Part I: I.1
Texas Instruments TI-82 Graphics Calculator
Getting started with the TI-82
I.1.1 Basics: Press the ON key to begin using your TI-82 calculator. If you need to adjust the display contrast, first press 2nd, then press and hold (the up arrow key) to lighten or (the down arrow key) to darken. As you press and hold or , an integer between 0 (lightest) and 9 (darkest) appears in the upper right corner of the display. When you have finished with the calculator, turn it off to conserve battery power by pressing 2nd and then OFF. Check the TI-82s settings by pressing MODE. If necessary, use the arrow keys to move the blinking cursor to a setting you want to change. Press ENTER to select a new setting. To start, select the options along the left side of the MODE menu as illustrated in Figure I.1: normal display, floating decimals, radian measure, function graphs, connected lines, sequential plotting, and full screen display. Details on alternative options will be given later in this guide. For now, leave the MODE menu by pressing CLEAR.

Figure I.1: MODE menu

Figure I.2: Home screen
I.1.2 Editing: One advantage of the TI-82 is that up to 8 lines are visible at one time, so you can see a long calculation. For example, type this sum (see Figure I.2): Then press ENTER to see the answer. Often we do not notice a mistake until we see how unreasonable an answer is. The TI-82 permits you to redisplay an entire calculation, edit it easily, then execute the corrected calculation. Suppose you had typed 56 as in Figure I.2 but had not yet pressed ENTER, when you realize that 34 should have been 74. Simply press (the left arrow key) as many times as necessary to move the blinking cursor left to 3, then type 7 to write over it. On the other hand, if 34 should have been 384, move the cursor back to 4, press 2nd INS (the cursor changes to a blinking underline) and then type 8 (inserts at the cursor position and the other characters are pushed to the right). If the 34 should have been 3 only, move the cursor to 4 and press DEL to delete it. Technology Tip: To move quickly to the beginning on an expression you are currently editing, press up arrow key); to jump to the end of that expression, press (the down arrow key). (the
Even if you had pressed ENTER, you may still edit the previous expression. Press 2nd and then ENTRY to recall the last expression that was entered. Now you can change it. In fact, the TI-82 retains many prior entries in a last entry storage area. Press 2nd ENTRY repeatedly until the previous line you want replaces the current line.
Graphing Technology Guide
Copyright by Houghton Mifflin Company. All rights reserved.
Technology Tip: When you need to evaluate a formula for different values of a variable, use the editing feature to simplify the process. For example, suppose you want to find the balance in an investment account if there is now $5000 in the account and interest is compounded annually at the rate of 8.5%. The formula for r nt the balance is P 1 , where P principal, r rate of interest (expressed as a decimal), n number n of times interest is compounded each year, and t number of years. In our example, this becomes 50001 .085) t. Here are the keystrokes for finding the balance after t 3, 5, and 10 years (results are shown in Figure I.3).

Here is a situation where this is especially useful. Suppose a person makes $5.85 per hour and you are asked to calculate earnings for a day, a week, and a year. Execute the given keystrokes to find the persons incomes during these periods (results are shown in Figure I.4.): Pay period 8-hour day 5-day week 52-week year Keystrokes 5.ENTER 5 ENTER 52 ENTER Balance $46.80 $234 $12,168
Figure I.4: ANS variable I.1.7 The MATH Menu: Operators and functions associated with a scientific calculator are available either immediately from the keys of the TI-82 or by the 2nd keys. You have direct key access to common arithmetic operations (x 2, 2nd , x -1, ^, 2nd ABS), trigonometric functions (SIN, COS, TAN) and their inverses ( 2nd SIN-1, 2nd COS-1, 2nd TAN-1 ), exponential and logarithmic functions (LOG, 2nd 10x , LN, 2nd e x ), and a famous constant (2nd ). A significant difference between the TI-82 graphing calculators and most scientific calculators is that the TI-82 requires the argument of a function after the function, as you would see a formula written in your textbook. For example, on the TI-82 you calculate 16 by pressing the keys 2nd 16 in that order. Here are keystrokes for basic mathematical operations. Try them for practice on your TI-82. Expression
Keystrokes 2nd (3 x 2 + 4 x 2) ENTER 2+3 x -1 ENTER 2nd ABS (-) 5 ENTER LOG 200 ENTER 2.34 2nd 10 x 5 ENTER
Display 5 2.2.301029996 234000

5 log 200 2.34

Additional mathematical operations and functions are available from the MATH menu. Press MATH to see the various options (Figure I.5). You will learn in your mathematics textbook how to apply many of them. As an example, calculate 7 by pressing MATH and then either 4 or ENTER; finally press 7 ENTER to see 1.912931183. To leave MATH menu and take no other action, press 2nd QUIT or just CLEAR.
Figure I.5: MATH menu The factorial of a nonnegative integer is the product of all the integers from 1 up to the given integer. The symbol for factorial is the exclamation point. So 4! (pronounced four factorial ) is 24. You will learn more about applications of factorials in your textbook, but for now use the TI-82 to calculate 4! The factorial command is located in the MATH menus PRB sub-menu. to compute 4!, press these keystrokes: 4 MATH 4 ENTER or 4 MATH ENTER ENTER. Note that you can select a sub-menu from the MATH menu by pressing either once than to press three times to get to the PRB sub-menu. or. It is easier to press

Functions and Graphs

I.2.1 Evaluating Functions: Suppose you received a monthly salary of $1975 plus a commission of 10% of sales. Let x your sales in dollars; then your wages W in dollars are given by the equation W 1975 .10x. If your January sales were $2230 and your February sales were $1865, what was your income during those months? Heres one method to use your TI-82 to perform this task. Press the Y= key at the top of the calculator to display the function editing screen (Figure I.6). You may enter as many as ten different functions for the TI-82 to use at one time. If there is already a function Y1, press or as many times as necessary to move the cursor to Y1 and then press CLEAR to delete whatever was there. Then enter the expression 1975 .10x by pressing these keys: 1975 +.10 X,T,. (The X,T, key lets you enter the variable X easily without having to use the ALPHA key.) Now press 2nd QUIT to return to the main calculations screen.

Figure I.11: Split screen: Y= below
Figure I.12: Graph of y x3 4x
The viewing window in Figure I.12 shows the part of the graph that extends horizontally from 10 to 10 and vertically from 10 to 10. Press WINDOW to see information about your viewing window. Figure I.13 shows the WINDOW screen that corresponds to the viewing window in Figure I.12. This is the standard viewing window for the TI-82.
Figure I.13: Standard WINDOW
The variables Xmin and Xmax are the minimum and maximum x-values of the viewing window. Ymin and Ymax are its minimum and maximum y-values. Xscl and Yscl set the spacing between tick marks on the axes. Use the arrow keys and to move up and down from one line to another in this list; pressing the ENTER key will move down the list. Press CLEAR to delete the current value and then enter a new value. You may also edit the entry as you would edit an expression. Remember that a minimum must be less than the corresponding maximum or the TI-82 will issue an error message. Also, remember to use the (-) key, not (which is subtraction), when you want to enter a negative value. Figures I.1213, I.14 15, and I.1617 show different WINDOW screens and the corresponding viewing window for each one.
Figure I.14: Square window
Figure I.15: Graph of y x3 4x
To initialize the viewing window quickly to the standard viewing window (Figure I.13), press ZOOM 6 [ZStandard]. To set the viewing window quickly to a square window (Figure I.14), press ZOOM 5 [ZSquare]. More information about square windows is presented later in Section I.2.4.
Figure I.16: Custom window
Figure I.17: Graph of y x3 4x
Sometimes you may wish to display grid points corresponding to tick marks on the axes. This and other graph format options may be changed by pressing WINDOW to display the FORMAT menu (Figure I.18). Use arrow keys to move the blinking cursor to GridOn; press ENTER and then GRAPH to redraw the graph. Figure I.19 shows the same graph as in Figure I.17 but with the grid turned on. In general, youll want the grid turned off, so do that now by pressing WINDOW , use the arrow keys to move the blinking cursor to GridOff, and press ENTER and CLEAR.
Figure I.18: WINDOW FORMAT menu
Figure I.19: Grid turned on for y x3 4x
I.2.3 Graphing Step and Piecewise-Defined Functions: The greatest integer function, written x, gives the greatest integer less than or equal to a number x. On the TI-82, the greatest integer function is called Int and is located under the NUM sub-menu of the MATH menu (see Figure I.5). So, calculate 6.by pressing MATH 4 6.78 ENTER. To graph y x, go into the Y= menu, move beside Y1, and press CLEAR MATH Figure I.20 shows this graph in a viewing window from 5 to 5 in both directions.

4 X,T, GRAPH.

Figure I.20: Connected graph of y x
Figure I.21: Dot graph of y x
The true graph of the greatest integer function is a step graph, like the one in Figure I.21. For the graph of y x, a segment should not be drawn between every pair of successive points. You can change from Connected line to Dot graph on the TI-82 by opening the MODE menu. Move the cursor down to the fifth line; select whichever graph type you require; press ENTER to put it into effect, and GRAPH to see the result. Make sure to change your TI-82 back to Connected line, because most of the functions that you will be graphing should be viewed this way.

The TI-82 can graph piecewise-defined functions by using the options in the TEST menu (Figure I.22) that is displayed by pressing 2nd TEST. Each TEST function returns the value 1 if the statement is true, and the value 0 if the statement is false.
Figure I.22: 2nd TEST menu x < 0 (using Dot graph) enter the following keystrokes x 0 Y= ( X,T, x 2 + 1) ( X,T, 2nd TEST ) + ( X,T, 1 ) ( X,T, 2nd TEST ) (Figure I.23). Then change the mode to Dot graph and press GRAPH to display the graph. Figure I.24 shows this graph in a viewing window from 5 to 5 in both directions. For example, to graph the function f x

xx 1, 1,

Figure I.23: Piecewise-defined function
Figure I.24: Piecewise-defined graph
I.2.4 Graphing a Circle: Here is a useful technique for graphs that are not functions, but that can be split into a top part and a bottom part, or into multiple parts. Suppose you wish to graph the circle whose equation is x2 y2 36. First solve for y and get an equation for the top semicircle, y 36 x2, and for the bottom semicircle, y 36 x2. Then graph the two semicircles simultaneously. Use the following keystrokes to draw the circles graph. Enter 36 x2 as Y1 and 36 x2 as Y2 (see Figure I.25) by pressing Y= CLEAR 2nd ( 36 X,T, x 2 ) ENTER CLEAR (-) 2nd ( 36 X,T, x 2 ). Then press GRAPH to draw them both.
Figure I.25: Two semicircles
Figure I.26: Circles graph standard WINDOW
If your range were set to the standard viewing window, your graph would look like Figure I.26. Now this does not look like a circle, because the units along the axes are not the same. This is where the square viewing window is important. Press ZOOM 5 and see a graph that appears more circular.

Figure I.27:

vertical horizontal 24 3
Figure I.28: A square circle
Technology Tip: Another way to get a square graph is to change the range variables so that the value of 2 Ymax - Ymin is approximately 3 times Xmax - Xmin. For example, see the WINDOW in Figure I.27 and the corresponding graph in Figure I.28. This method works because the dimensions of the TI-82s display are such that the ratio of vertical to horizontal is approximately 2. 3 The two semicircles in Figure I.28 do not connect because of an idiosyncrasy in the way the TI-82 plots a graph. Back when you entered 36 x2 as Y1 and 36 x2 as Y2, you could have entered -Y1 as Y2 and saved some keystrokes. Try this by going back to the Y= menu and pressing to move the cursor down to Y2. Then press CLEAR (-) 2nd Y-VARS 1 1. The graph should be just as it was before. I.2.5 TRACE: Graph y x3 4x from Section I.2.2 in the standard viewing window. (Remember to clear any other functions in the Y= screen.) Press any of the arrow keys , , , and see the cursor move from the center of the viewing window. The coordinates of the cursors location are displayed at the bottom of the screen, as in Figure I.29, in floating decimal format. This cursor is called a free-moving cursor because it can move from dot to dot anywhere in the graph window.

Figure I.29: Free-moving cursor Remove the free-moving cursor and its coordinates from the window by pressing GRAPH, CLEAR, or ENTER. Press an arrow key again and the free-moving cursor will reappear at the same point you left it.
Figure I.30: TRACE Press TRACE to enable the left and right arrow keys to move the cursor from point to point along the graph of the function. The cursor is no longer free-moving, but is now constrained to the function. The coordinates that are displayed belong to points on the functions graph, so the y-coordinate is the calculated value of the function at the corresponding x-coordinate (Figure I.30). Now plot a second function, y .25x, along with y x3 4x. Press Y=, move the cursor to the Y2 line, and enter.25x, then press GRAPH to see both functions.
Figure I.31: Two functions
Figure I.32: y x3 4x and y .25x
Note in Figure I.31 that the equal signs next to Y1 and Y2 are both highlighted. This means both functions will be graphed as shown in Figure I.32. In the Y= screen, move the cursor directly on top of the equal sign next to Y1 and press ENTER. This equal sign should no longer be highlighted (see Figure I.33). Now press GRAPH and see that only Y2 is plotted (Figure I.34).
Figure I.33: Y= screen with only Y2 active
Figure I.34: Graph of y .25x
Many different functions can be stored in the Y= list and any combination of them may be graphed simultaneously. You can make a function active or inactive for graphing by pressing ENTER on its equal sign to highlight (activate) or remove the highlight (deactivate). Now go back to the Y= screen and do what is needed in order to graph Y1 but not Y2. Now activate both functions so that both graphs are plotted. Press TRACE and the cursor appears first on the graph of y x3 4x because it is higher up in the Y= list. You know that the cursor is on this function, Y1, because of the numeral 1 that is displayed in the upper right corner of the screen (see Figure I.30). Press the up or down arrow key to move the cursor vertically to the graph of y .25x. Now the numeral 2 is displayed in the upper right corner of the screen. Next press the left and right arrow keys to trace along the graph of y .25x. When more than one function is plotted, you can move the trace cursor vertically from one graph to another with the and keys. Technology Tip: Trace along the graph of y .25x and press and hold either or. Eventually you will reach the left or right edge of the window. Keep pressing the arrow key and the TI-82 will allow you to continue the trace by panning the viewing window. Check the WINDOW screen to see that Xmin and Xmax are automatically updated. If you trace along the graph of y x3 4x, the cursor will eventually move above or below the viewing window. The cursors coordinates on the graph will still be displayed, though the cursor itself can no longer be seen. When you are tracing along a graph, press ENTER and the window will quickly pan over so that the cursors position on the function is centered in a new viewing window. This feature is especially helpful when you trace near or beyond the edge of the current viewing window. The TI-82s display has 95 horizontal columns of pixels and 63 vertical rows. So when you trace a curve across a graph window, you are actually moving from Xmin to Xmax in 94 equal jumps, each called x. You Xmax Xmin would calculate the size of each jump to be x . Sometimes you may want the jumps to 94 be friendly numbers like 0.1 or 0.25 so that, when you trace along the curve, the x-coordinates will be incremented by such a convenient amount. Just set your viewing window for a particular increment x by making Xmax = Xmin 94 x. For example, if you want Xmin 5 and x 0.3, set Xmax 0.3 23.2. Likewise, set Ymax = Ymin 62 y if you want the vertical increment to be some special y. To center your window around a particular point, h, k), and also have a certain x, set Xmin = h 47 x and Xmax h 47 x. Likewise, make Ymin k 31 y and Ymax k 31 y. For example, to center a window around the origin 0, 0), with both horizontal and vertical increments of 0.25, set the range so that Xmin 0.25 11.75, Xmax 0.25 11.75, Ymin 0.25 7.75, and Ymax 0.25 7.75.

10 1.85

Figure I.41: Before a zoom in
Figure I.42: After a zoom in
As you see in the ZOOM menu (Figure I.37), the TI-82 can Zoom In (press ZOOM 2) or Zoom Out (press ZOOM 3). Zoom out to see a larger view of the graph, centered at the cursor position. You can change the horizontal and vertical scale of the magnification by pressing ZOOM 4 [SetFactors.] (see figure I.43) and editing XFact and YFact, the horizontal and vertical magnification factors (see Figure I.44). The default zoom factor is 4 in both directions. It is not necessary for XFact and YFact to be equal. Sometimes, you may prefer to zoom in one direction only, so the other factor should be set to 1. As usual, press 2nd QUIT to leave the ZOOM menu.
Figure I.43: ZOOM MEMORY menu
Figure I.44: ZOOM MEMORY SetFactors.
Technology Tip: The TI-82 remembers the window it displayed before a zoom. So, if you should zoom in too much and lose the curve, press ZOOM 1 [ZPrevious] to go back to the window before. If you want to execute a series of zooms but then return to a particular window, press ZOOM 2 [ZoomSto] to store the current windows dimensions. Later, press ZOOM 3 [ZoomRcl] to recall the stored window. I.2.7 Value: Graph y x 3 4x in the standard viewing window (Figure I.12). The TI-82 can calculate the value of this function for any given x (between the Xmin and Xmax values). Press 2nd CALC to display the CALCULATE menu (see Figure I.45), then press 1 [value]. The graph of the function is displayed and you are prompted to enter a value for x. Press 1 ENTER. The x-value you entered and its corresponding y-value are shown at the bottom of the screen and the cursor is located at the point 1, 3 on the graph (see Figure I.46).
Figure I.45: CALCULATE menu
Figure I.46: Finding a value
Note that if you have more than one graph on the screen, the upper right corner of the TI-82 screen will display the numeral corresponding to the equation of the function in the Y= list whose value is being calculated. Press the up or down arrow key to move the cursor vertically between functions at the entered x-value. I.2.8 Relative Minimums and Maximums: Graph y x3 4x once again in the standard viewing window (Figure I.12). This function appears to have a relative minimum near x 1 and a relative maximum near x 1. You may zoom and trace to approximate these extreme values. First trace along the curve near the relative minimum. Notice by how much the x-values and y-values change as you move from point to point. Trace along the curve until the y-coordinate is as small as you can get it, so that you are as close as possible to the relative minimum, and zoom in (press ZOOM 2 ENTER or use a zoom box). Now trace again along the curve and, as you move from point to point, see that the coordinates change by smaller amounts than before. Keep zooming and tracing until you find the coordinates of the relative minimum point as accurately as you need them, approximately 1.15, 3.08.

Figure I.47: Finding a minimum I-16
Follow a similar procedure to find the relative maximum. Trace along the curve until the y-coordinate is as great as you can get it, so that you are as close as possible to the relative maximum, and zoom in. The relative maximum point on the graph of y x3 4x is approximately 1.15, 3.08. The TI-82 can automatically find the relative minimum and relative maximum points. Press 2nd CALC to display the CALCULATE menu (Figure I.45). Choose 3 [minimum] to calculate the minimum value of the function and 4 [maximum] for the maximum. You will be prompted to trace the cursor along the graph first to a point left of the minimum/maximum (press ENTER to set this lower bound). Then move to a point right of the minimum/maximum and set an upper bound and press ENTER. Note the two arrows at the top of the display marking the lower and upper bounds (as in Figure I.47). Next move the cursor along the graph between the two bounds and as close to the minimum/maximum as you can; this serves as a guess for the TI-82 to start its search. Good choices for the lower bound, upper bound, and guess can help the calculator work more efficiently and quickly. Press ENTER and the coordinates of the relative minimum/maximum point will be displayed (see Figure I.48).
Figure I.48: Relative minimum on y x3 4x Note that if you have more than one graph on the screen, the upper right corner of the TI-82 screen will display the numeral corresponding to the equation of the function in the Y= list whose minimum/maximum is being calculated. I.2.9 Inverse Functions: The TI-82 draws the inverse function of a one-to-one function. Graph y xas Y1 in the standard viewing window (see Figure I.49). Next, press 2nd DRAW to display the DRAW menu. Use to move down and then choose 8 to draw the inverse function (see Figure I.50). Press 2nd Y-VARS ENTER (see Figure I.51). These keystrokes instruct the TI-82 to draw the inverse function of Y1. The original function and its inverse function will be displayed (see Figure I.52). Note that the calculator must be in function mode in order to use DrawInv. To clear the graph of the inverse function, press 2nd DRAW 1 [ClrDraw].
Figure I.49: Graph of y xGraphing Technology Guide

Figure I.50: DRAW menu

Figure I.51: DrawInv
Figure I.52: Graph of y xand its inverse function
I.2.10 Tangent Lines: Once again, graph y xin the standard viewing window (see Figure I.49). The TI-82 can draw the tangent line to a graph of a function at a specified point. While on the home screen, press 2nd DRAW 5 [Tangent(] 2nd Y-VARS , 1 ) ENTER (see Figure I.53). These keystrokes instruct the TI-82 to draw the tangent line to the graph of Y1 at x 1. The graph of the original function and the tangent line to the graph at x 1 will be displayed (see Figure I.54). To clear the tangent line, press 2nd DRAW 1.

Figure I.53: Tangent

Figure I.54: Graph of y xand tangent line at x 1

Solving Equations and Inequalities
I.3.1 Intercepts and Intersections: Tracing and zooming are also used to locate an x-intercept of a graph, where a curve crosses the x-axis. For example, the graph of y x3 8x crosses the x-axis three times (see Figure I.55). After tracing over to the x-intercept point that is farthest to the left, zoom in (Figure I.56). Continue this process until you have located all three intercepts with as much accuracy as you need. The three x-intercepts of y x3 8x are approximately 2.828, 0, and 2.828.

10 2.18

Figure I.55: Graph of y I-18
Figure I.56: Near an x-intercept of y x3 8x TI-82 Graphics Calculator
Technology Tip: As you zoom in, you may also wish to change the spacing between tick marks on the x-axis so that the viewing window shows scale marks near the intercept point. Then the accuracy of your approximation will be such that the error is less than the distance between two tick marks. Change the x-scale on the TI-82 from the WINDOW menu. Move the cursor down to Xscl and enter an appropriate value. The x-intercept of a functions graph is a root of the equation f x 0. So press 2nd CALC to display the CALCULATE menu (Figure I.45) and choose 2 [root] to find a root of this function. Set a lower bound, upper bound, and guess as described in Section I.2.8. The TI-82 shows the coordinates of the point and indicates that it is a root (Figure I.57).
Figure I.57: A root of y x3 8x TRACE and ZOOM are especially important for locating the intersection points of two graphs, say the graphs of y x3 4x and y .25x. Trace along one of the graphs until you arrive close to an intersection point. Then press or to jump to the other graph. Notice that the x-coordinate does not change, but the y-coordinate is likely to be different (see Figures I.58 and I.59). When the two y-coordinates are as close as they can get, you have come as close as you now can to the point of intersection. so zoom in around the intersection point, then trace again until the two y-coordinates are as close as possible. Continue this process until you have located the point of intersection with as much accuracy as necessary. The points of intersection are approximately 2.062, 0.515, 0, 0, and 2.062, 0.515.

3.2 3.2

Figure I.58: Trace on y
Figure I.59: Trace on y .25x
You can also find the point of intersection of two graphs by pressing 2nd CALC 5 [intersect]. Trace with the cursor first along one graph near the intersection and press ENTER; then trace with the cursor along the other graph and press ENTER. Marks are placed on the graphs at these points. Finally, move the cursor near the point of intersection and press ENTER again. Coordinates of the intersection will be displayed at the bottom of the window. More will said about the intersect feature in Section I.3.3.

Next graph y tan x in the standard window first, then press ZOOM 7 [ZTrig] to change to a special window for trigonometric functions in which the Xscl is 1.5708 or 90 and the vertical range is from to 4. The TI-82 plots consecutive points and then connects them with a segment, so the graph is not exactly what you should expect. You may wish to change from Connected line to Dot graph (see Section I.2.3) when you plot the tangent function.

Scatter Plots

I.5.1 Entering Data: This table shows total prize money (in millions of dollars) awarded at the Indianapolis 500 race from 1995 to 2003. (Source: Indy Racing League) Year Prize (in millions) 1995 $8.$8.$8.$8.$9.$9.$9.$10.$10.15
Well now use the TI-82 to construct a scatter plot that represents these points and to find a linear model that approximates the given data. The TI-82 holds data in up to six lists. Before entering this new data, press STAT 4 [ClrList] 2nd L1, 2nd L2 , 2nd L3 , 2nd L4 , 2nd L5 , 2nd L6 ENTER to clear all data lists. This can also be done from within the list editor by highlighting each list title (L1, etc) and pressing CLEAR ENTER. Now press STAT 1 [Edit] to reach the list editor. Instead of entering the full year, let x 5 represent 1995, x 6 represent 1996, and so on. Here are the keystrokes for the first three years: 5 ENTER 6 ENTER 7 ENTER and so on, then press to move to the first element of the next list and press 8.06 ENTER 8.11 ENTER 8.61 ENTER and so on (see Figure I.68). Press 2nd QUIT when you have finished.
Figure I.68: Entering data points You may edit statistical data in the same way you edit expressions in the home screen. Move the cursor to any value you wish to change, then type the correction. To insert or delete data, move the cursor over the data point you wish to add or delete. Press 2nd INS and a new data point is created; press DEL and the data point is deleted. I.5.2 Plotting Data: Once all the data points have been entered, press 2nd STAT 1 to display the Plot1 PLOT screen. Press ENTER to turn Plot1 on, select the other options shown in figure I.69, and press GRAPH. (Make sure that you have cleared or turned off any functions in the Y= screen, or those functions will be graphed simultaneously.) Figure I.70 shows this plot in a window from 0 to 15 in both directions. You may now press TRACE to move from data point to data point.

Figure I.69: Plot1 menu

Figure I.70: Scatter plot
To draw the scatter plot in a window adjusted automatically to include all the data you entered, press ZOOM 9 [ZoomStat]. When you no longer want to see the scatter plot, press 2nd ENTER. The TI-82 still retains all the data you entered. I.5.3 Regression Line: The TI-82 calculates the slope and y-intercept for the line that best fits all the data. The TI-82 can calculate regression lines in two equivalent forms. After the data points have been entered, press STAT 5 [LinReg(ax + b)] ENTER to calculate a linear regression model with the slope named a and the y-intercept named b (Figure I.71). By pressing STAT 9 [LinReg(a + bx)] ENTER, the TI-82 produces a linear regression model with the roles of a and b reversed. The number r (between 1 and 1) is called the correlation coefficient and measures how well the linear regression equation fits the data. The closer r is to 1, the better the fit; the closer r is to 0, the worse the fit. STAT 1, move the cursor to OFF, and press PLOT

Figure I.76: Matrix B
Add the two matrices say A and B, create B (with the same dimensions as A) and then press MATRX 1 MATRX 2 ENTER. Subtraction is performed in a similar manner. Now set the dimensions of matrix 3 C to and enter the matrix: as C. For matrix multiplication of C by A, press 1
MATRX 3 MATRX 1 ENTER. If you tried to multiply A by C, your TI-82 would signal an error because the dimensions of the two matrices do not permit multiplication in this way. I.6.3 Row Operations: Here are the keystrokes necessary to perform elementary row operations on a matrix. Your textbook provides more careful explanation of the elementary row operations and their uses. To interchange the second and third rows of the matrix A that was defined in Figure I.75, press MATRX 8 [rowSwap ( ] MATRX 1 , 2 , 3 ) ENTER (see Figure I.77). The format of this command is rowSwap(matrix, row1, row 2). To add row 2 and row 3 and store the results in row 3, press MATRX ENTER. The format of this command is row+(matrix, row1, row2). 9 [row + ( ] MATRX 1 , 2 , 3 )
To multiply row 2 by 4 and store the results in row 2, thereby replacing row 2 with new values, press MATRX 0 [*row( ] (-) 4 , MATRX 1 , 2 ) ENTER. The format of this command *row(scalar, matrix, row ).
Figure I.77: Interchange rows 2 and 3
Figure I.78: Add 4 times row 2 to row 3
To multiply row 2 by 4 and add the results to row 3, thereby replacing row 3 with new values, press MATRX ALPHA A [*row + (] (-) 4 , MATRX 1 , 2 , 3 ) ENTER (see Figure I.78). The format of this command is *row+(scalar, matrix, row1, row2). Technology Tip: Note that your TI-82 does not store a matrix obtained as the result of any row operations. So when you need to perform several row operations in succession, it is a good idea to store the result of each one in a temporary place. You may wish to use matrix E to hold such intermediate results. For example, use elementary row operations to solve this system of linear equations:
x 2y 3z 9 x 3y 4. 2x 5y 5z 17
First enter this augmented matrix as A in your TI-82 :
9 4. Next store this matrix in 17
E (press MATRX 1 STO MATRX 5 ENTER) so you may keep the original in case you need to recall it.
Here are the row operations and their associated keystrokes. At each step, the result is stored in E and replaces the previous matrix E. The matrix in row-echelon form is shown in Figure I.79. Row Operation Add row 1 to row 2. Add 2 times row 1 to row 3. Add row 2 to row 3. Multiply row 3 by 1. 2 Keystrokes MATRX 9 MATRX 5 , 1 , 2 ) STO MATRX 5 ENTER MATRX ALPHA A (-) 2 , MATRX 5 , 1 , 3 ) STO MATRX 5 ENTER MATRX 9 MATRX 5 , 2 , 3 ) STO MATRX 5 ENTER MATRX 2 , MATRX 5 , 3 ) STO MATRX 5 ENTER
Figure I.79: Row-echelon form of matrix after row operations So, z 2, y 1, and x 1. I.6.4 Determinants and Inverses: Enter this square matrix as A: 1 determinant 1 2

You should find that the determinant is 2, as shown in Figure I.80. Because the determinant of the matrix is not zero, it has an inverse, A -1. Press MATRX 1 x -1 ENTER to calculate the inverse of matrix A, also shown in Figure I.80. x 2y 3z 9 Now lets solve a system of linear equations by matrix inversion. Once more, consider x 3y 4. 2x 5y 5z The coefficient matrix for this system is the matrix 0 , that was entered as matrix A in the 5 previous example.
, go to the home screen and press MATRX 5

3 0. To calculate its 5

1 [det] MATRX 1 ENTER.

Figure I.80: A and A -1

Figure I.81: Solution matrix
9 Now enter the matrix 4 as B. Then press MATRX 1 x -1 MATRX 2 ENTER to calculate the 17 solution matrix (Figure I.81). The solution is still x 1, y 1, and z 2.

Sequences

I.7.1 Iteration with ANS Key: The ANS feature permits you to perform iteration, the process of evaluating n1 n1 a function repeatedly. As an example, calculate for n 27. Then calculate for n the answer to the previous calculation. Continue to use each answer as n in the next calculation. Here are keystrokes to accomplish this iteration on TI-82 calculator (see the results in Figure I.82). Notice that when you use ANS in place of n in a formula, it is sufficient to press ENTER to continue an iteration. Iteration 5 Keystrokes 27 ENTER ( 2nd ANS 1 ) 3 ENTER ENTER ENTER ENTER Display 27 8.666666667 2.555555556.5185185185 -.1604938272
Figure I.82: Iteration Press ENTER several more times and see what happens with this iteration. You may wish to try it again with a different starting value. I.7.2 Terms of Sequences: Another way to display the terms of a sequence is to enter the sequence and the number of terms you want listed. For example, to find the first five terms of the sequence un n 4, press 2nd LIST 5 [seq( ] (-) ALPHA N + 4, ALPHA N , 1 , 5 , 1 ) ENTER (see Figure I.83). The format of this command is seq(expression, variable, begin, end, increment ).
Figure I.83: Terms of sequence un n 4 I.7.3 Arithmetic and Geometric Sequences: Use iteration with the ANS variable to determine the nth term of a sequence. For example, find the 18th term of an arithmetic sequence whose first term is 7 and whose common difference is 4. Enter the first term 7, then start the progression with the recursion formula, 2nd ANS4 ENTER. This yields the 2nd term, so press ENTER sixteen more times to find the 18th term, 75. For a geometric sequence whose common ration is 4, start the progression with 2nd ANS 4 ENTER. You can also define the sequence recursively with the TI-82 by selecting Seq in the MODE menu (see Figure I.1). Once again, lets find the 18th term of an arithmetic sequence whose first term is 7 and whose common difference is 4. Press Mode ENTER 2nd QUIT. Then press Y= to edit either the TI-82s two sequences, Un and Vn. Make un unby pressing 2nd Un -1 + 4. Now make uby pressing WINDOW and setting UnStart = 7 and nStart = 1 (because the first term is u1 where n 1). Press 2nd QUIT to leave this menu and return to the home screen. To find the 18th term of this sequence, calculate u18 by pressing 2nd Y-VARS ( 18 ) ENTER (see Figure I.84).

Figure I.96: List editor

Figure I.97: Mean and median
You can also find the mean and median of the above data by finding the 1-Var Stats (one-variable statistics) of the data. Using the data you entered in Figure I.96, press STAT 1 2nd L1 ENTER. You should obtain a list of several different statistical values. The first line represents the mean of the data which is approximately 75F (see Figure I.98). The second line is the sum of the data, the third line is the sum of the squares of the data, the fourth line is the sample standard deviation of the data, the fifth line is the population standard deviation of the data, the sixth line is the number of data values, the seventh line is the minimum value of the data, the eighth value is the first quartile of the data, and the ninth line is the median of the data which is 76.5F (see Figure I.99). The tenth line is the third quartile of the data and the eleventh line is the maximum value of the data.
Figure I.98: 1-Var Stats You can scroll through the list of statistical values by pressing
Figure I.99: 1-Var Stats or.

I.10 Programming

I.10.1 Entering a Program: The TI-82 is a programmable calculator that can store sequences of commands for later replay. Press PRGM to access the programming menu. The TI-82 has space for many programs, each called by a title you give it. The title should be descriptive and can be eight characters, letters, or numerals long (but the first character must be a letter). In the program, each line begins with a colon : supplied automatically by the calculator. Any command you could enter directly in the TI-82s home screen can be entered as a line in a program. There are also special programming commands. You may interrupt programming input at any stage by pressing 2nd QUIT. To return later for more editing, press PRGM , move the cursor down to the programs name, and press ENTER. You may remove a program from memory by pressing 2nd MEM 2 [Delete] 6 [Prgm]. Then move the cursor to the programs name and press ENTER to delete the entire program. I.10.2 Executing a Program: To execute a program you entered, press PRGM and then the number or letter it was named. If you have forgotten its name, use the arrow keys to move through the program listing to find its description. Then press ENTER to select the program and enter again to execute it. If you need to interrupt a program during execution, press ON. The instruction manual for your TI-82 gives detailed information about programming. Refer to it to learn more about programming and how to use other features of your calculator.

Getting Started

with the

TI-82 STATS

Important information
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2003 Texas Instruments Incorporated

Contents

About the TI-82 STATS...1 About this book...2 TI-82 STATS keys...3 Turning the TI-82 STATS on and off..4 Home screen...5 y and keys...7 and y 5...8 Entering an expression..9 TI-82 STATS menus..10 Editing and deleting...13 Using and ....15 Using parentheses...17 Storing a value...19 Graphing a function...21 Changing mode settings...23 Setting the graphing window..26 Using q...28 Building a table....29 Using the CATALOG...31 Performing simple calculations..32 Using the equation solver..35 Entering data into lists...37 Plotting data...39 iii
Calculating a linear regression...43 Calculating statistical variables..44 Using the MATRIX Editor..45 Error messages...49 Resetting defaults...50 Connecting to a computer...51 Quick reference....51 Texas Instruments (TI) Support and Service..53 Battery precautions...54

About the TI-82 STATS

The TI-82 STATS includes these features: Graphing - store, graph, and analyze up to 10 functions, up to 6 parametric functions, up to 6 polar functions, and up to three sequences. Sequences - generate sequences and graph them over time. Tables - create function evaluation tables to analyze many functions simultaneously. Matrices - enter and save up to 10 matrices and perform standard matrix operations on them. Lists - enter and save as many lists as memory allows for use in statistical analyses. Statistics - perform one- and two-variable, list-based statistical analyses, including logistic and sine regression analysis; plot the data as a histogram, xyLine, scatter plot, modified or regular box-and-whisker plot, or normal probability plot.
The CD included with your TI-82 STATS package also includes an electronic guidebook, which is a complete reference manual for the TI-82 STATS. If the CD is not available, you can download a copy of the electronic guidebook from the Texas Instruments web page at education.ti.com/guides

About this book

This Getting Started Guide was designed for: students who are using a graphing calculator for the first time. student who are using the TI-82 STATS for the first time. students who need a quick review of procedures for common operations on the TI-82 STATS.

This book gives a quick overview of each topic, along with keystroke instructions for easy examples. All examples assume that the TI-82 STATS is using default settings. For complete information on any topic, see the electronic guidebook on the CD that came with your TI-82 STATS. symbol at the top of the page in this guide. Look for the These notes direct you to the chapter in the Guidebook that provides complete details about the topic.

TI-82 STATS keys

y Provides access to the function or character shown above each key in green. Provides access to the characters shown above each key in orange.
}~| Let you move the cursor in four directions.
Clears (erases) the entry line or deletes an entry and answer on the home screen. Evaluates an expression, executes an instruction, or selects a menu item.
Turns on the TI-82 STATS.
Turning the TI-82 STATS on and off
To turn on the TI-82 STATS, press. The key is located at the lower left corner of the TI-82 STATS.
For more details, see Guidebook Chapter 1.
To turn off the TI-82 STATS, press the y key followed by the key. OFF is the second function of. When you turn off the TI-82 STATS, all settings and memory contents are retained. The next time you turn on the TI-82 STATS, the home screen displays as it was when you last used it.

Automatic Power Down

To prolong the life of the batteries, Automatic Power Down (APD) turns off the TI-82 STATS automatically after about five minutes without any activity. The next time you turn on the calculator, it is exactly as you left it.

Home screen

When you turn on your TI-82 STATS the first time, you should see this screen:
If you cannot read the text on the screen, press the y key and then press and hold or }. Pressing lightens the screen and } darkens the screen. To clear this text from your screen, press twice. You should now see the home screen, a blank screen with a flashing cursor. The home screen is where you enter problems and see results.
If you pressed above and you still do not see a blank home screen, press the y key followed by the z key (to select QUIT).

Home screen (continued)

Example:
Add 2 + 3 on the home screen.

Press Result

Entry line Answer line
Note: Results are displayed on the next line (the answer line), not on the entry line.

Example: Multiply 5 x 4.

y and keys
Most keys on the TI-82 STATS can perform two or more functions. To use a function printed on a key, press the key. To use a function printed above a key in green or orange, you must first press the y key or the key.

Second functions are printed above the keys in green (the same color as the y key). Some secondary functions enter a function or a symbol on the home screen (sin-1 or , for example). Others display menus or editors. To view the ANGLE menu, for example, look for ANGLE (printed in green) above the key near the top of the TI-82 STATS keyboard. Press the y key (and then release it) and then press. In this book and in the TI-82 STATS Guidebook, this key combination is indicated by y ;, not y. When you see these key combinations, press each key separately, not at the same time.
Note: The flashing cursor changes to when you press the y key. If you press the y key accidentally, you can undo the action by pressing y a second time.
The key lets you enter the alphabetic characters and some special symbols. To enter T, for example, press (and then release it) and then press. In this book and in the TI-82 STATS Guidebook, this key combination is indicated by [ T ]. If you have several alphabetic characters to enter, press y 7 to avoid having to press the key multiple times. This locks the alpha key in the On position until you press a second time to unlock it.
Note: The flashing cursor changes to when you press the key. If you press the key accidentally, you can undo the action by pressing a second time.

and y 5

The key erases the home screen. This key is located just below the four blue arrow keys at the upper right corner of the TI-82 STATS keyboard. If you press during an entry, it clears the entry line. If you press when the cursor is on a blank line, it clears everything on the home screen. Although it does not affect the calculation, it is frequently helpful to clear the previous work from the home screen before you begin a new problem. As you work through this guide, we recommend that you press each time you begin a new Example. This removes the previous example from the home screen and ensures that the screen you see matches the one shown in the example.
If you accidentally press a menu key, pressing will sometimes return you to the home screen, but in most cases you must press y 5 to leave the menu and return to the home screen.

Entering an expression

An expression consists of numbers, variables, operators, functions, and their arguments that evaluate to a single answer. 2X + 2 is an expression. Type the expression, and then press to evaluate it. To enter a function or instruction on the entry line, you can: Press its key, if available. For example, press. or Select it from the CATALOG. For example, press y N, press to move down to log(, and press to select log(. or Select it from a menu, if available. For example, to find the round function, press , press ~ to select NUM, then select 2:round(. Enter and evaluate the expression p Q 2.

TI-82 STATS menus

Many functions and instructions are entered on the home screen by selecting from a menu. To select an item from the displayed menu:
Press the number or letter shown at the left of that item. or Use the cursor arrow keys, or }, to highlight the item, and then press.
Some menus close automatically when you make a selection, but if the menu remains open, press y 5 to exit. Do not press to exit, since this will sometimes delete your selection. Example: Enter
27 on the home screen entry line.

Result

Menus containing an arrow next to the final item continue on a second page.
TI-82 STATS menus (continued)
Example: Change the FORMAT menu setting to display grid points on the graph.
Turn off the display of grid points.
Note: Press y 5 or to close the FORMAT menu and return to the home screen. 11
Summary of menus on the TI-82 STATS

Press To display

LINK menu to communicate with another calculator. MEMORY menu to check available memory and manage existing memory. MATH menu to select a math operation. VARS menu to select variable names to paste to the home screen. STAT PLOTS menu to define statistical plots. CATALOG menu to select from a complete, alphabetic list of all TI-82 STATS built-in functions and instructions. FORMAT menu to define a graphs appearance. MATRIX menu to define, view, and edit matrices. DRAW menu to select tools for drawing on graphs. DISTRIBUTIONS menu to select distribution functions to paste to the home screen or editor screens. TEST menu to select relational operators (=, , {, |, etc.) and Boolean operators (and, or, xor, not) to paste to the home screen.

y. y>

Editing and deleting
You can change any expression or entry using the backspace | key, the delete { key, or the insert y 6 key. You can make a change before or after you press. Enter the expression 52 + 1, and then change the expression to 52 + 5.

Enter the expression 52 + 1, and then change the expression to 52 - 5.
Editing and deleting (continued)
Change the example above to 52 + 2 - 5 using y [ to recall the expression and y 6 to insert + 2 into the expression.

Using and

Many calculators (including the TI-82 STATS) make a distinction between the symbols for subtraction and negation. Use to enter subtraction operations. Use to enter a negative number in an operation, in an expression, or on a setup screen.

Subtract 10 from 25.

Add 10 to L25.

Using and (continued)

Example: Subtract L10 from 25.
Note: Notice that the TI-82 STATS displays a slightly different symbol for negation and subtraction to make it easier for you to distinguish between the two. The negative symbol is raised and slightly shorter.

Using parentheses

Since all calculations inside parentheses are completed first, it is sometimes important to place a portion of an expression inside parentheses.
For more details, see Guidebook Chapter 3.
Multiply 4*1+2; then multiply 4*(1+2).
Note: The closing parenthesis is optional. The operation will be completed if you omit it. The exception to this rule occurs when there is another operation following the parenthetical operation. In this case, you must include the closing parenthesis.
Using parentheses (continued)
Example: Divide 1/2 by 2/3.

Calculate 16 ^ 2.

Calculate (L3)2.
Note: Try each of these examples without the parentheses and see what happens!

Storing a value

Values are stored to and recalled from memory using variable names.
Store 25 to variable A and multiply A by 2.

2 [A]

[A] 2
Storing a value (continued)
Example: Find the value of 2X3 - 5X2 - 7X + 10 when X = M0.5.

(stores L.5 to X)

You can remove a value stored to a variable using the DELVAR function or by storing 0 to the variable. Example: Delete the value (L.5) stored to X above by storing 0.

Graphing a function

o Displays the Y= Editor, where you can enter one or more functions or expressions to graph.
s Displays the graph you have defined.
p Lets you set the viewing window to produce the best display of your graph.
Lets you enter one of four symbols: X (if you are in Function mode), T (in Parametric mode), q (in Polar mode), or n (in Sequence mode).
q Lets you quickly adjust the window to a predefined setting.
r Lets you move the cursor along the graphed function using | and ~.
Graphing a function (continued)

To graph a function, you must: 1. Display the Y= Editor. 2. Enter the function. 3. Display the graph.
Note: If you previously changed graph type in the mode settings, you must change the type back to Func (the default setting) before you graph.
Example: Graph the function Y = X 2 + 1.
If Y1 is not blank, see Note.
Note: If Y1 is not empty, press. If there are additional entries in the Y= Editor, press until all are clear.

Changing mode settings

The mode settings determine how entries are interpreted and how answers are displayed on the TI-82 STATS. Example:
Change the mode setting for decimals from Float to 3 decimal places.

123456

Note: You must press to change a mode setting. If you highlight the setting and then exit the mode menu without pressing , the setting will not be changed.
Changing mode settings (continued)
The mode menu includes the following settings:
Setting Numeric notation Choices
Normal: for example, 12345.67 Sci (scientific): for example, 1.2345674 Eng (engineering): for example, 12.345673 Float: lets the number of decimal places change
based on the result (up to 10 digits)

Decimal

0 - 9: sets the number of decimal places to a
value (0 - 9) that you specify Angle measure Type of graph
Radian: interprets angle values as radians Degree: interprets angle values as degrees Func (functional): plots functions, where Y is a

function of X

Par (parametric): plots relations, where X and Y

are functions of T

Pol (polar): plots functions, where r is a function
Seq (sequence): plots sequences

Plot type

Connected: draws a line connecting each point
calculated for the selected functions
Dot: plots only the calculated points of the
selected functions Sequential or simultaneous graphing Real or complex mode Screen display
Sequential: draws graphs one at a time Simul (simultaneous): draws all selected graphs at

the same time

Real: displays real numbers, such as 1, 1/2, 3 a+b (rectangular complex): displays as 3+2 re^q (polar complex): displays as re^q Full: displays full screen Horiz: displays a horizontal split screen G-T: displays a vertical split screen (graph & table)
The importance of mode settings
Example: Multiply 2/3 Q 2.
Your first reaction to this example is that the calculator has produced a wrong answer. But you have set it to round to 0 decimal places (the nearest whole number), so for this setting the answer is correct. If you set rounding (decimals displayed) to 0 and then forget to reset it for later calculations, you may be surprised by some of your answers! With mode set to the default setting of Float, the result will be:

Setting the graphing window
To obtain the best view of the graph, you may need to change the boundaries of the window. To display the WINDOW Editor, press p.

Ymax Xmin Xscl

Xmax Ymin Yscl
Window variables (shown in WINDOW Editor)
Corresponding viewing window (shown on Graph window)
The Xmin, Xmax, Ymin, and Ymax variables represent the boundaries of the viewing window. Xmin: the minimum value of X to be displayed. Xmax: the maximum value of X to be displayed. Ymin: the minimum value of Y to be displayed. Ymax: the maximum value of Y to be displayed. Xscl (X scale): the distance between the tick marks on the X axis. Yscl (Y scale): the distance between the tick marks on the Y axis. Xres: pixel resolutionnot usually changed except by advanced users. To change the values: 1. Move the cursor to highlight the value you want to change. 2. Do one of the following: Type a value or an expression. The old value is erased when you begin typing. or Press to clear the old value; then type the new one. 3. Press , , or }. 26
Setting the graphing window (continued)
Note: Values are stored as you type them; you do not need to press. Pressing simply moves the cursor to the next window variable.
4. After you have made all changes, press y 5 to close the WINDOW Editor (or s to display the graph). Example: Change the window settings to display a maximum X value of 25, a minimum X value of L25, a maximum Y value of 50, and a minimum Y value of L50.

2525 5050

Using q
The TI-82 STATS has ten predefined window settings that let you quickly adjust the graph window to a predetermined level of magnification. To display this menu, press q.
Selection 1: ZBox Result Lets you draw a box (using the cursor pad) to define the viewing window. After you position the cursor and press , magnifies the graph around the cursor. After you position the cursor and press , displays more of the graph. Sets the change in X and Y to increments of.1 when you use r. Adjusts the viewing window so that X and Y dimensions are equal. Sets the standard (default) window variables. Sets the built-in trigonometry window variables. After you position the cursor and press , sets the change in X and Y to whole number increments. Sets the values for currently defined statistical lists. Fits Ymin and Ymax between Xmin and Xmax.

2: Zoom In

3: Zoom Out

4: ZDecimal

5: ZSquare

6: ZStandard 7: ZTrig

8: ZInteger

9: ZoomStat

0: ZoomFit

Building a table

Tables are useful tools for comparing values for a function at multiple points.
For more details, see Guidebook Chapter 7.
Build a table to evaluate the function Y = X3 N 2X at each integer between L10 and 10.
(sets function graphing mode)
Building a table (continued)
(sets TblStart; default settings shown for the other fields are appropriate)
Note: Press repeatedly to see the changes in X and Y.

Clearing the Y= Editor

Before proceeding with the remaining examples in this guide, clear the Y= Editor.

Using the CATALOG

The CATALOG is an alphabetic list of all functions and instructions on the TI-82 STATS. Some of these items are also available on keys and menus. To select from the CATALOG: 1. Position the cursor where you want to insert the item. 2. Press y N. 3. Press or } to move the 4 indicator to the function or instruction. (You can move quickly down the list by typing the first letter of the item you need. You do not need to press. The CATALOG defaults to Alpha-lock mode.) 4. Press. Your selection is pasted on the home screen.
For more details, see Guidebook Chapter 15.
Notes: Items are listed in alphabetical order. Those that do not start with a letter (+, , , p, and so on) are at the end of the list. You can also paste from the CATALOG to an editor, such as the Y= Editor.
Example: Enter the rand function on the home screen.

y N [R]

The indicates that Alpha-lock is on.
Performing simple calculations
Changing a decimal to a fraction
Example: Add 1/2 + 1/4 and change your answer to a fraction.
Note: You can perform an operation using the last answer without entering the value again. When you do this, (as you did in the step 2 above), the TI-82 STATS enters Ans on the screen.
Finding the least common multiple
Example: Find the least common multiple of 15 and 24.
Performing simple calculations (continued)

Finding the square root

Example: Find the square root of 256.

yC256

Finding the factorial of numbers
Example: Compute the factorial of 5 and 30.

30~~~4

Scientific notation
Solving trigonometric functions
Example: Find the sine of an angle of 72.

72 y;

Note: If you are solving multiple problems using angles, be sure that mode is set to Degree. If you are in Radian mode and do not wish to change the mode, you can use y ; (as you did in this example) to add the degree symbol to the calculation and override the Radian mode setting.

Adding Complex Numbers

Example: Add (3+5) + (2-3).

35yV 23yV

Note: The character is the second function of (the decimal key).
Using the equation solver
You can use the TI-82 STATS equation solver to solve for a variable in an equation. Find the roots for the equation X2 - 13X - 48 = 0.
Note: If you do not see eqn:0= as shown above, press } (the up arrow), and then press to erase the existing equation.
Using the equation solver (continued)
The two roots are M3 and 16. Since you did not enter a guess, the TI-82 STATS used 0 (the default guess) and first returned the answer nearest 0. To find other roots, you must enter another guess. In this example, you entered 100.

Entering data into lists

You can enter data into lists using either of two methods: Using braces and on the home screen or Using the statistical list editor.
For more details, see Guidebook Chapter 11 and Chapter 12.

Using

Example: Store 1, 2, 3, and 4 to list 1 (L1).
Entering data into lists (continued)
Using the statistical list editor
Example: Store 5, 6, 7, and 8 to list 2 (L2).
(if L2 already contains data)
(displays the contents of the list on the home screen)

Plotting data

When you have statistical data stored in lists, you can display the data you have collected in a scatter plot, xyLine, histogram, box plot, or normal probability plot. You will need to: 1. Determine which lists contain your data. 2. Tell the calculator which lists of data you want to plot and define the plot. 3. Display the plot.
For more details, see Guidebook Chapter 12.
Determine which lists contain your data
Note: In some cases, you may have several lists stored and you may have to press ~ several times to find the correct lists.

Plotting data (continued)
Tell the calculator which lists you want to plot
(turns plots off if any plots are on)

(turns Plot1 on)

(enters L1 as the Xlist)

(enters L2 as the Ylist)

(selects + as the plotting mark)
Note: This step is optional and is not necessary unless there is a previous entry in the Y= Editor. If there are additional entries in the Y= Editor, press until all are clear.

Display the plot

(selects ZoomStat)
Note: If you would like to add the regression line to a scatter plot, follow the instructions on page 43, adding Y1 to the end of the instruction: LinReg(ax+b) L1, L2, Y1. (Press ~ to add Y1.) Press s to see the regression line.
Calculating a linear regression
If you wish to calculate the linear regression for data, you can do so using the LinReg instruction from the CALC menu. Example: Calculate the linear regression for the data entered in L1 and L2 (on pages 37 and 38).
Note: The information on the last screen means that the points in L1 and L2 [(1,5) (2,6) (3,7) (4,8)] all lie on the line Y = X + 4.
Calculating statistical variables
The TI-82 STATS lets you easily calculate one-variable or twovariable statistics for data that you have entered into lists.
Using the data that you entered into L1 on page 37, calculate one-variable statistics.

Using the MATRIX Editor

Creating a new matrix
For more details, see Guidebook Chapter 10.
Note: When you press , the cursor automatically highlights the next cell so that you can continue entering or editing values. To enter a new value, you can start typing without pressing , but you must press to edit an existing value.
Using the MATRIX Editor (continued)
Using matrices to solve systems of equations
You can solve several equations simultaneously by entering their coefficients into a matrix and then using the rref (reduced rowechelon form) function. For example, in the equations below, enter 3, 3, and 24 (for 3X, 3Y, and 24) in the first row, and 2, 1, 13 (for 2X, 1Y, and 13) in the second row.

Solve and

3X + 3Y = 24 2X + Y = 13
You can interpret the resulting matrix as: [5] represents 1X + 0Y = 5 or X = 5 [3] represents 0X + 1Y = 3 or Y = 3 The solution to this system of equations is X = 5, Y = 3.

Error messages

Occasionally, when you enter a function or instruction or attempt to display a graph, the TI-82 STATS will return an error message.
For more details, see Guidebook Appendix B.
Enter the least common multiple function lcm( followed by only one number.
If you select 1:Quit, you return to the home screen with the cursor on a new entry line. If you select 2:Goto, you return to the original entry line; the cursor is flashing at the location of the error. You can now correct the error and continue. You can find a complete list of error conditions with explanations in the Guidebook, Appendix B: General Information.

Resetting defaults

If you are getting unexpected results, or if another person has used your calculator and may have changed the settings, you should consider resetting defaults on the TI-82 STATS.
For more details, see Guidebook Chapter 18.

WARNING:

If you reset All Memory in step 3 above, you will delete stored variables, lists, applications, and programs. Be sure you have backed up any essential data before you select this option.

Connecting to a computer

You can connect your TI-82 STATS to a personal computer using TI Connect software and a TI Connectivity cable. The software is included on the CD in the TI-82 STATS package. When you connect to the TI Connect software, the TI-82 STATS calculator will be identified by TI Connect as a TI-83 calculator. Everything else should function as expected. For more information, consult the TI Connect Help.

Quick reference

Press y} y y~ y|
Darken the screen Lighten the screen Move the cursor to the end of an expression Move the cursor to the beginning of an expression Page down to the next screen (on menus) Page up to the next screen (on menus) Place your last entry on the current entry line on the home screen Place Ans (a reference to your last answer) on the current entry line on the home screen, allowing you to use the answer in the next calculation Delete the character under the cursor Insert additional characters at the cursor Move the cursor from line to line Move the cursor from character to character within a line Clear the current line. (If the cursor is on a blank line, clears everything on the home screen.)

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Texas Instruments (TI) Support and Service

For general information

For more information about TI products and services, contact TI by e-mail or visit the TI Internet address. E-mail inquiries: Home Page: ticares@ti.com education.ti.com
Service and warranty information
For information about the length and terms of the warranty or about product service, refer to the warranty statement enclosed with this product or contact your local Texas Instruments retailer/distributor.

Battery precautions

Take these precautions when replacing batteries. Do not leave batteries within the reach of children. Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. Do not mix rechargeable and non-rechargeable batteries. Install batteries according to polarity (+ and - ) diagrams. Do not place non-rechargeable batteries in a battery recharger. Properly dispose of used batteries immediately. Do not incinerate or dismantle batteries.