Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200

CHAPTER 1 Note 1A Reentry Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200 If you want to do further calculation on a result you ve just found, and that result is the first number in the expression you now want to evaluate, you can simply continue the expression. For example, if you ve just calculated a result of 3.647483, and you want to multiply by 16, press 1 6 ENTER. If, on the other hand, you want to take the square root of that number, press 2nd [ ] 2nd [ANS], close the parentheses, and then press ENTER to calculate 3.6474 83. After you ve pressed ENTER the expression just calculated remains in the entry line and now has a black background. You can edit the expression by using the left or right arrow keys to move across it. Delete characters by pressing [DEL]; insert or replace characters by pressing 2nd [INS] (the cursor will change between the insert cursor, a blinking black line, and the replacement cursor, a blinking black square experiment to see how these work). You can recall any previous entry or result to the entry line by arrowing up to it and pressing ENTER. You can also recall the previous entry to the entry line by pressing 2nd [ENTRY]. Pressing 2nd [ENTRY] repeatedly allows you to go back, one by one, to previous entries. Alternatively you can go to a previous result by pressing 2nd [ANS]. The 1 in the ans(1) that appears in the entry line indicates that the immediately previous answer will be recalled. If you change ans(1) to ans(2) you will recall the second answer back, and so on. Using 2nd [ENTRY] allows you to edit a previously entered expression and get a new result. Using 2nd [ANS] allows you to use a previously calculated result but does not allow you to alter it. Note 1B Home Screen Recursion The command 2nd [ANS] allows you to use the result of your last calculation in your next calculation. Also, if you press ENTER without pressing another key, the calculator will recompute the last expression. Using these two commands together gives you a recursion machine. Begin by entering the starting value of a sequence. Press ENTER. Now enter the rule, using 2nd [ANS] in place of u n 1.Press ENTER repeatedly to generate the sequence. For example, this screen shows u 1 47 u n 2u n 1 8 where n 2 If you go too far in the sequence, you cannot back up. You must start the process over by entering the starting value again, then the rule. You also have to start over if you lose count of the number of terms in your sequence. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 1 3

Note 1B Home Screen Recursion TI-89/TI-92 Plus/Voyage 200 You can keep answers to a fixed length by setting the number of decimal places displayed. If, for example, a problem deals with money, you might want to display only two decimal places. Press MODE to go to the Mode screen, arrow down to Display Digits, and arrow right to see the options. Arrow up to 3:FIX 2 and press ENTER twice to select and confirm your choice. Note 1C Navigating Screens and Menus You ll use a variety of screens while working with the calculator. These are the ones you ll use most often. Home Screen Press HOME. (On a TI-92 Plus or Voyage 200, press [HOME].) Or, on any of the three calculators, press APPS and select Home. You ll do almost all your calculations on this screen. (Note: When you press APPS on a TI-89 or Voyage 200, you get either a drop-down menu or a desktop with icons. You can turn the Apps Desktop on or off in the Mode screen. When you press APPS on a TI-92 Plus or a TI-89 with an older operating system, you get only a drop-down menu.) Mode Screen Press MODE to change the number of decimal places displayed, whether graphs are displayed connected or with dots, and other settings as necessary. Arrow down to the setting you want to change, then arrow right to see the options. Graph Screen Press [GRAPH] or press APPS and select Graph to display graphs. 4 CHAPTER 1 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 1C Navigating Screens and Menus TI-89/TI-92 Plus/Voyage 200 Window Editor Screen Press [WINDOW] or press APPS and select Window Editor to set the window of values you want to graph. Y Editor Screen Press [Y ] or press APPS and select Y Editor to enter equations that you want to graph or evaluate. Stat Edit Screen To enter and work with data, press APPS and select Data/Matrix Editor or Stats/List Editor. (The Stats/List Editor is an optional application that may or may not be installed on the calculator. On a TI-89, TI-92 Plus, or Voyage 200 with the Apps Desktop turned off, press APPS 1:FlashApps in order to select Stats/List Editor.) There are several screens you can use to enter and edit data; see Note 1G for more detail. Plot Setup Screen Go to a Stat Edit screen and press histogram, or other statistics plot. F2 (Plot Setup) to set up a box plot, Table Setup Screen Press [TblSet] to make a table of values. Table Screen Press [TABLE] or press APPS and select Table to view a table. Commands There are keys for the most common commands you ll use numbers and operations, for example, and [DEL] (delete) and 2nd [INS] (insert). You ll choose other commands from menus and submenus. You can also simply type the command into the entry line. Include the opening parentheses if necessary but not the number or semicolon. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 1 5

Note 1C Navigating Screens and Menus TI-89/TI-92 Plus/Voyage 200 For example, to use the lcm( command, on the Home screen press 2nd [MATH], select 1:Number by pressing ENTER, arrow down to B:lcm(, and press ENTER.Return to the Home screen and lcm( will be in the entry line. Now type two integers, such as 18 and 24, separated by a comma, close the parentheses, and press ENTER. The calculator displays the least common multiple of 18 and 24, which is 72. Finding a Command To find a command, you can press CATALOG. (On a TI-92 Plus or Voyage 200, press 2nd [CATALOG].) Press the first letter of the command (you are now in Alpha mode) or use the arrow keys to find the command, and then press ENTER to insert the command into the Home screen entry line. When you select a command from the catalog, the required and optional parameters for that command are given in the status line at the lower left of the screen. Parameters in brackets are optional. For example, lcm( shows EXPR1,EXPR2 meaning that this command requires an expression followed by a comma followed by another expression. It is understood that you must close the parentheses. When you access a command through the catalog, the parameter help in the status line remains visible after you have returned to the Home screen so you can see how to complete the command. Note 1D Sequence Mode Sequence mode is a powerful way of working with recursive formulas. Press MODE, arrow right, select 4:SEQUENCE, and press ENTER to return to the Home screen. Notice SEQ is displayed in the status line at the bottom of the screen to remind you that you are in Sequence mode. Follow these steps to enter the recursive formula u 1 47 u n 2u n 1 8 where n 2 First, go to the Y Editor screen. u1 the recursive rule; in this example enter 2 alpha [u] 1 [n] 1 8. (On a TI-92 Plus or Voyage 200, ignore just press the appropriate letter key.) alpha alpha and ui1 the value of the starting, or initial, term; in this example enter 47. 6 CHAPTER 1 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 1D Sequence Mode TI-89/TI-92 Plus/Voyage 200 Next, go to the Window Editor screen. nmin the n-value of the starting term; in this example enter 1. nmax a number greater than nmin. To display recursive sequence values on the Home screen, the other Window Editor values don t matter. For graphing sequences you will have to set the other values; see Note 1E. You can find values of individual terms of the sequence on the Home screen. To find u 1,press alpha [u] 1 (1) ENTER.To edit the entry line (which now has a black background), press the right arrow key and replace the 1 in the parentheses with a term you want to find, such as 4, and press ENTER. Note 1E Graphing Sequence Mode You can graph sequences to display numbers generated by recursive formulas. The x-axis will represent the values of n, and the y-axis will represent the values of u(n). Go to the Window Editor screen. Set the window values to show the part of the graph you want to see. nmin the smallest value of n you want graphed on the x-axis. This should be the n-value of the starting term. nmax a value a little larger than the greatest value of n you want graphed. plotstrt the first term of the sequence you want graphed. This is almost always 1. plotstep the terms you want graphed. For example, if you want to plot every other term, plotstep 2. plotstep is almost always 1. xmin and xmax the minimum and maximum values on the x-axis. These usually will be about the same as nmin and nmax, unless you want a close-up look at some part of the graph. xscl and yscl the distance between tick marks on the two axes. The number of divisions should be less than 25. If there are too many tick marks, the axes will appear too thick. ymin and ymax the range of function values you want graphed. Usually ymin will be slightly less than the smallest function value and ymax will be slightly greater than the largest function value. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 1 7

Note 1E Graphing Sequence Mode TI-89/TI-92 Plus/Voyage 200 Press [GRAPH] to see the graph. These screens show graphing 20 terms of each sequence. The check mark to the left of a sequence rule on the Y Editor screen indicates that the rule is active and will graph. If you enter more than one sequence into the Y Editor screen, all will have check marks and all will be graphed at the same time. To make a plot inactive, turn a check mark off by arrowing to the rule and pressing F4 ( ). Note 1F Looking for the Rebound Press 2nd [VAR-LINK] and arrow down to see if the program ranger is on your calculator. If it is not on your calculator, you must download it before you can proceed. See the section Loading the Program at the end of this note. With a link cable, connect the CBR (Calculator-Based Ranger) to the calculator. Be sure to push in each plug firmly. From the Home screen, type ranger() into the entry line and press ENTER. Press ENTER again to start the actual program and to go to the Main Menu. Choose 3:Applications and select your units. Choose the application 3:Ball Bounce. Press ENTER again for more instructions. You may now disconnect the CBR while you are collecting data. Hold the ball nearly a meter above the floor and the CBR a half meter above the ball. Release the ball as you press the trigger. If the ball bounces to the side or your timing is not coordinated, simply repeat the drop and triggering. You do not have to rerun the program. 8 CHAPTER 1 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 1F Looking for the Rebound TI-89/TI-92 Plus/Voyage 200 When you think you have a good set of bounce data, reconnect the CBR to the calculator and press ENTER. You ll see a graph of your data. If you don t have good data showing at least five bounces, press ENTER and choose 5:Repeat Sample to repeat the experiment. When you are finished, press ENTER and choose 7:Quit. Loading the Program With a TI-89 calculator, you must download the ranger program from the Calculator Programs and Data CD. The program on the CBR for the TI-92 Plus may seem to load into the TI-89, but it will not work. With a TI-92 Plus or a Voyage 200, use a link cable to connect the CBR to the calculator. Be sure to push in each plug firmly. Press 2nd [VAR-LINK] F3 (Link) 2:Receive. The status line at the lower right of the screen should indicate that the calculator is busy. Open the pivot head of the CBR and press 92. This loads the program into the calculator. Note 1G Naming and Storing Data Your calculator stores data in folders. The name of the current folder is displayed in the status line at the lower left of the screen. You can change your current folder to other available folders by going to the Mode screen and selecting Current Folder. The calculator comes with a default folder named main. You can create additional folders to help keep your work organized; consult your calculator manual for assistance. Data are stored as a list variable or as a data variable (or as a matrix). A list variable must be entered and stored in a single list or column. A data variable may be a single list or column of data, or it may be data stored in more than one column. Matrices are not considered in this note; see Note 6A. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 1 9

Note 1G Naming and Storing Data TI-89/TI-92 Plus/Voyage 200 You can access a data variable through the Data/Matrix Editor, and a list variable through either the Data/Matrix Editor or the Stats/List Editor. To access these screens, press APPS and select Data/Matrix Editor or Stats/List Editor. (The Stats/List Editor is an optional application that may or may not be installed on the calculator. On a TI-89, TI-92 Plus, or Voyage 200 with the Apps Desktop turned off, press APPS 1:FlashApps in order to select Stats/List Editor.) For more detail on accessing these screens, see the sections Entering Data Through the Data/Matrix Editor and Entering Data Through the Stats/List Editor. Entering Data from the Home Screen Data you enter from the Home screen will be stored as a list variable. On the Home screen, you create a list by typing a sequence of elements separated by commas and enclosed in braces, { }. To enter and store a list, you must name it and decide in which folder you want to save it. The current folder appears in the Home screen status line. (To change folders, go to the Mode screen.) A variable name can have up to eight characters and cannot begin with a number. You cannot use a name that has another calculator meaning. You ll get an error message if you try to use an unacceptable name. To enter and save a list m1 with elements 1, 3, 9, 7, 5, 11, press 2nd [{] 1,3,9,7,5,11 2nd [}] STOÍ alpha [m] 1 ENTER. (On a TI-92 Plus or Voyage 200, omit alpha and just press the appropriate letter key.) To view a stored list on the Home screen, enter the list s name and press ENTER.When you want to view a list, make sure the status line indicates that you are in the same folder where the list is stored. If you are not in the correct folder, go to the Mode screen and change the folder setting. Lists that are entered from the Home screen can also be accessed and viewed through the Data/Matrix Editor or the Stats/List Editor; see the procedures Entering Data Through the Data/Matrix Editor and Entering Data into a List Through the Stats/List Editor that follow. Entering Data Through the Data/Matrix Editor You can enter data as either a list variable or a data variable directly into the Data/Matrix Editor. a. Open the Data/Matrix Editor screen and select 3:New. b. Choose the variable Type and the Folder that you want. Arrow down to the next line. c. Enter the variable name into the Variable line. A variable name can have up to eight characters and cannot begin with a number. Some names are not allowed because they have another calculator meaning. You ll get an error message if you try to use an unacceptable name. d. Press ENTER ENTER. e. Enter your data. 10 CHAPTER 1 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 1G Naming and Storing Data TI-89/TI-92 Plus/Voyage 200 Notice that the variable type appears at the upper-left corner of the screen. If you select Type:List and you enter data into a second column, the variable type will automatically switch to Data. Entering Data into a List Through the Stats/List Editor If your calculator has the Stats/List Editor application, you can enter list variable data directly into a list on the Stat/List Editor screen. The screen shows six lists with names list1, list2,...,list6. Enter data into one (or more) of the six lists. Each list is stored separately as a list variable. You can name a new list by arrowing up to a list name and then arrowing right to one column past the last named list. Type your new name and enter the data. On the Home screen you can also enter data into one of these lists by following the procedure Entering Data from the Home Screen and naming your list list1, list2, and so on. Clear a list by highlighting its name and pressing CLEAR ENTER. You can reset your Stat/List Editor lists to the original six lists by pressing F1 (Tools) 3:Setup Editor ENTER. Viewing and Editing Data To view or edit stored data, go to the Data/Matrix Editor screen and select 1:Current or 2:Open. 1:Current will display the most recent list or data variable you ve used with the Data/Matrix Editor. You can arrow down and edit any data. 2:Open will allow you to choose Type:List or Data and then select the variable name of the type you want displayed. If Type is List, only the names of list variables will be displayed under Variable. List variables created through the Stats/List Editor will also be displayed. If your Type is Data, only the names of data variables will be displayed under Variable. Press ENTER ENTER to display the data on the Data/Matrix Editor screen for viewing and editing. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 1 11

Note 1G Naming and Storing Data TI-89/TI-92 Plus/Voyage 200 You can also view and edit lists that were created on the Stats/List Editor by opening the editor and arrowing to the data you want to change. You can enter or edit values on a Stat Edit screen by typing numbers, expressions, fractions, or functions. The form of an entry depends on the Exact/Approx setting on the Mode screen; see Note 0B. Use the commands in F6 (Util) to assist in your editing. Deleting a List or Data Variable To delete the list or data variable from the calculator s memory, press [VAR-LINK], arrow to the name you want to delete, and then press F1 and ENTER to confirm. 2nd 1:Delete Note 1H Stat Plots To set up a plot of stored data, first go to the Y Editor screen and turn off or clear any functions that you don t want displayed on top of your stat plot. Then follow these steps: a. Open the data. If the data you want to plot are stored as a data variable, press APPS, select Data/Matrix Editor, and open the data. If the data you want to plot are stored as a list variable you can open the data in the same way, or you can open any data in the Data/Matrix Editor or the Stats/List Editor from the same folder as the data you want to plot. (See Note 1G if you need help displaying data.) b. Press F2 (Plot Setup) and arrow to the line of the plot you want to define, usually the first available line. (In the Stats/List Editor, press F2 (Plots) and select 1:PlotSetup...) c. Press F1 (Define). d. Select the Plot Type. Plot Type will determine the other selections you must make. Arrow down to the next required selection. Do not press ENTER or you ll void the plot definition and return to the Stat Plot screen. e. For scatter plots, xyline plots, and modified box plots select the Mark to use in the plot. If you graph more than one plot at the same time, use a different Mark for each plot. Arrow down. 12 CHAPTER 1 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 1H Stat Plots TI-89/TI-92 Plus/Voyage 200 f. Enter the name of the list variable(s) or the column(s) (columns c1, c2, etc., from the current data display) to be used in the stat plot. Make sure the list variable name is in the folder you are in. For one-variable plots (box plots and histograms) enter one list variable name or column name; for scatter plots and xyline plots enter two names, one for the x-axis values and one for the y-axis values. The number of x- and y-values must be the same. g. For one-variable data, Frequency indicates the number of times each data point occurs in the data set. Usually Freq and Categories? is set as NO indicating that each element is used once. If the frequencies of the data values are stored in another list or column, change Freq and Categories? to YES, and then for Freq enter the name of the list or column that contains the frequencies. h. Press ENTER to save your settings and to return to the Stat Plot screen. You should see a summary of your plot settings on the plot line you selected to use. The check mark at the left of the line indicates that the plot is active and ready to be displayed. You can make the plot inactive by pressing F4 ( ) while the plot line is highlighted. In this way you can define a number of plots but only display one or two at a time. Before viewing the plot, you need to decide what part of the graph you want to view. Press [WINDOW]. xmin a number slightly less than the smallest x-value you want displayed. xmax a number slightly greater than the largest x-value you want displayed. xscl and yscl the distance between tick marks on the two axes. The number of divisions should be less than 25. If there are too many tick marks, the axes will appear too thick. ymin a number slightly less than the smallest y-value. xmax a number slightly greater than the largest y-value. xres 1. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 1 13

Note 1H Stat Plots TI-89/TI-92 Plus/Voyage 200 On the Mode screen if Graph is not set to Function, the Window Editor screen may have additional settings. Ignore the settings other than the ones here. For more information about setting the Window Editor screen for box plots and histograms, see Notes 2C and 2D. Press [GRAPH] to see the plot. Note 1I Tracing If you have a plot displayed and you press F3 (Trace), a spider will appear on the plot. Use the right and left arrow keys to move the spider along the plot. The spider s position is given at the bottom of the screen. For scatter plots, the data are traced in the order they appear in the lists, so pressing the left arrow key may not move the spider left. One-variable plots always trace the same way: histograms from the left and box plots from the center. If you have displayed several plots at once, the spider will begin on the first stat plot that is turned on. Pressing the up and down arrow keys makes the spider jump to another stat plot. The plot you are currently tracing is given at the upper-right corner of the screen. Note 1J Linking Lists You can copy data (list and data variables) from one calculator into another. This can save time and ensure that you re working from the same data set as others. You will need a link cable and two compatible calculators. The TI-89, TI-92 Plus, and Voyage 200 calculators can all share data information. Push the plug firmly into the ports of both calculators. Press 2nd [VAR-LINK] on each calculator. On the receiving calculator, press F3 (Link) 2:Receive. VAR-LINK: WAITING TO RECEIVE and BUSY should be in the status line at the bottom of the screen. 14 CHAPTER 1 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 1J Linking Lists TI-89/TI-92 Plus/Voyage 200 On the calculator with the data, arrow down to the data (LIST or DATA) you want to send and press F3 (Link). If you want to send more than one set of data, highlight each set and press F4 ( ) to mark it for sending. Once you ve marked all the data sets you want to send, press F3 (Link). Ifyou are sending to a TI-89, TI-92 Plus, or Voyage 200, select 1; ifyou are sending to a TI-92, select 3. Ifeither calculator gives an ERROR: Link transmission message, push the link cable in again and start over. If the variable name you are sending already exists in the receiving calculator, it will display an Overwrite message. Press ENTER to replace the old data with the new data. When the transmission is complete the transmitted variable name(s) appears on the Var-Link screen of the receiving calculator. Note 1K Sequence Tables You can view many elements of a sequence at once by using sequence tables. First enter the sequence into the Y screen. (See Note 1D if you need help entering a sequence.) Then press [TBLSET]. tblstart is the smallest n-value for which you wish to see a sequence value. The value of tbl specifies which terms will actually be displayed. For this example, if tbl 3 the table will display every third term. Set Graph <-> Table to OFF and Independent to AUTO. Press ENTER to save the settings. If you aren t taken directly to the Window Editor screen, press [WINDOW]. Set nmin to the least n-value for which the sequence formula is defined. The other Window screen settings don t matter. Press [TABLE] to display the table. Arrow up or down to see more n-values and right or left to see values of other entered sequences. Highlighting a sequence value shows you significant digits that are not displayed on the table. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 1 15

TI-89/TI-92 Plus/Voyage 200 Note 1L Random Numbers There are several ways to generate a list of random numbers within an interval. Random Integers To find a random integer between 1 and 20, on the Home screen press 2nd [MATH] 7:Probability 4:rand(, enter 20), and press ENTER. If you want five random numbers, either press ENTER five times, or press 2nd [MATH] 3:List 1:seq( 2nd [MATH] 7:Probability 4:rand(, enter 20),x,1,5,1), and press ENTER. Changing the 20 to 50 and the 5 to 8 will generate a list of eight random integers between 1 and 50. If you ask for more numbers than show on one line of the screen, arrow up to the list and scroll left or right to see the rest of the list. Random Decimal Numbers Press 2nd [MATH], select 7:Probability, 4:rand(, close the parentheses, and press ENTER to display a random decimal number between 0 and 1. To generate a random decimal number between 0 and 8, enter 8*rand( ). Errors If you are getting exactly the same random numbers as someone else, try changing the seed value. Press 2nd [MATH], select 7:Probability, 6:RandSeed, and then enter a number other than 0. Note 1M Finance Mode The Finance solver will solve problems about simple loans, mortgages, and investments. It is an optional application that may or may not be installed on the calculator. Press APPS and select the Finance icon from the Apps Desktop, or press APPS 1:FlashApps and select Finance. Enter known values into all but one position. Then, into the one position you don t know, enter any value to act as a placeholder. Move the cursor to the unknown position and press F2 (Compute). The solver will correct the erroneous entry. In general, negative amounts indicate money you give to the bank and positive amounts indicate money you receive. N the total number of payments. I% the annual interest rate as a percent. PV the principal or starting value (this is negative for investments). PMT the payment or regular deposit (this is negative for investments). FV the final value. 16 CHAPTER 1 Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200

Note 1M Finance Mode TI-89/TI-92 Plus/Voyage 200 PpY payments per year. CpY interest calculations per year. PMT:END BEGIN indicates whether payments are made at the end or beginning of each month. As you move the cursor down the list, the meaning of each abbreviation appears in the status line at the bottom of the screen. This screen shows calculating the monthly payment to completely repay a 5-year (60-month) $12,000 loan at 5.25% interest, with payments made at the end of each month. The answer, PMT, is negative because it is a payment made to the bank. Discovering Advanced Algebra Calculator Notes for the Texas Instruments TI-89, TI-92 Plus, and Voyage 200 CHAPTER 1 17