# For another way to generate recursive sequences, see Calculator Note 1D.

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1 !"# 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 calculated a result of , and you want to multiply by 16, press [ ] [1] [6] [EXE]. If, on the other hand, you want to take the square root of that number, press [SHIFT] [x 2 ] { } and then [SHIFT] [(-)] {Ans} [EXE] to calculate You can also recall and edit a previous expression. Press [AC /ON ] to clear the screen, and use the up-arrow to scroll through previously input expressions until you find the one you would like to edit. Once you have recalled the expression, you can use the right- and leftarrows and enter replacement characters. To delete characters press [DEL], and to insert new characters press [SHIFT] [DEL] {INS}. When you are finished, press [EXE] to recalculate the revised expression.!\$ %" The command [SHIFT] [(-)] {Ans} on the calculator allows you to use the result of your last calculation in your next calculation. Also, if you press [EXE] without pressing another key, the calculator will recompute the last expression. Combining these two features allows you to perform on-screen recursion, calculating a new number by repeating the operation using the result of the previous calculation. You can create patterns of numbers (sequences) using the following procedure: a. Enter the starting number of your sequence and press [EXE]. b. Enter an expression using Ans. You can get Ans by pressing any of the operation keys, such as [+], [-], [ ], [ ], [^], or [x 2 ] or by pressing [SHIFT] [(-)] {Ans}. c. Press [EXE] for the result (the second term of the sequence). d. Press [EXE] repeatedly to generate successive terms in the sequence. For another way to generate recursive sequences, see Calculator Note 1D.!&'"'""%\$ " You will use a variety of screens and menus while working with the calculator. These are a few you will use most often. 4

2 Set Up Screen Options on the Set Up Screen will vary depending on the mode in which you are currently working. For example, from the RUN Mode, if you press [SHIFT] [MENU] {SET UP}, you will see: Scrolling down, you will see more options. You can change set-up options by highlighting the option and pressing [F1] through [F6]. Your Set Up Screen will most often appear as above. If you are working in the GRAPH Mode, your Set Up Screen will have other options. Graph Function Menu The Graph Function Menu appears when you choose the GRAPH Mode from the MAIN MENU. You can use this menu to store, edit, and recall functions and to draw their graphs. View Window Use the View Window to specify the range of the x- and y-axes, and to set the spacing between the increments on each axis. You should always set the View Window parameters you want to use before drawing a graph. Press [SHIFT] [F3] {V-Window} to display the View Window. 5

4 Example: Find the value of 5! 7! 2!. In the RUN Mode, press [OPTN] [F6] [F3] to access the PROBability submenu. Press [5] [F1] [ ] [7] [F1] [ ] [2] [F1]. The PROBability submenu will remain on the screen until you press [EXIT]. Therefore, you will not need to press a series of keys each time you wish to use the factorial symbol (!). (!"\$ % The Casio 9750G Plus/9850GB Plus has a built-in feature for performing recursion. Whereas Discovering Advanced Algebra uses the variable u for recursion, the calculator uses the variable a. From the Main Menu, select the RECUR icon to enter the RECUR Mode. Before inputting a recursion formula, you must specify its type. In the Recursion Menu, press [F3] (TYPE). Press the function key for the recursion formula type you want to set. For linear recursion between two terms, press [F2]. Input a recursion formula and generate a table. For example, u 1 = 47 (or a 1 = 47) u n = 2u n-1 8 where n 2 (or a n+1 = 2a n 8 where n 1) Press [2] [F4] (n,an ) [F2] (a n ) [-] [8] [EXE] to enter the recursive formula. Press [F5] (RANG) [F2] to display the table range settings. Enter a starting value of 1 and an ending value of 10 to specify the range of values for n. Also, set the initial value (a 1 ) as 47. Press [EXE] or [EXIT] to return to the Recursion Menu. Press [F6] to view the table containing the first 10 terms of the sequence. Use the arrow keys to scroll through the table. If you would like to generate a table for two recursive sequences at a time, simply enter a second recursive formula for b n+1. When the table is generated, it will include values for both sequences. You can change the initial value of the sequence by changing the value of a 1 or the recursive formula by changing the value of a n+1. 7

5 !)*"'&+" Whenever a table is generated in the RECUR Mode, the function menu that appears at the bottom of the screen includes the options to draw a connected-type or plot-type graph of the sequence(s) generated. Before drawing a graph, you must first specify which sequence(s) will be drawn and in what color. Press [EXIT] to back up to the very first Recursion Menu where your sequences are defined. Highlight each formula, and Press [F1] (SEL+C). Pressing [F1] will toggle between draw/non-draw status. Pressing [F2] through [F4] will specify a color in which the sequence will be drawn. Return to the Recursive Menu by pressing [EXIT]. Press [F6] to generate the table of values. Press [F5] if you want a connect-type graph or press [F6] if you want a plot-type graph.,!-"'.*/"% With a link cable, connect the EA-100 to the calculator. Be sure to push in each plug firmly. Choose the PRGM icon from the Main Menu. Arrow down to the program REBOUND. Press [F1] (EXE). If the REBOUND program is not listed, you will need to load the program provided at " #\$%&'() & \$** &+',' )&+'-# #.+ ) /01# " %8 7, 7 7,.'9:,*;< => 5= 7 : 9,*;<7=>??,*;<"=>?? => ( 0 05 (5,.% => 8

6 !""'(" The calculator contains six folders, each with six preset lists. You can enter 255 elements into a list if enough memory is available. You can enter data directly into lists from either LIST or STAT Mode. Clearing Data From the Main Menu, select the LIST or STAT icon and press [EXE]. In these notes, LIST Mode is used. If a list already has data in it, position the cursor so that any cell of the list is highlighted, then press [F4] (DEL-A). Press [F1] (YES) to delete all the cells in the list. Entering Data Directly into a List Follow the steps below to enter data, for example, {400, 455, 390, 450, 360, 320, 480, 480}, into a list. a. Select LIST or STAT from the Main Menu. b. Enter each number into List 1. After entering each data value, press [EXE]. If you wish to add a data value in the middle of the list, move the cursor to the place of insertion, press [F5] (INS), then enter the new number and press [EXE]. To remove an entry from a list, highlight the entry and press [F3] (DEL). Entering Data into a List from the Run Screen If you are working with a short list, you may want to enter it while in the RUN Mode. To enter the data {1, 2, 3, 4} into List 1, follow the steps below. a. Enter RUN Mode. b. Press [OPTN] [F1] (LIST) to display the list data manipulation menu. c. You will need to press [SHIFT] [ ] to obtain the open brace and [SHIFT] [ ] to obtain the close brace. d. Enter {1, 2, 3, 4} and then press [ ] [F1] (List) [1] [EXE]. e. You can check to see that the new data are stored in List 1 by selecting LIST or STAT Mode from the Main Menu. 9

7 You can also enter a list into the RUN Mode without storing it in a stat list by entering the values as in step b above. Press {1, 2, 3, 4} and then [EXE].!)* To set up a graph of statistical data stored in a list, you must first enter the STAT Mode from the Main Menu. Then press [F1] (GRPH) [F6] (SET). From the Set-Up Screen, you can set up any or all of the three statistical graphs (StatGraphs) available on the calculator. Use the following steps. Be aware that some options are not available depending on which graph type you choose. a. Press [F1], [F2], or [F3] to set up StatGraph1, StatGraph2, or StatGraph3 respectively. b. Scroll down to the Graph Type, and choose one of the following: [F1] scatter diagram [F2] xy line graph [F3] normal probability plot Other graph types can be found after pressing [F6] for more options. [F1] histogram [F2] med-box graph [F3] mean-box graph [F4] normal distribution curve [F5] line graph c. Scroll down to the XList, and press [F1] through [F6] to select the list where your independent variable is located. d. Scroll down to the YList (if applicable), and press [F1] through [F6] to select the list where your dependent variable is located. e. Scroll down to the Frequency (if applicable), and press [F1] if you want a frequency of 1, or choose the list where the frequencies are stored. Usually Frequency is set to 1. f. Scroll down to the Mark Type (if applicable), and press [F1], [F2], or [F3] according to your preferences. g. Scroll down to Graph Color, and press [F1], [F2], or [F3] according to your preferences. h. Scroll down to Outliers (if applicable), and press [F1] or [F2]. Before viewing the graph, you need to set an appropriate viewing window. Press [SHIFT] [F3] {V-Window}. Xmin = a number slightly less than the smallest x-value you want displayed. 10

8 Max = a number slightly greater than the largest x-value you want displayed. scale = the distance between tick marks on the x-axis. The number of divisions should be less than 25. If there are too many tick marks, the axis will appear too thick. Ymin = a number slightly less than the smallest y-value. max = a number slightly greater than the largest y-value. scale = see Xscale. For more information about setting the window for box plots and histograms, see Notes 2C and 2D. Press [EXIT] to return to the statistical data lists. Press [F1] (GRPH) and [F1], [F2], or [F3] to draw the selected graph. 0!"' If you have a statistical graph displayed and you press [SHIFT] [F1] {TRACE}, a spider will appear somewhere on the graph. Use the right and left arrow keys to move the spider along the graph. 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 list, so pressing the left arrow may not move the spider left. Histograms and box plots trace from left to right. If more than one set of data are graphed, the spider will begin on the first. Pressing the up or down arrow will cause the spider to jump from one graph to another. The graph being traced will be identified at the top of the screen. 1!"-"' You can copy lists 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. Push the plug firmly into the ports at the bases of both calculators. From the Main Menu of both calculators, choose the LINK icon. On the receiving calculator, press [F2] (RECV). This calculator should read Receiving... at the top of the screen. 11

9 On the calculator with the data, select [F1] (TRAN). Press [F1] (SEL) to see a list of all items (programs, lists, etc.) that you may send. Arrow down to highlight the list you want to send, and press [F1] (SEL). This marks the list but does not send it. Mark each list you wish to send. When you have marked all the lists, press [F6] (TRAN) and [F1] (YES). If either calculator gives a Transmit ERROR message, then push the link cable in again and start over. If the list you are sending already exists in the receiving calculator, choose [F1] (YES) to replace this list with the new list. 2!+"/ See Calculator Note 1D.!"%3 3/ There are several ways to generate a list of random numbers within an interval. Random Decimals To find a random decimal between 0 and 1, in the RUN Menu press [OPTN] [F6] [F3] (PROB) [F4] (Ran#) [EXE]. If you want a random decimal between 0 and 20, press [F4] [ ] [20] [EXE]. Random Integers To find a random integer between 0 and 20, you must enter Int(Ran# 20). Press [EXIT] until there are no more menus across the bottom of the screen. Press [OPTN] [F6] [F4] [F2] (Int). Then press [EXIT] [F3] (PROB) [ ( ] [F4] [ ] [20] [EXE]. If you want five random integers, press [EXE] five times. 12

10 \$!4\$ 5,""6\$ % The TVM (Financial) Mode provides you with the tools to perform the following types of financial calculations. - Simple interest - Compound interest - Investment appraisal (Cash Flow) - Amortization - Interest rate conversation - Cost, selling price, margin - Day/date calculations On the Main Menu, select the TVM icon to enter the Financial Mode. When you do, the Financial 1 screen appears on the display. Press [F2] (CMPD) from the Financial 1 screen to display the input screen for compound interest calculation. n = number of compound periods I% = annual interest rate PV = present value (loan amount in case of a loan; principal in case of savings) PMT = payment for each installment (payment in case of loan; deposit in case of savings) FV = future value (unpaid balance in case of loan; principal plus interest in case of savings) P/Y = installment periods per year C/Y = compounding periods per year A period (n) is expressed as a positive value. Either the present value (PV) or future value (FV) is positive, while the other is negative. After entering any six of the seven values, you can press [F1] to [F5] to calculate the value you want to find. This first screen shows the values input to calculate 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 second screen shows the display after pressing [F4] (PMT). The answer, PMT, is negative because it is a payment made to the bank. 13

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