Casio ClasspadReplacement calculator screens for the Core material Chapter 1: Univariate data Page 30 Using the calculator to find the mean, median and modeUse the calculator to find the mean and median of the following data : 2, 3, 5, 4, 3, 6, 5, 7, 3, 8, 1, 7, 5, 5, 9 Tap on the Statistics icon I in the applications menu.

Use list 1; check that the cursor is in the first position of list 1.Type 2 into the first position; this value will appear at the bottom of the screen as [ 1] = 2. Key E to move to the next position in the list. Type the remaining data values into list 1 keying E after each entry.

Note: There are 15 data values in the set so the screen shows all the data is entered in list 1.

To find the descriptive statistics for the data Tap Calc in the menu bar to get you into the menus for finding descriptive statistics. We are dealing with only one variable so tap the option One-Variable

The Set Calculation screen allows you to select the list that contains the relevant data. Tap OK

All the available descriptive statistics for this variable appear on the screen :- On this screen the first statistic, • •, is the mean. The mean of the data is 4.867 (to 3 decimal places)

The second statistic: x� = 73 means that the sum of the data v

all k symbol � meaning alues as 73; the Gree

5’ refers to the fact that there are

tics

ber summary hich is covered in section 1F

‘sum of’. The next three statistics we will consider in section 1E. ‘n = 1 15 data values in the set. Scroll down to access other statisMed = 5 means the median is 5 Mode = 5 gives the mode for this data set The other statistics on this part of the screenare the statistics of the five-numw

1

Page 34 Using the calculator to find the range and inter-quartile range:

Key the data into a list. The data does not have to be ordered.

Tap Calc in the menu bar to get you into the menus for

finding descriptive statistics. We are dealing with only one variable so tap the option One-Variable

The Set Calculation screen allows you to select the list that contains the relevant data. Tap OK

The screens at right show all the statistics for the data. Scrolling down will reveal the lower part of the screen.

The range is maxX – minX = 14 – 3 = 11

The IQR = Q3 – Q1 = 9 – 5 = 4

Page 38 Using the calculator to find the standard deviation

Key the data into a list.

Tap Calc in the menu bar to get you into the menus for finding descriptive statistics.We are dealing with only one variable so tap the option One-VariableThe Set Calculation screen allows you to select the list that contains the relevant data. Tap OK

2

The sample standard deviation that we use is

The sample standard deviation is 2.5166.....

Note: The variance is not given on the screen. The variance can be found by squaring the standard deviation.

Page 38 Standard deviation for grouped data Key the data into the lists using list 1 for the data values and list 2 for the frequency.

Tap Calc in the menu bar to get you into the menus for finding descriptive statistics.We are dealing with only one variable so tap the option One-VariableThe Set Calculation screen allows you to select the lists that contains the data (list 1) and the frequency (list 2)Tap OK

The sample standard deviation that we use is

The sample mean is 3.38 and the sample standarddeviation is 1.3536...

3

Page 47 Using the graphing calculator to find descriptive statistics and construct a boxplot.Using the data from the example above: 2, 3, 5, 4, 3, 6, 5, 7, 3, 8, 1, 7, 5, 5, 9 Key the data into a list.TTap on

Tap on SetGraph in the menu bar and tap Setting...to access the Set StatGraphs screen

Turn Draw OnThe type of graph is a MedBoxThe data is in list 1Tick the Show Outliers box. Tap Set to get back to the lists screen

Tap the graph icon y to display the boxplot in the bottom half of the screen .

Tap Analysis in the menu bar and select Tracethen use the cursor keys to see the values of the five number summary displayed on the graph.

4

Page 50 Example 20 Using the calculator:

Page 51 Using the calculator to draw the boxplot in Example 20.

Tap on SetGraph and tap Setting...to access the Set StatGraphs screen

Turn Draw onThe type of graph is a MedBoxThe data is in list 1Tick the Show Outliers box. Tap Set to get back to the lists screen

Tap the graph icon y to display the boxplot in the bottom half of the screen .

Tap Analysis in the menu bar and choose Trace then the cursor keys to seethe values of the five number summary displayed on the graph.

Page 55 Using the random number generator on the calculator: Go to the Main menu Jand press the Keyboard k .Access the catalogue by tapping on cat.Locate rand(Tap twice for rand( to appear on the screen.

Type in the range of integers that we are considering 1,45) and then tap EXE Other random numbers in the same range can be obtained by tapping EXE repeatedly.

5

To obtain a list of six random numbers in the range 1 to 45 inclusive i. Locate randList in the catalogue. Tap twice to for randList( to appear on the screen. ii. Type in 6,1,45) ; the number of random numbers required and the range of numbers, all separated by commas. Close the bracket and press EXEA list of six random numbers in the range 1 to 45 will be generated. Other sets of random numbers in the same range can be found by tapping repeatedly EXE

Page 56 Example 21

Core Chapter 2 : Bivariate data Page 63 Using the calculator to graph parallel boxplots. Enter the data into the lists:Tap on SetGraph and tap Setting...to access the Set StatGraphs screen

Set-up the first boxplot: Turn Draw onThe type of graph is a MedBoxThe data is in list 1Tick the Show Outliers box.

Set-up the second boxplot: Tap on the 2 for the second graph The data for the second graph is in list 2.

Similarly set-up the third graph ; the data for the third graph is in list 3.After setting-up all three graphs tap on Set

6

Tap on the graph icon y to produce the parallel boxplots. Tap the Resize option at the bottom of the screen to get a full screen graph.

Page 69 Using the calculator to construct a scatterplot Enter the data into the lists; the independent variable (height) in list 1 and the dependent variable (weight) in list 2Tap on SetGraph and tap Setting...to access the Set StatGraphs screen Set-up the graph as shown, tapping Set to get back to the lists screen.

Tap on the graph icon to produce the graph. Tapping Analysis, then Trace and then using the cursor keys allows you to identify the points.

Page 75 Using the calculator to find Pearson’s correlation coefficient Enter

Enter the data into the lists; the independent variable in list 1 and the dependent variable in list 2 Produce a scatterplot for the data; it will reveal any errors made in entering the data and any outliers. It will also indicate whether the data is linear. The scatterplot indicates strong, positive, linear correlation between the variables.

7

Tap on Calc and then on Linear Reg This means that we are fitting a linear model or linear regression of the form y = ax + b to the data. Regression will be discussed in greater detail in Chapter 3 Complete the Set Calculation screen as shown, tapping OK when finished. The appropriateStat Calculation screen will appear.

The linear regression screen for this data is shown at right. Pearson’s correlation coefficient r is 0.9130....for this example. This r value indicates a strong, positive correlationas indicated by the scatterplot.

Page 78 Calculation of the coefficient of determination.

r2 is found on the linear regression screen of the calculator. r2 = 0.8336.... Alternatively, if the value of r is known, then this can simply be squared.

Core Chapter 3 : Linear regression

Page 88 Using the calculator to find the three median regression line. Enter the data into the lists and draw a scatterplot to make sure the data is entered correctly. Tap Calc from the menu bar and select MedMed Line.

Complete the Set Calculationsscreen as shown at right:

8

Tap OK and the coefficients for the equation of the three-median regression line are shown. The equation in this case is

Tap OK and the regression line appears on the scatterplot.

Page 91 Using the calculator to find the least squares regression line. Enter the data into the lists and draw a scatterplot to make sure the data is entered correctly.

Tap Calc in the menu bar and select Linear Reg

Complete the Set Calculationsscreen as shown at right: Tap OK

The figures for Linear Regression appear on the screen. The values a and b are the coefficients for the equation of the least-squares regression line. a is the slope of the line and b is the intercept. The equation is Note: Least squares regression lines are often written in the form which in this case would be The slope is always the number multiplying the independent variable x.

Tap OK and the least squares regression line appears on the scatterplot.

9

Page 98 Using the calculator to find and plot the residuals. Using the data from Page 91:Tap Calc to access the Set Calculations screen. Choose LinearRegression. Change Copy Residual from Off to list 3. This will paste the residual values into list 3. Tap OK

Tap SetGraph and go into Settings...Turn Off graph 1

Tap on graph 2 and complete the settings as shown.Tap on Set and then the graph icon y.

The residual plot is shown on the lower half of the screen.

10

Page 104 Example 4 a. Enter the data into the lists and construct a scatterplot .

The data does not appear to be linear.

Fit a least-squares regression line to the data and construct a residual plot: From the menu bar tap Calc and thenSettings...

Complete the

Complete the Set Calculations screen as shown. Tap OK.

The Linear regression screen appears. Tap OK.

The least squares regression line appears on the scatterplot.

Tap the label of list 3 to fill the column with the residual values.

Set-up graph 2 for the residual plot (turn graph 1 Off). Tap Set.

The residual plot shows a pattern suggesting that the linear model is not the best fit.

11

b. We can apply the x2 transformation by adding an extra row containing x2 values in the table. To do this on the table go to the Callocation for list 4 and, using the keyboard, type in list1^2.

Tap on the label of list 4 and the column will fill with the values from list 1, squared.

Go to SetGraph in the menu bar and choose Settings... to construct a scatterplot ofy(list 2) versus x2(list 4).

Tap Set and then the graph icon y.The scatterplot of y versus x2 appears to be linear.

Go to SetGraph and Settings... and complete the Set Calculation screen so that the residuals for this transformed graph are in list 5.

Tap OK to see the Linear Regression screen and(Tap OK) to fill list 5 with the residuals.

12

Tap SetGraph and Setting... and complete the screen for graph 3 as shown (make sure the other graphs are turned Off)

Tap Set and the graph icon y to construct the residuals plot for the transformation. The residuals plot confirms that the relationship between y and x2 is linear.

c. From the linear regression screen above we can write the equation. The slope, a, is 0.4186... and the intercept, b, is 1.0781... so the equation connecting y and x2 is

Page 109 Example 5 a. Enter the data and construct a scatterplot.

The data is clearly not linear and has the general shape.

We therefore consider the four transformations

where x represents the day and y represents the audience size.

day

audience size

For each of the transformations we add the appropriate column to the data in the lists, construct a scatterplot including a least squares regression line, and a residual plot.

Transformation logx

13

Transformation logy

Transformation

Transformation

See the text for the remainder of Example 5.

14

Core Chapter 4 : Time series Page 136 Example 6 To graph the deseasonalised data open the Statistics application and enter the time period 1 to 48 in list 1 and the deseasonalised data in list 2.

The time period data, 1 to 48, can be entered into list1 using a sequence: Tap on Cal for list1 and then the soft keyboard and cat to select seq([alternatively you could type seq( ] then specify the sequence as sequence, variable, starting value, ending value, step)These values are shown at right. Tap EXE and list1 will fill with the values 1 to 48.Enter the deseasonalised data into list2.

Tap SetGraph in the menu bar and choose Setting... to get to the SetStatGraphs screen. Choose xyLine for a time-series graph. Tap Set.

15

isplayed.

Tap Calc and choose Linear Reg. Complete as shown.

Tap OK and the slope (a) and intercept (b) for the least-squares regression line will be d

Tap OK and the graph will be drawn along with the least squares regression line. (Shown as a full screen here)

Casio ClassPad Replacement calculator screens for Module 1 : Number Patterns Chapter 5 : Arithmetic and Geometric Sequences Page 157 Finding terms of a sequence using the calculator. Method 1 Tap on the Graph and Table: W application. Complete the screen as shown Tap on the table icon # in the toolbar. A table of values appears in the lower screen. Scroll down to find the 25th term. Note: You may need to choose the maximum value for x in the table. Tap on the 8 icon to enter the Table Input screen. Change the End value to at least 25. Tap OK Method 2 On the Menu screen tap on the Sequence application, H. Choose Explicit as the type of sequence and type in the sequence using the n available on the toolbar. To create a table for the sequence tap 8 to display the Sequence TableInput box. Enter the required values and tap OK. Tap on the table icon # in the toolbar. A table of values appears in the lower screen. Scroll down to find the 25th term.

1

Page 158-159 Displaying a sequence using a calculator This section does not have an equivalent on the Casio CassPad. Page 159 Example 2 On the menu screen tap on the Main application J.

a. Type and tap E and the answer will be given as a fraction. b. Type in the two subtractions and it is seen that the answers, given as fractions, are not the same value so the sequence is not arithmetic. Page 160 Example 3 On the Menu screen tap on the Sequence application, H. Choose Explicit as the type of sequence and type in the sequence,

,using the n available on the toolbar. To create a table for the sequence tap 8 to display the Sequence TableInput box. Enter the required values (End value must be at least 25) and tap OK. Tap on the table icon # Note : The appearance of the formula may change when you create the table. A table of values appears in the lower screen. Scroll down to find the 25th term. Page 162 Example 5 Choose Explicit as the type of sequence and type in the sequence, ,using the n available on the toolbar. To create a table for the sequence tap 8 to display the Sequence TableInput box. Enter the required values ( The End value must be fairly large in this case; you may have to change the value to find the term that is equal to 927) and tap OK. Tap on the table icon # Scroll down the table until you come to the value 927 for anE. This means that term 186 has the value 927.

2

Page 162 Example 6 Choose Explicit as the type of sequence and type in the sequence, 0, using the n available on the toolbar. To create a table for the sequence tap 8 to display the Sequence TableInput box. Enter the required values ( The End value must be fairly large in this case; you may have to change the value to find the term that is more than 1000) and tap OK. Tap on the table icon #. Scroll down the table until you come to the first value of an that is greater than 1000. Term 24 is the first term that is greater than 1000. Page 164 Graphing Arithmetic Sequences. Choose Explicit as the type of sequence and type in the sequence,

, using the n available on the toolbar. Tap on the table icon #. To plot the sequence the table window must be active. Tap on Graph in the top menu bar and choose G-plot. This will plot the sequence values as disconnected points. Tap on the graph icon $ to Tap Analysis and choose Trace then use the cursor keys to trace the points on the graph. Page 167 Example 9 It is possible to include a column in the table showing the sum of n terms. Tap on the diamond ♦in the menu bar Choose ∑display and turn On Tap on the table icon # and three columns will fill; the third column gives the sum of n terms of the sequence. Scroll down to find that the sum of 25 terms of the sequence is 1975.

3

Page 168 Example 12 Choose Explicit as the type of sequence and type in the sequence,

, using the n available on the toolbar. Tap on the diamond ♦in the menu bar Choose ∑display and turn On Tap on the table icon # and the three columns will fill; the third column, ∑anE, contains the sum of n terms of the sequence. Scrolling down this column will show that the sum of 26 terms will first exceed 50,000. Page 174 Example 15 Choose Explicit as the type of sequence and type in the sequence,

, using the n available on the toolbar. Tap on the table icon # and scroll down to find the value of the 10th term is 1536. Page 175 Example 16 b. Choose Explicit as the type of sequence and type in the sequence,

, using the n available on the toolbar. Tap on the table icon # and scroll down to see that the value of term six is 81. Tap on Graph and choose G-Plot. The graph should appear. The window for the graph may not be correct . Tap on the window icon6 and set it up as shown. Note : the xmin (n) value is 1 and the xmax value is 6. The corresponding terms(an values) have values from 1/3 to 81 so ymin is set at 0 and ymax is set at 90 to cover these two values.

4

c. Scrolling down the table will show that term 13 is the first term that has a value greater than 100,000 Page 176 Example 17 Choose Explicit as the type of sequence and type in the sequence,

, using the n available on the toolbar. Tap the table icon #and then the Graph. Choose G-plot and the graph should appear. If the window is not correct then tap Zoom and choose Auto or Quick Initialise. The graph shown at right is Zoom Auto. Alternatively values can be chosen for the window by tapping 6 The maximum y (anE) value is 16 and the minimum is -8. Page 177 Example 19 Tap on main menu J and then the keyboard k key. Select the 2D option and tap on the nth root icon Type in 4, arrow right, and type 5.0625. Tap EXE and the answer 1.5 appears.

5

Page 179 Example 21 The last term is 1/729, which, as a decimal, is 1.3717...×10-3 or 0.0013717... Enter the sequence and tap on the table icon. Scrolling down reveals that term 7 has the value 1.3717...×10-3 so we are looking for the sum of 7 terms. From the table the sum of 7 terms is 1.49931.... Alternatively, the sum of the 7 terms can be calculated by substituting in the formula. The answer will be given as a fraction. Highlight the fraction answer and tap on u to give the answer as a decimal. Page 180 Example 22 The first term is 5 and the common ratio is 2 so the formula for the nth term is 5×2n-1 Type in the sequence and tap on the table icon#. Scrolling down the table shows that the sum of 11 terms is the minimum number of terms to give a sum of at least 10,000. Note: The sum column is On in this case. Tap on the diamond ♦in the menu bar. Choose ∑display and turn On.

6

Page 185 Example 24 Enter the sequence as shown and tap on the table icon#. Scroll down the table until you come to a value that is greater than 20,000. Since Vn is defined as the amount after n years then we can say that after 12 years the value of the investment is at least $20,000. Note: By highlighting the amount a12, the value to10 decimal places appears below, and it can be seen that, rounded to the nearest dollar, this is $21291. Page 185 Example 25 Enter the sequence as shown and tap on the table icon#. Scroll down the table until you come to a value that is greater than 6,000. The population will reach 6000 twelve years after 1990; in the year 2002. Page 186 Example 26 d. Enter the sequence as shown and tap on the table icon#. Scroll down the table until you come to a value that is greater than 2000. They will first be making an investment of more than $2000 on Maria’s 25th birthday. e. Scrolling down the ‘sum’ table to n = 21 shows the total sum of $28 676.49 has been made up to and including Maria’s 21st birthday. Note : To include the ‘sum’ column Tap on the diamond ♦in the menu bar Choose ∑display and turn On Page 189 Example 28 e. Enter the sequence as shown and tap on the table icon#. Make sure that you have ∑display turned On Scrolling down the ‘sum’ table to a sum of $12.83 show that this occurs when n = 20. A phonecall of 20 minutes costs $12.83.

7

Page 193 Example 30 d. Enter both the sequences and tap the table icon #. Scroll down the table until you come to the values where bnE > anE This first occurs at the beginning of the eighth year. To draw the graph : Tap on the window icon 6 and complete as shown. The ‘y’ values can be seen on the table : the minimum value is $1000 and the values for term 10 are approximately $2000 Tap OK to bring up the graph: Tap Analysis, choose Trace and use the cursor keys to help distinguish which points belong to which sequence. Chapter 6 : Difference Equations Page 203 Generating a sequence on the calculator. Difference equations are known as recursive sequences so we use this option when entering the rules for difference equations. The variable an for this type of sequence is found on the menu bar. Page 203 Example 4 This sequence is of the form an+1 = 2an -1; a1 = 5 so tap on the p next to ^. Choose&

hese.

ar.

Enter the sequence as shown and tap the table icon #. Tap on the window icon 6 and set up the window as shown. The value of term one is 5 and the value of term seven is 257 so y- values are set to cover t Tap OK and the graph will appe

8

Page 213 Example 10 c. Enter the sequence as shown; make sure the Sequence Table Input 8 screen starts at 0. Tap on the window icon 6 and set up the window as shown. The value of term one is 500 and the value of term nine is 84 so y- values are set to cover these. Tap on OK to bring up the graph. d. From the table it can be seen that after week 9 the size of the colony will not be sufficient to provide 120 mice for research purposes. e. Enter the sequence as shown and tap on the table icon #. From the table it can be seen that the population is now increasing as the weeks increase. The window will need to be changed to graph this sequence: Tap OK to show the graph.

9

f. Enter the sequence as shown and tap on the table icon #. From the table it can be seen that the population is remaining constant at 500 as the weeks increase. Tap on Graph and choose G-Plot. Tap on the graph icon $. The graph shows that the population is stable at 500. Page 218 Using the calculator for second-order difference equations. To enter a second-order difference equation firstly the type of equation needs to be chosen. Tap on& and choose ( which means that the equation is of the type

Complete the screen as shown accessing the variables from the top menu. Tap on the table icon, #. To graph the first seven terms first choose an appropriate window observing the required values from the table. Tap OK to show the graph.

Tap Analysis in the menu bar and choose Trace to track the sequence on the graph using the cursor keys.

10

Casio ClassPad Replacement calculator screens for Module 2 : Geometry and Trigonometry. Chapter 6: Geometry. No replacement screens. Chapter 7 : Trigonometry Page 267 Example 1 Tap on the main menuJ and press the Keyboard buttonk. Tap on TRIG. Note: The default option for measuring angle is Radians but for the calculations in Further Maths you will be working in Degrees. Tap on Rad (for radians) on the bottom menu and it should change to Deg (for degrees). The calculator will now assume all angles are in degrees and will give answers as degrees. To give all answers as decimals tap on Standard in the bottom menu and change this to Decimal Tap on sin then 46) Tap EXE. Sin (46o) = 0.7193 correct to 4 decimal places. Page 267 Example 2 Tap on the main menuJ and press the Keyboard buttonk. Tap on TRIG and check that the calculator is in Degree mode. Tap on cos-1 then 0.8649) Tap EXE and the answer is given as a decimal degree. cos (30.1287o) = 0.8649 To change the answer into degrees, minutes and seconds (DMS): Tap on Interactive in the top menu, choose Transformation and then the bottom option toDMS Tap OK and the answer will be given in degrees, minutes and seconds ie. 30 degrees, 7 minutes and 43 seconds. Page 270 Example 5 Tap on the main menuJ and press the Keyboard buttonk. Tap on TRIG and check that the calculator is in Degree mode. Tap on cos-1 then 26 ÷ 38) Tap EXE and the answer is given as a decimal degree.

cos (46.8264..o) = To change the answer into degrees, minutes and seconds (DMS): Tap on Interactive in the top menu, choose Transformation and then the bottom option toDMS Tap OK and the answer will be given as 46 degrees, 49 minutes and 35 seconds.

1

Page 272 Example 6 Follow the same instructions as for Example 5 above. Page 272 Example 7 Follow the same instructions as for Example 5 above to find the angle then tap 12 ÷ cos (ans) and tap EXE. Alternatively

You can use the calculator to solve the equation On the Main menu highlight the answer 30.9637... by running the stylus over the number. Go to Edit in the tool bar and select copy. Go to Menu and select the solve equation N option. Tap k and TRIG. Tap cos , tap Edit from the tool bar and tap Paste. This should paste the value from the Main application into the equation so that you have cos(30.9637... To complete the equation tap ) = 12 ÷ x Tap solve 1 and the calculator will solve the equation for you. This means that you do not have to transform your equations to solve them. Page 275 Example 8 There are three methods for doing this and other examples on the calculator. It is worthwhile trying all the methods so that you can see which one suits you. Method 1 The Interactive menu from the menu bar will enable you to access the ‘solve equation’ facility on this calculator which means that you do not have to transpose equations to solve them. a. Go to Main J menu. Tap k and TRIG. Tap Interactive from the menu bar and select Equation/Inequality and solve. Select solve numerically and complete the screen as shown typing the equation sin(x)/15=sin(30)/9 into the equation line. Tap OK and OK on the Warning box (the warning box appears because this example is an example of the ambiguous case of the sine rule).

2

The calculator will solve the equation for you; angle B is 56.4426...o Enter 180 – x – 30. Tap on EXE to find angle A; angle A is 93.5573..o b. Tap Interactive from the menu bar and select Equation/Inequality and solve. Enter the equation , using y as the variable in this case and ans to use the previous answer (angle A). Tap OK to give the answer; y = 17.9653... Method 2 The whole calculation can be done on the Main application however, the equations will have to be transposed as in the text. Method 3 Note: Example 8 is an example of the ambiguous case of the sine rule which means there are two possible solutions (not examined in Further Maths). The sequence for drawing the triangle in this case needs to be angle first then the side lengths. Tap on Geometry Gin the menu and then on the triangle O in the toolbar. Use the stylus to construct a triangle. Tap on two of the sides and then the arrow on the rightp. The ‘measure angle’ Qsymbol will be on the left. The angle between the highlighted sides in this case is measured as 74.47589o. Highlight this figure and change it to 30. Highlight the tick box to the right. Tap on the screen and then tap on the side AC T

Tap on the arrow on the right of the toolbar and select the icon that measures lengthx.

The length of the highlighted side in the triangle drawn will be shown. Highlight this figure and change it to 15 then highlight the tick box. Touch the screen again to get back to the triangle. ap on the screen and then tap on the side AB T T

3

Tap on the arrow on the right of the toolbar and select the icon that measures lengthx. Highlight the length and change it to 9 units. Tick the box on the right. The diagram should now look like the one in the text. a. Tap on the sides AB and BC. The angle B will be measured as 56.44269o

Tap on the sides AB and AC. The angle A will be measured as 93.55731o

b. Tap on the side BC and the length will be calculated for you and appear in the toolbar. The length is 17.96532 cm.

Note: Drawing the triangles requires some practice but is worthwhile as then there are no calculations to be made. The area of the triangle above can also be found by highlighting all the sides and then the area icon E will appear on the left and the area (67.36994 cm2) is given in the toolbar. Page 277 Example 10 Using the main Japplication from the icon panel, pressing k and selecting the TRIG option. Make sure that you have selected Decimal and Degree on the status bar. Calculations are typed as shown followed by EXE for each calculation. Alternatively i. You can draw the diagram, entering the lengths and angles as shown above in Example 8, and use the diagram to solve for AD ii.

4

Page 280 Example 11 Use the main J application from the icon panel and pressing k Enter the calculation as shown using the x2 option and going to the TRIG window for cos (use I to get back to the mth option) Tap ans) EXE to find the square root of the previous answer. Alternatively Tap on Geometry Gin the menu and then on the triangle O in the toolbar. Use the stylus to construct a triangle. Tap on the side AB. Tap on the arrow on the right of the toolbar and select the icon that measures lengthx. The length of the highlighted side in the triangle drawn will be shown. Highlight this figure and change it to 16 then highlight the tick box. Repeat this process for side AC changing the length to 23 units. (You may need to zoom out if the triangle extends off the screen; Select View and Zoom Out from the tool bar) Tap on the sides AB and AC and change the angle between them to 40o The triangle is now set-up as for the example. Tap on side BC and its length (14.8725 cm) is shown on the tool bar .

Page 281 Example 12 Construct the triangle in the Geometry application (See example 11 above.) Tap on the side marked x; AC in this case, to find that the length is 12.6965.... m

5

Page 281 Example 13 Tap on Geometry Gin the application menu and then on the triangle O in the toolbar. Use the stylus to construct a triangle. Tap on the side AB. Tap on the arrow on the right of the toolbar and select the icon that measures lengthx. The length of the highlighted side in the triangle drawn will be shown. Highlight this figure and change it to 8 then highlight the tick box. Repeat this process for sides AC and BC changing the lengths to 9 and 11 units respectively.

By tapping on two sides the magnitude of the angle appears in the toolbar above and all the angles of the triangle are

found.

Page 283 Example 14 Tap on Geometry Gin the application menu and then on the parallelogram o in the toolbar. Use the stylus to construct a parallelogram. Tap on the side AB. Tap on the arrow on the right of the toolbar and select the icon that measures lengthx. The length of the highlighted side in the triangle drawn will be shown. Highlight this figure and change it to 15 then highlight the tick box. Repeat the process for side AD changing its length to 21 units. Highlight both sides AB and AD to change the angle between them to 65o.

6

Go back to the toolbar and select the line segment icon y. Use the stylus to draw a line from B to D and from A to C. Tap on G to stop the line drawing function. Tap on BD and go to the length toolbar. BD is 19.99376 cm long. Tap on the screen and then AC to find its length is 30.53276 cm. Page 287 Example 15 a. Tap on Geometry Gin the application menu and then on the triangle O in the toolbar. Use the stylus to construct a triangle. Tap on the side AB. Tap on the arrow on the right of the toolbar and select the icon that measures lengthx. The length of the highlighted side in the triangle drawn will be shown. Highlight this figure and change it to 25 then highlight the tick box. Repeat the process for side CB changing it to 18. Highlight both sides AC and CB to change the angle between them to 105o. Tap on all three sides and the area icon E should appear. The area of the triangle is 217.333 cm2 b. The area of the triangle can best be found using

as in the text but to check you could construct a triangle as described above changing the lengths of the sides to 16, 12 and 20 cm. Tap on all three sides and the area icon E should appear. The area of the triangle is 96 cm2. Page 288 Example 16 Tap on Geometry Gin the application menu and then on the triangle O in the toolbar. Use the stylus to construct a triangle. Tap on the side BC. Tap on the arrow on the right of the toolbar and select the icon that measures lengthx. The length of the highlighted side in the triangle drawn will be shown. Highlight this figure and change it to 30 then highlight the tick box. Repeat the process for side AB changing it to 24. Highlight both sides AB and AC to change the angle between them to 44o. Highlight all three sides and the area icon E should appear.

7

The area of the triangle is 351.8176 cm2. Chapter 9 Applications of Geometry and Trigonometry Page 294 Example 2 Tap on Geometry Gin the application menu and then on the triangle O in the toolbar or the line segment icon y. Use the stylus to construct a triangle. Tap on the side AB. Tap on the arrow on the right of the toolbar and select the icon that measures lengthx. The length of the highlighted side in the triangle drawn will be shown. Highlight this figure and change it to 7.5 then highlight the tick box. Repeat the process for side AC changing it to 5. Highlight both these sides to change the angle between them to 68o. Highlight CB to find its length; 7.2907... km b. Highlight both BC and AC to find that the angle between these sides is 39.48427o. The bearing is found by subtracting this angle and 68o from 360o. The angle can be highlighted, copied and pasted into the main J screen. Page 299 Example 5 Tap on Geometry Gin the menu and then on the line segment icon y. Use the stylus to construct the diagram. Tap on AB to change it to 50 and pairs of sides to establish the angles between them. a. Tap on the side AD b. Tap on the side BC (length 65.57 m) (length 59.16 m)

8

c. Tap on the side AC (length 96.91 m) Tap on the points D and C (length 111.19 m) d. Construct a line joining D to C and highlight the triangles ADC and ABC to find the areas. (Areas 3159.9 m2 and 1211.424 m2 resp.) These values can be copied and pasted into the main J screen to calculate the total area.

9

Casio ClassPad Replacement screens for Module 3 : Graphs and relations Chapter 10: Construction and interpretation of graphs. Page 339 Example 8 Choose Graph and Table W from the application menu. Enter 5x – 3 next to y1 and tick the box next to this equation. Tap the graph icon$ in the toolbar. Tap Zoom in the menu bar and choose one of the zoom options that will show the features of the graph. In this case I have chosen Box then used the stylus on the graph to constructed a box around the graph enclosing the intercepts with the axes. To find the intercepts with the axes: Tap on the right arrowu in the tool bar. The first icon = on the left finds the y-intercept. Tap on this to show that the y-intercept is -3.

The second icon Y on the left finds the x-intercept. Tap on this to show that the x-intercept is 0.6 Page 347 Example 14 Choose Graph and Table W from the application menu. Enter -2x + 7 next to y1 and tick the box next to this equation. Enter 4x - 5 next to y2 and tick the box next to this equation. Tap the graph icon$ in the toolbar. Tap Zoom in the menu bar and change the window if the point of intersection is not on the screen. Tap Analysis then G-Solve then Intersect and the point of intersection (2, 3) appears on the graph screen.

1

Page 349 Using the calculator to solve simultaneous equations. Tap on the Main J application and press the keyboard buttonk. Choose

e top box and the second

to the outer box. ap EXE w to get the answer.

n the Statistics applicationI and enter the data in the

Set StatGraphs screen, p Set and then the graph icon y.

the 2D option) and choose Enter the first equation in thequation in the lower box. The two variables x,y are typed inT Page 371 Using the calculator for Example 28 Tap olists. Tap on G in the toolbar to reach theta To test the x2 tranformation.: Go to the Cal row of List 3. Tap on the soft keyboardk and select the qwerty keyboard abc and type list1^2. Tap on the l

abel of list3 and the list will fill with e squares of list1.

up as shown n the screen at right.

graph y icon and the graph will appear: the points ppear to be linear.

th Graph x2 versus y; set-o Tap Set and then thea

2

Repeating the process for the x3 transformatiThe poi

on: nts on the graph do not appear to be

near.

x and y is of the form

li If it is known that the relationship between then the calculator can be

e Set Calculation screen

so the equation of t e relationship between x and y is

used to find the values of k and n. Go to Calc in the menu bar, choose Power Reg and thwill appear. Set-up this screen as shown and then tap OK. The Stat Calculation screen will show that the value of k (a) is 3.19 and the value of n (b) is 2

h

The graph shows the original points with the regression line

tted.

nd solving simultaneous equations is simp

fi Chapter 11: Linear programming There are no replacement screens for this chapter however it is possible to graph inequalities on the calculator a lified by using the calculator. Page 385 Example 3 Go to the Graph and Table menu W You will need to transpose any equations that do not have y as the subject. Constraint : Tap on the y = icon in the toolbar choose

ick the box next to this relation. Z and type 0.

T Constraint Tap on the y = icon in the toolbar choose ' and type 0.

ck the box next to this relation. Ti

Constraint Tap on the y = icon in the

petoolbar, choose X

ty and tick the box next to this relation.

Constraint

Type and tick the box next to this relation.

3

4

ap on the graph icon $ and the feasible region will be shaded.

ain menu J and press the keyboard

he top box and the er

to the outer box. ap EXE w to get the nswer.

T The point of intersection of y3 and y4 can be found: Tap on the M buttonk. Choose the 2D option) and choose Enter the first equation in tsecond equation in the lowbox. The two variables x,y are typed inTa

Casio ClassPad Replacement calculator screens for Module 4: Business Related Mathematics Chapter 12 : Financial transactions and asset values. Page 437 Example 13 Tap on the Statistics I application and enter the numbers 0 to 7 in list1. Go to the Cal row of list2 and type . Tap on the label of list2 to fill the list with the inflated values for each year. Tap on the Set StatGraphs icon G and set-up the scatterplot. Tap Setand then tap the graph icon y.

Page 443 Example 18 Tap on the NumSolve applicationN. Type in the equation Tap on Solve and the value x = 5.36118... is given. Rounding this value up we can say that after 6 years the value will be less than $4000. Chapter 13: Loans and Investment Page 452 Example 1 Tap on the Financial icon in the application menu. The initial screen, at right, will appear. Tap on Simple Interest to access the simple interest calculation screen. Complete the screen as shown entering the term of 4 years as 4 × 365 days and the amount invested (an amount ‘going out’) as -2460. Tap on the button SI next to the box to calculate the simple interest and the button SFV to calculate the simple future value (principal + interest). Note : Make sure the Format for Days in Year is on 365

1

Page 452 Example 2 Tap on the Financial application and choose Simple Interest.

Enter the time period as and the loan value as 18000 (an amount ‘coming in’, so positive) Tap the buttons next to the last two boxes to find the interest paid and the total amount owing. Page 452 Example 3 Tap on the Financial application and choose Simple Interest. Enter the time period as 185 days and the loan value as 2500 (an amount ‘coming in’ so positive) Tap the buttons next to the last two boxes to find the interest paid and the total amount owing. Page 454 Example 4 Tap on the Financial application. a. On the initial screen there is a Day Count calculator that will calculate the number of days between two dates. Entering the two dates as month, day, year and tapping on the Days button will give 174 days from day 1 to day 2. If both days are to be included then you will need to add one day. b. and c. Tap on the Calculations and choose Simple Interest. Note : The simple interest calculator will only calculate the interest and the (principal + interest). For examples where you are required to calculate the principal, the time period or the interest rate you will need to use the transposed formula and substitution.

2

Page 463 Example 11 From the initial Financial application screen choose Compound Interest. N is the number of instalment periods; 5 years in this example. I% is the Annual interest rate; 5.5% in this example. PV is the present value or initial investment; $10 000 in this example. PMT is the amount paid each period; $0 in this example. FV is the future value; the amount that needs to be calculated in this example. In this example there is 1 instalment period per year, P/Y, and the interest is calculated once per year (C/Y) a. Tap the FV box and the amount of the investment after 5 years is calculated.

b. Highlight the FV value and tap the copy box x in the toolbar. Tap on the Main menu Jand paste the value on the screen. Type – 10000 and tap EXE to calculate the interest. Page 464 Example 12 From the Financial application choose Compound Interest. a. b. Enter the N value as 5×4 c. Enter the N value as 5×365

Page 465 Example 13 From the Financial application choose Compound Interest. a. Interest is 893.09 b. $14 883.62 is in the account after 3 years (36 months)

3

c. Copy the FV value from part b. by tapping on the copy icon x in the toolbar. Tap on the Main applicationJ and paste this value. Complete the calculation as shown. Page 467-8 Finding times and periods for compound interest. From the Financial application choose Compound Interest. The value of N can be calculated easily by the calculator by entering the other values in the calculation and then tapping on the N box. Note the signs for PV and FV. Page 469 Example 14 From the Financial application choose Compound Interest. The value of N can be calculated by the calculator by entering the other values in the calculation and then tapping on the N box. a. the minimum number of time periods is 41 b. 41 time periods (months) is 3 years, 5 months. Page 470 Example 15 From the Financial application choose Compound Interest. The values of N can be calculated by the calculator by entering the other values in the calculation and then tapping on the N box. It will take 321 days for the investment to grow from $1700 to $1800.

4

Page 471- 473 Using the calculator to plot interest graphs. Tap on the Statistics I application and enter the numbers 0 to 10 in list1. Go to the Cal row of list2 and type . Tap on the label of list2 to fill the list with the compound interest values for each year.

Go to the Cal row of list3 and type . Tap on the label of list3 to fill the list with the (principal + simple interest) values for each year. Tap on the Set StatGraphs icon G and set-up the scatterplots. Tap the graph icon y. Tap Analysis then Trace and use the cursor keys to find the value of particular points on the graph. Page 477 Example 17 a. From the initial Financial application screen choose Compound Interest. N is the number of instalment periods; 5×12 months in this example. I% is the Annual interest rate; 6% in this example. PV is the present value or initial investment; -$1000 in this example (outgoing amount). PMT is the amount paid each period; -$250 in this example (outgoing amount). FV is the future value; the amount that needs to be calculated in this example. P/Y and C/Y are both 12 as there are 12 payments per year and 12 compounding period per year. Tap on the FV box to get the amount accumulated.($18 791.36) b. Alternatively this calculation can be done on the Amortization screen. The sum of the interest can be accessed on this screen. Amortization lets you calculate the interest and principal portions of a payment or payments. PM1 is the number of the first instalment period in the interval under consideration; 1 in this example PM2 is the number of the last instalment period in the interval under consideration; 60 in this example. Note: The initial investment and regular payment can be entered as positive amounts on this screen and the balance and sum of interest payments are also positive. If they are entered as negative amounts then the balance and sum of interest will be negative. The sum of the interest for the 5 years is $2791.26

5

Page 478 Example 18 Using the Compound Interest screen from the Financial application: Set-up as shown. Tap on the N box to find the number of months to save $10 000. It will take 25 months to save $10 000. Page 485 Examples 22 and 23 Calculations of the amount owing using the annuities formula can be done on the Main application. Page 488 Example 25 From the initial Financial application screen choose Compound Interest. $10000 is borrowed (incoming amount, so positive) for 5 years and interest is charged at 7% p.a. compounding yearly. A repayment of $2000 (outgoing amount, so negative) is made each year. Tap on the FV box to find the amount still owing after 5 years: $2524.04. This is shown as a negative value indicating that it is still owing (outgoing). Page 489 Example 26 a. Enter the instalment period (N) as 4.5 × 12 There are 12 repayments and compounding periods per year. The amount still owing is $9619.15

6

b. Enter the instalment period (N) as 4.5 × 4 There are 4 repayment and compounding periods per year. The amount still owing is $9793.21 Page 489 Example 27 The repayment amount (PMT) is required in this example. If the loan is ‘paid out’ this means that the future value is zero. The monthly repayment is $492.02 to pay out the loan in 5 years. Page 490 Example 28 The loan is for 20 years so there are 20 × 12 = 240 instalment periods (N) The repayments (outgoing amount, so negative) are $1250 per month. The loan is to be paid out in the 20 years so FV is zero. Tap on PV to find the amount that can be borrowed; $158,760.54

Page 491 Example 29 Calculate the yearly repayment amount for the loan then tap on the spread sheet icon in the toolbar Tap on Edit and choose Fill Sequence. You will need to enter the annuities formula

in the Expr. box. Complete the remainder of the screen as shown. Tap OK. Highlight the 25 values in column A and tap on the graph icon D and the graph of the amount owing each year will be drawn.

7

Page 491 Example 30 Enter the values for I%, PV, PMT, FV, P/Y and C/Y as shown. Tap on N to find the number of instalment periods; 28.004 will need to be rounded-up to 29.

Page 492 Solving for the principal, P Enter N as 20 × 12 months and the other values as shown. Tap on PV for the amount that can be borrowed; $158 760.54 Page 492 Example 31 Enter N as 10 × 26 fortnights and the other values as shown. Tap on I% to give an interest rate of 6.10% Page 496 Example 32 Solving for N, for a loan of $20 000 at 7.5% interest and repayments of $120, brings an Error message. This occurs because $120 is less than the interest on the loan for a month so the loan will be increasing in value and will never reach zero.

8

Page 496 Example 32 a. Solve for N entering the values for I%, PV, PMT, FV, P/Y and C/Y as shown. N = 158, rounding-up. Tap on Calculations in the menu bar and choose Amortization. The values for I%, PV, PMT, FV, P/Y and C/Y will carry over to this screen. Complete the PM1 and PM2 values as 1 and 158 respectively then scroll down and tap on ΣInt $11 484.67 is paid in interest for this loan. b. Solve for N entering the values for I%, PV, PMT, FV, P/Y and C/Y as shown. N = 61, rounding-up. Tap on Calculations in the menu bar and choose Amortization. The values for I%, PV, PMT, FV, P/Y and C/Y will carry over to this screen. Complete the PM1 and PM2 values as 1 and 61 respectively then scroll down and tap on ΣInt $4055.39 is paid in interest for this loan. c. Solve for N entering the values for I%, PV, PMT, FV, P/Y and C/Y as shown. N = 38, rounding-up. Tap on Calculations in the menu bar and choose Amortization. The values for I%, PV, PMT, FV, P/Y and C/Y will carry over to this screen. Complete the PM1 and PM2 values as 1 and 38 respectively then scroll down and tap on ΣInt $2497.50 is paid in interest for this loan.

9

Page 498 Example 33 a. Solve for N entering the values for I%, PV, PMT, FV, P/Y and C/Y as shown. N = 14, rounding-up. Tap on Calculations in the menu bar and choose Amortization. The values for I%, PV, PMT, FV, P/Y and C/Y will carry over to this screen. Complete the PM1 and PM2 values as 1 and 14 respectively then scroll down and tap on ΣInt $12570.67 is paid in interest for this loan. b. Solve for N entering the values for I%, PV, PMT, FV, P/Y and C/Y as shown. N = 53, rounding-up. Tap on Calculations in the menu bar and choose Amortization. The values for I%, PV, PMT, FV, P/Y and C/Y will carry over to this screen. Complete the PM1 and PM2 values as 1 and 53 respectively then scroll down and tap on ΣInt $11680.76 is paid in interest for this loan. c. Solve for N entering the values for I%, PV, PMT, FV, P/Y and C/Y as shown. N = 158, rounding-up. Tap on Calculations in the menu bar and choose Amortization. The values for I%, PV, PMT, FV, P/Y and C/Y will carry over to this screen. Complete the PM1 and PM2 values as 1 and 158 respectively then scroll down and tap on ΣInt $11 484.67 is paid in interest for this loan.

10

Page 499 Example 34 a. Calculate the repayment amount (PMT) per month; $757.39 Tap on Calculations in the menu bar and choose Amortization. The values for I%, PV, PMT, FV, P/Y and C/Y will carry over to this screen. Complete the PM1 and PM2 values as 1 and 240 respectively then scroll down and tap on ΣInt The total cost of the loan is interest + fees = $81 774.62 + 240 × $8 = $83 694.62 b. Calculate the repayment amount (PMT) per month; $769.31 Tap on Calculations in the menu bar and choose Amortization. The values for I%, PV, PMT, FV, P/Y and C/Y will carry over to this screen. Complete the PM1 and PM2 values as 1 and 240 respectively then scroll down and tap on ΣInt The total cost of the loan is (interest only) $84 633.88 Option A is a cheaper loan. Page 500 Example 35 a. Calculate the repayment amount; $1075.56 per month for option A Go to the Simple Interest screen to calculate the amount that is to be repaid per month for option B: The total amount that is to repaid is $114 000 so the monthly repayments are $114000/96 = $1187.50

11

b. The total amount of interest paid for option A is $28 253.96 and for option B it is $39 000. The difference is $10746.04; more interest paid for option B. c. An equivalent reducing balance loan rate to option B can be found by using the repayment amount from option B and tapping on I%. An equivalent rate is 11.23% Page 503 Example 36 The Simple Interest screen can be used to calculate the total amount that has to be repaid; $1296 Monthly instalments will be $1296/6 = $216 Page 504 Effective rate of interest Nick is making six monthly payments of $150 on a loan of $800. This has an equivalent reducing balance interest rate of 41.67%.

12

Casio ClassPad Replacement screens for Module 5: Networks and Decision Mathematics Chapter 14: Undirected graphs and networks No replacement screens for this chapter. Chapter 15: Directed graphs and networks Page 564 Finding connectivity matrices on a calculator. Go to the Main application J then k. Go to the 2D keyboard and choose the CALC option Tap on the 2 × 2 matrix symbol 8 and a 2×2 matrix will appear on the screen. In this case we want a 5 × 5 matrix so tap 3 times on 7 and this will produce three more rows. Tap on 6 3 times to produce three more columns and so we end with a 5 × 5 matrix.T Tap on the first element and tap 0 to enter the first element.. Use the arrows to go to the next element and continue entering the elements. Some of the elements in the matrix are entered in the screen at right When all the element are entered in the matrix tap outside the matrix and save W the matrix as a variable, (tap VAR) A, in this case. Tap w

1

It is now possible to find powers of the matrix A. Tap A ^ 2 w Tap A + A^2 w

2

Casio ClassPad Replacement screens for Module 6: Matrices Chapter 16 Matrix representation and its application. Page 625 Using a calculator for matrix operations. Go to the Main J application thenk. Go to the 2D keyboard and choose the CALC option Tap on the 2×2 matrix symbol 8 and a 2×2 matrix will appear on the screen. In this case we want a 3×3 matrix so tap once on 7 and this will produce another row. Tap on 6 once to produce another columns and so we end with a 3×3 matrix.T Tap on the first element and tap 1 to enter the first element. Use the arrows to go to the next element and continue entering the elements. All the elements in the matrix are entered on the screen at right.

To save the matrix tap outside the matrix and save W the matrix as a variable, (tap VAR) A, in this case. Tap wand the matrix is saved as A. Establish the other matrix as B

1

To calculate A × B : type A × B (make sure you are using variables for A and B) and then w To calculate 2A + B : type 2A + B (make sure you are using variables for A and B) and then w Note : To clear the matrices from the screen tap Edit and then Clear All. To clear the matrices from the variable names tap Edit and then Clear All Variables. Page 630 Powers of matrices To find A2 : Type A^2 w To find A3 : Type A^3 w Page 637 Using the calculator to find inverses. Set-up matrix A Tap A ^ -1 w to find the inverse of A. Check that A × A-1 = I

2

Page 638 Example 10 Set-up matrix B Tap on the 2×2 icon, 8. In this case we want a 4×4 matrix so tap twice on 7 and this will produce two more rows. Tap on 6 twice to produce two more columns and so we end with a 4×4 matrix.T Enter the elements into the matrix and save it as B. Tap on ans^-1wto find the inverse with the elements as decimals. Highlight the inverse matrix and tap the decimal-fraction icon . in the toolbar. The elements in the matrix will now be presented as fractions. Page 640 Example 12 Set-up matrix A: Tap8and then 6 and then 7 to establish a 3×3 matrix. Enter the elements and then save the matrix as matrix A Set-up matrix B: Tap7 twice to establish a 3×1 matrix. Enter the elements and save as matrix B. To solve the simultaneous equations we need to calculate A-1×B Type A-1×Bw

3

Chapter 17 Transition matrices Page 648 Example 1 Establish the transition matrix A and the initial state matrix B. c. The state matrix for Tuesday is AB The state matrix for Friday is A4×B d. To see the progression to steady state, A5, A10 and A15 have been calculated. The steady state proportion of students buying their lunch at the canteen is 0.375 or 37.5%. Summary Page 657 Using the calculator for matrix operations. Establish matrices A and B.

• Addition: Tap A + B w

• Multiplication by a scalar: Tap 3A w

Tap 4A – 2B w.

4

Multiplication Tap AB w

• Powers of a square matrix Tap A^2w Tap A^5w

• Determinant of a matrix Go to Interactive in the menu bar and choose Matrix-Calculation Tap det then tap A and OK Alternatively type det(A) The determinant of matrix A is 10 Similarly the determinant of matrix B is 5.

• The inverse of a matrix Establish the matrix B. Check that the determinant is not zero.

To find the inverse: Tap B^-1w and the inverse is given with the elements as decimals. Highlight the matrix and tap the ‘decimal to fraction’ icon . and the elements of the matrix

5

will be given as fractions.