB1: INT÷ Displays quotient and remainder. 2: 8 D...

Math, Angle, and Test Operations 2-9 NDERIV( (numerical derivative, MATH MATH , item 6) returns an approximate derivative of an expression with respect to aspecified variable, given the value at which to calculate thederivative, and H (optional; if none is specified, 1 í - 3 is used). NDERIV( expres...

2-12 Math, Angle, and Test 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 returna list calculated on an element-by-element basis. MATH NUM PRB1: RAND Random number generator. 2: nPr Numbe...

2-14 Math, Angle, and Test 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 iscopied to the cursor location. ANGLE1: ¡ Degree notation. 2: r Radian notation. 3: R 8 Pr( Returns r , given X and...

3-2 Fractions 8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01 9:53 AM Page 2 of 10 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 the...

3-4 Fractions 8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01 9:53 AM Page 4 of 10 From the MODE screen, you can select simplification and display format optionsfor fraction results. AUTOSIMP mode simplifies fractions automatically. Simplification t...

Fractions 3-5 8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01 9:53 AM Page 5 of 10 MANSIMP mode lets you simplify fractions manually. MANSIMP was designed for teaching and learning fractions concepts. In MANSIMP mode, you can simplify fractions and ...

3-6 Fractions 8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01 9:53 AM Page 6 of 10 The TI . 80 lets you enter fractions directly from the keyboard. A simple fraction is a fraction with no whole-number part; forexample, 3 à 4 or 4 à 3 . To enter a si...

Fractions 3-7 8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01 9:53 AM Page 7 of 10 In general, you can use fractions in expressions just as you would use othernumbers. The results of the expressions, however, may or may not be fractions. The absolut...

3-8 Fractions 8003ENG.DOC TI-80, Chp 3, ENG, 135x205mm Bob Fedorisko Revised: 02/15/01 9:52 AM Printed: 02/15/01 9:53 AM Page 8 of 10 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 thecursor location. ...

Function Graphing 4-1 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. Getting Started: Graphing a Circle ................... 4 - 2 Defining a Graph .................................. 4 -...

4-2 Function Graphing 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 viewingwindow. To graph a circle, you must enter separate formulas for the upper andlower portions of the circle. Then use ZSQUARE to ...

Function Graphing 4-3 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 defineda graph, you can plot it, display it, and explore it. There are six basic steps to defining a graph, although youmay not nee...

4-4 Function Graphing 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 afunction, check to be sure that the mode settings are appropriate. Press 3 to display the mode settings. The current setting...

Function Graphing 4-5 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 graphone or more of these functions at a time. Press ( to display the Y= edit screen. In the example below, the Y1 and Y2 fu...

4-6 Function Graphing 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...

Function Graphing 4-7 You can the calculate the value of a Y= function at a specified value of X. To display the Y= list, press ( . Enter these functions for Y1 , Y2 , and Y3 : X 2 , X+2 , and Y1(Y2(X)) . @ a ¸ @ « 2 ¸ 2 G 1 c 2 G 2 c @ d d To evaluate the functions, first specify the value of X. No...

4-8 Function Graphing Only functions that are selected (turned on) are graphed. All four functions maybe selected at one time. 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 Graphing 4-9 The Window variables determine the boundaries and other attributes of theviewing window. The Window variables are shared by all graphing modes. The viewing window of the TI - 80 is the portion of the coordinate plane defined by XMIN , XMAX , YMIN , and YMAX . The distance betwe...

4-10 Function Graphing To leave the Window screen: ¦ 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 froma program, begin on a blank line. 1. Enter the value (which can be an expres...

Function Graphing 4-11 Pressing , graphs any functions selected on the Y= edit screen. The current mode settings apply, and the current values of the Window variables define theviewing window. Grid points correspond to the axis tick marks. To turn the gridpoints on and off use GRIDON and GRIDOFF . T...

4-12 Function Graphing While a graph is displayed, you can move the free-moving cursor anywhere onthe graph and display the coordinates of any location on the graph. 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 ...

Function Graphing 4-13 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. 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 i...

4-14 Function Graphing To trace another selected function on the graph, press 8 or 7 to move the cursor to that function. The cursor moves to thenew 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 se...

Function Graphing 4-15 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 areaccessible from programs. ZOOM1: ZBOX Draws box to define viewing window. 2: ZOOM IN Magnifies graph around cursor. 3: ZOOM OUT Vi...

4-16 Function Graphing 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 d...

Function Graphing 4-17 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 = L 3 . 1 YMIN = L 2 . 3 XMAX = 3.1 YMAX = 2.3 XSCL = 1 YSCL = 1 ZSQUARE replots the fu...

4-18 Function Graphing The Zoom factors, XFACT and YFACT, determine the extent of the change for theviewing window created by ZOOM IN or ZOOM OUT on a graph. Zoom factors are positive numbers (not necessarily integers)greater than or equal to 1. They define the magnification orreduction factor used ...

Parametric Graphing 5-1 This chapter describes how to graph parametric equations on the TI . 80. Before doing parametric graphing, you should be familiar with Chapter 4, FunctionGraphing. Getting Started: Path of a Ball ...................... 5 - 2 Defining and Displaying a Parametric Graph ...........

5-2 Parametric Graphing 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 anangle of 60 ¡ with an initial velocity of 15 meters per second. (Ignore air resistance.) What is the maximum height? When do...

Parametric Graphing 5-3 Parametric equations consist of an X component and a Y component, eachexpressed in terms of the same independent variable T. They are often used tograph equations over time. Up to three pairs of parametric equations can bedefined and graphed at a time. The steps for defining ...

5-4 Parametric Graphing 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 para...

Parametric Graphing 5-5 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...

5-6 Parametric Graphing As in function graphing, three tools are available for exploring a graph: the free-moving cursor, tracing, and zooming. The free - moving cursor works the same in parametric graphing as in function graphing (page 4-12). Pressing + puts the Trace cursor on the first selected e...

6-2 Tables Getting Started is a fast-paced introduction. Read the chapter for details. Evaluate the function Y=X 2 – 4X+3 at each integer between L 10 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 SET...

Tables 6-3 The independent variable for a table is the independent variable in the currentgraphing mode (X for FUNC mode and T for PARAM mode). You define theminimum value and the incremental value for the independent variable on theTABLE SETUP screen. To display the TABLE SETUP screen, press 2 # . ...

6-4 Tables The selected functions from the Y= list define the dependent variables. You canhave as many dependent variables as there are functions in the current graphingmode (four for FUNC mode and six for PARAM mode). Enter the functions to define the dependent variables in the Y= editor. FUNC Mode...

Tables 6-5 The table displays up to six values for the independent variable, along with thesix corresponding values of one dependent variable, at a time. Once the table isdisplayed, you can press 6 , 7 , 9 , and 8 to move around and scroll the table, displaying other independent and dependent values...

Draw Operations 7-1 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, FunctionGraphing. Getting Started: Shading a Graph .................... 7 - 2 DRAW DRAW Menu ............................... 7 - 3 Drawin...

7-2 Draw Operations Getting Started is a fast-paced introduction. Read the chapter for details. Shade the area below the function Y=X ä N 2 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 th...

Draw Operations 7-3 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 displayedwhen you access the menu, as described under each operation. DRAW POINTS1: CLRDRAW Clears all drawn elements. 2: LINE( Draws a line between...

7-4 Draw Operations While a graph is displayed, LINE( lets you use the cursor to define a line on thegraph. If a graph is not displayed, the instruction is copied to the Home screen. To define a line directly on a graph: 1. When a graph is displayed, select LINE( from the DRAW DRAW menu (item 2). 2....

Draw Operations 7-5 While a graph is displayed, HORIZONTAL and VERTICAL let you define lines onthe graph using the cursor. If a graph is not displayed, the instruction is copiedto the Home screen. To draw horizontal and vertical lines directly on a graph: 1. When a graph is displayed, select HORIZON...

7-6 Draw Operations DRAWF (draw function) draws a function on the current graph. DRAWF must beentered on the Home screen or in the program editor. DRAWF (draw function, DRAW DRAW , item 5) is not an interactive operation. It draws the specified expression as afunction in terms of X on the current gr...

Draw Operations 7-7 There are three shading instructions on the DRAW DRAW menu: SHADE_Y>,SHADE_Y<, and SHADE(. These instructions are not interactive; they must beentered on the Home screen or in the program editor. SHADE_Y> ( DRAW DRAW, item 6) takes up to four arguments (functions of X )....

Draw Operations 7-9 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 specificall...

7-10 Draw Operations 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 isdisplayed when you access the menu, as described under each operation. DRAW POINTS1: PT-ON( Turn on a point. 2: PT-OFF( Turn off a point. 3: PT-...

Draw Operations 7-11 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( . When you use these instructions from the Home screen or aprog...

7-12 Draw Operations All points, lines, and shading drawn on a graph with DRAW operations aretemporary. They remain only until you execute a CLRDRAW (clear drawing)instruction or a change prompts Smart Graph to replot the graph, at which timeall drawn elements are erased. To clear drawings from the ...

8-2 Lists Getting Started is a fast-paced introduction. Read the chapter for details. Calculate the first eight terms of the sequence 1 à A 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 beginnin...

Lists 8-3 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 onthe keyboard. A list may have a maximum of 99 elements. To use a list in an expression, you may: ¦ Use the name of the list...

8-6 Lists Press 2 = to display the list operations on the LIST OPS menu. OPS MATH1: SORTA( Sorts lists in ascending order. 2: SORTD( Sorts lists in descending order. 3: DIM Accesses the list dimension. 4: SEQ( Creates a sequence. Note: SORTA( and SORTD( are the same as SORTA( and SORTD( on the STAT ...

8-8 Lists SEQ( (sequence, LIST OPS , item 4) requires five arguments: an expression, a variable to be incremented, a beginningvalue, 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 f...

Lists 8-9 Pressing 2 = 9 accesses the list math operations on the LIST MATH menu. OPS MATH 1: MIN( Returns minimum element of a list. 2: MAX( Returns maximum element of a list. 3: MEAN( Returns mean of a list. 4: MEDIAN( Returns median of a list. 5: SUM Returns sum of all elements in a list. 6: PROD...

Statistics 9-1 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 amodel, and plotting data. Getting Started: Building Height and City Size ......... 9 - 2 Setting Up a Statistical Ana...

9-2 Statistics 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 alinear regression. Then plot the data. Predict how many buildings of more than12 stories you would expect to find in a city of 30...

9-8 Statistics The data for statistical analyses is stored in lists. The TI . 80 has six list variables (L ã through L è ) that you can use in STAT calculations. Several types of statistical analyses are available. Follow these basic steps to perform statistical analyses. 1. Enter the statistical da...

Statistics 9-9 Pressing A accesses the STAT list editor and several instructions for use with lists (L ã through L è ). The instructions are discussed on page 9-13. EDIT CALC1: EDIT ... Displays list editor. 2: SORTA( Sorts list in ascending order. 3: SORTD( Sorts list in descending order. 4: CLRLIS...

9-10 Statistics The STAT list editor has two “contexts,” viewing and editing. The currentcontext determines the result of a key press. In both contexts, the full value ofthe highlighted element is displayed on the bottom line. In the viewing context, you can move quickly from one listelement to the ...

9-12 Statistics You can enter or edit an entire list by moving the cursor to a list name on the topline of the STAT list editor and then pressing ¸ . The bottom line displays L n =Ln × 1, if there is data already in the list. Type any expression that returns a list, and press ¸ . The new list is dis...

Statistics 9-13 Items 2 through 4 on the STAT EDIT menu  SORTA(, SORTD(, and CLRLIST  let 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. Notethat SORTA( and SORTD( are the same as SORTA( and SORTD( o...

9-14 Statistics 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. EDIT CALC1: 1-VAR STATS Calculates 1-variable statistics. 2: 2-VAR STATS Calcula...

Statistics 9-15 These calculations return statistical results based on the list(s) you reference. Ifyou reference a third list name as an argument for 2-VAR STATS or any of theregression models, the list is interpreted as the frequencies of occurrence forthe data pairs in the first two lists. 1-VAR ...

Statistics 9-17 The statistical variables are calculated as indicated below. Some are displayedwhen 1-VAR STATS or 2-VAR STATS are calculated. You can access thesevariables for use in expressions through the VARS STATISTICS... menus. If youedit a list, all statistical variables are cleared. Variable...

9-18 Statistics You can plot statistical data that you have entered in lists. The types of plotsavailable include scatter plots, x-y lines, box and whisker plots, and histograms.You can define up to three plots at a time. To plot statistical data: 1. Enter the statistical data as lists (page 9 - 9 a...

9-22 Statistics You can enter statistical data, calculate statistical results, and fit data to modelsfrom a program. Enter the statistical data directly into lists (Chapter 8) in theprogram. To calculate statistical results or fit data to a model from aprogram: 1. On a blank line in the program edit...

Statistics 9-23 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 definitionsare used. To define a statistical plot in a program: 1. Enter the data into list(s). On a blank line in the program ed...

9-24 Statistics To display a plot, use any of the Zoom instructions (Chapter4), or use the DISPGRAPH instruction (Chapter 10). Displaying a StatPlot from aProgram

Programming 10-1 This chapter describes specific programming instructions and explains how toenter and execute programs on the TI . 80. Getting Started: Rolling a Die ....................... 10 - 2 About TI - 80 Programs ............................. 10 - 4 Creating and Executing Programs .............

10-2 Programming 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 theyhad been entered from the keyboard. Write a simple program to simulate therolling of a single die. It should prompt for the number ...

Programming 10-5 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 beexecuted from the Home screen can be included in a program. A programcommand always begins with a colon (:). To create a new program: 1. ...

10-6 Programming The program editor also lets you edit an existing program. As you edit, you canenter commands just as you did when you created the 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 i...

Programming 10-11 The PRGM I/O (program input/output) instructions are accessed only from theprogram editor. They control input to and output from a program, allowing youto enter values and display answers during program execution. While theprogram editor is displayed, press K . The selected menu it...

10-14 Programming 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. To call one program from another, begin on a blank line in theprogram editor and do one of the following. ¦ Press K 6 to display...

Applications 11-1 This chapter contains application examples that incorporate the TI . 80 features described in the preceding chapters. Several of the examples use programs. Probability Experiments: Coins, Dice, and Spinners ... 11 - 2 The Unit Circle and Trigonometric Curves ............ 11 - 3 Pro...

Applications 11-3 You can use the parametric graphing feature of the TI . 80 to show the relationship between the unit circle and any trigonometric curve. Graph the unit circle and the sine curve to demonstrategraphically the relationship between them. Any function that can be plotted in function gr...

11-4 Applications This program uses the Newton-Raphson method to find the roots (zeros) of afunction numerically. Find the roots of ex ì 3X. This program uses the Newton-Raphson method to find a rootof Y1 based on an initial guess. The program prompts for the initial guess. One way to make this init...

Applications 11-5 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 differ...

11-6 Applications This program uses Simpson’s method to estimate the definite integral of afunction. Estimate the definite integral of ‰ 0 1.5 (6 ì 6x 5 )dx and graph the area of the integral. The program estimates the definite integral for Y1 using Simpson’s method. It prompts for the lower and upp...

11-8 Applications 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 alsodemonstrates a method for including menus in a program. PROGRAM:WINMEM:CLRHOME:DISP "WINDOW MEMORY":DISP "1:STORE WINDOW&#...

11-10 Applications You can use the parametric graphing feature of the TI . 80 to graph the inverse relation of any function by defining the function in X ã T and Y ã T and its inverse in X ä T and Y ä T . The function Y=.2X 3 ì 2X+6 can be expressed in parametric form as X T =T and Y T =.2T 3 ì 2T+6...

11-12 Applications The test functions of the TI . 80 can be used to build piecewise defined functions. Define and graph this piecewise defined function. f(x)= x ñ , for x ≤ 3 1.5x+1, for 3 < x < 5 6 ì x, for x ≥ 5 The TEST functions, which return 1 if true and 0 if false, can be used to build ...

11-14 Applications Examine the inequality . 4X ò ì 3X+5< . 2X+4 graphically. Use the TEST functions to explore the values of X where the inequality is true and where it is false. 1. Press 3 . Select DOT , SIMUL , and the default mode settings. Press 2 " , and turn off all stat plots. 2. Press...

Applications 11-15 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 definedby the polar equation r=a q . A polar equation r=f( q ) can be graphed by applying the conversion formulas, x=f( q ) cos( q ) and...

11-16 Applications 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 corr...

Memory Management 12-1 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 storeditems that you are no longer using. You can also reset the calculator, erasing alldata and programs. Checking Available Mem...

12-2 Memory Management The MEMORY CHECK RAM screen displays the total amount of availablememory and the amount of memory used by each variable type. This allows youto determine the amount of memory available for new items such as programsand the amount used by old items that you no longer need. To c...

Memory Management 12-3 You can delete the contents of any variable (real number, list, or Y= function) orprogram from memory to increase available memory. 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 th...

12-4 Memory Management Resetting the TI . 80 restores memory to the factory settings, including deleting the contents of all variables and programs and resetting all system variables tothe original settings. Because you can increase available memory by deletingindividual items, you should rarely nee...

Tables and Reference Information A-1 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 inprograms. It also includes other reference information that can help you. Table of TI - 80 Functions and Instructions...

A-2 Tables and Reference Information A function (F) returns a value or a list and can be used in expressions; aninstruction (I) initiates an action. Some, but not all, have arguments. † indicates that the instruction is available for copying only from the program editor. a À b º c Sets the display f...

Tables and Reference Information A-3 CONNECTED Sets connected linegraphing format. (I) † 3 á CONNECTED â 1 - 11 COS value Returns the cosine of value . (F) X 2 - 4 COS list Returns a list of thecosine for each list element. (F) X 2 - 4 COS ê value Returns the arccosine of value . (F) 2 R 2 - 4 COS ê...

A-4 Tables and Reference Information DISPGRAPH Displays the currentgraph. (I) † K I/O á DISPGRAPH â 10 - 13 Division: valueA à valueB Returns valueA divided by valueB . (F) e 2 - 4 Division: list à value Returns list elements divided by value . (F) e 2 - 4 Division: value à list Returns value divide...

Tables and Reference Information A-5 EXPREG Xlistname , Ylistname Fits Xlistname and Ylistname to the exponential model. (I) A CALC á EXPREG â 9 - 16 EXPREG Xlistname , Ylistname , freqlistname Fits Xlistname and Ylistname to the exponential modelwith frequency freqlistname . (I) A CALC á EXPREG â 9...

A-6 Tables and Reference Information FPART value Returns the fractional partof value . (F) I NUM á FPART â 2 - 10 FPART list Returns a list of thefractional parts for each list element. (F) I NUM á FPART â 2 - 10 value 8 FRAC Returns value in fraction form, according to thecurrent fraction displayfo...

Tables and Reference Information A-7 HORIZONTAL Y Draws a horizontal line atvalue Y . (I) 2 F DRAW á HORIZONTAL â 7 - 5 IF condition : commandA : commands If condition = 0 (false), skips commandA . (I) † K CTL á IF â 10 - 7 IF condition :THEN: commands :END Executes commands from THEN to END if cond...

A-8 Tables and Reference Information IPART value Returns the integer part of value . (F) I NUM á IPART â 2 - 10 IPART list Returns a list of theinteger part for each list element. (F) I NUM á IPART â 2 - 10 LBL label Assigns label to the command. (I) † K CTL á LBL â 10 - 10 Less Than: valueA < va...

Tables and Reference Information A-9 LNREG Xlistname , Ylistname Fits Xlistname and Ylistname to the logarithmic model. (I) A CALC á LNREG â 9 - 16 LNREG Xlistname , Ylistname , freqlistname Fits Xlistname and Ylistname to the logarithmic model withfrequency freqlistname . (I) A CALC á LNREG â 9 - 1...

A-10 Tables and Reference Information MIN( listA , listB ) Returns a list of thesmaller of each pair ofelements in listA and listB . (F) 2 = MATH á MIN( â 8 - 9 MIN( list , value ) or MIN( value , list ) Returns a list of thesmaller of each list element compared to value . (F) 2 = MATH á MIN( â 8 - ...

Tables and Reference Information A-11 Negation: ë value Returns the negative of value . (F) · 2 - 6 Negation: ë list Returns a list with each list element negated. (F) · 2 - 6 NORMAL Sets normal display mode. (I) † 3 á NORMAL â 1 - 10 Not Equal: valueA ƒ valueB Returns 1 if valueA ƒ valueB . Returns...

A-12 Tables and Reference Information PAUSE Suspends execution of theprogram until ¸ is pressed. (I) † K CTL á PAUSE â 10 - 9 Pi Returns the value of π rounded to 13 digits. (F) 2 T 2 - 6 PLOT n ( type , Xlist , Ylist ) Plots stat plot n (1 - 3) of type ( ¼ or ½ ) for Xlist and Ylist coordinate pair...

Tables and Reference Information A-13 PRGM_ programname Executes the program programname . (I) † K CTRL á PRGM_( â 10 - 10 PROD list Returns the product ofelements in list . (F) 2 = MATH á PROD â 8 - 10 P 8 Rx( R , q ) Returns the rectangularcoordinate x , given the polar coordinates R and q . (F) 2...

A-14 Tables and Reference Information PWRREG Xlistname , Ylistname Fits Xlistname and Ylistname to the power model. (I) A CALC á PWRREG â 9 - 16 PWRREG Xlistname , Ylistname , freqlistname Fits Xlistname and Ylistname to the power model with frequency freqlistname . (I) A CALC á PWRREG â 9 - 16 QUAD...

Tables and Reference Information A-15 REMAINDER( list , value ) Returns a list ofremainders from thedivision of each elementin list by value. I NUM á REMAINDER( â 2 - 11 REMAINDER( listA , listB ) Returns a list ofremainders from thedivision of each elementin listA by the each element in listB. I NU...

A-16 Tables and Reference Information R 8 Pr( Xlist , Ylist ) Returns a list of r coordinates, given the X coordinates in Xlist and the Y coordinates in Ylist . (F) 2 E á R 4 P q ( â 2 - 15 R 8 P q ( X , Y ) Returns the polarcoordinate q , given the rectangular coordinates X and Y . (F) 2 E á R 4 P ...

Tables and Reference Information A-17 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) 2 F DRAW á SHADE( â 7 - 9 SHADE_Y> func1 , func2 , . . . Sh...

A-18 Tables and Reference Information SORTD( listname ) Sorts the elements of listname in descending order. (I) 2 = OPS á SORTD( â 8 - 6 SORTD( keylistname , dependlist1 , dependlist2 , . . . ) Sorts the elements of keylistname in descending order with dependlist1 , dependlist2 . . . as dependent li...

Tables and Reference Information A-19 TAN list Returns a list of thetangent for each list element. (F) Y 2 - 4 TAN ê value Returns the arctangent of value . (F) 2 S 2 - 4 TAN ê list Returns a list of thearctangent for each list element. (F) 2 S 2 - 4 THEN See IF:THEN TRACE Displays a graph andenters...

A-20 Tables and Reference Information Menus begin in the upper left of the keyboard. Default values are shown. ( ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ) ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ( FUNC mode) Y1=Y2=Y3=Y4= ( PARAM mode) X ã T = Y ã T = X ä T = Y ä T = X å T = Y å T = (FUNC mode) WINDOW XMIN= ì 10 XMAX=10 XSCL=1 YMIN= ì 10 YMAX...

Tables and Reference Information A-21 2 " ÚÄÄÄÄÄÙ 2 " (in program editor) ÚÄÄÄÄÄÄÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄ¿ STAT PLOTS1:PLOT1 ... OFF ¼ L1 L2 Â 2:PLOT2 ... OFF ¼ L1 L2 Â 3:PLOT3 ... OFF ¼ L1 L2 Â 4:PLOTSOFF5:PLOTSON PLOTS1:PLOT1(2:PLOT2(3:PLOT3(4:PLOTSOFF5:PLOTSON TYPE1: ¼ 2: ½ 3: ¾ 4: ¿ MARK1: Â...

A-22 Tables and Reference Information 2 = ÚÄÄÁÄÄÄÄÄÄÄÄÄ¿ OPS1:SORTA(2:SORTD(3:DIM4:SEQ( MATH1:MIN(2:MAX(3:MEAN(4:MEDIAN(5:SUM6:PROD I ÚÁÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ MATH1:INT ÷ 2: 4 DEC 3 : 3 4: 3 ‡ 5 : X ‡ 6:NDERIV( NUM1:ROUND(2:IPART3:FPART4:INT5:MIN(6:MAX(7:REMAINDER( PRB1:RAND2:nPr3:nCr4:!5:RANDI...

Tables and Reference Information A-23 K ÚÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄ¿ K (in program editor) ÚÁÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿ EXEC1: name 2: name 3: name © EDIT1: name 2: name 3: name © NEW1:CREATE NEW CTL1:IF2:THEN3:ELSE4:FOR(5:END6:PAUSE7:LBL8:GOTO9:PRGM_0:RETURNA:STOP I/O1:INPUT2:DISP3:DISPGRAPH4:CLRHOME EXEC1: n...

A-24 Tables and Reference Information L ÚÄÙ VARS1:WINDOW ... 2:STATISTICS … 3:TABLE…4:SIMPFACTOR… L á WINDOW… â ÚÄÄÄÄÄÄÁÄÄÄÄÄ¿ L á TABLE… â ÚÄÄÄÄÄÄÙ X/Y1:XMIN2:XMAX3:XSCL4:YMIN5:YMAX6:YSCL7: @ X 8: @ Y 9:XFACT0:YFACT T1:TMIN2:TMAX3:TSTEP TABLE1:TBLMIN2: @ TBL L á SIMPFACTOR… â ÚÄÄÄÄÙ SIMPFACTOR1:FAC...

Tables and Reference Information A-25 2 ¯ ÚÄÙ MEMORY1:CHECK RAM…2:DELETE…3:RESET… 2 ¯ á CHECK RAM… â ÚÄÄÄÄÙ 2 ¯ á DELETE… â ÚÄÄÄÄÄÄÙ 2 ¯ á RESET… â ÚÄÄÄÄÄÄÙ MEM FREE 7014REAL 14LIST 0Y-VARS 80PRGM 14 DELETE: ú name memory name memory name memory © © ( names include defined programs, lists, Y= equati...

A-26 Tables and Reference Information The variables listed below are used by the TI - 80 in various ways. Some have restrictions on their use. 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 du...

Service and Warranty Information B-1 This appendix provides supplemental information that may be helpful as youuse the TI . 80. It includes procedures that may help you correct problems with the calculator. Battery Information ............................... B - 2 Accuracy Information .................

B-2 Service and Warranty Information The TI . 80 uses two CR2032 lithium 3-volt batteries. As you use the TI . 80, the battery voltage will gradually drop, and the display will dim. You can adjust the contrast to darkenthe display when this happens. If the display is dim andadjusting the contrast to...

Service and Warranty Information B-3 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 batterycompartment cover, push down slightly ...

B-4 Service and Warranty Information Slide the metal battery cover away from the battery. Thebattery pops up. Remove the old battery. Insert a new battery, positive side (+)up. Hold the new battery in place and slide the metal batterycover back into position over the battery. Changing theBatteries(C...

Service and Warranty Information B-5 Push the red switch all the way down to free the metal batterycover 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 theBatteries(Continued)

B-6 Service and Warranty Information Hold the new battery in place and slide the metal batterycover back into position over the battery. Push the red switch to its center position to lock the metalcovers and batteries into place. Note: The calculator will not turn on unless the red switch is in the ...

Service and Warranty Information B-7 Replace the plastic battery compartment cover. Turn thecalculator 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 t...

B-8 Service and Warranty Information To maximize accuracy, the TI . 80 carries more digits internally than it displays. Values in memory are stored using up to 13 digits with atwo-digit exponent. ¦ You can store values in the Window variables using up to10 digits (13 digits for XSCL , YSCL , and TST...

Service and Warranty Information B-9 Following is a table of functions and the range of input valuesfor each. Function Input Values SIN x , COS x , TAN x 0  | x | < 10 10 (degree) SIN - 1 x , COS - 1 x - 1  x  1 LN x , LOG x 10 - 100 < x < 10 100 e x - 10 100 < x  230.2585092993 10 x...

B-10 Service and Warranty Information If you have difficulty operating the calculator, the following suggestions mayhelp you to correct the problem. Follow these procedures if you have difficulties. 1. If you cannot see anything on the display, perhaps the display contrast needs adjusting. Press and...

Service and Warranty Information B-11 When the TI . 80 detects an error, it displays ERR: message and the error menu. The general procedure for correcting errors is described onpage 1 . 22. The error messages, their possible causes, and suggestions for correction are shown below. ARGUMENT A function...

B-12 Service and Warranty Information INCREMENT ¦ 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. INVALID You are attempting to reference a variable or...

Service and Warranty Information B-13 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. ¦...

B–14 Service and Warranty Information 99APXB2.DOC TI-80, Service & Waranty Bob Fedorisko Revised: 02/15/01 11:34 AM Printed: 02/15/01 11:36 AM Page 14 of 3 Support and Service Information Product Support Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands For general questions, co...

Service and Warranty Information B-1 5 8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/27/01 12:20 PM Printed: 02/27/01 12:25 PM Page 12 of 13 Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Electronic Product This Texas Instruments (“TI”) e...

B-1 6 Service and Warranty Information 8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/27/01 12:20 PM Printed: 02/27/01 12:25 PM Page 13 of 13 Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments electronic pr...

Index I-1 A a variable, 9 - 15 to 9 - 17, A - 26 a À b º c MODE , 1 - 9, 1 - 11, 3 - 4, A - 2 8 a À b º c , 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 - 1...

I-6 Index R (Cont.) Residuals, 9 - 6, 9 - 7 RETURN , 10 - 7, 10 - 10, A - 15 root x ‡ , 2 - 7, 2 - 8, A - 15, B - 9 ROUND( , 2 - 10, A - 15 Running programs, 10 - 5 R 8 Pr( , R 8 P q ( , 2 - 14, 2 - 15, A - 15, A - 16 S SCATTER plot, 9 - 18, 9 - 20 SCI MODE , 1 - 7, 1 - 9, 1 - 10, A - 16 Scientific ...

Index I-7 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 V Variables, x, 1 - 12, 1 - 13, A - 26 VARS menu, 1 - 19 VERTICAL , 7 - 3, 7 ...