DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 9

CHAPTER 1

Calculator Notes for the fx-9750G Plus and CFX-9850GC Plus

Note 1A Setting the Mode

Each mode on your calculator has different settings that you can change. While in RUN mode, press SHIFT [SET UP]. Arrow down to see more settings. The settings displayed in the screens above are the ones that you will use most often in this course while in RUN mode. Other modes may have different choices on their setup screens. If your calculator does not display these settings in RUN mode, follow these steps to change them. a. Use the arrow keys to highlight the setting you want. b. Press a function key to register your selection. Sometimes pressing F6 () gives more options. c. When you have selected the settings you want, press EXIT to exit from the setup screen. In this class, you will need to change some of these settings during the year. The list may not mean much to you now, but your textbook will refer you to this note several times during the course. All of these settings do not appear in all modes. The following is a description of the mode settings that you may need (or want) to change. There are other settings in some modes that should not concern you in this course. a. Stat Wind (statistics window) should be set to Man in this course. b. Graph Func (graph function) gives you the choice to display or not display the function on the screen with its graph. c. Func Type (function type) refers to the type of function (or relation) currently active on the calculator. Y is the usual setting. The Parm (parametric) setting and inequality settings are also used. Press F6 () to see the inequality options. d. Draw Type refers to the way graphs are drawn. Con (connected) means that each calculated point will be connected to the next. Plot means that each calculated point is drawn by itself. e. Plot/Line allows you to choose one of three colors for your graph. f. Dual Screen allows you to split the screen to show two graphs or a graph and its table of values. g. Angle allows you to choose the type of angle measure. In this course, you will use only deg (degree) measure. This setting is not important until you reach the chapter on distance. h. Coord (coordinates) allows you to show or not show the coordinates of points while tracing. i. Grid allows you to show or not show the grid points on a graph screen. j. Axes allows you to show or not show the axes on a graph screen. k. Label allows you to show or not show the label for the axes.

(continued)

2007 Key Curriculum Press
Discovering Algebra Calculator Notes for the Casio fx-9750G Plus and CFX-9850GC Plus
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 10
Note 1A Setting the Mode (continued)
fx-9750G Plus and CFX-9850GC Plus
l. Display refers to the way in which numbers are written. The options are Fix (fixed), Sci (scientific), Norm (normal), and Eng (English). Usually the setting should be Norm. Sci is used in the chapter on exponents. After you choose Sci, you also decide on the total number of digits you want displayed. The Fix setting is useful in hiding long decimal answers and will make some numbers clearer. After choosing Fix, you choose how many digits appear to the right of the decimal point. This setting is helpful in applications involving money, for example, where one wants two decimal places showing. Change this setting back to Norm when you dont need a special display. If you find that your screen looks strange when you try to do something, its a good idea to look at the setup screen and check to see if any settings have been changed.

Note 1B Entering Lists

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 LIST or STAT and press EXE. If a list already has data in it, position the cursor so that any cell of the list is highlighted, and 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 want to add a data value in the middle of the list, move the cursor to the place of insertion, press F5 (INS), and then enter the new number and press EXE. To remove an entry from a list, highlight the entry and press F3 (DEL).
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 11
Note 1B Entering Lists (continued) 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 screen. To enter the data {1, 2, 3, 4} into List 1, follow the steps below. a. Press OPTN F1 (LIST) to list the data. b. Press SHIFT [ { ] 1 , 2 , 3 , 4 SHIFT [ } ]. (The brace symbols are above the multiplication and division signs.) c. Press F1 (List) 1 EXE. d. You can check to see that the new data is in the list by selecting LIST or STAT from the Main Menu.
You can also enter a list into the Run screen without storing it in a stat list by entering the values as in step b above. Press EXE.

Deleting a List

To delete a single list while in LIST mode, highlight any entry in the list and press F4 (DEL-A) F1 (Yes). In STAT mode, press F6 (), then F4 (DEL-A) F1 (Yes). To delete all lists, select MEM from the Main Menu. Highlight Memory Usage and press EXE. Arrow down to highlight List File and press F1 (DEL) F1 (FILE1) F1 (Yes).
Switching Between List Files
You can store up to six lists (List 1 through List 6) in each file (File 1 through File 6). To switch between list files, select LIST from the Main Menu and press EXE. Press SHIFT [SET UP] to display the List setup screen. Press the appropriate function key to select the file you want.

Moving a List

To move a list, begin by highlighting the heading of an empty list. Press OPTN F1 (LIST) F1 (List), enter the number of the list whose contents you want to copy, and press EXE. The list data appears. You can now delete or overwrite the data in the original list, and the data will remain in the new list.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 12
fx-9750G Plus and CFX-9850GC Plus Note 1C Mean, Median, and Mode
Enter the data into a list. (See Note 1B if you dont remember how to enter data into a list. This example uses the same data as the first list entered in Note 1B.) a. Press MENU , select RUN, and press EXE. b. Press OPTN F1 (LIST). c. Press F6 to see more menu options. d. To find the mean, press F3 (Mean) F6 F6 F1 (List), and the number of the list that contains the data. Then close the parentheses, press EXE , and press F6 to see more menu options. e. To find the median, press F4 (Med) F6 F6 F1 (List), the number of the list that contains the data, and EXE.
You can also calculate all the statistical values of a data set at once, including the median, mean, mode, and summary values. a. Press MENU. Highlight STAT and press EXE. Highlight any cell in your list. b. Press F2 (CALC). c. Press F1 (1VAR) to access the statistical values.
Use the down arrow to display the entire list of values.
x 416.875 x 3335 x2 1.414425 xn 54.93959751 xn1 58.73290025 n8 minX 320 QMed 425 Q3 467.5 x xn x xn maxX 480 Mod
the mean the sum of the x-values the sum of the squares of the x-values the population standard deviation the sample standard deviation the number of data values the minimum of the list the first quartile the median the third quartile data mean population standard deviation data mean population standard deviation the maximum of the list the mode of the list
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 13
fx-9750G Plus and CFX-9850GC Plus Note 1D Box Plots Entering the Data
Enter the data set into a list. In this example, List 1 is {400, 455, 390, 450, 360, 320, 480, 480}. (See Note 1B if you need help entering data.)
Setting the VIEW WINDOW Values
Select STAT from the Main Menu. While the statistical data list is displayed, press SHIFT [SET UP] F2 (Man) EXIT.
Press SHIFT [V-Window] and input the following values on the View Window screen. Press EXE after each entry.

Xmin: 300

(This value is a number slightly less than the minimum of the data.) (This value is a number slightly greater than the maximum of the data.) (This number does not affect a box plot.)

max: 500

scale: 1 Ymin: 0 max: 10
(This number is not important for a box plot. Any number greater than Ymin will work.)
Press EXIT or EXE when you are done entering values. The view window shown is [300, 500, 1, 0, 10, 0].

Displaying the Box Plot

This example uses the data in List 1, but you can choose any list. a. Press MENU to display the Main Menu. Highlight STAT and press EXE. b. Press SHIFT [SET UP]. Arrow down to Grid and press F2 (Off). Press EXE. c. Press F1 (GRPH) to display the graph menu. d. Press F6 (SET) to enter the graph settings menu. Press a function key to select a graph. e. Arrow down to Graph Type. Press F6 (). Press F2 (Box) to select MedBox. (Pressing F3 (Box) also gives a box plot; but it is a MeanBox, which is not used in this course.) f. Arrow down to XList to display list choices. Press F1 to select List 1. g. Arrow down to Graph Color. Press a function key to select the graph color. h. Arrow down to Outliers and select On or Off by pressing the corresponding function key.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 14
Note 1D Box Plots (continued)
i. Press EXIT to return to the Graph screen. Press F4 (SEL). Use the down arrow and F1 or F2 to turn on the graph you selected and to turn off the other graphs. Press F6 (DRAW) to draw the graph. (You can also graph from the Graph screen by pressing the function key corresponding to the number of the graph that you want to display.)

Tracing on a Box Plot

Press SHIFT [Trace]. The trace option allows you to see the five summary values for the box plot by pressing the left and right arrow keys. When you press the up and down arrow keys, you move from one box plot to another. (See the Graphing More Than One Box Plot section that follows.) Look in the upper-left corner of the calculator screen to see which plot the calculator is tracing.
Graphing More Than One Box Plot
The calculator can graph up to three box plots at once. Follow the directions for making a box plot and press F4 (SEL). Use the arrow keys and F1 or F2 to choose DrawOn or DrawOff for each graph. Be sure the list you select when setting up each box plot is the same list in which youve entered the data. Using a different color for each plot is an effective way to display them.

Errors

If you dont see a graph and you selected Stat Wind:Manual, check Xmin and Xmax to make sure that your data lies between those values. If the minimum value is greater than the maximum value, the axis will be inverted. If you get a Dim ERROR, you selected a blank list. If anything appears on the graph other than the statistical graph you set, press SHIFT [Sketch] F1 (Cls).
Note 1E Histograms Entering the Data
Enter the data into a list. In this example, List 1 is {400, 455, 390, 450, 360, 320, 480, 480}. (See Note 1B if you need help entering the data.)

Select STAT from the Main Menu. While the data list is displayed, press SHIFT [SET UP] F2 (Man) EXIT.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 15
Note 1E Histograms (continued)
Press SHIFT [V-Window] and input the following values into the View Window screen.
(This value is a number slightly less than the minimum of the data.) (This value is a number slightly greater than the maximum of the data.) (This number sets the distance between the tick marks on the horizontal axis. This number is not critical, but if its too small, the tick marks will make the horizontal axis appear too thick.) (Using a negative value allows you to see the horizontal axis. This value should be about a quarter of a fifth of the Ymax value, but the opposite sign.) (This value should be the height of the tallest bar. You might have to revise this value when you look at the graph. Tracing on the graph can help you determine the maximum bar height.) (This value does not affect a histogram.)

scale: 10

Ymin: 0.5

max: 2

scale: 0
Press EXIT or EXE when you are done entering values. The view window shown is [300, 500, 10, 0.5, 2, 0].

Displaying the Histogram

This example assumes the data is in List 1, but you can choose any list.

a. b. c. d.

Press MENU to see the Main Menu. Highlight STAT and press EXE. Press SHIFT [SET UP]. Arrow down to Grid and press F2 (Off). Press EXE. Press F1 (GRPH) to display the Graph menu. Press F6 (SET) to enter the Graph settings menu. Press a function key to select a graph.
e. Arrow down to Graph Type. Press F6 () to display the 1-variable graph types. Press F1 (Hist) to select Hist.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 16
f. Arrow down to XList to display list choices. Press F1 to select List 1. g. Arrow down to Graph Color. Press a function key to select the graph color. h. Press EXIT to return to the Graph menu. Press F4 (SEL). Use the down arrow and F1 or F2 to turn on the graph you selected and to turn off the other graphs. Press F6 (DRAW). (You can also graph from the Graph screen by pressing the function key corresponding to the number of the graph that you want to display.) The Set Interval menu will appear with the values of Start and Pitch automatically set. You may change both values. Start is the minimum x-value shown on the graph, and Pitch changes the width of the bars on the graph. A smaller pitch value results in narrower bars. Press EXE to accept the new values (if any) and F6 (DRAW) to draw the graph.

Tracing on a Histogram

SHIFT [Trace].
Use the left and right arrow keys to move the cursor.
You will get a Ma ERROR message if you attempt to make a histogram with too many intervals (bars). Increase the pitch to correct this error. If anything appears on the screen other than the statistical graph you set, press SHIFT [Sketch] F1 (Cls).

Note 1F Scatter Plots Entering the Data
Enter the x-coordinates (horizontal axis) into one list and the y-coordinates (vertical axis) into another list. List 1 and List 2 are used for this example. (See Note 1B if you need help entering the data.) Note: The data can also be entered while in the Stat screen. Any changes made to lists while in STAT mode show up in the same lists in LIST mode and vice versa. In this example, {27, 10, 18, 5, 47, 36, 8} is entered into List 1 and {20, 2, 22, 3, 45, 28, 15} is entered into List 2.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 17
Note 1F Scatter Plots (continued) Setting the VIEW WINDOW Values
Select STAT from the Main Menu. While the data list is on display, press SHIFT [SET UP] F2 (Man) EXIT. Press SHIFT [V-Window] and input the following values on the view window screen.

Xmin: 0

(This value is a number slightly less than the minimum of the x-coordinates.) (This value is a number slightly more than the maximum of the x-coordinates.) (This number is the distance between tick marks. You can use 0, that is, no tick marks, or a value usually less than or Xmax equal to 0 Xmin. If your scale value is too small, the x-axis 1 will disappear.) (This number is slightly less than the minimum of the y-coordinates. In this example, 0 would work, but a negative number allows you to see the x-axis.) (This number is slightly more than the maximum of the y-coordinates.) (This number is the distance between tick marks. You can use 0, that is, no tick marks, or a value usually less than or equal to Ymax Ymin. If your scale value is too small, the y-axis will appear 10 too thick.)

max: 50

scale: 5

Ymin: 10

The view window shown is [0, 50, 5, 10, 50, 5].
Displaying the Scatter Plot
Press MENU to see the Main Menu. Highlight STAT and press EXE. Press SHIFT [SET UP]. Arrow down to Grid and press F2 (Off). Press EXE. Press F1 (GRPH) to display the Graph menu. Press F6 (SET) to enter the Graph settings menu. Press a function key to select a graph. e. Arrow down to Graph Type. Press F1 (Scat) to select Scatter. f. Arrow down to XList to display list choices. Press F1 to select List 1. Similarly, choose List 2 for YList. g. Arrow down to Mark Type and select a mark. h. Arrow down to Graph Color. Press a function key to select a graph color.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 18
Note 1F Scatter Plots (continued)
Tracing on a Scatter Plot
Press SHIFT [Trace]. Use the left and right arrow keys to move the cursor.
Graphing More Than One Scatter Plot at a Time
The calculator can graph up to three scatter plots at the same time. Follow the directions for making a scatter plot and press F4 (SEL). Use the arrow keys and F1 or F2 to choose DrawOn or DrawOff for each graph. Be sure the list you select when setting up each scatter plot is the same list in which youve entered the data. Choose a different mark and color for each plot.

A Dim ERROR message means that the two lists do not have the same number of entries. The same error message could appear if you accidentally turned on a graph you are not using or if you named the wrong list. To clear extra graphs from the screen, press SHIFT [Sketch] F1 (Cls).

Note 1G POINTS Program

Link or manually enter the POINTS program into your calculator. (See Note 0F or Note 0G.) The POINTS program plots a single point in a graphing window that measures from 5.5 to 5.5 on the horizontal axis and from 3.5 to 3.5 on the vertical axis. You identify and enter the coordinates of the point rounded to the nearest 0.5 unit. a. To execute the program, select PRGM from the Main Menu and press EXE. Arrow to POINTS and press EXE. Press EXE again to start the program. b. Study the screen and determine the coordinates of the marked point, then press EXE. c. Enter the x-coordinate and press EXE. You will see the graph screen again. Press EXE , enter the y-coordinate, and press EXE. d. If you enter the wrong coordinates, the calculator will ask you to try again. Look at the graph and repeat steps b and c. e. If you enter the wrong coordinates a second time, the calculator will display the correct answer.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 19
Note 1G POINTS Program (continued)
File Name:POINTS 0N " POINTS" "ALWAYS PRESS EXE" "TO GO ON." ClrText "LOOK AT THE POINT ON" "THE GRAPH." ClrText "DETERMINE ITS" "COORDINATES." Int (Ran#1000)S Int (Ran#1000)T If S2=Int (S2) Then 1S Else 1S IfEnd If T2=Int (T2) Then 1T Else 1T IfEnd {S(Int ((Ran#10+1)3)}List 1 {T(Int ((Ran#10+1)4)}List 2 Lbl 1 S-WindMan ViewWindow 3.9,3.9,1,2.3,2.3,1 S-Gph1 DrawOn,Scatter,List 1, List 2,1,Square DrawStat
For 3A To 3 For 2B To 2 PlotOn A,B Next Next ClrText "(A,B) IS THE POINT." "WHAT IS A"?C "WHAT IS B"?D If C=List 1[1] Then If D=List 2[1] Then "GOOD" Goto 2 IfEnd IfEnd If N=0 Then N+1N ClrText "LOOK AGAIN" Goto 1 Else ClrText "NO. PRESS EXE TO SEE" "THE ANSWER." Plot List 1[1],List 2[1] Lbl 2
Note 1H Connecting the Points
The xyLine connects a sequence of points with line segments. The order in which the points are connected is the order in which the coordinates appear in the lists. Enter the data and set the window as described in Note 1F.
Displaying the Connected Points
Press MENU to see the Main Menu. Highlight STAT and press EXE. Press SHIFT [SET UP]. Arrow down to Grid and press F2 (Off). Press EXE. Press F1 (GRPH) to display the Graph menu. Press F6 (SET) to enter the Graph settings menu. Press a function key to select a graph. e. Arrow down to Graph Type. Press F2 (xy) to select xyLine. f. Arrow down to XList to display list choices. Press F1 to select List 1. Similarly, choose List 2 for YList. g. Arrow down to Mark Type and select a mark. h. Arrow down to Graph Color. Press a function key to select the graph color.

DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 20
Note 1H Connecting the Points (continued)
i. Press EXIT to return to the Graph menu. Press F4 (SEL). Use the down arrow and F1 or F2 to turn on the graph you selected and turn off the other graphs. Press F6 (DRAW) to draw the graph. (You can also graph from the Graph screen by pressing the function key corresponding to the number of the graph that you want to display.)
If the points are not listed in ascending order by their x-coordinates, your xyLine will be scrambled, with segments crisscrossing each other. While the data lists are on the screen, press F6 F1 (SRT-A) to sort in ascending order. The prompt How many lists? will appear to ask how many lists you want to sort. Press 2 EXE to indicate two lists. Respond to the next prompt by pressing 1 EXE to select List 1 as the base list, and after the last prompt, press 2 EXE to select List 2 as the second list. Notice that the sort command puts List 1 in ascending order but maintains the original pairings between List 1 and List 2. (See Note 10B.)

Tracing Connected Points

Use the right and left arrows to move the cursor.
A Dim ERROR message means that the two lists do not have the same number of entries. The same error would appear if you accidentally turned on a graph youre not using or if you named the wrong list when you set up the graph. If anything appears on the graph other than the graph you set, press SHIFT [Sketch] F1 (Cls) to clear the extra graphs from the screen.
Note 1I Reading a Distance Using the EA-100 or EA-200
To read a distance, you will need a Casio EA-100 or EA-200 Data Analyzer, an Ultrasonic Motion Sensor (distance probe), and a meterstick or meter tape. Your EA-100 or EA-200 does not need to be connected to a calculator to measure distance. a. Connect your EA-100 or EA-200 to a distance probe from the sonic port on the right side of the EA-100 or EA-200. b. Turn on the EA-100 or EA-200. c. Press MODE until the EA-100 or EA-200 begins flashing SAMPLING and DONE alternately. Your EA-100 or EA-200 is now ready to measure and display in the multimeter mode. d. Push the CH-View button several times until the EA-100 or EA-200 display indicates SONIC M.

To distance probe

DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 21
Note 1I Reading a Distance Using. (continued)
You should see the distance probes blinking red light and hear it clicking as it samples measurements (in meters) to the nearest object in front of it. As you point the distance probe at various objects, your EA-100 will display the distances to the nearest object in meters. Shown on the previous page is a reading of an object that is 3.14 meters from the probe. e. Use your meterstick (tape) and hold the distance probe so that the front of the probe is exactly 1 meter from the wall, and then take a reading. Determine whether the distance is measured to the front, middle, or back of the probe. This knowledge is important for accurate length measurements. You will need to repeat this step if you change equipment because not all devices work the same.

If you do not get a reading, check to make sure the distance probe is plugged into the port marked SONIC and that the link cable is securely connected.

Note 1J Equations

To graph an equation on your calculator, the equation must be in the form y some expression. If the equation contains variables other than x and y, you need to rewrite it using only x and y as variables. a. From the Main Menu, select GRAPH. b. Enter the equation using the variable x. Press ,, to enter the variable x. Press EXE.
c. Setting a window for graphing equations is not as easy as setting a window for data. If it is an application problem, think about what values make sense for both x and y. You may need to try different windows to find one that is appropriate. The following graph has a view window of [10, 10, 1, 10, 10, 1]. Press EXIT to return to the Graph Func screen. d. Press F6 (DRAW).
e. If you want the axes labeled, as in the previous screen, press SHIFT [SET UP], scroll down to Label, and press F1 (On). Press EXIT to return to the graph.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 22
Note 1J Equations (continued) Tracing Equations and Plots on the Same Graph
In STAT mode, enter the data and draw a scatter plot. Store the scatter plot in one of the six picture memories. To store in Pic1, press OPTN F1 (PICT) F1 (STO) F1 (Pic1). In GRAPH mode, enter the equation, set the view window, and graph the equation. Remember, your view window must accommodate both the data and the equation. Press OPTN F1 (PICT) F2 (RCL) F1 (Pic1) to recall a graph stored in Pic1. You will see the scatter plot and the equation(s) graphed on the same screen. To trace the equation, press SHIFT [Trace]. Note the label in the upper-left corner of the screen. When you are tracing an equation, the equation is displayed. To trace the scatter plot, store the equation graph in picture memory, graph the scatter plot, and recall the equation graph. Trace works on either the scatter plot or the equation, but not on both at the same time. It works on whichever you graph first.
If you see a Syn ERROR message, check your equation and count the number of left and right parentheses to make sure they match. Look for numbers with two decimal points. Check that you used the negative or subtraction sign correctly. If you see the Graph screen but nothing appears, you might have a problem with your equation or your view window settings. Remember that your view window must accommodate both the equation and the scatter plot. Try changing one or both of these.

Note 1K Formula-Generated Lists
Enter the data into a list. (See Note 1B.) Move the cursor to another list, arrow up to highlight the list name, and press EXE. Enter the formula for the operations you want to perform. For example, if List 2 is defined as List 1 plus 47, highlight List 2, press OPTN , and then press F1 (LIST) F1 (List) If you get an error message, press AC/ON. Make sure you have highlighted the name of the list before you enter the list operation. You can perform operations with list variables the same way you do with numbers. You can add, subtract, multiply, divide, or do any other mathematical operation.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 23
Note 1K Formula-Generated Lists (continued)
For another example, let List 1 be a list of rectangle lengths and let List 2 be a list of the corresponding widths. Move the cursor so that it highlights List 3 and enter the formula for the area of a rectangle, List 1 List 2, by pressing OPTN F1 (LIST) F1 (List) 1 F1 (List) 2. Press EXE.

List Formulas

If you change the values in the list referred to in a formula, you must reenter the formula to update the values in the new list. For example, let List 1 be {2, 3, 4} and define the name of List 2 to be 3 List 1. Now, edit one of the entries in List 1; for example, change the 3 to 5. To change the second entry in List 2, you must reenter the formula for List 2.

Note 1L Matrices

To enter MATRIX mode, arrow to MAT on the Main Menu and press EXE. The MATRIX mode allows you to work with up to 26 matrices: Mat A, Mat B,. , Mat Z. To define and store a matrix, Mat A, for example, highlight Mat A on the Matrix screen. If a matrix is not defined, :None shows to the right of its name. The dimensions of a matrix are given as rows by columns. Enter the first dimension, the number of rows, and press EXE. Then, enter the second dimension, the number of columns, and press EXE. Notice that after you enter both dimensions, the matrix on the screen will be set at the appropriate size. On this calculator, matrix dimensions are limited to 255 rows or 255 columns.

Entering a Matrix

After entering the dimensions, the cursor will be at row 1, column 1. Enter the value and press EXE. The cursor moves across the first row, then down to the next row. Continue to enter values and to press EXE after each entry. You can edit any entry by arrowing to the position and reentering the value.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 24
Note 1L Matrices (continued)
After you enter all the values, press EXIT to store the matrix and to return to the Matrix screen. Notice that the dimensions are listed beside Mat A. Any matrix that shows dimensions on the Matrix screen is defined.

Displaying a Matrix

To display Matrix A, choose Mat A on the Matrix screen and press EXE. The letter A appears in the upper-left corner of the screen and the complete matrix is displayed. To return to the Matrix screen, press EXIT. If you want a matrix to represent money, you can set the calculator so that all numbers are rounded to two decimal places. To change the setting, press SHIFT [SET UP] and highlight Display. Press F1 (Fix) and F3 to select two decimal places. Press EXIT to return to the Matrix screen. As you use the arrow keys to move around the matrix, the highlighted values will be displayed to two decimal places at the bottom-right corner of the screen.

Changing or Deleting a Matrix from the Calculator
You can always change a matrix entry by arrowing to the matrix name on the Matrix screen and pressing EXE , then arrowing to the entry you want to change. If you reenter the dimensions, you will define a new matrix replacing the one you had. You might, however, want to conserve memory space and delete a matrix (or all matrices) from your calculator. To delete a matrix, go to the Matrix screen and press F1 (DEL) F1 (YES). To delete all matrices, press F2 (DEL-A) F1 (YES).
If you get a MEM ERROR message, it means there is not enough free memory to create a matrix of the size that you chose. A Dim ERROR message probably indicates that you named a matrix that is not defined.
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 25
fx-9750G Plus and CFX-9850GC Plus Note 1M Multiplying a Matrix by a Number
To multiply a matrix by a number, multiply each cell value of the matrix by the number. For example, to multiply Mat A (from Note 1L) by 50, select RUN from the Main Menu. Then press OPTN F2 (MAT) F1 (Mat) ALPHA [A] EXE. The matrix answer appears on the screen.
Multiplying a number by a matrix, Mat A 50, for example, is done in the same way. Press OPTN F2 (MAT) F1 (Mat) ALPHA [A] EXE.
A Dim ERROR message probably indicates that you named a matrix that is not defined.
Note 1N Adding or Subtracting Matrices
To add or subtract two matrices, the matrices must have the same dimensions. Define Mat B to have dimensions 3 2, and enter the values below. (See Note 1L.) 1, 1 8.9 1, 2 9.1 2, 1 2.35 2, 2 2.65 3, 1 1.5 3, 2 1.6 Define Mat C to have dimensions 3 2, and enter the values below. 1, 1 2.5 1, 2 2.25 2, 2, 2 1.25 3, 1 .65 3, 2 .5
DA2_FX9850GB_01.qxd 12/30/05 09:58 AM Page 26
Note 1N Adding or Subtracting Matrices (continued)
Go to the Run screen from the Main Menu. Press OPTN F2 (MAT) F1 (Mat) ALPHA [B] F1 (Mat) ALPHA [C] EXE. The matrix showing on the screen is the sum of Matrix B and Matrix C.
If you get a Dim ERROR message, youve tried to add (or subtract) two matrices that dont have the same dimensions or you have named a matrix that is not defined.
Note 1P Multiplying Two Matrices
To multiply two matrices, the number of columns in the first matrix must match the number of rows in the second. For example, if the first matrix has dimensions and the second matrix has dimensions 3 2, the three columns of the first matrix will match the three rows of the second. The multiplication will be defined. Enter Mat D and Mat C as shown in the screens below. (See Note 1L.)
Display Mat D Mat C on the Run screen using the following keystrokes: OPTN F2 (MAT) F1 (Mat) ALPHA [D] F1 (Mat) ALPHA [C]. Press EXE and the product will appear on the screen. The dimensions of the product are (the number of rows of the first matrix) (the number of columns of the second matrix). In this example, a matrix times a matrix has a answer.

If you get an ERR:DIM MISMATCH message, the number of columns in the first matrix does not match the number of rows in the second. An ERR:UNDEFINED message probably indicates that you named a matrix that is not defined.

DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 55

CHAPTER 10

Calculator Notes for the fx-9750G Plus and CFX-9850GC Plus
Note 10A List of Random Integers
There are several ways to generate a list of random integers within an interval. Here we will combine the three commands Seq, Int, and Ran# to generate a sequence of up to 255 terms. We will also look at a short program that will allow you to repeat the procedure quickly. You will see that with slight modifications, you can apply the commands and program to a number of familiar situations.
Integers from 1 through 100
The following procedure will generate a sequence of four random integers from 1 through 100. From RUN mode: a. Press OPTN F1 (LIST) F5 (Seq). b. Press OPTN F6 () F4 (NUM) F2 (Int). c. Press ( OPTN F6 () F3 (PROB) F4 (Ran#). d. Press x 0 ) , ,, , 1 , 4 , 1 )
After completing steps ad, press EXE. Press EXE EXE EXE and so on. Notice that each time you press EXE , a new sequence is generated.
By changing the 100 in step d to 50 and the 4 to 10, the same procedure would generate a sequence of ten random integers from 1 through 50. To make changes, press EXIT until you see the Run screen displaying Done. Then, press the left REPLAY arrow key. Use the arrow keys, DEL , and SHIFT [INS] to access the formula and change it. If you add another step to the procedure, your calculator can store the sequence into a list. (See Note 10B.) Add the following step: e. Press OPTN F1 (LIST) F1 (List) 1. Now when you press EXE , you do not see the sequence, but you see Done. Press MENU , select STAT or LIST, and look at List 1.
Unfortunately, when you change modes to look at the list and then return to RUN mode, your screen is blank and you need to reenter the steps. You can avoid this inconvenience by storing your work in Function Memory and recalling it when you need it again. Add the following step to the procedure: f. Press OPTN F6 () F6 () F3 (FMEM) F1 (STO) F1 (f1).

(continued)

2007 Key Curriculum Press
Discovering Algebra Calculator Notes for the Casio fx-9750G Plus and CFX-9850GC Plus
DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 56
Note 10A List of Random Integers (continued)
fx-9750G Plus and CFX-9850GC Plus
The Function Memory screen shows what you have stored in each function key. Press EXIT twice to return to the Run screen, or press MENU to go elsewhere. Now if you leave RUN mode and then return to it, you can recall the stored procedure by repeating step f, substituting F2 (RCL) for F1 (STO).
When you recall your formula, it is active and you can use the REPLAY arrow keys, DEL , and SHIFT [INS] to go back into the formula and change it. For example, you can change the interval, send it to a list or not, change the list you send it to, and so on. You do not have to reenter the entire formula each time you want a variation. You can store different versions of the formula with different Function Memory numbers. If you turn your calculator off and then back on, your formulas will still be stored in memory and can be accessed by following step f with the F2 (RCL) substitution. An alternative to the preceding procedure is to use a program called RNDINT. Download, link to, or manually enter the RNDINT program. (See Notes 0F and 0G.) The program allows you to set the interval and to decide how many random integers you want in a sequence within the interval. The program stores the sequence in List 1 and displays it on the Run screen.
File Name:RNDINT ClrText "WHAT IS THE LOWEST" "VALUE"?L ClrText "WHAT IS THE "HIGHEST" "VALUE"?H ClrText "HOW MANY VALUES"?N Seq(Int (Ran#(H-L+1))+L,X,1,N,1)List 1 List 1
To use the RNDINT program to generate a sequence of four random integers from 1 through 100, follow the steps below. a. Press MENU and select PRGM. Arrow down to RNDINT and press F1 (EXE), or press EXE. b. In response to the question WHAT IS THE LOWEST VALUE?, press 1 EXE. c. In response to the question WHAT IS THE HIGHEST VALUE?, press 0 EXE. d. In response to the question HOW MANY VALUES?, press 4 EXE. e. The Run screen shows a sequence of four integers. The same sequence is in List 1. You can check List 1 by going to STAT or LIST.
DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 57
Note 10A List of Random Integers (continued) Two Possible Outcomes: Coin Toss/True-False Test
Suppose you want to simulate the results of 100 coin tosses with 0 representing tails and 1 representing heads. Use the REPLAY arrow keys, DEL , and SHIFT [INS] to change step d in the Integers from 1 through 100 section to the following: d. Press x 2 ) , ,, , 1 , 0 , 1 ). The results of this sequence of commands can be stored in a list. (See step e in Integers from 1 through 100.) You will use this formula later. You might want to store it in Function Memory. (See step f in Integers from 1 through 100.)

You can also use the RNDINT program to simulate the results of 100 coin tosses. Run the program and answer 0 to the question WHAT IS THE LOWEST VALUE?. Answer 1 to the question WHAT IS THE HIGHEST VALUE?, and answer 100 to the question HOW MANY VALUES?. The results appear on the Run screen and in List 1.
Six Possible Outcomes: Tossing a Die
Suppose you want to simulate the results of four throws of a die. Use the REPLAY arrow keys, DEL , and SHIFT [INS] to change step d in Integers from 1 through 100 to the following: d. Press x 6 ) , ,, , 1 , 4 , 1 ) 1. The results of this sequence of commands can be stored in a list. (See step e in Integers from 1 through 100.) You might want to store it in Function Memory. (See step f in Integers from 1 through 100.)
You can also use the RNDINT program to simulate the results of throwing a die four times. Run the program and answer 1 to the question WHAT IS THE LOWEST VALUE?. Answer 6 to the question WHAT IS THE HIGHEST VALUE?, and answer 4 to the question HOW MANY VALUES?. The results appear on the Run screen and in List 1.
DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 58
Note 10A List of Random Integers (continued) Two Possible Outcomes: Random Walk
Suppose you want to simulate a random walk back and forth on a road by generating a sequence of four 1s and 1s. Use the REPLAY arrow keys, DEL , and SHIFT [INS] to change steps a and d in Integers from 1 through 100 to the following: a. Press 2 OPTN F1 (LIST) F5 (Seq). d. Press x 2 ) , ,, , 1 , 4 , 1 ) 1. The results of this sequence of commands can be stored in a list. (See step e in Integers from 1 through 100.) You might want to store it in Function Memory. (See step f in Integers from 1 through 100.)
To use the RNDINT program to simulate the random walk, generate a list of four 0s and 1s as in the Coin Toss/True-False Test procedure. That sequence is stored in List 1. Press MENU and select STAT. Define List 2 as 2List11. (See Note 1K.) Your sequence of 1s and 1s is in List 2. Remember, however, that each time you run the program, you will have to redefine List 2. As an alternative, you can carefully edit the RNDINT program to give your desired results. (See Note 0G.) a. Press MENU and select PRGM. b. Arrow down to RNDINT and press F2 (EDIT). c. Arrow to the next-to-last command line that begins with Seq. Use SHIFT [INS] to insert 2 before Seq and add 1 after the last closing parenthesis. d. Press EXIT and then F1 (EXE) to execute the altered program. Use 0 as the lowest value, 1 as the highest value, and 4 as the number of values. Your sequence is in List 1. Every time you execute the program, you generate a new sequence. When you are finished, change the program back to its original form.

Viewing an Entry in a List
To avoid having to scroll through a list to see a distant entry, you can view any term directly on the Run screen. If in List 1 you have 50 random
DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 59
integers from 1 through 100 and you want to see the fortieth term, from the RUN mode press OPTN F1 (LIST) F1 (List) 1 [[] []] EXE.
You can use the same command in any mode. For example, in LIST you can enter the seventieth term of List 1 as the first term of List 2.

Errors

The longest sequence you can make has 255 entries. If you get an Arg ERROR, a Mem ERROR, or a Dim ERROR message, you are probably trying to construct a sequence that is too long, or you are referring to a term of a list that does not exist.

Note 10B List Operations

(See Note 1B for instructions on entering a list.)

Sorting a List

When working with long lists, it is often more convenient to order the numbers in the list rather than to scan the list for the smallest, greatest, middle, or any other value. Press MENU and select LIST, then press F1 (SRT-A) for ascending order or F2 (SRT-D) for descending order. In response to the prompt How Many Lists?(H), press 1 EXE if you want to sort only one list. In response to the prompt Select List(L), press 1 EXE if you want to sort List 1.
Suppose that you have two related lists and you want to sort List 2 in ascending order, but you want each entry in List 1 to stay with its corresponding entry in List 2. From the Main Menu, select LIST and press F1 (SRT-A). Press 2 EXE when you see the prompt How Many Lists?(H). Press 2 EXE when you see the prompt Select Base List(B), and press 1 EXE when you see the prompt Select Second List(L). Notice that in the screen on the far right below, the entries in List 2 are in ascending order and the original pairings have not changed.
DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 60
Note 10B List Operations (continued) Filling a List with a Sequence
The sequence command Seq(X,X,1,50,1) will generate the sequence of integers from 1 through 50. The command Seq(X,X,10,40,2) will generate the sequence of even numbers from 10 through 40. To access Seq, select RUN from the Main Menu and press OPTN F1 (LIST) F5 (Seq). Then complete the command and press EXE.

To fill List 1 with your sequence, press EXIT once or twice until you see your commands followed by Done. Press the left REPLAY arrow key to reactivate the commands and clear Done from the screen, and then press OPTN F1 (LIST) F1 (List) 1 EXE. (See Note 2C for more on instant replay.)
You can also fill a list with a sequence in LIST or STAT by defining the list name with the Seq command as in the screen below. (See Note 1K.)

Cumulative Sum of a List

This calculator has a list function that will find the cumulative sums of a list and enter those sums into another list. For example, if List 1 is the sequence of integers from 1 through 10, then to generate the cumulative sums of List 1 and enter them into List 2, press
OPTN F1 (LIST) F6 () F6 () F3 (Cuml) F6 () F1 (List) 1 F1 (List) 2 EXE

Other List Functions

In RUN mode, you can find the mean, median, sum, and other important numbers associated with a list by pressing OPTN F1 (LIST) F6 (). Press F6 ()
DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 61
Note 10B List Operations (continued)
to see more options. Always specify the list name and close any parentheses. (Also see Note 1C.)

min max mean median sum

the minimum value in a list the maximum value in a list the mean of the list entries the median of the list entries the sum of the list entries.
To get the screen below, press
OPTN F1 (LIST) F6 () F2 (Max) OPTN F1 (LIST) F1 (List) 2 ) EXE
Note 10C Calculator Coin Toss 100 Trials
a. Enter the sequence of integers from 1 through 100 into List 3. This list will number the trials. (See Note 10B.) b. Enter 100 randomly generated 0s and 1s into List 1. List 1 will represent the 100 coin tosses. Let 0 represent tails and 1 represent heads. (See Note 10A.) c. Use Cuml to calculate the cumulative sums of List 1 and store them in List 2. (See Note 10B.) List 2 d. Calculate the ratio and store the results in List 4. (See Note 1K.) List 3 e. Make a scatter plot using List 3 for the x-values and List 4 for the y-values. Use the small dot as the mark. Set appropriate view window parameters. (See Note 1F.) f. Enter the probability of tossing a head into Y1 in the Graph Func screen in GRAPH mode. Graph this equation along with the scatter plot. (See Note 1J.)

200 Trials

By changing 100 to 200 in steps a and b in the previous section, you can modify 100 coin tosses to work for 200 tosses. You can also enter the short program that follows so that you can rerun the simulation without reentering the commands each time. This program only enters data into lists. You then need to make a scatter plot and graph the probability as in steps e and f in the preceding section.

can be changed from 1 to the probability of an event that does not have 2 outcomes that are equally likely.
DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 62
Note 10C Calculator Coin Toss (continued)
File Name:PROBSIM Seq(X,X,1,200,1)List 3 Seq(Int (Ran#2),X,1,200,1)List 1
Prog "CUMSUM" List 2List 3List 4

Note 10D Permutations

To find numbers of permutations, use the nPr command. To find the nPr command, go to the Run screen, and press OPTN F6 F3 (PROB) F2 (nPr). First, enter the value of n, which is the number of objects. Then, enter the nPr command, and enter the value of r, which is the number of objects chosen. Then press EXE. For example, to find the number of arrangements of 5 objects chosen 3 at a time, enter 5 nPr 3. The answer shows that there are 60 arrangements.

Note 10E Combinations

To find numbers of combinations, use the nCr command. To find the nCr command, go to the Run screen, and press OPTN F6 F3 (PROB) F3 (nCr). First, enter the value of n, which is the number of objects. Then, enter the nCr command, and enter the value of r, which is the number of objects chosen. Then press EXE. For example, to find the number of groupings of 5 objects chosen 3 at a time, enter 5 nCr 3. The answer shows that there are 10 different groupings.

Note 10F Factorials

To find the factorial command, press to evaluate 5!, press 5 OPTN F6 F3 F1
OPTN F6 F3 (PROB) F1 (x !). EXE

For example,

DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 63
Note 10F Factorials (continued)
In the order of operations, factorial has higher precedence than negation, so 3! is equivalent to (3!).

Note 10G CITIES Program

The CITIES program will simulate random travel among six cities, stopping when a previously visited city is revisited. Run the program and choose whether youd like to view one, ten, or some other number of trips. If you choose 1. ONE TRIP, youll see travel among the six cities labeled AF, and the histogram will show you the total number of cities visited on this trip. When the program stops, retrieve the histogram by choosing STAT from the Main Menu, and then pressing F1 (GRPH) F1 (GPH1). Then, press EXE to simulate another trip, or quit.
If you choose 2. TEN TRIPS, youll see ten trips simulated, and the histogram will show how many cities were visited during the ten trips. As the program runs, you will see a map of the six cities and a trace of the route taken during each trip. When the program stops, retrieve the histogram by choosing STAT from the Main Menu, and then pressing F1 (GRPH) F1 (GPH1). Selecting F2 (GPH2) instead will allow you to see the tenth route taken before the program finished. The first screen shown below indicates that four cities were visited during the tenth trip. The second screen shows that in the ten trips, two trips visited one city, four trips visited two cities, two trips visited three cities, and two trips visited four cities.

If you choose 3. CHOOSE TRIPS, you can choose any number of trips up to the limit of your calculators available memory. The program wont show each trip, but it will show a histogram with the number of trips that visited 1, 2, 3, 4, 5, and 6 cities. After you run this option, press SHIFT [QUIT] EXE to continue.
DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 64
Note 10G CITIES Program (continued)
F-Line List 3[K],List 4[K],List 3[K],List 4[K] F-Line List 3[K],List 4[K],List 3[K],List 4[K] F-Line List 3[K],List 4[K],List 3[K],List 4[K] Int (Ran#(6))+1C K+1K List 5[C]List 3[K] List 6[C]List 4[K] F-Line List 3[K-1],List 4[K-1],List 3[K],List 4[K] LpWhile List 2[C]=0 K-1List 1[J] S-Gph1 DrawOn S-Gph2 DrawOn DrawGraph Plot 2,4 Plot 5,4 Plot 6,2.5 Plot 5,1 Plot 2,1 Plot 1,2.5 ClrGraph ViewWindow 0,7,1,0,5,1 Next Goto 0 Lbl 3 S-Gph2 DrawOff S-Gph3 DrawOff "N"?N Seq(0X,X,1,N,1)List 1 ViewWindow 0,6,0.5,0,N2,1 For 1J To N {0,0,0,0,0,0}List 2 0K Int (Ran#(6))+1C Do K+1K 1List 2[C] Int (Ran#(6))+1C LpWhile List 2[C]=0 KList 1[J] Next S-Gph1 DrawOn,Hist,List 1,1 DrawStat Lbl 4
Filename:CITIES ClrList ClrGraph Lbl 0:1N "CITY HOPPING" "WHEN DONE PRESS MENU,STAT TO VIEW GRAPHS" "1. ONE TRIP" "2. TEN TRIPS" "3. PICK N" "4. QUIT" ?A ClrText A=1Goto 1 A=2Goto 2 A=3Goto 3 A=4Goto 4 Lbl 2:10N Lbl 1 {0,0,0,0,0,0,0,0,0,0}List 1 {0,0,0,0,0,0}List 3 {0,0,0,0,0,0}List 4 S-Gph1 DrawOn,Hist,List1,1 S-Gph2 DrawOn,xyLine,List3,List4,1, Square ClrGraph S-Gph3 DrawOn,Scatter,List 5, List 6,1,Cross {2,5,6,5,2,1}List 5:{4,4,2.5,1, 1,2.5}List 6 ViewWindow 0,7,1,0,5,1 For 1J To N {0,0,0,0,0,0}List 2 1K Int (Ran#(6))+1C List 5[C]List 3[K] List 6[C]List 4[K] S-Gph2 DrawOff DrawGraph Plot 2,4 Plot 5,4 Plot 6,2.5 Plot 5,1 Plot 2,1 Plot 1,2.5 Do 1List 2[C] F-Line List 3[K],List 4[K],List 3[K],List 4[K]
DA2_FX9850GB_10.qxd 12/30/05 10:06 AM Page 65
fx-9750G Plus and CFX-9850GC Plus Note 10H Infinite Sums
To find the sum of terms of a recursive sequence, you can use a recursive routine. Rather than finding the terms of a recursive sequence, as you did in Chapters 0 and 3 (See Notes 0D and 3A), here youll find the sum of the terms of a recursive sequence. For example, to find the sum of 1 . you create the sequence 1, 1.5, 1.75, and so on. This sequence shows the sum of the first one term, the first two terms, the first three terms, and so on. Using the sum feature, (, you can look at what happens to this sequence as you add more terms of the sequence. To find the sum after any number of terms has been added, write a formula that will generate each term. n1 Each term is defined by 1 , where n is the term number. 2 To enter this formula into your calculator, follow these steps: a. From the Run screen, press OPTN F4 (CALC) F6 F3 ((). b. Now, you are ready to build the formula. Press ALPHA [N] to enter the letter N as the index variable. The formula is followed by values that tell the calculator how to evaluate the sum. If, for instance, you want to find the sum of the first 11 terms, you enter N, 1, 11, 1. This tells the calculator to sum the expression with N terms, starting at N 1 and ending at N 11, increasing by one unit each time. The sum appears to be approaching 2. Test this conjecture by finding the sum of more terms.

Now, consider the sum 1 2 3 3 3

4 3 3

5 3 3

1 3

Notice that one factor in each term is the counting number, another factor in each term is always 1, and the remaining factor is a power of 2, 0 n1 beginning with 2. So an expression for the terms is n 1 2. Enter 3 the formula into the calculator as described before and evaluate the sum after some number of terms. In this case, the sum appears to approach 3. Experiment by taking the sum of a greater number of terms to confirm this guess.