how do i ……………on the classpad 300? working with ungrouped univariate data .....68 6.1.2...

How do I ……………on

the ClassPad 300? For Units 1 - 4

Mathematics VCE Study Design,

accreditation period 2006 - 2009.

Content refers to Operating System 3.0 of the ClassPad 300.

Written by Elena Zema

Former Head of Mathematics - Mildura Senior College.

Edited by Anthony Harradine

Baker Centre, Prince Alfred College.

Work in progress, version 2.0.

For

Operating System 3.0

How do I ……………on the ClassPad 300?

Version 2 – Februrary 2007.

Written by Elena Zema

Edited by Anthony Harradine

Copyright © Zema and Harradine 2007.

This resource was proudly funded by the Casio Education Australia in their ongoing efforts to provide the very best support to teachers and students using Casio technology.

Contents

Introduction – Key ClassPad 300 features. ................................................ 7 A. Catalogue, Action menu, Interactive menu and 2-D.............................................7

Catalogue and Action menu.........................................................................7 Interactive Menu ..........................................................................................8 The 2-D palette. ..........................................................................................8

B. The basics about variables.....................................................................................9

Section 1 - Main application calculations ................................................. 11 1.1 Basic arithmetic calculations .............................................................................11 1.2 Defining variables to have a numerical value....................................................16 1.3 Defining a list variable using the list editor .......................................................17 1.4 Basic function calculations ................................................................................19 1.5 Working with angles ..........................................................................................20

1.5.1 - To change the default settings to operate in degrees with decimal output...............................................................................................................................20 1.5.2 - Expressing angles in degrees to degrees, minutes and seconds ...............21 1.5.3 - Expressing angles in degrees, minutes and seconds to degrees ...............22 1.5.4 - Convert angles in degrees to radians. .......................................................23 1.5.5 - Convert angles in radians to degrees. .......................................................24

1.6 Basic trigonometric calculations........................................................................25 1.7 Basic statistical calculations ..............................................................................27 1.8 Basic probability calculations ............................................................................29

1.8.1 - Random Number Generator......................................................................29 “rand” function...........................................................................................29 “randList” function ....................................................................................30 “RandSeed” command ...............................................................................31

1.9 Basic symbolic calculations..............................................................................32 Simultaneous Equations.............................................................................35

Section 2 – Exploring functions ................................................................. 37 2.1 Create a table of values ......................................................................................37

Customising your plot view .................................................................................38 2.2 Enter & plot functions........................................................................................38

2.2.1 Using the trace function ..............................................................................40 2.3 Finding significant points on a graph.................................................................41

2.3.1 To find the x intercept/s (or root/s): ............................................................41 2.3.2 To find the y intercept/s: .............................................................................42 2.3.3 To find the stationary points: ......................................................................42

Maximum point/s .......................................................................................42 Minimum point/s........................................................................................43 Point/s of inflection....................................................................................43

2.3.4 To find an x-value given a specific y-value:...............................................44 2.3.5 To find a y-value given a specific x-value:.................................................44

2.4 Finding the intersection point/s on a two graphs ...............................................45 2.5 Finding the distance between two points ...........................................................45

Section 3 Navigating/Managing the graph window................................. 46 3.1 Configuring graph view window parameters.....................................................46 3.2 Zooming the graph window...............................................................................47 3.3 Scrolling and panning the graph view window..................................................49

Scrolling the graph view window ..............................................................49 Panning the graph view window................................................................49

Section 4 Advanced function graphing options ....................................... 50 4.1 Enter and plot functions using parameters.........................................................50 4.2 Graphing an inequality.......................................................................................51 4.3 Graph functions defined in terms of other functions .........................................52 4.4 Draw the inverse of a function...........................................................................53 4.5 Restrict the domain of a function.......................................................................55

Section 5 – Calculus .................................................................................... 56 5.1 Limits .................................................................................................................56 5.2 Rates of Change .................................................................................................57

5.2.1 Average rates of change..............................................................................57 5.2.2 Instantaneous rates of change .....................................................................58

5.3 Derivatives .........................................................................................................60 5.3.1 Sketching the derivative function ...............................................................63 5.3.2 Tangent to a curve.......................................................................................64

5.4 Integration ..........................................................................................................65 5.4.1 Indefinite integrals ......................................................................................65 5.4.2 Definite integrals (without a graphical display)..........................................66 5.4.3 Definite integrals (with a graphical display)...............................................67

Section 6 – Statistical Calculations............................................................ 68 6.1 Univariate data ...................................................................................................68

6.1.1 Working with ungrouped univariate data ...................................................68 6.1.2 Working with grouped univariate data .......................................................69 6.1.3 Histogram....................................................................................................70 6.1.4 Box plot.......................................................................................................71

Box plot with outliers.................................................................................72 (Modified box plot)....................................................................................72

6.2 Cumulative frequency curves (or ogives) ..........................................................73 6.4 Bivariate data .....................................................................................................74

6.4.1 Scatter plot ..................................................................................................76 6.4.2 Correlation coefficient, r and coefficient of determination, r2 ...................77 6.4.3 Calculating the Least-squares line ..............................................................78 6.4.4 Sketch Least-squares line............................................................................78 6.4.5 Using the Least-squares line .......................................................................79

Section 7 – Numeric Solver Application ................................................... 80 7.1 Using the numeric solver ...................................................................................80

Section 8 – Matrices.................................................................................... 82 8.1 Inputting matrix data..........................................................................................82

8.1.1 Matrix calculations......................................................................................83 Addition .....................................................................................................83 Subtraction .................................................................................................83 Multiplication.............................................................................................84 Computing a given power of a matrix. ......................................................84 Inverse........................................................................................................84 Determinant................................................................................................85

8.2 Solving simultaneous equations using matrices ................................................85 8.3 Geometric transformations using matrices ........................................................86 8.4 Transition matrices (Markov chains) .................................................................87

Section 9 – Sequences ................................................................................. 88 9.1 Define, tabulate & plot a sequence. ...................................................................89 9.2 Summing of a sequence .....................................................................................90 9.3 Difference equations ..........................................................................................91

Section 10 - Advanced function graphing options ................................... 92 10.1 Graphing hybrid (mixed or piecewise) functions ............................................92 10.2 Graphing reciprocal functions..........................................................................93 10.3 Graphing rational functions .............................................................................94 10.4 Graphing sum and difference functions ...........................................................95 10.5 Graphing absolute value (modulus) functions .................................................96 10.6 Graphing product functions .............................................................................97 10.7 Graphing composite functions .........................................................................98

Section 11 – More on Calculus. ................................................................. 99 11.1 Area between two curves .................................................................................99 11.2 Mean value of a function ...............................................................................100 11.3 Second derivative...........................................................................................101 11.4 Volumes of solids of revolution.....................................................................102 11.5 Direction fields for a differential equation.....................................................103

Section 12 – Probability distributions..................................................... 105 12.1 Discrete probability distributions...................................................................105

12.1.1 Finding probabilities, the mean, variance & standard deviation associated with discrete random variables. .........................................................................105 12.1.2 Finding probabilities, the expected value, the variance & the standard deviation associated with the binomial distribution...........................................109

12.2 Continuous probability distributions..............................................................114 12.2.1 Finding k, graphing and finding the mean and variance. ........................114 12.2.2 Standard normal distribution...................................................................116 12.2.3 Inverse cumulative normal distribution ..................................................117

Section 13 - Graphing relations, circles and ellipses ............................. 118

Section 14 - Complex Numbers ............................................................... 121

Section 15 - Financial Calculations - TVM ............................................ 123

Section 16 - Vectors................................................................................... 125 16.1 Viewing vectors. ............................................................................................125 16.2 Operating with vectors. ..................................................................................127 16.3 Vectors that are functions of time..................................................................128

Appendices - Text-book cross referencing ............................................. 130

Units 1 & 2 ................................................................................................. 130 A.01 Cambridge Essential Advanced General Mathematics .................................130 A.02 Cambridge Essential Mathematical Methods 1 & 2 CAS.............................132 A.03 Cambridge Essential Mathematical Methods 1 & 2 .....................................134 A.04 Cambridge Essential Standard General Mathematics ...................................136 A.05 Heinemann VCE Zone General Mathematics...............................................138 A.06 Heinemann VCE Zone Mathematical Methods 1 & 2 ..................................140 A.07 Jacaranda Maths Quest 11 General Mathematics A .....................................142 A.08 Jacaranda Maths Quest 11 General Mathematics B......................................143 A.09 Jacaranda Maths Quest 11 Mathematical Methods.......................................144 A.10 Macmillan MathsWorld Technology Toolkit (TI-89) ..................................145

A.11 Pearson Longman General Maths Dimensions (An advanced course) 1 & 2................................................................................................................................147 A.12 Pearson Longman Mathematical Methods Dimensions 1 & 2 .....................148

Units 3 & 4 ................................................................................................. 151 A.13 Cambridge Essential Further Mathematics 3 & 4 .........................................151 A.14 Cambridge Essential Mathematical Methods 3 & 4 CAS.............................153 A.15 Cambridge Essential Mathematical Methods 3 & 4 .....................................155 A.16 Cambridge Essential Specialist Mathematics 3 & 4 .....................................157 A.17 Heinemann VCE Zone Further Mathematics................................................159 A.18 Heinemann VCE Zone Mathematical Methods 3 & 4 ..................................161 A.19 Heinemann VCE Zone Specialist Mathematics............................................162 A.20 Jacaranda Maths Quest 12 Further Mathematics 2nd ed................................163 A.21 Jacaranda Maths Quest 12 Mathematical Methods 2nd ed ............................165 A.22 Jacaranda Maths Quest 12 Specialist Mathematics 2nd ed............................166 A.23 Pearson Longman Mathematical Methods Dimensions 3 & 4 .....................167 A.24 Pearson Longman Specialist Maths Dimensions 3 & 4................................170

Introduction – Key ClassPad 300 features.

A. Catalogue, Action menu, Interactive menu and 2-D.

Catalogue and Action menu.

The CP 300 was made to enable the user to enter mathematics as we write it on paper (natural input) and conduct mathematical processes without the use of syntax. Every command the CP 300 possess resides in the

catalogue. Launch the application, raise the soft

keyboard and tap the (alogue tab. Set the form to be all. Locate the lim( command.

Suppose we want to determine the

−→ − 2

1

2

lim

xx. We

would now have to remember what the syntax for this command is: lim(function, variable, variable value, limit

direction). So, if you like syntax, you can use the CP 300 in this way. A shortcut to the catalogue, if you like this way of operating, is the Action menu. It contains many of the most commonly used command from the catalogue.

However, a syntax free way of working exists –

read on…

Interactive Menu

The interactive menu contains the same options as the Action menu. However, it is used differently.

In the application, enter the expression

− 2

1

x. Then select it by dragging

across it with the stylus. Then tap the Interactive menu, then Calculation and then lim. You can see that a box appears prompting you to input the required information – no recall of syntax required. Entering the correct inputs and pressing tapping OK returns the result. Note that in some cases the CP 300 displays the input in natural form. In other cases the syntax is included on the screen. (Note that OS 3 allows commands from the Interactive menu to be used without

first entering and highlighting an input. This supplement will continue to use the

‘old’ method.)

The Interactive menu acts like a wizard so you do not have to remember what information the CP 300 needs, it tells you what it needs.

The 2-D palette.

The 2-D palette allows you to enter a lot of the mathematics you deal with as you see it in books and

write it on paper. Raise the soft k and tap the )

tab. This reveals 2-D palette. (Tap and to reveal other options.) We can achieve that seen opposite. Not all processes can be entered in this way. So, you are able to choose the way you want to work. The

) palette removes the need for excessive bracket entry, which has always been a difficulty with electronic technology.

B. The basics about variables

You will notice on the hard keypad the keys x y Z. When pressed they input a bold italic letter.

You can also input letters using the panel on the soft keyboard. Note that when doing this the letters are not bold and italic. Note the outputs. CP 300 understands xyz

to be zyx ×× , thus removing the need to enter

multiplication signs all the time. CP 300 understands xyz to be the name of some other variable. If we wanted to, we could enter x×y×z – your choice, but it is easy to forget them sometimes! This feature helps us to enter algebraic expressions as we see and write then, provided we use the bold and italic letters.

We are not restricted to just x y Z. On the 9 and ) palettes of the

soft keyboard the option holds 52 variables for you to use.

Note that it is possible to define a variable to be a numeric value. If this has occurred, it can be annoying when trying to perform symbolic computation. To be sure the variables a to z are not defined to be some numeric value use the Clear All Variables command in the Action menu. This command does not clear capitalized variables. To do this, enter the ‘delvar’ followed by a space and then the variable you want to ‘clear’. Or, retrieve the delvar command from the catalogue.

C. Active windows, menus and tool bars The CP 300 has a large screen. It allows us to have two applications visible the same time.

For example we can have the application and the application visible at once.

Launch the application then do as the directions in picture (below) ask.

We now have two windows open, one with a darker boundary – the top one in this case. Tap in the bottom window – what do you notice?

Notice that the menu options and the toolbar change. The menu options and the icons on the tool bar belong to the application whose window is active (has the bolder border). This is an important thing to remember as we proceed.

Section 1 - Main application calculations

1.1 Basic arithmetic calculations

This section explains how to carry out basic mathematical operations in the Main application. To launch the Main Application:

Tap M within the menu of on the icon panel.

Or, if an application is already launched, tap M

on the icon panel.

Once launched, the Main application window will be displayed as below:

Menu bar

Toolbar

Work area – input

displayed on left,

output displayed on

the right.

Status bar – displays

current mode settings

Icon panel

To change the mode the calculator is operating in, you can simply tap on the

specific mode name in the status bar to change it. Alternatively, tap OOOO on the

menu bar.

Note: To switch between outputs as exact values to decimal approximations, put the

cursor in either the input or output line and tap . (located on the tool bar).

Example Demonstration 2

3

5

1) Use either the hard

keyboard or 9 soft keyboard to enter the calculation.

2) The calculation can also be entered using natural

input via the ) soft keyboard.

2

5

1. Use the 9 soft keyboard to enter the calculation.

2. The calculation can also be entered using natural


5 76

1. Use the hard keyboard

or 9 soft keyboard to enter the calculation. (Tap . to get decimal output.)



( ) ( )47 101.2109.4 ×÷×

1. Use the hard keyboard

or 9 options on the soft keyboard to enter calculation. (Tap . to get decimal output.)



Is 64 46 < ? The judge( function will judge the validity of an equality or inequality. Use

the (alogue on the soft keyboard to enter judge( or just type it in.

(Use the 9 options on the soft keyboard, select the

tab, in order to enter the inequality sign.)

Find prime factors of 360? 1. Key in the number, then

highlight/select it.

2. Tap the Interactive option on the menu bar, tap Transformation, and then select factor.

Note: The Action menu

or (alogue on the soft keyboard could also have been used for this example.

Evaluate 324log10

1. Use the 9 options on the soft keyboard to enter calculation.


format via the ) soft keyboard.

(Tap . to get decimal output.)

Note: Logarithms of bases other than 10 can be computed.

1.2 Defining variables to have a numerical value

Use the variable assignment key W, to assign a numerical value to a variable. This

key can be found in the 9 options and the ) options on the soft keyboard.

Example Demonstration

4

11

a) Find the hypotenuse, h.

b) Find the angle, θ . Using Pythagoras’ Theorem, assign the following; a = 11, o = 4,

( )22oah += . The angle,

θ can be found using

= −

hyp

opp1sinθ .

You can to use the 9 options including

the options or the

) options on the soft keyboard. You can then edit the initial inputs and all calculations will be recalculated below where the cursor is placed.

Note that variables need to be clear of defined numeric

values before doing symbolic calculations. See the section

“The basics about variables” to see how to clear the

definitions from within the Main application.

θ

1.3 Defining a list variable using the list editor

This list editor makes short work of creating and using list variables (or lists data). The list editor can be accessed from within the Main, Graph and Table, Statistics and eActivity applications. To access the list editor window from the Main application:

• Select n from the tool bar, then (. The list editor window will open, and

occupy the bottom half of the main work area.

• Note that the menu bar, tool bar options and status bar change when the list editor window is active.

To enter data:

• Select a list, key in data and press E after each

entry.

• The list name can also be changed. Simply select the current list name (e.g. list1) and change it to an appropriate name (e.g. time, height etc).

• List variables can be used in various calculations, graph applications and so on as variables are globally recognized in the CP 300. Some examples are shown below working in the Main application, the List Editor and the Graph and Table application.

Also in Graph and table,

1.4 Basic function calculations


Evaluate 222 ++ xx when

4=x . Method 1:

1. Raise the (alogue on the soft keyboard.

2. Find Define, and tap

it twice to input this command. (Alternatively type Define and then a space

using the 0 keypad.) Key in the equation and

press E.

3. Now type in f(4) and

press E.

Method 2: 1. Key in the equation and

highlight. 2. Tap Interactive on

the menu bar, then tap Define.

3. Enter the function name

and variable/s into the Define box. (The Expression should already be entered.) Tap

. 4. Now type in f(4) and

press E.

1.5 Working with angles

When working with angles, always begin by checking that the CP 300 is set to compute in the angle units you are working with. Look at the status bar to find out which angle the CP 300 is set to use. The default setting is radians. It is highly desirable (and critical in some cases) to include the units of the angle when you make an input. When the units are displayed in the input, the CP 300 then knows what the units of the input are. If no units are given it will assume the units are the units it is set to compute in. If the units are given, it will consider the input to be those units, regardless of what it is set to compute in. The output will always be in the units to which the CP 300 has been set to compute in.

Note: The ClassPad utilizes r, not c,

as a notation for the units of radians.

It may be useful, when working with degrees (or when you require a decimal

approximation and not an exact value), to set the ClassPad to output the approximate

decimal answer. See below for details.

1.5.1 - To change the default settings to operate in degrees with decimal output.

Key Operation

Alternatively,

1. Tap O on the menu bar, or Settings on the Icon Panel.

2. Select Basic Format.

3. Change the Angle setting (by using the drop box) to Degree.

4. It may be useful, when working with degrees (or when you require a decimal

approximation and not an exact value), to set the ClassPad to output the

approximate decimal answer. Tick the Decimal Calculation box under the Advanced settings.

5. Tap .

To change the angle mode the calculator is operating in, simply tap on the specific angle indicator in the status bar to change it.

Notice the status bar has changed, and the ClassPad will now be operating in degrees and return outputs that are decimal approximations.

1.5.2 - Expressing angles in degrees to degrees, minutes and seconds

Example

Express °65.34 in degrees, minutes, seconds.

Key Operation

1. Enter the angle and put a degree ( o ) symbol after it. The degree symbol is on

panel within the 9 panel of the soft keyboard. While this is not absolutely necessary it is a good habit to have – see later sections for the reason.

2. Highlight the angles and then tap Interactive on the menu bar.

3. Select Transformation, then toDMS.

1.5.3 - Expressing angles in degrees, minutes and seconds to degrees

Example

Express 9334 ′° as a decimal degree value.

Key Operation 1. From the Interactive menu tap Transformation and then select

dms.

2. Enter in the degree, minute and second values.

3. Tap . 4. Tapping Standard on the status bar will change the settings to Decimal.

Once changed, press E . The last input line will be recalculated.

1.5.4 - Convert angles in degrees to radians.

Example

Express 9334 ′° in radians.

Key Operation 1. Change the CP 300 to compute in radians if it is not presently (look at the

status bar). See section 1.5.1 for instructions.

2. Repeat the procedure from Section 1.5.3. Add the degree symbol at the end

(found on the panel of the 9tab of the soft k).

3. To convert from the exact value to the decimal approximation, highlight the

answer and tap .. (Or, tap Standard on the status bar. This will change the settings to Decimal.)

Note:

It is in this situation that the inclusion of the degree symbol is critical. It tells the

CP 300 your input is in degrees. Without this, it would assume the input is in

radians as the CP 300 is set to radian mode.

1.5.5 - Convert angles in radians to degrees.

Example

Express c

8

5πin degrees, minutes, seconds.

Key Operation

1. Change the CP 300 to compute in degrees if it is not presently (look at the

status bar). See section 1.5.1 for instructions.

2. Enter the angle, including the radian symbol, then highlight. 3. From the Interactive menu tap Transformation and then select

toDMS.

4. Tap E.

1.6 Basic trigonometric calculations

When working with angles, always begin by checking that the CP 300 is set to compute in the angle unit you are working with. Look at the status bar to find out which angle the CP 300 is set to use. The default setting is the radian. It is highly desirable (and critical in some cases) to include the unit of the angle when you make an input. When the unit is displayed in the input, the CP 300 then knows what the unit of the input is. If no unit is given it will assume the unit is the unit it is set to compute in. If the unit is given, it will consider the input to be that unit, regardless of what it is set to compute in. The output will always be in the units to which the CP 300 has been set to compute in.

Note: The ClassPad utilizes r,not c

, as a notation for the units of radians.

It may be useful, when working with degrees (or when you require a decimal

approximation and not an exact value), to set the ClassPad to output the approximate

decimal answer. See section 1.5.1 for instructions. This section assumes you have read all of Section 1.5.


Evaluate )'4225sin( ° .

Method :

1. Using the 9 options on the soft keyboard, select the

tab, and tap

. 2. Use the Interactive

menu, tap Transformation and then select dms.

3. Enter the angle and tap .

Evaluate

c

7

5cos

π

1. Use the 9 soft keyboard, select the

tab, in order to view/enter the trigonometric functions.

2. Type in/or use the

) options on the soft keyboard to enter the angle.

Evaluate )45.190tan( ° and

sin(c

4

π).

This example illustrates how the CP 300 can be set to compute in radians, but if the input is in degrees, it is respected and vice versa.

Find θ in radians if

3.0sin =θ . 1. Be sure the CP 300 is

set to compute in radians.

2. Using the 9 options on the soft keyboard, select the

tab.

3. Key in expression

(using the ) options if you wish).

4. To convert from exact values to approximate, highlight the answer and tap ..

Find θ in degrees, minutes and seconds if 75.0cos =θ .

1.7 Basic statistical calculations

While using the Main application, you can easily access the Statistics application. Key Operation

1. Tap on the tool bar and select (

2. Enter data into list1 (or an empty list)

3. Select Calc then One-Variable.

4. Select the XList using the drop down menu. Tap .

5. The Stat Calculation screen will appear containing a basic statistical summary of the selected listed data.

There is another method for computing statistics for a list of data. The list name can be copied and then pasted into the Main application work area. We can then the Interactive menu options as seen below.

It is also possible to enter the data directly into the Main application using the following: { }, see below.

1.8 Basic probability calculations

Raise the soft keyboard. Select the options on 9 palette. The factorial, combination and permutation commands are found here.

1.8.1 - Random Number Generator

The random number generator on the ClassPad can generate:

• Non-sequential random numbers.

• Sequential random numbers. The ClassPad has three ‘random’ functions:

• rand – generates random numbers.

• randList – generates a list of random numbers.

• RandSeed – configures settings for random number generation (i.e. switch between non-sequential and sequential). The ClassPad can generate nine different patterns of sequential random numbers – this function is also used to choose a specific pattern.

“rand” function


Generate random numbers between 0 and 1. Method : 1. Type in/ or locate

rand( in the

catalogue. Press E.

2. To generate more

random numbers,

simply press E again.

Generate random integers between 25 and 50 inclusive. Method : 1. Type in/ or locate

rand( in the catalogue. Enter the start and end values separated with a comma.

2. Press E.

3. To generate more

random numbers using these limits, simply

press E again.

“randList” function


Generate 20 random numbers between 0 and 1. Method : 1. Type in/ or locate

randList( in the catalogue. Enter the number of random numbers you wish to find and close with a bracket.

2. Press E.

Alternatively:

1. Open a Stat list editor window.

2. Go to the Cal cell of list1 and type in/ or locate randList( in the catalogue. Enter the number of random numbers you wish to find and close with a bracket.

3. Press E.

Generate 20 random integers between 1 and 100 inclusive. Method : 1. Type in/ or locate

rand( in the catalogue. Enter 20,1,100 and close with a bracket.

2. Press E.

3. Or use Stat list editor

application, as in the previous example.

“RandSeed” command

This command requires an integer between 0 and 9 for the argument. RandSeed 0 – non-sequential random number generation. RandSeed (integer from 1 to 9) – uses that particular value as a seed for specification for sequential random number generation.


Generate sequential random numbers using 4 as the seed value. Method : 1. Type in RandSeed

(and a space) or locate it in the catalogue. Enter 4, then

press E.

2. To generate random

numbers - Type in/ or locate rand( in the catalogue. Press E.

3. To generate more random numbers,

simply press E again.

1.9 Basic symbolic calculations

When entering symbols it is good practice to use the bold italic letters available on the hard keyboard and

on the 9 and) soft keyboards under the

option. See the Introduction for reasons. To achieve answers in the same format as those displayed in the following examples; go to Settings and select Basic Format. Under the Advanced options, tick Descending Order. Tap . Before doing symbolic computation, clear variables of any numeric definitions. To do so for all lower case variables a to z use the Clear All Variables command.


axxx ++ 23

( )( )yx

yx

+

− 22

)(3 ab −

Expand

a. 2)( yx +

b. 4)( yx +

To complete example b. edit the calculations from example a. Highlight and then drag and drop the first input into a new working line and edit the 2 to be a 4 and then

press E.

Factorise 162 −x

Factorise 62 −x : a) over Q – the rational

numbers b) over R – the real

numbers

Divide 15 +x by 2−x .

Is 22 4ba − equal to )2)(2( baba +− ?

Note: You could also have used the expand command.

Express yx 3

3

2

5+ as a

single fraction.

Solve ,2

12sin =x

a) for all x.

b) for 20 << x . 1. Enter in the equation

and highlight. 2. Select Interactive,

Equation/Inequality then solve.

3. Then use the “for”

operator, U, to key in the condition.

(The tab, holds the “for” operator.)

Solve the following simultaneous equations:

52

153

+=

=+−

xy

yx

1. Key in the function,

using the template

on the ) palette of the soft keyboard (choose the option).

Note: To enter a system with more than 2 equations,

repeatedly tap the template.

Alternatively, use the solve function and following syntax:

Simultaneous Equations

solve({-x+3y=15,y=2x+5},{x,y})

Calulator output

Solve 072 <−x for x.

The ClassPad can display the solution to this inequality both numerically and graphically.

To see the solution

graphically, select the

inequality. Open the graph

application, then “drag and

drop” the inequality from

Main to the Graph window .

The graph window will

illustrate the values of x for

which the inequality is true.

Solve 325

9+= CF for C.

Note: The Interactive menu options have been used in these examples. The

Action menu options, direct typing or accessing commands from the (alogue on the soft keyboard could also have been used for these examples.

Section 2 – Exploring functions

2.1 Create a table of values

Method Demonstration

1. Tap m on the icon

panel.

2. Open the W

application.

3. Tap in the working line of y1 (or an empty line). Define y1 to be

53 +x .

4. Press E to complete

the process. Notice the box in front of the function is now ticked.

5. Tap 8 on the tool

bar. This will display the Table Input box.

6. Enter the domain you are interested in as well as the steps within the domain to be displayed, and then tap .

7. Select # on the tool

bar. This will generate a table of values and will be displayed in a Table

window. (Note that the menu bar and tool bar

options change when the table window is active).

Note: This process is a helpful guide to choosing sensible settings for the graph view window.

Customising your plot view

1. Tap O on the menu bar,

or Settings on the Icon

Panel.

2. Select Graph Format.

3. Check settings.

4. Tap .

2.2 Enter & plot functions

There are two methods of plotting functions:

1. via the W application.

2. via the M application window.

Method Demonstration

Method 1.

1. Tap m on the icon

panel.

2. Open the W

application. 3. Tap in the working line

of y1 (or an empty line). Define y1 to be

103 +x .

4. Press E to complete

the process. Notice the box in front of the function is now ticked.

5. Check your graph view

window settings by tapping 6 located on the tool bar. If necessary, change your window settings, then tap .

6. Tap $ to have a graph of the function appear. (Note that the menu bar,

tool bar options and status bar change when the graph window is active).

Alternatively,

highlight the function

and drag it into the

graph window to

have the graph of the

function appear.

Method 2

1. Tap M on the icon

panel. 2. Input the function. (In

this example,

103 += xy .)

3. Press E.

4. Insert a graph window by selecting $ from the tool bar. A graph window should appear. (Note that the menu bar,

tool bar options and status bar change when the graph window is active).

5. Highlight the entire function and drag it into the graph window. The graph of the function will automatically appear in this window.

Try it out for yourself:

Graph the following functions. Remember to always check your graph view window, and

if necessary change the settings, in order to view the graph of the function.

a) 52 −= xy

b) 1354 =+ yx

c) 23)( 2 −= xxf

d) 3xy =

e) 1644 23 +−−= xxxy

f) xy sin=

g) xy 2=

h) )2(log xy e=

i) x

y1

=

j) ( )2−= xy

k) xy =

2.2.1 Using the trace function

The trace function allows you to move along a graph. The coordinates of the position where the cursor is displayed in the graph view window. To operate the trace function, the graph view window needs to be active so the tool

bar is visible. Tap the Analysis option on the menu bar and select Trace. Alternatively, tap p on the tool bar to scroll and view other options. Tap =. The cursor will automatically be placed at x = 0. The cursor can be moved along the graph by pressing the cursor key, left or right, or by tapping the left or right graph controller arrows (on the edges of the graph window). If multiple graphs are sketched, press the cursor key, up or down, (or tap the up or down graph controller arrow) to jump between graphs.

If you wish to move the cursor to a specific x-value, after activating the Trace function, press a number key to display the Enter Value box. Key in the value and tap .

2.3 Finding significant points on a graph

At times, you will be required to do the following:

• Find x and y intercepts

• Find stationary points (i.e. Maximum/minimum points, points of inflection)

• Calculate an x-value given a specific y-value or vice versa. The following instruction will assume that you have already drawn a graph of the function.

2.3.1 To find the x intercept/s (or root/s):

The graph window needs to be active in order to use the appropriate tool bar. Tap the Analysis option on the menu bar. Tap G-solve, and then select Root. Alternatively, tap p on the tool bar to scroll and view other options. Tap Y This will locate and display the x intercept. Where there is more than one x intercept to be found, simply use the cursor key (left and right) to allow the next intercept to be located.

2.3.2 To find the y intercept/s:

Tap the Analysis option on the menu bar, tap G-solve, and then select y-Intercept. This function will locate and display the y intercept.

Note: While you can graph ( )22 −= yx ) in this application some of the Analysis

options can not be performed. However, in the Conics application C analysis

tools can be used.

2.3.3 To find the stationary points:

Maximum point/s

Tap the Analysis option on the menu bar, tap G-solve, and then select Max. Alternatively, tap p on the tool bar to scroll and view other options. Tap U. This function will locate and display the local maximum point of the function within

the bounds of the screen. Where there is more than one maximum point to be found, simply use the cursor key (left and right) to allow the next maximum point to be located.

n

Minimum point/s

Tap the Analysis option on the menu bar, tap G-solve, and then select Min. This function will locate and display the minimum point of the function. Where there is more than one minimum point to be found, simply use the cursor key (left and right) to locate the next minimum point.

Note: Alternatively, tap p on the tool bar to scroll and view other options. Tap I.

Point/s of inflection

Tap the Analysis option on the menu bar, tap G-solve, and then select Inflection. This function will locate and display the point of inflection of the function. Where there is more than one point of inflection to be found, simply use the cursor key (left and right) to locate the next point of inflection.

2.3.4 To find an x-value given a specific y-value:

Tap the Analysis option on the menu bar, tap G-solve, and then select x-Cal. This function will locate and display the x and y coordinates. Where there is more than one x-value given for a specific y-value to be found, simply use the cursor key

(left and right) to allow the next x-value to be located.

2.3.5 To find a y-value given a specific x-value:

Tap the Analysis option on the menu bar, tap G-solve, and then select y-Cal. This function will locate and display the x and y coordinates.

2.4 Finding the intersection point/s on a two graphs

Tap the Analysis option on the menu bar, tap G-solve, and then select Intersect. This function will locate and display the intersection point of the graphs. Where there is more than one intersection point to be found, simply use the cursor key (left and right) to allow the next intersection point to be located.

Note that if three or more functions are drawn and the intersection of two is required, the CP 300 will flash the cursor on one function. Use the up and down cursor keys to

select the functions you require and press E when the required function is selected.

2.5 Finding the distance between two points

This function will locate and display the distance between two specific points. Tap the Analysis option on the menu bar, tap G-solve, and then select Distance. Press a number key to display the Enter Value box. Key in the coordinates and tap . The coordinates will be displayed in the graph view window and the distance calculated in the message box.

Alternatively, you can use the stylus to tap the two points on the screen.

Section 3 Navigating/Managing the graph window

This section assumes that the ClassPad is operating in the W application.

Also, check the Graph Format settings (see page 37 for further details).

3.1 Configuring graph view window parameters

1. Tap 6 located on the tool bar. (Or, tap O, then select View Window.)

This feature displays the View Window dialog box.

2. If necessary, make the appropriate changes, depending on the nature of the

intended graph. Tap . (Note: The menu bar, tool bar options and status bar change when the graph window is active). Brief explanation of View Window parameters (rectangular coordinates):

xmin – minimum value of x-axis ymin – minimum value of y-axis

xmax – maximum value of x-axis ymax – maximum value of y-axis

xscale – marker spacing of x-axis yscale – marker spacing of y-axis

xdot – value of each screen pixel horizontally

ydot – value of each screen pixel vertically

The x/y dot and x/y dot values will change automatically when the x/y maximum and minimum values are changed.

Graph

Editor

Window

Graph

View

Window

Message box

A number of View Window configurations are saved in the memory of the CP 300. Tap the Memory drop down menu when the view window setting input box is open. Brief explanation of some of the preset parameters: Initial – square window settings (Default). Undefined – auto-configuration of the view window box. You can also Store and Recall your own settings.

3.2 Zooming the graph window

The ClassPad features an extensive selection of Zoom commands that can be used for either a specific region of a graph or to enlarge and/or reduce an entire graph.

Brief explanation of some of the Zoom commands:

Zoom command Demonstration Box Select the Box zoom option and then select a region of the graph you want enlarge with the stylus by dragging a rectangle on the screen. Once the stylus has been taken off the screen, the selected region will be enlarged to fill the entire graph window display. You can also access this command from the tool bar. Tap p on the tool bar to scroll and view other options. Tap Q.

Factor This command allows you to configure the zoom factor settings.

Zoom In

Quick Zoom There are seven of these commands: Quick Initialize Quick Trig Quick log(x) Quick e^x Quick x^2 Quick –x^2 Quick Standard These quick zoom commands will redraw the graph using preset built-in View Window parameters.

3.3 Scrolling and panning the graph view window

Scrolling the graph view window

Once a graph has been sketched, it can be scrolled left, right, up or down using the cursor key or the graph controller arrows.

Note: The graph controller arrows will only be active if the Graph Format settings are set with the G-Controller box ticked (see page 37 for further details).

Panning the graph view window

To operate this function, the graph view window needs to be active in order to use the appropriate tool bar. Tap p on the tool bar to scroll and view other options. Tap z. Position the stylus on the graph view window, and drag the window to an appropriate location. Once the stylus is removed, the graph will be redrawn at that particular location.

Section 4 Advanced function graphing options

This section four assumes that the ClassPad is operating in the W application.

4.1 Enter and plot functions using parameters


Let cbxaxf +−= 2)()( ,

where a, b and c are integers. How is the function transformed under the following conditions?

a. a = 1, b = 0 and c

varies b. a = 1, b varies and c

= 0 c. a varies, b = 0 and c

= 1 Method: a. Key the following into y1:

}2,1,0,1,2{)0(1 2 −−+−x

Use the ) soft

keyboard and tap to enter the parameter list or

just use the { on the 9 palette. b. Key the following into y2:

0})2,1,0,1,2{(1 2 +−−−x

c. Key the following into y3:

1)0}(2,1,0,1,2{ 2 +−−− x

You could also define a list

as a variable and use that

variable.

a)

b) c)

4.2 Graphing an inequality


Sketch 12 +≤ xy .

Method: If you already have an equality entered, tap on the equal sign, (=). This will display the Type box, enabling you to select the form you wish to graph. Select the appropriate form and tap . Tap $ to graph the region.

Alternatively,

You can use the option available on the tool bar. Tap d or Type in the menu bar.

Sketch the region bounded by the following:

• 12 +≤ xy and

• xy −> 3 and

• 0≥x and

• 0≥y .

4.3 Graph functions defined in terms of other functions


Sketch 2)( xxf = . Explain

graphically, the outcome of the following transformations

a. )(xf−

b. 2)( +xf

c. )(2 xf

d. )4( −xf

Method: 1. In the Main application

window: Type in, (followed by a space), or locate Define in the catalogue. Key in the function and

press E.

2. Launch the application. Make y1 be

f(x). Press E after

each entry.

3. Tap $ to graph the function. Functions can be sketched simultaneously or individually, depending on whether the check box is ticked.

4. You can also specify the graph line style. Simply tap the line style next to the function and the Graph Plot Type window will appear. Select your desired type and press .

Line style

Alternative method.

Make y1 = 2x .

Then define the remaining functions in terms of y1(x).

4.4 Draw the inverse of a function


Sketch 2)( xxf = and its

inverse. Method: 1. Enter the function into

y1. Press E.

2. Select the Analysis option, tap Sketch followed by Inverse.

3. The inverse of the function will automatically appear in the Graph View

Window. The inverse function will also be defined in the message box.

Alternative method:

1. Key the function into the Main application

window. Highlight the function and the select Interactive on the menu bar, tap Assistant, followed by invert.

2. Select variables you wish to invert in the invert window and press .

3. The function and its inverse of the function will appear on the right hand side of the screen (work area).

4. This can be sketched if required, by opening a graph view window. (Tap $ on the tool

bar.) Select each in turn and “drag and drop” them into the graph view window.

4.5 Restrict the domain of a function


Sketch xy = , where 0≥x .

Method: Key in the function, then

the “for” operator, U, followed by the restricted domain.

(Using the 9 palette on the soft keyboard, select the

tab, in order to view/enter the “for” and inequality operators.)

Sketch xy = , where

22 <<− x . Method: Key in the function, then

the “for” operator, U, followed by the restricted domain.

(Using the 9 soft

keyboard, select the tab, in order to view/enter the “for” and inequality operators.)

Note that the “for”, U, can be use in conjunction with the solve command to find

solutions within a given domain.

Section 5 – Calculus

5.1 Limits


Find

a.

∞→ xx

1lim

b.

+→ xx

1lim

0

c.

−→ xx

1lim

0

Method: 1. Key in the limit

statement, using the

limit feature, , on

the ) soft keyboard (choose the option).

2. To enter the direction of the limit, use the + and - operators available on

the 9 soft keyboard, tap to view/select. (Note: you can also use the standard + and – operators.)

Alternatively,

The limit statement could be entered using the Action or Interactive options on the menu bar, or catalogue.

5.2 Rates of Change

5.2.1 Average rates of change


Calculate the average rate of change for

22)( 2 ++= xxxf on the

intervals: a. x = 3 and x = 3.1 b. x = 3 and x = 3.05 c. x = 3 and x = 3.001 d. x = 3 and x = 3 + h

Method: 1. Define the function,

press E.

2. Using the ) palette on the soft keyboard, enter a fraction template then enter the average rate of change.

3. Calculations can easily performed by selecting the previous input, dragging and dropping it into the next working line and then editing it.

5.2.2 Instantaneous rates of change


Calculate the instantaneous rate of change where

22)( 2 ++= xxxf at x = 3.

Method: To find the instantaneous rate of change, find the limit (as h approaches 0) of the average rate of change for the interval [3 , 3+h]. 2. Define the function,

press E.

3. Key in the function,

using the limit template,

, on the ) palette of the soft keyboard (choose the

option).

Alternative method:

1. Key in and select the function.

2. Tap Interactive, then Calculation, followed by lim.

3. Enter variable, point and direction into the lim box. Tap .

Note that the Direction

input can be -1 if you want

the limit approaching from

the left, 1 for the right and 0

for both.

5.3 Derivatives


Find a. the derivative of

22)( 2 ++= xxxf

b. )2(f ′

c. )3(−′f

Method for part (a): 1. Define the function,

press E.

2. Key in the problem,

using the derivative

feature, , on the

) soft keyboard (choose the option).

Alternative method for part

(a) See screen captures 1 &

2.:


2. Tap Interactive, then Calculation, followed diff.

3. Select differentiation. Enter variable and order into the diff box. Tap

.

Method for part (b): Key in the function, then

the “for” operator, U, followed by the argument.

(Use the 9 soft

keyboard, select the tab, in order to view/enter the “for” operator.)

1. 2.

Alternative method for part

(c):


2. Tap Interactive, then Calculation, followed diff.

3. Select Derivative at value, then enter variable, order and derivative into the diff box. Tap .

4. This feature helps you to use syntax to solve the task.

Using the W application, find )2(f ′

where 22)( 2 ++= xxxf .

Method: 1. In this example the

function has been defined and stored as f(x).

2. Key in the function as f(x) into the graph

editor window. Press

E. Tap $ to graph.

3. Check the Graph

Format settings. [Tap

O, then Graph Format.] Make sure Derivative/Slope is ticked. Tap .

4. With the graph view

window active, tap Analysis, then Trace.

5. Press 2. The Enter Value box appears. Tap .

6. The derivative at that point, along with the coordinates of the function will be displayed in the graph view window.

5.3.1 Sketching the derivative function


Sketch 22)( 2 ++= xxxf

and its derivative, )(' xf .


function has been defined and stored as f(x).

2. Key in the function as f(x) into the graph

editor window. Press

E.

3. Key in the derivative

function, using the derivative template,

, on the ) palette of the soft keyboard (choose the

option). Press

E. Tap $ to graph.

4. You can also specify the

graph line style. Simply tap the line style next to the function and the Graph Plot Type window will appear. Select your desired type and press .

Graph line style

5.3.2 Tangent to a curve.


Sketch 22)( 2 ++= xxxf

and the tangent at 2−=x . Find the equation of the tangent.


function has been defined as f(x).

2. Key in the function into the graph editor

window. Press E.

Tap $ to graph.


window active, tap Analysis, then Sketch, followed by Tangent.

4. Enter -2 and the Enter Value box will appear. Tap .

5. Crosshairs will appear at that point. You must

press E in order for

the tangent to appear.

6. The tangent at that

point, along with the coordinates of the function will be displayed in the graph

view window.

The equation of the

tangent appears in

the message box.

5.4 Integration

5.4.1 Indefinite integrals


Find the integral of

2610)( 34 ++= xxxf .

Method: Key in the function, using

the integral feature, ,

on the ) soft keyboard (choose the option).

Press E.

Note: Do not enter lower & upper terminals for indefinite integrals. Alternative method:


2. Tap Interactive, then Calculation,

followed by ∫ (the

integral sign).

3. Select Indefinite integral. Enter the variable you are integrating with respect to into the variable box. Tap .

When working with indefinite integrals, don’t forget you will need to include the constant of integration, c, when writing down your answer.

5.4.2 Definite integrals (without a graphical display)


Calculate dxex

x

∫ +4

1

25

.

Method: Key in the function, using

the integral template, ,

on the ) soft keyboard (choose the option).

Press E.

Note: Don’t forget to enter lower & upper limits for definite integrals. Alternative method:



followed by ∫ , the

integral sign.

3. Select Definite integral. Enter the variable you are integrating with respect to, the lower and upper

limits into the ∫ input

box. Tap . Note: This method will

provide an ‘exact’ result if

possible.

5.4.3 Definite integrals (with a graphical display)

Using the W application, compute and display and interpretation of

dxex

x

∫ +4

1

25

.

Method: 1. Key the function into

the graph editor. Press

E. Tap $ to graph.


window active, tap Analysis, then G-Solve, followed by

∫dx .

3. Press 1 and the Enter

Value box will appear. Key in the lower and upper intervals and tap

.

4. The function, along with the area interpretation of the integral will be displayed in the graph view window. The decimal approximation of the integrals value will be displayed in the message box.

Note that this method will return a decimal approximation for the integral.

Section 6 – Statistical Calculations

In this section we use the I application.

6.1 Univariate data

6.1.1 Working with ungrouped univariate data


The height of 20, year 11 students from across Australia has been recorded. The results, in centimeters, are: 185, 176, 184, 175, 173, 183, 182, 184, 174, 174, 169, 179, 190, 175, 178, 203, 145, 188, 177, 162. Calculate the five number summary (min, Q1, median, Q3, max.) for the sample and make a histogram. Method:

1. Enter data into list1 (or an empty list).


3. Select the XList using the drop down menu. Tap .


To draw a histogram of these data use the SetGraph then Setting ...menu.

6.1.2 Working with grouped univariate data


The following table shows the number of “Smarties” in each of 50 packets .

# of Smarties Frequency

40 1 41 8 42 29 43 7 44 4 45 1

a. Calculate the mean, median and mode.

b. Find the total number of Smarties in 50 packets.

Method: 1. Enter data into list1

and frequency into list2 (or empty lists).


3. Select list1 for the XList and list2 for the Freq using the drop down menu. Tap .


Note: Name the list before

entering your data. Once

named, the list is

considered to be a

variable.

6.1.3 Histogram


The frequency table shows the length (l) of 80 fish caught in a fishing competition.

Length (mm) Frequency

295 ≤ l<305 8

305 ≤ l<315 17

315 ≤ l<325 19

325 ≤ l<335 13

335 ≤ l<345 10

345 ≤ l<355 6

355 ≤ l<365 4

365 ≤ l<375 3

Draw a histogram. Method: 1. Enter the midpoints of

each class into list1, frequency into list2.

2. Tap G on the tool

bar. (Or, select SetGraph from the menu bar, then Setting.)

3. Adjust the Set StatGraphs options. Press .

4. Tap y on the tool bar to sketch the curve.

5. The Set Interval box will appear – set HStart to 300 and HStep to 10 (this is critical). Press .

6. The histogram will appear in the StatGraph window. (Press Analysis, then Trace, to display the XList and Freq on the histogram.)

6.1.4 Box plot


The height of 20 year 11 students from across Australia has been recorded. The results, in centimeters, are: 185, 176, 184, 175, 173, 183, 182, 184, 174, 174, 169, 179, 190, 175, 178, 203, 145, 188, 177, 162.

1) Construct a box plot with this data.

2) Hence, state the five figure summary (min, Q1, median, Q3, max) for the sample.

Method:

1. Enter data into list1 (or an empty list).



3. Adjust the Set StatGraphs options. Type: MedBox. Make sure

you do not tick the Show OutliersShow OutliersShow OutliersShow Outliers box. Tap .

4. Tap y on the tool

bar to sketch the boxplot.

5. The box plot will appear in the StatGraph window.

6. Tap Analysis, then Trace. Use the cursor key or graph

controller arrows (left/right) to jump between values.

Box plot with outliers

(Modified box plot)

- utilises the IQR×5.1 rule,

which defines limits for “outliers”. To make modified box plot, make sure you tick the Show OutliersShow OutliersShow OutliersShow Outliers box. We have set up StatGraph 2

as a modified box plot and

then drawn both StatGraph

1 and StatGraph 2.

6.2 Cumulative frequency curves (or ogives)


The frequency table shows the length of 80 fish caught in a fishing competition.

Length (mm) Frequency

300 – 309 8

310 – 319 17

320 – 329 19

330 – 339 13

340 – 349 10

350 – 359 6

360 – 369 4

370 - 379 3

a. Add a cumulative

frequency column to the table.

b. Represent the data using cumulative frequency curve.

Method: 1. Enter length data into

list1, frequency data into list2 and cumulative frequency values into list3.




4. Tap y on the tool bar to sketch the curve.

6.4 Bivariate data

This section will use the following example to demonstrate bivariate data analysis with the ClassPad. Example: Swimming Pool Attendance and Daily Maximum Temperature The operators of a local swimming pool record the following data:

Day Max. temp C° Attendance

1 18 870

2 17 819

3 30 2168

4 16 714

5 20 1435

6 22 1458

7 16 819

8 12 406

9 14 231

10 15 572

11 16 603

12 17 839

13 15 572

14 15 806

15 18 1218

16 19 1007

17 23 931

18 21 1215

19 19 995

20 21 275

21 25 1894

22 29 2301

23 26 2207

24 24 2109

25 30 2564

Task: a) Calculate the summary statistics

for the two variables. b) Construct a scatter plot to

examine the relationship between attendance and temperature.

c) Calculate Pearson’s product–moment correlation coefficient, r.

d) Calculate the coefficient of determination, r2

. e) Calculate the equation of the least

squares line. f) Sketch the least squares line. g) Use your equation to predict the

attendance on a day of maximum

temperature at C°23 and compare

your result to Day 17.


Task: a) Calculate the summary statistics for the two variables. Method:

1. Enter temperature into list1 and attendance into list2. to rename the lists.

2. Select Calc then Two-Variable.

3. Select Programs\temp for the XList and Programs\attend for the YList using the drop down menu. Tap .

4. The Stat Calculation screen will appear containing summary statistics of the selected two variable data. Scroll down to see the y variable statistics.

6.4.1 Scatter plot

b) Construct a scatter plot to examine the relationship between temperature and attendance.

Method: 1. Tap G on the tool



3. Tap y on the tool bar to view the scatter plot.

6.4.2 Correlation coefficient, r and coefficient of determination, r2

c) Calculate Pearson’s product–moment correlation coefficient, r. d) Calculate the coefficient of determination, r2

. Method: These tasks can be performed simultaneously. 1. With the List Editor

window active, select Calc from the menu

bar, followed by Linear Reg.

2. Adjust the Set

Calculation options. Tap .

3. The Stat Calculation screen will appear containing, correlation coefficient, r, and the coefficient of determination, r2. (MSe is the mean square error.

Note: Once the Set Calculation window is

closed by tapping ,

the least squares line will

automatically be sketched

in a Statgraph window.

Note that this information

can also be accessed from

the StatGraph window when

active:

- select Calc from the menu bar, followed by Linear Reg.

6.4.3 Calculating the Least-squares line

e) Calculate the least squares regression line. (linear regression) The ouput screen from the previous section also includes the slope and intercept. Note: Once the Set Calculation window is

closed by tapping ,

the least squares line will

automatically be sketched in

a Statgraph window.

6.4.4 Sketch Least-squares line

f) Sketch the least squares line. An alternative to the method

seen above is:

1. To sketch the least squares line tap G on the tool bar. (Or, select SetGraph from the menu bar, then Setting.)

2. Adjust the Set StatGraphs options. Leave StatGraph 1 as is and set up StatGraph 2 as shown. Tap .

3. Tap y on the tool

bar.

6.4.5 Using the Least-squares line

g) Use your equation to predict the attendance on a day of maximum

temperature at C°23 and compare your result to Day 17. There are many different

ways to achieve this – here

is one method:

1. With the List Editor window (or StatGraph window) active, select Calc from the menu

bar, followed by Linear Reg.

2. Adjust the Set

Calculation options. Be sure to change the Copy Formula setting to y1. Tap .

3. Tap M on the icon

panel. Key in y1(23).

Press E. Note. When entering y1(23) or

y1(x), be sure to use the ‘y’

from the qwerty keyboard

and not the y from the hard

keyboard that denotes a

variable.

Section 7 – Numeric Solver Application

This section assumes that the ClassPad is operating the N application.

Note: While this application can be launched from the Menu and also be from the

Graph Editor, 3D Graph Editor and the Main application. Simply tap O when in

these applications.

Equations can be “dragged and dropped” from the above mentioned applications into the Numeric Solver window.

7.1 Using the numeric solver


The volume of a cone, radius r cm and height h

cm, is given by: 3

2hr

Vπ

= .

a) Find the volume of a cone with r = 12 cm and h = 7 cm.

b) Find the radius of a cone if h = 10 cm and V = 1500 cm3.

Method:

1. Key in the Equation: (Use the

) soft keyboard to enter the equation using natural input).

Tap E.

2. The list of expression’s variables will appear. Enter the values.

3. Select the variable you want to solve by checking the adjacent button.

4. Tap 1 on the tool

bar.

5. The Result will appear in a dialogue box. Tap .

Note that the Left-Right = 0

refers to the value of the

right hand side of the

equation subtracted from

the left hand side of the

equation of the value of the

variable computed. If this is

0, then we confident the

correct value of the variable

has been computed.

The lower and upper bounds for the solution can also be specified. If the solution is not within the specified range, an error will occur – see below.

Section 8 – Matrices

8.1 Inputting matrix data

The examples below use the ) soft keyboard to enter the matrix using natural input.


Define the following matrices.

=

34

12A

−

−=

240

112B

−

−

−

=

2

2

1

C

−=

21

12D

Method: Key in the matrix, using the

features, , on

the ) soft keyboard (choose the option).

8.1.1 Matrix calculations

This subsection will use the following exercise to demonstrate matrix calculations using the ClassPad 300. It assumes you have defined matrices A to D as shown in the previous section.

Given the following matrices:

=

34

12A

−

−=

240

112B

−

−

−

=

2

2

1

C

−=

21

12D

Addition

a) DA +

Subtraction

b) DA −2

Calculate the following:

a) DA + b) DA −2 c) BC

d) 2A

e) 1−A f) Adet

Multiplication

c) BC

Note that using the BC from the Qwerty key board will not give the result we want. B×C will. It is good practice to use the letters on the VAR panel – the bold and italic ones that denote a variable.

Computing a given

power of a matrix.

d) 2A

Inverse

e) 1−A

Determinant

f) Adet

Method:

1. Enter A. 2. From the menu bar,

tap Interactive, then Matrix-Calculation, followed by det.

8.2 Solving simultaneous equations using matrices


Using matrices, solve

103 =− yx and 152 =+ yx .

Method: We can express the simultaneous equations in matrix form:

=

−

1

10

52

13

y

x

And so BAy

x×=

−1

Enter

−

52

13as A and

1

10as B and then compute

BA ×−1

8.3 Geometric transformations using matrices


a) Determine the transformation matrix,

yxD , , for the

combination of transformations: a dilation by a factor of 5 parallel to the x axis followed by a dilation by a factor of 3 parallel to the y axis.

b) Find the coordinates of the transformed image of the point (7,9) under

yxD , .

Note that we know that each

point ),( yx is mapped onto

its image ),( yx ′′ by:

dycxy

byaxx

+=′

+=′

Therefore, in matrix form:

=

′

′

y

x

dc

ba

y

x

8.4 Transition matrices (Markov chains)


Claude has a coffee shop. He sells coffee and biscotti. He realises that if a person buys (and enjoys) a coffee on a particular day, there is a 75% probability that the person will return a buy coffee the next day. In addition, if a person buys biscotti one day then there is a 50% probability that they will purchase biscotti the next day. On Monday, 90% of Claude’s patrons bought coffee and 40% bought biscotti. a) Determine a transition

matrix, T that models this situation.

b) Determine the initial

state matrix, 0S .

c) What is the probability that a patron will purchase a coffee on Tuesday?

d) What is the probability that a patron will purchase a coffee on Friday?

Parts a) and b).

Part c) Part d).

Section 9 – Sequences

When you open the H application, the following will be displayed:

9.1 Define, tabulate & plot a sequence.


Consider the sequence

132 >+= nnnan , .

a) Enter the sequence into the ClassPad.

b) Tabulate the sequence.

c) Plot the sequence. Method: 1. This is an explicit

relationship and so tap the explicit tab.

2. Enter the sequence using the B available on the

menu bar. Press E.

3. To create a table for the sequence, tap 8, to display the Sequence Table Input box. Enter the desired conditions. Tap . Then tap #, to display the table.

4. To plot the sequence, the table window must be

active. Tap ! to plot. (Or, select Graph, then G-Plot on the menu

bar.)

a)

b)

c)

9.2 Summing of a sequence


Consider the arithmetic

series: ...392613 +++ a) Find the sum of the

first 20 terms. b) Find the sum of the

first n terms. c) What is the term

number that would sum to an answer of at least 4000?

Method: We note that, a = 13, d = 13. Therefore,

)( 11313 −+= nan .

1. Open the Main application.

Use the ) palette on the soft keyboard to enter the sum template

2. Using the expression

found in part (b), we can set it equal to 4000 and solve for n. Obviously, the solution would be a positive number.

Recall, to use the solve function: Select the equation. Tap Interactive menu, then tap Equation/Inequality, and then solve.

Part a) and b)

Part c)

9.3 Difference equations


Consider the sequence defined by the difference equation:

12 01 =+=+ ttt nn , .

a) Find the first seven terms of the sequence.

b) Find the 25th term. c) Find the sum of the

first 5 terms. d) Plot the sequence.

Method:

1. Enter the difference equation on the recursive form (since it is a recursive relationship) using the B available on the

menu bar. Press E.

2. To tabulate the sequence, tap 8, to display the Sequence Table Input box. Enter the desired conditions. Tap . Then tap #, to display the table.

3. To plot the sequence, the table window must

be active. Tap ! to plot. (Or, select Graph, then G-Plot on the menu bar.)

Part a)

Part b)

Part c)

Section 10 - Advanced function graphing options

This section four assumes that the ClassPad is operating in the W application.

10.1 Graphing hybrid (mixed or piecewise) functions


Sketch the graph of

−≤+

<<−+

≥

=

2,)2(

02,2

0,

)(2

xx

xx

xx

xf

Method: Key in the function, then

the “with” operator, U, followed by the restricted domain. Tap $ on the tool bar.

(Using the 9 palette on the soft keyboard, select the

tab, in order to view/enter the “with” and inequality operators.) An alternative way to plot a piecewise function is to use the piecewise command, for the syntax see opposite. We have use a nested system for the command: piecewise(condition, value if this condition is true, value if this condition is false) Note: Using this methods sees an (almost) vertical line joining the pieces at

0=x .

piecewise(x≤-2,(x+2)^2,piecewise(-2<x<0,x+2,x)

10.2 Graphing reciprocal functions


Sketch the graph of 1)( += xxf and the

reciprocal function, )(

1

xf.

Method: Key in the function into y1 and the reciprocal function into y2. Tap $ on the tool bar. You could also define the function 1)( += xxf in the

Main application. Then go to the Graph & Table application to graph the defined function

10.3 Graphing rational functions


Sketch the graph of

4

65)(

2

−

+−=

x

xxxf ,

showing axial intercepts and asymptotes.

Method: Key in the function into y1. Tap $ on the tool bar. Check your graph view

window settings by tapping 6 located on the tool bar.

If necessary, change your window settings, then tap

. Alternatively, you can use the Zoom commands to resize the graph view. Use the Table function to help you find any asymptotes. Select # on the tool bar. This will generate a table of values and will be displayed in a Table window.

10.4 Graphing sum and difference functions


Sketch the graph of

xxy

1+= .

Method:

To sketch the graph of the sum (or difference) function, the individual functions are sketched onto the same set of axes. Using the method of addition of ordinates, the sum (or difference) function can then also be sketched. Key in the sum (or difference) function into y1. y2 = x

y3 = x

1

Use the Table function to help you use the method of addition of ordinates. Select # on the tool bar. This will generate a table of values and will be displayed in a Table window. By adding the y-coordinates of y2 and y3 will give the y-coordinate value of the sum function, in this case y1. Graph (and view the table of) all three functions to check your answers.

10.5 Graphing absolute value (modulus) functions


Sketch the graph of

xy 2sin2= over the

domain [ ]π2,0 .

Method:

Key in the function, using absolute value then

the “with” operator, U, followed by the restricted domain.

(Using the 9 palette on the soft keyboard, for the absolute value function.

Also, to select the tab, in order to view/enter the “with” and inequality operators.) Check your graph view



. Alternatively, you can use the Zoom commands to resize the graph view.

10.6 Graphing product functions


Sketch the graphs of i) xxf =)(

ii) xxg sin)( =

iii) )()( xgxf .

Method: Check your graph view




10.7 Graphing composite functions


For the functions xxf sin)( = and

xxg =)( :

Sketch and state the domain of i) ))(( xgf

ii) ))(( xfg

Method: 1. Define the functions first. This way you can easily key in calculations and/or graph the functions. Check your graph view




Section 11 – More on Calculus.

11.1 Area between two curves


Find the area between the two curves over the given interval [0, 1]

21)( xxf −=

xxg −= 1)( .

Method: 1. Define the functions in

the Main application. 2. Tap $ to show the

graph view window. 3. ‘Drag and drop’

functions in the graph

view window. The graphs of the functions will automatically appear in this window.

4. Use the sketch to help you determine which function needs to be ‘subtracted’.

5. Tap in and make the Main application window active.



followed by ∫ , the

integral sign. 8. Select Definite

integral. Enter the variable you are integrating with respect to, the lower and upper

limits into the ∫ input

box. Tap .

11.2 Mean value of a function


Find the mean value of the

function 26)( xxf = over

the interval [0, 4]. Method: Use the variable assignment

key W, to assign a numerical value to a variable. This key can be

found in the 9 options

and the ) options on the soft keyboard. By using this method, you can easily change the upper and lower limits and/or the function. Simply “highlight”, key in changes

and press E. The final

answer will appear without having to re-input the integral.

11.3 Second derivative


Find )(xf ′′ if

xxxf 2)( 2

5

+=

Method: 1. Enter the function and

highlight. 2. Tap Interactive,

then Calculation, followed diff.

3. Select differentiation. Enter variable and order (2) into the diff box. Tap .

11.4 Volumes of solids of revolution


Consider the region bounded by the x-axis and the given lines for:

20;sin

π=== xandxxy .

Find the volume of solid of revolution generated when the region is rotated about the x-axis. Method: 1. Define the function in

the Main application. 2. Tap ! to show the

graph editor window. Enter the function and tap $ to graph.


window active, tap Analysis, then G-Solve, followed by

∫ dxxf 2)(π .

4. Key in the lower value (press 0) and the Enter Value box will appear. Key in the lower and upper intervals and tap .

5. The function, along with the volume interpretation of the integral will be displayed in the graph

view window. The decimal approximation of the volume will be displayed in the message box.

Note: To achieve an exact

solution, use the soft keyboard to input the volume of revolution.

11.5 Direction fields for a differential equation.

Enter the application. Enter the DE yy 2=′ . Tap to have a slope field

generated. Tap r to have the full screen view.

Now tap r again and tap the IC (Initial Conditions) tab. Set some ICs and then tap

the again. This will plot a path through the slope field, starting at (0,1) in this case. You can also plot the graph of a function to test your conjecture about the solution to the DE.

Tapping the 6 icon reveals the View Window settings and allows you to set at will. Note the Steps setting.

Note that the Spreadsheet on the CP 300 has CAS capabilities and so making a spreadsheet to display Euler’s Method numerically and graphically is quite simple. An eActivity that already does this is available from www.casioed.net.au.

Section 12 – Probability distributions

12.1 Discrete probability distributions

12.1.1 Finding probabilities, the mean, variance & standard deviation associated with discrete random variables.

As is true in most sections, there are numerous ways to complete the computations outlined in this section. We have chosen methods that keep the user working within

the Main application, M.


Suppose a random variable X has distribution: x 0 1 2 p(x)

8

2k

8

4 3k−

2

2 2k−

Find the value(s) of k and the values of p(x) in each case. Method: 1. Define the three

elements in the list as a function p(x).

2. Find the sum of p(x). 3. Then set the sum equal to 1

and solve the resulting equation.


Note: If the distribution is given in the form: p(x) = 5,3,1),14( =− xxkx

proceed as shown opposite to find P(X>1).


Find the mean, variance and standard deviation of the discrete random variable with distribution:

p(x) = 5,3,1,91

)14(=

−x

xx

Method: 1. Define p(x). 2. Compute the mean using

the mean formula. Note that two ways are illustrated opposite.

3. Now store the mean value

by defining a variable to have the value attained. Then use the compute the variance.

Note that any letter may be

used in place of µ (mu).

4. Finding the square root of

the variance value returns the standard deviation.


Find the mean, variance and standard deviation of the discrete random variable with distribution:

,.......3,2,1,4

1)( =

= xxp

x

Method: 1. Define p(x). 2. Compute the mean using

the appropriate formula formula.

3. Compute the variance

using the appropriate formula.

Note: Prior to doing this example we

have chosen to ‘Clear All

Variables’ from the Edit menu.

Also not that the use of the

symbols µ (mu) and σ (sigma)

are not necessary.

12.1.2 Finding probabilities, the expected value, the variance & the standard deviation associated with the binomial distribution.


Suppose a random variable X has binomial distribution with n = 10 and p = 0.4. Find P(X =4). Method 1: 1. Enter the Statistics

application, I.

2. From the Calc menu, choose Distribution.

3. Then choose the

Binomial PD option and tap .

4. Enter the values for x,

Numtrial and prob. Tap and the probability value for P(X =4) is returned.

Note: A nice plot of the distribution can be made by tapping the graph icon $ in the top left corner. The plot can be traced to compute any other individual probabilities for this distribution.

Method 2: This method requires us to use a more functional approach. 1. Enter the Main application

J.

2. Define the function

Bin(n,r,p) as the ‘binomial formula’.

3. We can use function

notation to compute the value of interest.


Suppose a random variable X has binomial distribution with n = 10 and p = 0.4. Find the P(X >6) Method 1: This method requires us to determine 1-P(X ≤ 6) 1. Enter the Statistics

application, I.

2. From the Calc menu, choose Distribution.

3. Then choose the

Binomial CD option and tap .

4. Enter the values for x,

Numtrial and prob. Tap and the probability value for P(X ≤ 6) is returned.

Note: A nice plot of the distribution can be made by tapping the graph icon $ in the top left corner. The plot can be traced to compute any other cumulative probabilities for this distribution.

5. Now return to the Main

application and compute 1 minus the probability value returned. prob can be found in the catalogue, or simply type it in.

Method 2: This method requires us to use a more functional approach. 1. Enter the Main application

J.



3. We can use the (‘sum’ function) to compute the cumulative probability required. Note the two different ways to achieve the result.


Suppose a random variable X has binomial distribution with n = 10 and p = 0.4. Find the mean, variance and standard deviation of X. Method: 1. Enter the Main application,

J.



3. Now apply the correct

formula for the mean of a binomial distribution, making use of the defined function Bin(n,r,p). Similarly for the variance and then standard deviation.

Note: For a binomial distribution, the mean can be computed by simply multiplying n by p and the variance by finding

)1( ppn −×× .

12.2 Continuous probability distributions.

12.2.1 Finding k, graphing and finding the mean and variance.


A continuous random variable, X, has distribution described

by 0,)( 2 ≥= − xkexf x . Find k,

draw the distribution and then find the mean, variance and standard deviation. Method: 1. Enter the Main application

J.

2. Define the function f(x). 3. We know that the total area

under this curve is 1 (as it is a probability distribution). So we can find k as seen opposite.

We could now solve for k,

but in this case k is clearly 2.

4. A quick way to graph this

function is to tap the application launcher icon and select $. Then in Main Work Area, enter f(x)|k=2 and press

E.Then ‘drag and drop’

the result into the Graph

View window.

5. Then utilise the correct

formulae for the mean and variance of a continuous random variable.

Note:

It is not necessary to use the Greek symbols (followed by the equal sign) in this computation.

12.2.2 Standard normal distribution.


Find )2Pr( <Z using the

cumulative normal distribution. Method:

1. In the I application, tap Calc then Distribution.

2. Select Normal CD. Tap .

3. Enter the lower and upper intervals, standard deviation and mean. Tap

. 4. The next screen will

give the probability and the option to sketch the probability region (this

is always a very good

idea). 5. Tap $ to sketch the

probability region.

12.2.3 Inverse cumulative normal distribution


Find the value of c if 9370.0)Pr( =<<− cZc .

Method:

1. In the I application, tap Calc then Distribution.

2. Select Inverse Normal CD. Tap

. 3. Enter the tail setting,

area, standard deviation and mean. Tap .

4. The next screen will give the unknown z values and the option to sketch the probability region (this is always a

very good idea). 5. Tap $ to sketch the

probability region.

Section 13 - Graphing relations, circles and ellipses This section explains how to graph circles and ellipses when the ClassPad is operating

in the C application. (You can also use this application to graph parabolas,

hyperbolas and other general conics.)

When you open the C application, the following will be displayed:

The following describes the buttons located on the tool bar while the Conics Editor

window is active.

The following describes the buttons located on the tool bar while the Conics Graph

window is active.

Note: - You can only input one

conics equation at a time in the Conics Editor window.

- This application contains various preset conic formats making equation input efficient.

- Various graph analysis tools can be used when the Conics Graph window is active.


Sketch the graph of the circle with centre (2, 2) and radius 1. Method: 1. Enter the equation by

soft keyboard input OR using the preset conics form menu – press q.

2. If using the preset menu, select the form you wish to graph. Tap

. 3. The selected form will

be displayed in the Conics Editor window. The equation can now be modified.

4. Tap ^ to graph. Note: Various graph analysis tools can be used when the Conics Graph

window is active.


Sketch the graph of the ellipse:

( ) ( )1

9

2

4

122

=−

+− yx

.

Method: 1. Enter the equation by

soft keyboard input OR using the preset conics form menu – press q.

2. If using the preset menu, select the form you wish to graph. Tap

. 3. The selected form will

be displayed in the Conics Editor window. The equation can now be modified.

4. Tap ^ to graph. Note: Various graph analysis tools can be used when the Conics Graph

window is active.

Section 14 - Complex Numbers To work with complex number calculations, the ClassPad needs to operate in Complex mode.

The Complex Submenu contains commands that can be used in complex number calculations.

Explanation of the commands: arg – will output the argument of a complex number. cong – will output the conjugate complex number. re – will output the real part of a complex number. im – will output the imaginary part of a complex number. cExpand – expands a complex expression to rectangular form. compToPol – converts a complex number into its polar form. compToTrig – converts a complex number into its trigonometric form.

To change the mode the calculator is operating in, you can simply tap on the specific mode name in the status bar to change it. Alternatively, tap

O on the menu bar.


For iz 31+= , find the

following: a) argument of z over [0, π2 ]. b) conjugate of z. c) real part of z. d) imaginary part of z.

Method: 1. Enter the equation by

soft keyboard input for i.

2. Tap Interactive, then Complex, followed by arg.

3. Continue using the Complex Submenu to complete the complex calculations.

Note: Conversions from Cartesian form to polar form can be made using the compToTrig and compToPol commands. And vice versa using the cExpand command.

Section 15 - Financial Calculations - TVM

Enter the TVM application ; you will see it has an amazing array of abilities

Tap Compound Interest. You will see that the variables associated with compound interest (including Annuity calculations) are laid out with input boxes ready to be filled. If you are not sure what they mean, tap into one and then tap Help at the bottom of the screen.

This is the Financial

Application Initial screen. It appears if you have not yet used the application or when you use the Clear All command in the Edit menu while using the application.

To configure the

settings, tap O and then Financial Format.

Suppose that we wish to determine the size of the repayments on a loan of $400 000 for which the interest rate is 6% p.a. compounded monthly and the term of the loan is for 30 years. Then we enter, as seen below left, and then simply tap the variable we wish to compute.

Now tap the Calculation menu and note the Amortization option. The appropriate values from our previous problem are carried over and now we can carry out some ‘what if’ exercises. We can do this for any period within the life of the annuity.

PM1 is the number of the first installment in the period being considered and PM2 is the number of the last installment in that period. Above we can see that after the first 10 installments are paid, the annuity has a balance of $39592.72.

Section 16 - Vectors

16.1 Viewing vectors.

Enter the Geometry application G. Tap the Draw menu icon drop down box and

select the vector tool. Then tap on the Cartesian Plane in two different spots, the first for the tail of the vector and the second for the head. A vector appears, labeled as r in this case.

Now tap on the selection tool and then on the vector itself. Then tap the “take me around the corner” icon to reveal the measurement bar.

You can now edit the components and change the vector.

Now tap on the Cartesian Plane in ‘free space’ to deselect the vector and tap on the point representing the vectors tail. You can then edit its co-ordinate, say to (0,0). Using the Zoom Out option from the View menu completes the task.

16.2 Operating with vectors.

Enter the Main application. Bring up the soft keyboard and tap the button on the 2D sheet. Enter a vector by tapping the column matrix template. Tapping it twice will allow you to enter a vector with three dimensions. You can add and subtract as you would expect.

In the Interactive menu you will see a Vector submenu and all of the commands it contains.

Most of these uses are self explanatory; the following screen shots illustrate some of the functionality. Enter the vector (s) first, highlight them and then choose Interactive, Vector and the command you require.

16.3 Vectors that are functions of time

Suppose tjtir sin2cos~~~

+= where t is time. What path does this describe?

This path can be plotted by considering this as a function in parametric form, namely:

ty

tx

sin2

cos

=

=

Enter the application. From the Type menu, tap ParamType and enter the x and y components. Tap the graph icon, $.

The path appears to be elliptical.

Note that the settings for the values for t can be found in the View Window setting window (scroll to the bottom).

Appendices - Text-book cross referencing

Units 1 & 2

A.01 Cambridge Essential Advanced General Mathematics

Text Page Description

How

do I …

Section

How do I

…

Page

8 Matrix calculation 8.1 82

8 Matrix calculation 8.1 82

15 Determinant & inverses for 2x2 matrices 8.1.1 84

16 Determinant & inverses for 2x2 matrices 8.1.1 84

33 Intersection point 2.4 45

46 Solve application 1.9/7.1 32/80

47 Factorise 1.9 32

48 Expand 1.9 32

48 zeros/roots/x-intercepts 2.3.1 41

49 Approximate 1.1 13

49 Common denominator 1.9 32

49 Proper fraction 1.9 32

49 solve 1.7 27

70 Highest common factor 1.1 11

70 Factor 1.1 11

109 Sequence 9.1 89

110 Sequence 9.1 89

132 Fixed point iteration 9.1 89



151 Expand – partial fractions 1.9 32

154 Expand – improper fractions 1.9 32

156 Simultaneous equations 2.4 45


199 Transformations 4.3 52

200 Transformations 4.3 52

250 Sketch function over a specific domain 4.5 55

251 Sketch function over a specific domain 4.5 55

255 E.g. 12 solving circular function equations 2.4 45

256 E.g. 12 solving circular function equations 1.9 32

260 E.g. 15 find axis intercepts 2.3.1 41

260 E.g. 15 find axis intercepts 1.9 32

280 Addition of ordinates 4.3 52

282 Solve circular function equations 1.9 32

285 Graphing reciprocal trig functions 2.2/2.4 38/45

288 Addition & double angle formulae 1.9 32

297 Solve circular function equations 1.9 32

482 Construct a histogram 6.1.3 70

503 Summary statistics 1.7 27

508 Construct a boxplot 6.1.4 71

510 Construct a boxplot with outliers 6.1.4 72

514 Construct a histogram 6.1.3 70

515 Construct a boxplot with outliers 6.1.4 72


529 Scatterplot 6.4.1 76

539 Pearson's correlation coefficient, r 6.4.2 77

549 Least squares regression 6.4.3 78


553 Pearson's correlation coefficient, r 6.4.2 77

554 Least squares regression 6.4.3 78

A.02 Cambridge Essential Mathematical Methods 1 & 2 CAS


How do

I …

Section

How do I

…

Page

4 Solve 1.9/7.1 32/80

5 Solve 1.9 32

10 simultaneous equations - solve 1.9 32

10

simultaneous equations - intersection point

2.4

45

15 solve inequality 1.9 32

18 solve 1.9 32

30 solve 1.9 32

30 plot 2.2 38

68 inputting matrix data 8.1 82

68 matrix calculations/+/-/scalar x 8.1.1 83

72 matrix calculations/x 8.1.1 84

75 matrix calculations/inverse/det 8.1.1 84/85

79 simultaneous equations - matrices 8.2 85

87 expand 1.9 32

91 factor 1.9 32

103 enter & plot 2.2 38

106 solve 1.9 32

108 iteration/sequence 9.1 89

114 simultaneous equations - solve 1.9/2.4 32/45


158 define function 1.4 19

159 restrict domain 4.5 55

169 inverse function 4.4 53

178 define function 1.4 18\9

197 division polynomials 1.9 32

201 Factor 1.9 32

204 Solve 1.9 32

207 plot cubic 2.2 38

207 Stationary points 2.3.3 42


212 Solve 1.9 32

220 intersection point 2.4 45

220 Maximum 2.3.3 42


221 Solve 1.9 32





307 matrix multiplication 8.1.1 84

314 transition matrix 8.4 86

333 nCr 1.8 29


389 exp calculation 1.9 32

396 solve 1.9/7.1 32/80

407 define & solve 1.4/1.9 19/32

419 degree, radian mode 1.5.1 20


439 solve/ intersection point 1.9/2.4 32/45

440 solve/ intersection point 1.9/2.4 32/45

452 trig 1.6 25

507 limits 5.1 56

510 derivative 5.3 60



536 tangent 5.3.2 64


552 f'(x)=0 5.3 60

603 indefinite integral 5.4.1 65

615 definite integral 5.4.2 66

640 Introduction A, B, C 7

642 Using Algebra menu 1 11

642 solve 1.9/7.1 32/80

643 factor 1.9 32

644 expand 1.9 32

645 zeros 2.3.1 41

645 approx 1.1 13

645 common denominator 1.9 32

645 propFrac 1.9 32

645 (nSolve) 1.9 32

646 Trig & A:Complex 1.6 25

646 Graphing 2.0/3.0 37/46

648 Defining functions 1.4 19

649 Probability & Counting 1.8 29

649 Trigonometric functions 1.6 25

650 Using the calculus menu 5 56

650 Differentiate 5.3 60

650 Integrate 5.4 65

651 Limit 5.1 56

651 min/max 2.3.3 42

A.03 Cambridge Essential Mathematical Methods 1 & 2


How

do I …

Section

How do I

…

Page

5 Graph Application – intersection point 2.4 45

5 Solver 7.1 80


67 Solve – find x-intercepts 2.3.1 41

82 Iteration – sequence 9.1 89


116 Draw Circle – method 1 (graph app) 2.2 38

133 Y for domain after defining y1 1.4 19

145 Draw inverse 4.4 53

148 Translation 4.3 52

152 Dilation 4.3 52

170 Plot y1, y2 in terms of y1 etc 4.3 52

183 Create a table of values 2.1 40

185 Maximum 2.3.3 42

185 Minimum 2.3.3 42

192 Graph quartics 2.3 41

199 Maximum 2.3.3 42


271 nCr 1.8 29

294 Create a table of values 2.1 37

322 Find y given x 2.3.4 44

322 Find x given y 2.3.5 44

332 Solver 7.1 80

356 DEG – RAD mode 1.5.1 20

367 Trigonometric function graph 4.5 55


420 plot/trace/zoom 2.2.1/3 40/46

482 Stationary points 2.3 41

484

Finding a tangent to a curve at a given point 5.3.2 64

486 Maximum 2.3.3 42

486 Minimum 2.3.3 43



541 Integration 5.4.2 66

565 Introduction A, B, C 7

567 Using Algebra menu 1 11

567 solve 1.9/7.1 32/80

568 factor 1.9 32

569 expand 1.9 32

570 zeros 2.3.1 41

570 approx 1.1 13


470 propFrac 1.9 32

570 (nSolve) 1.9 32

571 Trig & A:Complex 1.6 25

571 Graphing 2, 3 37/46


577 Probability & Counting 1.8 29

579 Trigonometric functions 1.6/1.9 25/32

580 Using the calculus menu 5 56

580 Differentiate 5.3 60

580 Integration 5.4 65

581 Limit 5.1 56


A.04 Cambridge Essential Standard General Mathematics


How

do I …

Section

How do I

…

Page

12 Histogram 6.1.3 70

33 Summary statistics 1.7/6.1 27/68

38 Box plot 6.1.4 71

44 Box plot with outliers 6.1.4 72

61 Table of values 2.1 37

76 sequence 9.1 88


86 Simultaneous equations 1.9/2.4 32/45

97 straight line graph 2.2 38

97 Table of values 2.1 37

109

Equation of a line from 2 points/linear regression

6.4.3

78


139 Linear regression/ least squares regression 6.4.3 78

215 simple interest/plot 2.2 38

215 simple interest/table of values 2.1 37

224 compound interest/plot 2.2 38

224 compound interest/table of values 2.1 37

230 Flat rate depreciation & book value/ plot 2.2 38

230

Flat rate depreciation & book value/ table of values

2.1

37

234

Reducing balance depreciation & book value/plot

2.2

38

234

Reducing balance depreciation & book value/table

2.1

37

248 Degree mode 1.5.1 20

263 Calculator tip/define variables 1.2 16

304 Generate arithmetic sequence 9.1 88

305 Position counter arithmetic sequence 9.1 88

321 Generate geometric sequence 9.1 88

321 Position counter geometric sequence 9.1 88

340 Difference equations 9.3 91

364 graph feasible region 4.2 51




444 matrix calculations/det/inverse 8.1.1 85/84

448 simultaneous equations/matrix 8.2 85

466 calculate/basic 1.1 11

467 straight line graph 2.2 37\8

468 table of values 2.1 37

468 Simultaneous equations/solve 1.9/2.4 32/45


471 Boxplot 6.1.4 71

472 Boxplot with outliers 6.1.4 72

473 Mean & standard deviation 1.7 27


475 sequence generate 9.1 89

476 simple interest/plot 2.2 38

476 simple interest/table 2.1 37

476 compound interest/plot 2.2 38

477 compound interest/table of values 2.1 37




479 matrix calculations/det/inverse 8.1.1 85/84

480 simultaneous equations/matrix 8.2 85

A.05 Heinemann VCE Zone General Mathematics


How

do I …

Section

How do I

…

Page

8 basic arithmetic 1.1 11

25 solver 7.1 80

62 finding x-intercepts 2.3.1 41


63 zoom 3.2 47




70


2.4

45


96


2.4

45

103 scatterplot 6.4.1 76

103 linear regression 6.4.3 78

104 coefficient of determination, r^2 6.4.2 77


131 matrix + 8.1.1 83

132 matrix - 8.1.1 83



140 determinant 8.1.1 85

141 inverse 8.1.1 84

142 decimal to fraction 1.1 13



148 transition matrix 8.4 87


193 enter & plot 2.2 38


198 inequality 4.2 51

199 inequality 4.2 51

210 enter & plot 2.2 38

210 trace 2.2.1 40

211 enter & plot 2.2 38

211 functions in terms of functions 4.3 52


216 log graph 4.3 52

248 cumulative frequency curve 6.2 73

263 five figure summary 1.7 27

263 boxplot 6.1.4 71

265 modified boxplot 6.1.4 72

266 modified boxplot 6.1.4 72

267 mean &standard deviation 1.7 27

272 statistics 1.7 27

280 random numbers 1.8.1 29



301 Correlation coefficient, r 6.4.2 77

302 Coefficient of determination, r2 6.4.2 77


309 linear regression - sketch 6.4.4 78


384 Degree/radian mode 1.5.1 20

384 Trigonometric calculations 1.6 25




521 generate sequence 9.1 89

522 plot sequence 9.1 89

523 sum of a series 9.2 90

603 definite integral 5.4.2 66

A.06 Heinemann VCE Zone Mathematical Methods 1 & 2


How do

I …

Section

How do I

…

Page

12 enter & plot 2.2 38


14 Trace 2.2.1 40

21

simultaneous equations - intersection point 2.4 45


66 Solver 7.1 80

74 enter & plot 2.2 38

78 enter & plot fn with parameters 4.1 50

79 enter & plot fn with parameters 4.1 50


89 x intercepts 2.3.1 41

89 Maximum and minimum points 2.3.3 42



92


94




116 enter & plot 2.2 38


119 enter & plot 2.2 38






151 enter & plot 2.2 38


151 y intercept 2.3.2 42


155 enter & plot 2.2 38


158 enter & plot 2.2 38

165 enter & plot 2.2 38

166 enter & plot 2.2 38



245 find y given x 2.3.5 44

247 Tangent to a curve 5.3.2 64

270 enter & plot 2.2 38


272 piecewise/restrict domain 4.5 55

275 enter & plot 2.2 38


277 enter & plot 2.2 38


277 Limits 5.1 56

278 piecewise/restrict domain 4.5 55


291 Derivative 5.3 60

301 Tangent 5.3.2 64

307 Trace 2.2.1 40

307 sketch derivative 5.3.1 63

341 deg to dms 1.5.2 21



345 convert degrees to radians 1.5.4 23

345 convert radians to degrees 1.5.5 24

353 enter & plot 2.2 38





360 enter & plot 2.2 38


387 enter exponential function 1.1 11

393 enter & plot 2.2 38


394 enter & plot 2.2 38


397 enter & plot 2.2 38


404 log calculation 1.1 11


412 enter & plot 2.2 38


419 find y given x 2.3.5 44

436 factorial 1.8 29

438 nPr 1.8 29

451 nCr 1.8 29

A.07 Jacaranda Maths Quest 11 General Mathematics A


How

do I …

Section

How do I

…

Page

24 Solving matrix equations 8 82

28 Matrix multiplication 8.1.1 84

53 Converting decimals to fractions 1.1 12

103

Listing the terms of an arithmetic sequence

9.1 89

107 Sum of an arithmetic sequence 9.2 90

112 Listing the terms of a geometric sequence 9.1 89

116 Sum of a geometric sequence 9.2 90

146 histogram 6.1.3 70

162 Finding statistical information 1.7/6.1 27/68

171 Measures of variability 1.7/6.1 27/68

184 Box plot 6.1.4 71


239 linear regression – line of best fit 6.4.3 78

264 Random number generation 1.8.1 29


280 matrix calculations 8.1.1 83

308 Solving linear equations 1.9/7.1 32/80

319 Generating a table of values/sequence 2.1/9.1 37/88

358 Generating a table of values 2.1 37

363

Graphs of non-linear equations Find x intercepts (roots)

2.2 2.3.1

38

41

364 Solving non-linear equations using tables 2.1 37

365 Zoom functions/window settings 3 46

386 simultaneous equations – graphical 2.4 45


388 simultaneous equations - iteration 9.1 89

389 simultaneous equations - solver 7.1 80

391 simultaneous equations – table of values 2.1 37

407 Plot linear functions 2.2 38

421 Point of intersection 2.4 45

434 Line of best fit (linear regression) 6.4.4 78

490 Graphing linear inequations 4.2 51

499 Simultaneous linear inequations 4.2 51

539 Compound interest 6.4 74

548 Simple and compound interest functions 2 37

580 Straight line depreciation using solver 7.1 80

651 Ratios 1.1 12

741 Viewing perpendicular lines 3 46

A.08 Jacaranda Maths Quest 11 General Mathematics B


How

do I …

Section

How do I

…

Page

24 Solving matrix equations 8 82


46 Cube and nth root 1.1 12

129

Listing the terms of an arithmetic sequence

9.1

89

133 Sum of an arithmetic sequence 9.2 90

138 Listing the terms of a geometric sequence 9.1 89

142 Sum of a geometric sequence 9.2 90



185 matrix calculations 8.1.1 83

212 Solving linear equations 1.9/7.1 32/80

223 Generating a table of values/sequence 2.1/9.1 37/88

262 Generating a table of values 2.1 37

267

Graphs of non-linear equations Find x intercepts (roots)

2.2 2.3.1

38

41

268 Solving non-linear equations using tables 2.1 37

269 Zoom functions/window settings 3 46



292 simultaneous equations - iteration 9.1 89

293 simultaneous equations - solver 7.1 80

295 simultaneous equations – table of values 2.1 37

365 Plot linear functions 2.2 38

379 Point of intersection 2.4 45

392 Line of best fit (linear regression) 6.4.4 78

453 Direct variation using plots 2.2 38

470 Inverse variation using plots 2.2 38

540 Graphing functions 2.2 37

545 Finding distance using sequences 9.1/9.2 89/90


569 Simultaneous linear inequations 4.2 51

669 Viewing perpendicular lines 3 46

A.09 Jacaranda Maths Quest 11 Mathematical Methods


How

do I …

Section

How do I

…

Page

4 Solving linear equations with solver 7.1 80

4 Solving linear equations graphically 2.2/2.3 38/21

9 Using the Solve function 1.9/7.1 36/80

27 Finding x and y intercepts 2.3.1 41


32 simultaneous equations – matrices 8.2 85

38 Distance between two points 2.5 45

46 Intersection point 2.3.3 43

81 Repeated calculations 1.2 16

92 Finding significant points on a graph 2.3 41


98 Solving quadratic equations - graphs 2.3.1 41

125 Calculating functions using parameters 4.1 50

137

Sketching cubic functions Finding significant points on a graph

2.2 2.3

38

41



159 Modelling 6.4 74

188 Plotting points 6.4.1 76

210 Piecewise defined functions 4.5 55

244 Indicial equations - solver 1.9/7.1 35/80

248 Intersection point 2.3.3 43

289

Working with angles Degrees to radians Radians to degrees

1.5 1.5.4 1.5.5

20

23

24

357 Drawing a tangent to a curve 5.3.2 64

410 Plotting the derivative function 5.3.1 63

437 Finding stationary points 2.3.3 42


522 Factorials 1.8 29

528 Permutations 1.8 29

537 Combinations 1.8 29

A.10 Macmillan MathsWorld Technology Toolkit (TI-89)

Description

How do I …

Section

How do

I …

Page

1.1 How to perform simple arithmetic calculations 1.1 11

1.2 How to store and use numerical values 1.2 16

1.3 How to store and use lists 1.3 17

1.4 How to perform simple function calculations 1.4 19

1.5 How to work with angles 1.5 20

1.6 How to perform simple trigonometric calculations 1.6 25

1.7 How to perform simple statistical calculations 1.7 27

1.8 How to perform simple probability calculations 1.8 29

1.9 How to perform simple symbolic calculations 1.9 32

2.1 How to enter and plot functions 2.2 38

2.2 How to create a table of values 2.1 37

2.3 How to ‘jump to’ significant points on a graph 2.3 41

2.4 How to find the intersection point of two graphs 2.4 45

3.1 How to change the viewing window 3.1 46

3.2 How to zoom options 3.2 47

4.1 How to enter and plot a function using parameters 4.1 50

4.2 How to shade above/below a function graph 4.2 51

4.3 How to graph functions defined in terms of other functions 4.3 52

4.4 How to draw the inverse of a function 4.4 53

4.5 How to restrict the domain of a function 4.5 55

5.1 How to calculate average & instantaneous rates of change 5.2.1/5.5.2.2 57/58

5.2 How to calculate the numeric derivative 5.3 60

5.3 How to calculate and plot derivative functions 5.3.1 63

5.4 How to draw tangent lines 5.3.2 64

5.5 How to calculate the definite integral 5.4.2 66

6.1 How to store and summarise ungrouped univariate data 6.1.1 68

6.2 How to store and summarise grouped univariate data 6.1.2 69

6.3 How to construct cumulative frequency curves 6.2 73

6.4 How to construct a histogram 6.1.3 70

6.5 How to construct a box plot 6.1.4 71

6.6 How to store and summarise bivariate data 6.4 74

6.7 How to construct a scatter plot 6.4.1 76

6.8 How to calculate correlation coefficients 6.4.2 77

6.9 How to calculate the least-squares regression line 6.4.3 78

7.1 How to use the numeric solver APP 7.1 80

8.1 How to store and use matrices 8.1 82

8.2 How to solve equations with matrices 8.2 85

8.3 How to transform points and equations with matrices 8.3 86

8.4 How to work with transition matrices 8.4 87

9.1 How to define, plot and tabulate a sequence rule 9.1 89

9.2 How to sum a sequence 9.2 90

9.3 How to work with difference equations 9.3 91

10.1 How to define and use functions 1.4 19

10.2 How to use the symbolic solve command 1.9 32

10.3 How to work with general solutions 1.9 32

10.4 How to rearrange equations and expressions 1.9 32

10.5 How to work with limits 5.1 56

10.6 How to find the symbolic derivative 5.3 60

10.7 How to calculate indefinite integrals 5.4.1 65

A.11 Pearson Longman General Maths Dimensions (An advanced course) 1 & 2


How

do I …

Section

How do I

…

Page

13 Basic calculations/operations 1.1 11

25 Convert degrees to radians 1.5.4 23

27 Rational numbers (exact answers) 1.1 11

28 Fraction (recurring decimal) 1.1 11

87 Logarithms 1.1 11

110 Finding equation of a straight line 2 37


122 Input degrees, minutes and seconds 1.5 20


150 Convert radians to degrees 1.5.5 24

179

Solving trig equations(using graph/intersection) 2.4 45

228 Create histogram (enter data to list) 6.1.3 70

238 Boxplot 6.1.4 71

241

Basic statistical calculations (summary statistics) 6.1.1 68

252 Least squares regression line 6.4.3 78

267 (Addition &) Subtraction of matrices 8.1.1 83


273 Inverse of a matrix 8.1.1 84

273 Determinant 8.1.1 85

292/3 Sequences – define, tabulate and plot 9.1 89

297 Define arithmetic sequence 9.1 89

304 Summing of a sequence 9.2 90

308 Define geometric sequence 9.1 89

320 – 323 Difference equations 9.3 91

335/6 Linear regression 6.4.3 78

350 Linear regression 6.4.3 78

383 Convert into polar coordinates 13 119

385 Plotting polar curves 13 119

464 Complex number mode 14 122

A.12 Pearson Longman Mathematical Methods Dimensions 1 & 2


How do I

…

Section

How do I

…

Page

11 Solve linear equations 1.9 32

13 Simultaneous equations – graphically plot 2.2 38

13

Simultaneous equations – graphically intersection point

2.4

45

14 Simultaneous equations – solve 1.9/2.4 32/45

15 Simultaneous equations – matrices 8.2 85

17 Linear inequations 1.9 32

18 Transpose equations 1.9 32

27 Sketch linear graph 2.2/4.1 38/50

48 Expand 1.9 32

48 Factorise 1.9 32

52 Solve quadratic equations 1.9/7.1 32/80

73 - matrices 8.2 85

73 - define & solve 1.4 19

85 Division of polynomials 1.9 32

89 Factorise polynomials 1.9 32

92 Solve cubics 1.9 32

122 Define functions f(x) = 1.4 19

122 Solve f(x)=0 1.9 32

125 Inverse functions – graphically 4.4 53

125 Inverse functions – defined f(y)=x 4.4 53

148 Intersecting lines – sketch 2.2 38

148 Find x intercept 2.3.1 41

148 Find y intercept 2.3.2 42


148 Intersection point – using matrices 8.2 85

149 Solve with matrices 8.2 85

151

Equation of polynomial function – plot values

6.4.1

76

151 Simultaneous equations 1.9/7.1 32/80

151 Matrices 8.2 85

153 Inverse functions – (expand/simultaneous) 1.9 32

153 Turning point 2.3.3 42

153 Inverse functions – solve 4.4 53

153 Inverse functions – graph 4.4 53

153 Coordinate geometry – sketch 2.2 38

153 Maximum 2.3.3 42

153 Distance between 2 points 2.5 45

155 Matrix transformations – translation 8.3 86

155 Matrix transformations – reflection 8.3 86

155 Matrix transformations – dilation 8.3 86

156 Relations & functions – sketch circle 2.2 38

156 Circle inequality 4.2 51

156 Trigonometry (sohcahtoa) 1.6 25

184

Average & instantaneous rates – define function

5.2.1/5.2.2

57/58

184 Sketch 4.5 55

184 Draw tangent 5.3.2 64

184 Calculate gradient 5.3 60

184 Equation of tangent 5.3.2 64

186

Rate of change application – graph specific domain

5.2.1/4.5

57/55

186 Find x-value given a specific y-value 2.3.4 44

227 Generate random numbers 1.8.1 29

232

Probability distribution – quadratic regression 6.1.2 69

232 Define function p(x)/solve 1.4/1.9 19/32

247 Radian mode 1.5.1 20

247 Solve sin/cos angles 1.6 25

250 Solve sin/cos angles 1.6 25

261 Learning task 7F – radian 1.5.1 20

261 Learning task 7F – plot/window settings 2.2 38

265 Solve trigonometric equations 2.2 38

265 Solve trigonometric equations 2.4 45

266

Solve trigonometric equations over specific domain

1.9/4.5

32/55

267

Solve trigonometric equations over specific domain

1.9/4.5

32/55

269 Sketch y=tan(x) [0,2pi] 4.5 55

270 Radian mode 1.5.1 20

270 plot/window settings 2.2 38

E.g. 2&3 different tan graphs/domain 4.5 55

286 Sketch trig graph 2.2 38

286 Find y-value given a specific x-value 2.3.5 44



301 Solve exponential equations 1.9/7.1 32/80

302 Solve indicial equations 7.1 80

306 Exponential function graph – domain 4.5 55

306 Find y-value given a specific x-value 2.3.5 44


315 Solve exponential equations 1.9/7.1 32/80

319 Solve exponential equations 7.1 80

329 Euler's number – limits 5.1 56

330 Solve exponential equations 7.1 80

333 Solve logarithmic equations 7.1/1.4 80/19

333 Average rates of change 5.2.1 57

348 Limits 5.1 56

353 Positive & negative limits 5.1 56

363

Derivative of a function with respect to x at a specific point

5.3

60

366 [tangents & normals] 5.3.2 64

379 Sketch f'(x) from f(x) 5.3.1 63

386 Rates of change – plot points/table 6.4.1 76

387 Polynomial models of growth – plot 4.5 55

387 Predict y given x 2.3.5/1.4 44/19

388 Average rates of change 5.2.1 57

388 Limits 5.1 56

388 Differentiation 5.3 60

394 Instantaneous rate of change 5.3 60

400 Solve f'(x)=0 1.9 32

400 Maximum 2.3.3 42

400 Minimum 2.3.3 42

401 Find constants 1.9 32

401 Define function 1.4 19

401 Solve given conditions 1.9 32

415 Maximum 2.3.3 42

415 Minimum 2.3.3 42

428 Derivative of a function 5.3 60

428 Sketch over specific domain 4.5 55

428 Stationary points ** 2.3.3 42

429 Define function 1.4 19

429 Find derivative (operation at same time) 5.3 60

436 Antiderivative – indefinite integrals 5.4.1 65

438 Definite integrals 5.4.2 66


451 Area under a curve [bounded] 5.4.3 67

455 Area between two curves 5.4.3 67

466 Integral 5.4 67

466 Gradient at specific points/values 5.3 60

467 Integral 5.4.1 65

467 Solve function through a point (constant) 1.9/7.1 32/80

467 Maximum 2.3.3 42

488 Gradient of tangent 5.3.2 64

490 Gradient of tangent 5.3.2 64

490 Equation of tangent 5.3.2 64


491 Derivative of a function 5.3 60

491 Sketch over specific domain 4.5 55

498 Permutations 1.8 29

508 Combinations 1.8 29

518 Markov sequences/matrices 8.4 87

528

CAS to find first 6 rows of Pascal's triangle

1.8

29

529 Define probability function p(x) 1.4 19

531 Probability involving combinations 1.8 29

534 Transition matrices – matrix calculations 8.4 87

Units 3 & 4

A.13 Cambridge Essential Further Mathematics 3 & 4


How

do I …

Section

How do I

…

Page



62

Summary statistics – mean & standard deviation 6.1.1 68



103 Correlation coefficient 6.4.2 77

121 Equation of least squares regression line 6.4.3 78

183 Time series plot 2.2 38

237 Generate terms of arithmetic sequence 9.1 89

242 Generate terms of arithmetic sequence 9.1 89

249 Sum of arithmetic sequence 9.2 90

254 Generate terms of geometric sequence 9.1 89

273 Generate terms of geometric sequence 9.1 89

282

Generate sequence defined by difference equation 9.3 91

302

Generate /graph terms of Fibonacci sequence 9.1 89


415 Simultaneous equations – graphical 2.4 45

437 Scatterplot /linear regression 6.4 74

488 Simple interest – Financial solver 15 124

493 Compound interest – Financial solver 15 124

495 Financial solver 15 124




639 Entering a matrix 8.1 82

646 Add, subtract & scalar multiply matrices 8.1.1 83


669 Determinant and inverse of a matrix 8.1.1 85/84


Appendix

717 Name a list 1.3 17

719 Basic calculations 1.1 11



722 Summary statistics 6.1.1 68



725 Least squared regression line 6.4.3 78

731 Time series plot 2.2 38

732 Generate terms of a sequence 9.1 89

733

Generate sequence defined by difference equation 9.3 91

734 Simple interest – Financial Solver 15 124

735 Compound interest – Financial Solver 15 124

736 Financial Solver 15 124

737 Financial Solver 15 124

738 Enter a matrix 8.1 82

738 Matrix calculations 8.1.1 83

740 Determinant and inverse of a matrix 8.1.1 85/84


A.14 Cambridge Essential Mathematical Methods 3 & 4 CAS


How

do I …

Section

How do I

…

Page

8 Define & evaluate functions 1.4 19

19 Absolute value/modulus 10.5 96

24 Composite functions – sketch 10.7 98

28 Inverse functions 4.4 53

54 Matrix operations 8.1.1 83



104 Inverse Functions 4.4 53

120 Division of polynomials 1.9 34

122 Factor and solve 1.9 34

140 Graph – maximum /minimum 1.9 32

144 Solve 1.9/7.1 32/80

149 Solve 1.9/7.1 32/80

150 Solve 1.9/7.1 32/80

172 Solving log equations 7.1 80

178 Solving exponential functions 7.1 80

184 Solving exponential functions 7.1 80

216 Finding axes intercepts 2.3 41

222 Solve trig equations 1.9/7.1 32/80

226 Solution of circular function equations 1.9/7.1 32/80

243 Define and sketch functions 1.4/2.2 19/38

247 Inverse function 4.4 53

247 Solve function 1.9/7.1 32/80

281 Limits 5.1 56

283 Derivative at a point 5.3 60

292 Define & differentiate 5.3 60

311 Derivative – graph 5.3.1 63

312 Derivative – graph 5.3.1 63

324 Tangent to the curve 5.3.2 64



384 Limits 5.1 56

423 Indefinite integral 5.4.1 65

425 Indefinite integral 5.4.1 65

515 Binomial cdf 12.1.2 109

567 Definite integral 5.4.3 67

613 Normal cdf 12.2 115

614 Inverse normal 12.2.3 118

616 Normal area curves 12.2.2 117

Appendix

669 Introduction 1.1 11

671 Using Algebra menu 1.1 11

672 solve 1.9/7.1 32/80

672 factor 1.9 32

673 expand 1.9 32

674 zeros 2.3.1 41

674 approx 1.1 13


674 propFrac 1.9 32

675 (nSolve) 1.9 32

675 Trig & A:Complex 1.6/14 24/122

675 Graphing 2/3 7/46


678 Circular functions 1.6/1.9 25/32

679 Using the calculus menu 5/10 56/99

681 Probability 1.8 29

A.15 Cambridge Essential Mathematical Methods 3 & 4


How

do I …

Section

How do I

…

Page

8 Define & evaluate functions 1.4 19

19 Absolute value/modulus 10.5 96

25 Composite functions – sketch 10.7 98


98 Table application 2.1 37

116 Eg 16 minimum 2.3.3 42

116 Eg 16 maximum 2.3.3 42


179 Sketch trig function over specific domain 4.5 55

181 Sketch trig function over specific domain 4.5 55

215 Eg 6 inverse functions 4.4 53

215 Eg 7 inverse functions 4.4 53

219 Linear regression 6.4 74



260 Derivative of a function at a specific point 5.3 60

278 Graph of function & derivative 5.3.1 63

299 Tangent to the curve 5.3.2 64


401 Area under the curve – bounded 5.4.3 67


402 Plot antiderivative function 5.4 65

481 Binomial distribution 12.1.2 109

486 Plot of binomial pdf 12.1.2 109

492 Solve for n – sample size 12.2.1 115

506 Calculate probability/ area under curve 5.4.3 67

549 Normal distribution 12.2.2 117

549 Eg 4 normal distribution 12.2.2 117


551 Eg 6 inverse normal 12.2.3 118

551 Eg 7 inverse normal 12.2.3 118


Appendix

603 Introduction 1.1 11

605 Using Algebra menu 1.1 11

606 solve 1.9/7.1 32/80

606 factor 1.9 32

607 expand 1.9 32

608 zeros 2.3.1 41

608 approx 1.1 13


608 propFrac 1.9 32

609 (nSolve) 1.9 32

609 Trig & A:Complex 1.6/14 24/122

609 Graphing 2/3 7/46


614 Trigonometric functions 1.6/1.9 25/32

616 Using the calculus menu 5/10 56/99

621 Probability 1.8 29

A.16 Cambridge Essential Specialist Mathematics 3 & 4


How

do I …

Section

How do I

…

Page


8 Solve application 7.1 80

10 Tan graph 2.2 38

27 Eg 24 sequence 9.1 89

28 Eg 25 sequence 9.1 89

28 Sequence 9.1 89

43 Parametric equations 16 126

44 Parametric equations/conics 16 126

104 Graph cosec(x) 2.2 38

105 Graph cot(x) 2.2 38

108 Eg 4 simplifying trigonometric functions 1.9 32

108 Eg 5 solving trigonometric functions 1.9/7.1 32/80

112 Eg 6 Exact solutions 1.1 11

113 Eg 7 solve/expand trigonometric functions 1.9/7.1 32/80

125 Eg 18a maximum 2.3.3 42

125 Eg 18a minimum 2.3.3 42

125 Eg 18b y2=1/y1 10.2 93

138 Eg 1 complex mode/application 14 122

139 Eg 2b simplify complex expressions 14 122

140 Define/store complex expressions 14 122

142 Eg 7 14 122

145 Eg 8 complex conjugate 14 122

146 Eg 9a 10.5 96

149

Eg 10a absolute/angle [modulus/argument] 10.5 96

149 Eg 10b 10.5 96

158 Eg 15 Factorisation of quadratics 1.9 32

159 Eg 16 Factorisation of cubics 1.9 32

160

Eg 17 Factorisation of higher degree polynomials 1.9 32

163 Eg 19 solutions of quadratics 2.3 41

164 Solutions of quadratics = 0 2.3 41

199 Gradient at a specific point 5.3 60

204 Derivatives of x=f(y) 5.3 60

206 Graph inverse trigonometric functions 4.4 53

206

Derivative of inverse trigonometric functions 5.3/4.4 60/53

211 Eg 9b second derivative 11.3 101

220 (using eg 9b) derivative 5.3 60

220 (using eg 9b) second derivative 11.3 101

220 (using eg 9b) f'(x)=0 5.3 60

220 (using eg 9b) f''(x)=0 11.3 101

220 (using eg 9b) stationary points 2.3.3 42

240 Eg 28 implicit differentiation 5.4 65

241 [eg 29 implicit differentiation] 5.4 65

269 Eg 12c integration by substitution 5.4 65

298

Section 8.3 Integration using graphics calculator 5.4 65

303 [section 8.4 Volume of solids/revolution] 11.4 102

346 Section 9.6 Differential equations 11.5 103

349 Differential equations 11.5 103

352 Program for Euler's method 11.5 103

354

Section 9.8 Direction(slope) field for differential eqn 11.5 103

439

Eg 6 Parametric equations-plot eqns simultaneously 16 126

439

Eg 6 Parametric equations-intersection point 16 126

444 Vector Calculus (eg 12) 16 126

A.17 Heinemann VCE Zone Further Mathematics


How

do I …

Section

How do I

…

Page

13 Basic statistical calculations 1.7 27


17 Boxplots 6.1.4 71


26

Random numbers & basic statistical calculations 1.8.1 29

37 Boxplots 6.1.4 71



58 Least squares regression line 6.4.3 78

111 Plotting a sequence 9.1 89

117 Summing a sequence 9.2 90

121 Calculating nth roots 9 88

122 Tabulating sequence 9.1 89

127 Tabulating sequence 9.1 89

130 Recurring decimal (fraction) 9.1 89


146 Define, tabulate & plot a sequence 9.1 89

164

Define variables to have a numerical value 1.2 16

167 Exact answer (fraction) 1.1 11

175 Basic trig calculations (answers →DMS) 1.6 25

179 Basic trig calculations 1.6 25

228

Solving simultaneous equations graphically 2.4 45

237 Break-even analysis 2.4 45


260 Graphs of xkxy = 2.2 38

265 Graphs of non-linear relations 13 119

266 Plot points (regression) 6.4 74

296 Plot points (interest) 6.4 74

300 Graph/ table 2.1 37



319 Graph/ table 2.1 37


389 Inputting matrix data 8.1 82

391 Matrix addition & subtraction 8.1.1 83

394 Scalar multiplication 8.1.1 83


403 Inverse & determinant of a matrix 8.1.1 84/85

404 Solve simultaneous equations – matrices 8.2 85

412 Solve simultaneous equations – matrices 8.2 85

417 Transition matrices 8.4 87

A.18 Heinemann VCE Zone Mathematical Methods 3 & 4


How

do I …

Section

How do I

…

Page

6 Graphing polynomials 2.2 38

11 Graphing functions with restricted domain 4.5 55

22 Graph (graph view window settings) 2 37

29 Turning points (maximum /minimum) 2.3.3 42

35 Graph /table – hyperbola 10.2 93

39 Graph – truncus 10.2 93

41 Graph – negative powers 10.2 93

42 Graph /square root function 10.2 93

64 Graph – exponential functions 2 37

68 Reflection in x/y axis 4.4 53

69 x-intercept 2.3.1 41

71 Graph – logarithmic functions 2 37

98 Covert radians to degrees 1.5.5 24

99 Parametric mode 16 126

100 Graph – parametric 16 126

109 Graph – trig functions 2.2 38

124 Solve trig equations – intersection point 2.4 45

128 Graph – trig func. with restricted domains 4.5 55

144 Addition (& subtraction) of ordinates 10.4 95

151 Product of functions 10.6 97


169 Plotting data 6 68

182 Hybrid /piecewise functions 10.1 92

183 Limits (graph /table) 5.1 56


198 Derivative – chain rule 5.3 60

206 Derivative – log functions 5.3 60

209 Derivative – trig functions 5.3 60

237 Derivative – stationary points 5.3 60

249 Sketch gradient function 5.3.1 63

254 Maximum /minimum 2.3.3 42

268 Equation of tangents & normals 5.3.2 64

302 Definite integrals – graph & algebraic 5.4.3/2 67/66

307 Integral – signed area 5.4.3 67

311 Area between two curves 11.1 99

351 Binomial pdf 12.1.2 109


363 Markov sequences – transition matrices 8.4 87

374 Integral (pdf) 5.4.3 67

380 Normal distribution 12.2 115

386 Standard normal distribution 12.2.2 117

394 Inverse standard normal distribution 12.2.3 118

A.19 Heinemann VCE Zone Specialist Mathematics


How

do I …

Section

How do I

…

Page

37 Complex numbers 14 122

39 Complex addition & subtraction 14 122

42 Complex multiplication 14 122

47 Complex conjugate 14 122

48 Complex division 14 122

50 Powers of complex numbers 14 122

99 Sketch graph –

2

2)(x

baxxf +=

10.4 95

100 Solve function 7.1 80

113 Sketch circles & ellipses 13 119

120 Sketch hyperbolas 10.2 93

135 Reciprocal circular functions 10.2 93

160 Graph – inverse circular functions 10.2 93

166 Derivative – inverse circular functions 5.3 60

177 Indefinite integrals 5.4.1 65

202 Partial fractions (define & expand) 1.9 32



232 Volumes of solids of revolution 11.4 102

247 Second derivative 11.3 101

287

Numerical solution of differential equations 11.5 103

302

Non-constant velocity – graph derivative, solve for given value 5.3.1 63

304 Sketch function /derivative function 5.3.1 63

328 Area under curve 5.4.3 67

340 Parametric mode 16 126

395 Graph & table 2.1 37

A.20 Jacaranda Maths Quest 12 Further Mathematics 2nd ed


How

do I …

Section

How do I

…

Page


23 Summary statistics 6.1.1 68

30 Boxplot 6.1.4 71


35 Summary statistics – mean 6.1.1 68

41 Summary statistics – standard deviation 6.1.1 68


80 Parallel boxplots 6.1.4 71


101

Correlation coefficient & coefficient of determination 6.4.2 77

122 Three median method

128 Least-squares regression 6.4.3 78

136

Interpretation, interpolation & extrapolation 6.4.5 79

167 Time series 2.2 38

210 Equation solver 7.1 80

216 Equation solver – arithmetic sequence 9.1 89

219 Listing terms of arithmetic sequence 9.1 89

225 Summing sequence 9.2 90

237 Equation solver – geometric sequence 9.1 89

238 Listing terms of geometric sequence 9.1 89

245

Summing a given number of terms of a geometric sequence 9.2 90


298

Difference equations – graphical representation 9.3 91

438 Entering angles in degrees & minutes 1.5 20

438 Changing angles from degrees to DMS 1.5.2 21

500 Sketching straight line graphs 2.2 38

515 Solve simultaneous equations – graphical 2.4 45

528 Non-linear relations and graphs 2.2 38


586

Simple interest calculations – Financial solver 15 124

600 Compound interest – Financial Solver 15 124










711 Graph & table 2.1 37

842

Matrix operations – addition, subtraction, scalar 8.1.1 83


860 Inverse & determinant of a matrix 8.1.1 84/85


876 Transition matrices 8.4 87

A.21 Jacaranda Maths Quest 12 Mathematical Methods 2nd ed


How

do I …

Section

How do I

…

Page

12 Listing several values of a function 1.4 19

86 Graph – asymptotes 2.2 38

98 Graph – absolute value 10.5 96

103 Modeling – Plotting data 6.4 74

179 Graph – exponential function 2.2 38

218 Graphing inverse relations 4.4 53

322 Gradient of a function at a particular point 5.3 60


432 Integrals – Signed area 5.4.3 67

438 Area bound by graph & x-axis 5.4.3 67





614 Standard normal distribution 12.2.2 117

618 Normal cdf 12.2.2 117

625 Normal curve areas 12.2.2 117

627 Inverse normal distribution 12.2.3 118

A.22 Jacaranda Maths Quest 12 Specialist Mathematics 2nd ed


How

do I …

Section

How do I

…

Page

28 Graphing ellipses 13 119

53 Graph – window settings 2.1 38

71 Graphs – reciprocal trig functions 10.2 93

123 Simple algebra of complex numbers 14 122

146 Roots of complex numbers 14 122

224 Finding numerical derivatives 5.3 60

265 Graph – function and antiderivative 5.4 65


283 Definite integrals – graph 5.4.3 67

286 Area bounded by two curves 11.1 99

292 Volume of a solid of revolution 11.4 102

328 Solving first order differential equations 11.5 103

377 Graphing x-t graph & v-t 16.3 129

384 Graphing x-t graph & v-t 16.3 129

392 Numerical solver 7.1 80

434 Parametric plots 16 126

440 Magnitude & direction of vectors 16 126

469 Parametric plots 16 126

484 Derivatives – vector functions 16 126

A.23 Pearson Longman Mathematical Methods Dimensions 3 & 4


How do

I …

Section

How do I

…

Page


36 Addition (& subtraction) of ordinates 10 92

47 Sketch graphs – find intercepts 2.3 41

56 Solve equation – quadratic 7.1 80

63 Solve simultaneous equations 1.9 35

66 Factorise cubics 1.9 32

72 Factorise/sketch polynomials 1.9/2.2 32/38

78 Sketch/graph 2.2 38

84 Sketch/graph 2.2 38

87 Define/solve functions 1.4/1.9 19/32


95

Graphing polynomials – turning point/ point of inflection/ intercepts 2.3 41


97 Factor 1.9 32

97 Define/solve functions 1.4/1.9 19/32

99 Eg. 4 define 1.4 19

100 Graph/point of inflection 2.3.3 43

101

Inverse functions – define/solve/sketch point of intersection 4.4 53

102 Define 1.4 19

103 Eg.6 Graph absolute value function 10.5 96

103

Define function over specific domain and solve 4.5 55

105 Eg. 7 Define matrix 8.1 82

105

Solving simultaneous equations with matrices. 8.2 85

105 Graph domain/restrictions 4.5 55

106 Define and solve functions 1.4/1.9 19/32

106 Define/solve/graph composite functions 10.7 98

122

Solve exponential equations (using numerical solver & solve function) 7.1 80

124 Sketch exponential functions 2.2 38

139 Solve logarithmic equations 7.1 80

141 Sketch logarithmic equations 2.2 38

157 Solve/graph 7.1/2.2 80/38

159

Eg. 2 Modelling with logarithmic functions. Define/solve/graph 7.1 80

176 Basic trig calculations 1.6 25


220 Limits 5.1 56

222 Limits 5.1 56

224

Define functions 0

lim→h

(Differentiation

from first principles) 5.1 56


237 Derivative (& expand) 5.3 60

241 Derivative – chain rule 5.3 60

289 Stationary points. 2.3.3 42

297 Maximum value/graph 2.3.3 42

300 Minimum value/graph 2.3.3 42

309 Instantaneous rate of change 5.2.2 58

322

Stationary points. Limit/ intercept/maximum 2.3.3 42

323 Eg. 2 Stationary points with parameters 2.3.3 42

325 Intersection 2.4 45

326

Eg. 4 Average & instantaneous rates of change 5.2 57

327 Graph with restricted domain 4.5 55

328

Eg. 6 Circular functions & rates of change. 5.2 57

329

Maximum/average & instantaneous rates of change 5.2 57

330 Eg. 7 Circular functions & graphs 2.2 38

331

Maximum/minimum. Graph with restricted domain 2.3.3/4.5 42/55

332 Eg. 9 Stationary points 2.3.3 42

341 Integration – indefinite 5.4.1 65





384 Definite integrals (& finding limit) 5.4.2 66

392

Calculating area (with & without graphical display) 5.4.3 67

399 Area bounded by two curves 11.1 99

422

Eg. 1 Areas & graphs. Define/ integrate with & with out graphical display 11.1 99

423 Eg. 2 Rules of differentiation 5.3 60

424 Define/ solve/ derivative/ graph


425

Eg. 3 )(xf ′ / ∫ )(xf graphs with

parameters 5.3.1/ 5.4.3 63/67

426 Integral – solve with restrictions 5.4 65

427 Eg. 5 Find areas under curves 5.4.3 67

427

Eg. 6 Equation of tangent to a curve. Area between curves 5.3.2 64

429 Average value of a function

448 Combinations (nCr) 1.8 29

452 Markov sequences 8.4 87



486 Binomial distribution 12.1.2 109

489 List/plot binomial distribution 12.1.2 109

500 Eg. 1 defining a binomial distribution 12.1.2 109

501 Eg. 2 Calculating probabilities 12.1.1 105

509 Basic statistical calculations 1.7 27

513 Calculate probabilities/ definite integral 5.4.3 67

514 Mean/ standard deviation 12.2.1 115

522 Normal pdf 12.2.2 117

524 Inverse normal 12.2.3 118

536 Eg. 1 defining a pdf 12.2 115

537 Eg. 2 calculating probabilities 12.2 115

538

Eg. 3 Infinity & pdf. (Define/ definite integral/ graph) 12.2 115

540

Eg. 4 Measures of central tendancy & spread 12.2 115

542 Rule for defining normal distribution 12.2 115

543 Normal distribution 12.2 115

544

Eg. 6 Mean & standard deviation. Find z value. 12.2 115

A.24 Pearson Longman Specialist Maths Dimensions 3 & 4


How

do I …

Section

How do I

…

Page

11 Graph (including asymptotes) 2.2 38



12 Solve 0)( =′ xf 5.3 60

13 Graph 2.2 38



14 Graph 2.2 38

25 Graphing relations 13 119

27 Graph - ellipse 13 119

32 Graph - hyprerbola 13 119

54 Basic trigonometric calculations (radians) 1.6 25

55 Basic trigonometric calculations 1.6 25

58

Basic trigonometric calculations (exact value) 1.6 25

61 Trig expressions with restricted domain 1.9 32


65 Inverse trig calculations 4.4 53

67 Graph trig functions 2.2 38

68 Graph trig functions 2.2 38

79 Simplify complex expressions 14 122

95 De Moivre’s Theorem 14 122

102 Solving complex equations (quadratic) 14 122

103 Solving complex equations (cubic) 14 122

104 Solving complex equations 14 122

111 Graph – ellipse 13 119

113 Graph relations – hyperbola/circle 13 119


140 Derivative of inverse circular functions 5.3 60




144 Find equation of a tangent 5.3.2 64

144 Find equation of the normal 5.3.2 64

158

Second derivative/point of inflection (stationary points) with graph 11.3 101

159

Second derivative/point of inflection (stationary points) with graph 11.3 101

162 Solve 0)( =′′ xf to find turning points 11.3 101

163 Sketch 2.2 38


186 Indefinite integrals (& factor) 5.4.1 65





200 Indefinite integrals (inverse trig functions) 5.4.1 65

208 Indefinite integrals (trig functions) 5.4.1 65



248 Area under curve 5.4.3 67

260 Areas bounded by two curves 11.1 99

270 Volumes of solids of revolutions 11.4 102

272 Regions bounded by two curves 11.1 99

273 Regions bounded by two curves 11.1 99

305 Differential equations 11.5 103



311 Solve equations 7.1 80

352 – 354 Direction fields 11.5 103

445 Parametric forms (graph) 16 126

how do i ……………on the classpad 300? working with ungrouped univariate data .....68 6.1.2...

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