INTERNATIONAL BACCALAUREATE

MATHEMATICAL METHODS

STANDARD LEVEL

fx-9700GH + CFX-9850G

Calculator Supplement
This booklet is intended to be used in conjunction with the Mathematical Methods text ISBN: 8, published by IBID Press. It describes the keying sequences that can be used to perform the calculations described in the text for the Texas series of calculators. This booklet is not a manual for the calculator and does not describe all the features of the calculator that could be useful to students of the IB course. Students are advise to work through the manufacturers manual so that they become thoroughly familiar with their calculator. IBID press gratefully acknowledge the help and support of CASIO in the production of this supplement. Keying sequences are described by giving the key followed by the associated menu description which can usually be seen on the screen. Thus press F6 (DRAW) means press the F6 key above which you should see the word DRAW on the screen. These notes have been written using models fx-9700GH & CFX-9850G. The exact capabilities of this series of calculators varies from model to model. These notes are a guide only.
Copyright IBID Press, Victoria. First published in 1998 by IBID Press, Victoria, Published by IBID Press, Victoria. Library Catalogue:
This document is sold copyright free for use by the students of the purchasing institution only. While every care has been taken to trace and acknowledge copyright, the publishers tender their apologies for any accidental infringement where copyright has proved untraceable. They would be pleased to come to a suitable arrangement with the rightful owner in each case. This booklet has been developed independently of the International Baccalaureate Organisation (IBO). The text is in no way connected with, or endorsed by, the IBO.
Published by IBID Press, Box 9, Camberwell, 3124, Australia.

CHAPTER 1 CHAPTER 2

Section 2.1 Section 2.2 Section 2.3
Page 24. Set the desired modes before doing any calculations by choosing the RUN mode followed by the key sequence SHIFT SET UP. Use the down arrow to scroll the instructions to Display. F1 will allow you to x the number of decimal places in the display. Use F4 to select 3 decimal places.
Press EXE and then calculations can be performed in the FIX mode.
Scientic notation is set by selecting Sci from the setup menu. F4 selects scientic notation with 3 signicant gures. Numbers in scientic notation can be entered using the EXP key before the power of 10.
Page 25. Set Sci format with 3 gures to get the same output

Section 2.4

Page 28. The absolute value function is obtained by using OPTN F3 (CPLX), (complex numbers)

CHAPTER 3

Section 3.1
Page 40. The replay feature is automatic. Enter 5 and then press + 7. Successive pressing of EXE will generate the sequence.
Page 43. Choose the TABLE option from the main menu. Next, enter the rule that you want to tabulate. and then use F5 (RANG)

Press EXIT and then press F6 (TABL) to display the table. It may be necessary to adjust the table range to view the part of the table that you need. The arrow keys will only allow you to scroll through the values set in this range.

Section 3.2

Page 48. The replay is automatic in the RUN mode. Enter 50 and then press EXE. Next, press multiply and then 0.5 EXE. Repeated pressing of EXE will generate the sequence.
Page 49. Use the TABLE mode from the main menu. Enter the rule as a Y= function. Use TABLE SETUP (RANG F5) to select the terms that you want to generate, press EXIT and the TABL (F6).
Page 50. The calculator uses brackets in the standard algebraic manner. Use the RUN mode to perform this calculation.

CHAPTER 4

Section 4.1
Page 58. The power key is ^.
Page 61. Index calculations.

Section 4.2

Page 65. The base 10 logarithm key is marked log and the natural logarithm key, ln.
Page 67. The calculator has an automatic Ans memory that works in the same way as the model described in the main text.
Page 71. A good option is to display the graph of the function and then use G-Solve followed by F1 to select root.

Page 73.

Note that it is not necessary to use the ^ key when using this calculator to evaluate the exponential function.

CHAPTER 5

Section 5.1
Page 79. The combinatorial numbers are found using the OPTN key to select the options menu. The probability options are off screen and can be accessed using F6. F3 can now be used to show the probability functions. The combinatorial keys remain on screen and so sequential calculations can be completed quickly either by using the replay feature (left or right arrows) or by using the appropriate function keys.
The replay key clears the screen before redisplaying the previous calculation for editing.

CHAPTER 6

Section 6.1 Section 6.2 Section 6.3
Page. 94. Use the GRAPH option from the main menu. After making y the subject of both equations, enter these as functions. Use SHIFT V-Window (F3 key) to display the current window. Choose STD (F3) to choose the standard viewing window.
Press EXIT and then F6 (DRAW) to display the graph. The viewing window INIT (F1) provides a scale that is a multiple of the number of screen pixels, making trace operate more easily. SHIFT F1 (TRACE) can then be used to identify the intersection point.

In addition, SHIFT G-Solv (F5) followed by F5 (ISECT) will locate the intersection point.

Section 6.4

Page 98. Select the TABLE mode from the main menu. Next, enter the function rule and then use RANG (F5) to select the table range.
Press EXIT and then F6 (TABL) to display the table. F5 (G-CON) can then be used to display the connected graph or F6 G-PLT to display the disconnected points of the table. Remember that you may need to reset the viewing window to, for example, the standard window.
Page 99. Enter the new formula and set the table range. F5 G-Con can be used to display a connected graph. The CASIO handles the discontinuity correctly. F6 G-PLOT can be used to display the pointwise graph.

CHAPTER 7

Section 7.1 Section 7.2
Page 114. Use the graph mode, enter the function rule and select the INIT option from SHIFT F3 (V-Window).
Use SHIFT F2 (Zoom) followed by F4 (OUT) to zoom out whilst still preserving the correct multiple ratio between the viewing window and the screen pixels. It is now possible to use SHIFT F1 (TRACE) to locate the minimum. In this case the true minimum is missed. Alternatively Use SHIFT F5 (G-Solv) followed by F3 (MIN) and the arrows to automatically locate the minimum point.
Page 116. Use the GRAPH mode from the main menu and enter both formulas. Choose a suitable viewing window and display the graph.
Either use ZOOM and TRACE to nd the intersection points, of use the G-Solv facility described earlier to locate the intersection points.

CHAPTER 8

Section 8.1
Page 125. The window that will set the correct scales to display a circle is F1(INIT). This will set a scale that is directly related to the number of rows and pixels of the screen.
Set the basic function as Y1. Enter a negative sign (). Then use the VARS key followed by F4 (GRPH) and F1 to select the variable Y. Finally enter 1 EXE to record the second function Y2 as the negative of the rst Y1. Press F6 DRAW to display the complete circle with the correct aspect ratio.
If the standard viewing window is chosen, the circle will be displayed as an ellipse.

Page 127. Enter the rule under the Y= menu, choose a suitable viewing window using SHIFT F3. Press EXIT, F6 to draw the graph.

Section 8.2

Page 128. Dene Y1 as dow. x and Y2 as Y1 as before. Display the graph using a suitable win-

Section 8.3

Page 134. To plot absolute value functions, select the graph mode from the main menu. With the Y= screen active, press the OPTN button, followed by F5 (NUM) and F1 to select the Abs function. Enter the desired expression, choose an appropriate window and display the graph.
Other examples are entered in a similar way.
Page 136. Exponential functions are entered using the caret key ^.
With 0 < a < 1, the form of the graph is:

Section 8.4

Page 147. Use the graph mode and enter the function rule. Use SHIFT F3 (V-Window) to select an appropriate window and then press EXIT, F6 (DRAW) to show the graph. Note again that the CASIO handles the discontinuity correctly.
The third example on page 147 can be entered in a similar way.

CHAPTER 9 CHAPTER 10

Section 10.1
Page 176. First use the RUN mode and SHIFT SETUP to set the calculator to degree mode.
The angle instructions are found under the OPTN key, followed by F6 (more) and then F5 (ANGL).
The F4 key now allows you to enter degrees minutes and seconds. Enter the rst part of the calculation as normal until you have reached the sine expression. Press sin, 39 followed by F4. This records the 39 as degrees. Finally press 17 F4 EXE. This records the 17 as minutes and completes the calculation.
The F5 key acts as the degree, minute, second converter. Enter the inverse cosine calculation and press EXE. The result is displayed as degrees and decimal parts of a degree. If you then press F5 the display switches to degrees, minutes and seconds.

CHAPTER 11

Section 11.1
Page 194. To convert decimal degrees to degrees, minutes & seconds, enter the decimal angle, use the MATH menu and use F4 (DMS), press F1 EXE followed by F2 to obtain the answer.

CHAPTER 12

Section 12.1
Page 211. Begin with the graph mode from the main menu. Use SHIFT SET UP to check that the angle mode is set to radians.
Next, set the viewing window with SHIFT F3. Choose F2 (TRIG), press EXIT and F6 (DRAW) to display the graph. In this case, the viewing window is not quite correct. Edit the y window to be 2 to 5 and then display the graph.

Section 12.2

Page 214. Make sure that you are using the angle measurement scale (degrees or radians) that you intend (using SHIFT DRG).

CHAPTER 13

Section 13.1 Section 13.2 Section 13.3 Section 13.4 Section 13.5
Page 249. To enter vectors and matrices, choose the MAT (matrix) option from the main menu. The calculator offers a list of matrices that can be edited. Press the right arrow and enter the size of the matrix in this case 3 by 1.

Press EXE and you will see a picture of the vector whose entries can be edited. Enter B in a similar way.
Within the matrix mode, most of the available operations are manipulations of single vectors and matrices. Arithmetic with vectors and matrices is done by returning to the run mode through the main menu. Use the OPTN key followed by F2 (MAT) F1 (mat) to reach a screen that will allow you to recall the vectors and matrices stored previously. To perform the specied calculation with, press 3 F1 (Mat) ALPHA A 4 F1 (Mat) ALPHA B EXE.

CHAPTER 14

Section 14.1
Page 262. The statistical option from the main menu allows the entry of lists of statistical data. Enter the data as a list.
The data can now be displayed as a histogram. Press F1 (GRPH). It is necessary to set the parameters controlling the type of graph to be displayed. To do this press F6 (SET), move the highlighter to Graph Type, press F6 (more) and F1 (Hist) to select histogram as the graph type. Also, you must select the list in which the data is stored (L1) and the frequency. In this case we have entered raw data and so this should be 1. If grouped data was entered as L2, then this item should be adjusted to record this. Press EXE and F1 (GPH1) to display the graph.
The histogram displayed is different from that in the text because the calculator has chosen different class groupings. The default mode is for the calculator to select these automatically. If you want to choose this you must set this to manual. To do this press SHIFT SET UP. Change Stat Wind to Man (Manual) by pressing F2. Press EXIT, F1 (GRPH) and then F1 (GPH1) to select the statistical graph. On this occasion, you will see a screen that allows you to set the manner in which the data is grouped. In this case we want class intervals of 148-150, etc. so edit the screen to allow this. Press F6 (DRAW) to display the graph. Other choices from the set up screen can produce other versions of the graph.

Section 14.2

Page 269. Enter the grouped data as two lists. If necessary, delete existing lists by pressing F6 (more), F4 (DEL-A) F1 (YES). You may need to press F6 (more) to display the F2 (CALC) option. Press this and then press F1 (1-VAR) to calculate the single variable statistics of the data. You may also need to set the correct lists for the calculation. For these data these need to be L1 and L2. Press F6 (SET) and use the function keys to edit the rst two entries in the list.
All should now be set to calculate the 1 variable statistics. Press EXE followed by F1 (1VAR) to display these results. The two versions of the standard deviation are clearly labelled with their weighting. xn is the population standard deviation and xn-1 is the sample standard deviation.

Page 273. If necessary, clear existing lists. Press F6 (more), F4 (DEL-A) F1 (YES). Next, enter the raw data. as L1. Next, check that the lists are correctly set by pressing F6 (SET). Edit the screen to show that the data is in L1 with a frequency of 1. Press EXIT twice and then set the graph parameters as necessary by pressing F6 (SET). Move the highlighter to Graph Type. Press F6 (more) and F2 (Box) to select the median box plot.
It may be necessary to reset the scaling to automatic. To do this, press SHIFT SET UP and edit Stat Wind to Auto. Press EXIT and F1 (GPH1) to display the box plot. The trace feature now allows you to identify the main points on the graph. Press SHIFT F1 (Trace). Use the arrows to locate these.
To display the statistics, press EXIT twice followed by F2 (CALC) and then F1 (1-var). There are other gures that can be scrolled onto the screen using the down arrow. The manual denes these clearly.
Page 274. If the data is grouped, enter it as two lists. If necessary, clear existing lists rst. If necessary, press F6 (more) to obtain the CAL option. Press F2 to select this and then F6 to set the lists to be List 1 for the data and List 2 for the frequency. Press EXE and then F1 (1VAR) to calculate the one variable statistics. Again, the values that you want may not be on the rst screen to be displayed. Use the arrows to scroll to these.

CHAPTER 15 CHAPTER 16

Section 16.1 Section 16.2 Section 16.3 Section 16.4
Page 333. To nd a numerical slope, rst enter and display the graph of the function. Next, Select G-SOLV. It is a good idea to choose a range that will allow the cursor to move in integral steps. This diagram shows the x-interval [0,6.3].
Press F3 to display the gradients.

CHAPTER 17 CHAPTER 18

Section 18.1 Section 18.2 Section 18.3
Page 377. To nd the maxima and minima of functions using the CASIO calculator, select the graph mode from the main menu. Enter the required function using the Y= screen. Select a suitable window such as [2,5] for x and [2,2] for y. Display the graph (EXIT, F6 DRAW). Use SHIFT F5 (G-Solv) followed by F2 (and the right arrow) to locate the local maximum.
Page 378. Enter the required function f ( x ) = x 2 sin ( x ) , choose the viewing window suggested in the text. Select SHIFT F5 (G-Solv) followed by F2 (and the right arrow) to locate the local maximum. Remember to use SHIFT SETUP to check that the calculator is set in radian mode.

Section 18.4

Page 390. To nd the axis intercepts, use the GRAPH mode selected from the main menu. Enter the function using the Y= screen. Next, choose an appropriate viewing window and select G-Solve (SHIFT F5), then select F1 (ROOT) and possibly the right arrow to display the intercept.

Section 18.5

Page 401. Draw the graph and then use G-SOLV followed by F1 to nd the roots of the equation. Use the right arrow to nd the second solution.

CHAPTER 19

Section 19.1 Section 19.2 Section 19.3 Section 19.4
Page 422. The integral function is found under the OPTN key. Choose F4 (CALC) and F4 to choose the integral symbol. Enter the function and the limits of the integral separated by commas and nally EXE.
Page 430. An alternative is to use the graph mode from the main menu. Enter the function rule. You are advised to use a viewing window based on multiples of the scales of the INIT window as these give better x values when using TRACE and some of the G-Solv functions. Display the graph and choose SHIFT F5 (G-Solv), F6 to choose more options, F3 to choose the integral function. Use the arrow keys to mark the lower terminal (1) followed by EXE. Because the window has been chosen, you should nd that you can locate x = 1 exactly. Next locate the upper terminal (3) and press EXE. The area appears shaded and the value of the area is displayed.

CHAPTER 20 CHAPTER 21

CHAPTER 22 CHAPTER 23

Section 23.1

Page 484. Select the REG (regression) mode.
Set an appropriate range for this example. Then clear the statistical memory with SHIFT CLR F2 EXE.
Enter the data using the function keys for comma and data entry (F1, DT). To enter the pair 10,9, enter 10, press F3, enter 9, press F1.
As this happens, the scattergraph is displayed.
A regression line can be added by pressing Graph SHIFT F4 Line 1 EXE.

Section 23.2

Page 488. To calculate regression statistics, enter the data as described above. Remember to clear the memory rst. Next use F6 (Reg) to allow you to nd the regression parameters described in the text. Page 492. Adding the regression line to a scattergraph was described above.

CHAPTER 24

Section 24.1 Section 24.2 Section 24.3 Section 24.4
Page 509. Enter the required function under the graph menu.

Select a suitable range.

Select F6 DRAW to show the graph.
Page 511. Set the graph up as above. The result should be:

CHAPTER 25

Section 25.1
Page 517. Iterative processes can be processed in the COMP or RUN modes.
Page 519. Select the TABLE & GRAPH mode.
Choose the recursion mode F2 (RECR).
Enter the recursion formula.
Select F2 (RANGE) and enter your choice. The rst term is entered as the third of these numbers.

Press F1 to display the table. Note that the rst term is numbered zero as opposed to one in the case of the TI calculator.
Return to the TABLE mode, press F2 to select the RECR mode and press F6 (G-PLT) to plot the graph. The remainder of the examples in this section can be solved in a similar way.
Page 522. This iterative scheme can be implemented by enter1 ing the iteration formula: ------------- as a recursion formula: x2 + --------------. The rst guess must be entered as a 0. 2+1 an Scrolling down will produce additional iterates.

Section 25.2

Page 534. Select the graph mode and enter the polynomial.

Draw the graph.

Select G-SOLV followed by F1 (ROOT) to display the point at which the graph crosses the axis.
The second example can be solved by plotting both graphs, selecting G-SOLV and pressing F5 (ISECT) to nd the intersection point.

CHAPTER 26

Section 26.1 Section 26.2 Section 26.3 Section 26.4
Page 552. This problem would need to be solved as: A =
( x + 2 ( x 2 + x 2 ) ) dx =

1 ( 4 x 2 ) dx

Do not use the graph mode for this, RUN or COMP will do. Use G-dx and make the entry shown. After choosing an appropriate range, the result should be similar to:
Page 553 example 2. Enter the rule using the RUN mode and use G-dx to enter the appropriate rule and terminals.

The result is:

To obtain the correct answer we must use the symmetry of the diagram and nd one half of the true answer.

CHAPTER 27

Section 27.1
Page 562. To continue with matrix calculations it may be necessary to clear previously stored matrices. Edit the dimensions of matrix A to be 4 by 7.

Section 27.2

To perform matrix multiplication, use the MAT option from the main menu to enter both matri19
ces as A and B. Next, return to the RUN mode via the main menu and press OPTN followed by F2 (MAT). Now press F1 (Mat) followed by ALPHA A to enter the matrix A. Press the multiply key and enter matrix B by pressing F1 (Mat) followed by ALPHA B to enter matrix B and nally EXE to complete the calculation.
Section 27.3 Section 27.4 Section 27.5
Page 581. To use the matrix method to solve simultaneous equations, enter the two matrices as described above and return to the run mode. Press OPTN followed by F2 (MAT). Use F1 (Mat) and ALPH A to enter matrix A. Press SHIFT x 1 (not ^ (1))and then multiply by matrix B. Press EXE to evaluate the product.

Inverse matrices can be calculated as above. Note that the fractional values of the answer appear at the bottom right of the screen. To read the other entries, us the arrow key to move the highlight to the desired entry.