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.
For
Operating System 3.0
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.
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
Page 3
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
Page 4
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
Page 5
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
Page 6
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.
lim  1 

 . We
x → 2−  x − 2 
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.
Suppose we want to determine the
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…
Page 7
Interactive Menu
The interactive menu contains the same options as the Action menu. However, it is
used differently.
 1 
application, enter the expression 
 . Then select it by dragging
 x−2
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.
In the
(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.
Page 8
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 x × y × z , 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.
Page 9
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
visible at once.
Launch the
application and the
application
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.
Page 10
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.
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
Page 11
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.
Page 12
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
5
 
3
Demonstration
2
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.
5
2
1. Use the 9 soft
keyboard to enter the
calculation.
2. The calculation can also
be entered using natural
input via the ) soft
keyboard.
5
76
1. Use the hard keyboard
or 9 soft keyboard
to enter the calculation.
(Tap . to get
decimal output.)
2. The calculation can also
be entered using natural
input via the ) soft
keyboard.
Page 13
(4.9 ×10 )÷ (2.1×10 )
7
4
1. Use the hard keyboard
or 9 options on the
soft keyboard to enter
calculation. (Tap . to
get decimal output.)
2. The calculation can also
be entered using natural
input via the ) soft
keyboard.
Is 6 4 < 4 6 ?
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.
Page 14
Evaluate log10 324
1. Use the 9 options
on the soft keyboard to
enter calculation.
2. The calculation can also
be entered using natural
format via the )
soft keyboard.
(Tap . to get decimal
output.)
Note: Logarithms of bases
other than 10 can be
computed.
Page 15
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
θ
11
a) Find the hypotenuse,
h.
b) Find the angle, θ .
Using Pythagoras’
Theorem, assign the
following; a = 11, o = 4,
(
)
h = a 2 + o 2 . The angle,
θ can be found using
 opp 
 .
θ = sin −1 
 hyp 
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.
Page 16
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).
Page 17
•
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,
Page 18
1.4 Basic function calculations
Example
Evaluate x 2 + 2 x + 2 when
x =4.
Method 1:
Demonstration
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.
Page 19
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.
c,
Note: The ClassPad utilizes r, not 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
To change the angle mode the
calculator is operating in, simply
tap on the specific angle
indicator in the status bar to
change it.
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
.
Page 20
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 34.65° 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.
Page 21
1.5.3 - Expressing angles in degrees, minutes and seconds to
degrees
Example
Express 34°39′ 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.
Page 22
1.5.4 - Convert angles in degrees to radians.
Example
Express 34°39′ 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.
Page 23
1.5.5 - Convert angles in radians to degrees.
Example
c
5π
Express
in degrees, minutes, seconds.
8
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.
Page 24
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.
c
Note: The ClassPad utilizes r,not , 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.
Example
Evaluate sin(25°42' ) .
Method :
Demonstration
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
.
 5π c 

Evaluate cos

 7 
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.
Page 25
Evaluate tan(190.45°) and
sin(
πc
4
).
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
sin θ = 0.3 .
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 cosθ = 0.75 .
Page 26
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.
Page 27
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.
Page 28
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
Example
Generate random numbers
between 0 and 1.
Method :
1. Type in/ or locate
rand( in the
Demonstration
catalogue. Press E.
2. To generate more
random numbers,
simply press E again.
Page 29
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
Example
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.
Demonstration
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.
Page 30
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.
Example
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
Demonstration
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.
Page 31
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.
Example
3 x + 2 x + ax
(x
2
− y2
(x + y )
Demonstration
)
Page 32
3(b − a )
Expand
a. ( x + y ) 2
b. ( x + y ) 4
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 x 2 − 16
Page 33
Factorise x 2 − 6 :
a) over Q – the rational
numbers
b) over R – the real
numbers
Divide 5 x + 1 by x − 2 .
Is a 2 − 4b 2 equal to
(a − 2b)(a + 2b) ?
Note:
You could also have used
the expand command.
Page 34
5
3
+
as a
2x 3y
single fraction.
Express
1
Solve sin 2 x = ,
2
a) for all x.
b) for 0 < x < 2 .
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:
− x + 3 y = 15
Simultaneous Equations
y = 2x + 5
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:
solve({-x+3y=15,y=2x+5},{x,y})
Calulator output
Page 35
Solve x 2 − 7 < 0 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.
9
Solve F = C + 32 for C.
5
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.
Page 36
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
3x + 5 .
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.
Page 37
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
Method 1.
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
3 x + 10 .
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.
Page 38
Method 2
1. Tap M on the icon
panel.
2. Input the function. (In
this example,
y = 3 x + 10 .)
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) y = 2 x − 5
b) 4 x + 5 y = 13
c)
f ( x) = 3x 2 − 2
d) y = x 3
e) y = x 3 − 4 x 2 − 4 x + 16
f) y = sin x
h) y = log e (2 x)
1
i) y =
x
j) y = ( x − 2 )
k) y = x
g) y = 2 x
Page 39
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
Page 40
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.
Page 41
2.3.2 To find the y intercept/s:
Tap the Analysis option on the menu bar, tap G-solve, and then select yIntercept. This function will locate and display the y intercept.
Note: While you can graph x =
(y
2
)
− 2 ) 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
Page 42
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.
Page 43
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.
Page 44
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
. The coordinates will be displayed in the graph view
coordinates and tap
window and the distance calculated in the message box.
Alternatively, you can use the stylus to tap the two points on the screen.
Page 45
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.
Graph
Editor
Window
Graph
View
Window
Message 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
ydot – value of each screen pixel vertically
horizontally
The x/y dot and x/y dot values will change automatically when the x/y
maximum and minimum values are changed.
Page 46
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.
Page 47
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.
Page 48
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 GController 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.
Page 49
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
Example
Demonstration
2
Let f ( x) = a ( x − b) + c ,
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)
a. Key the following into
y1:
1( x − 0) 2 + {−2,−1,0,1,2}
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:
1( x − {−2,−1,0,1,2}) 2 + 0
b)
c)
c. Key the following into
y3:
{−2,−1,0,1,2}( x − 0) 2 + 1
You could also define a list
as a variable and use that
variable.
Page 50
4.2 Graphing an inequality
Example
Sketch y ≤ 2 x + 1 .
Demonstration
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:
• y ≤ 2 x + 1 and
• y > 3 − x and
• x ≥ 0 and
• y ≥ 0.
Page 51
4.3 Graph functions defined in terms of other functions
Example
Demonstration
2
Sketch f ( x) = x . Explain
graphically, the outcome of
the following
transformations
a. − f ( x)
b. f ( x) + 2
c. 2 f ( x)
d. f ( x − 4)
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
Page 52
Alternative method.
Make y1 = x 2 .
Then define the remaining
functions in terms of
y1(x).
4.4 Draw the inverse of a function
Example
Sketch f ( x) = x 2 and its
inverse.
Demonstration
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.
Page 53
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.
Page 54
4.5 Restrict the domain of a function
Example
Sketch y = x , where x ≥ 0 .
Demonstration
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 y = x , where
−2< x<2.
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.
Page 55
Section 5 – Calculus
5.1 Limits
Example
Find
Demonstration
1
a. lim 
x →∞ x
 
1
b. lim+  
x →0  x 
1
c. lim−  
x →0  x 
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.
Page 56
5.2 Rates of Change
5.2.1 Average rates of change
Example
Calculate the average rate
of change for
f ( x) = x 2 + 2 x + 2 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
Demonstration
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.
Page 57
5.2.2 Instantaneous rates of change
Example
Calculate the instantaneous
rate of change where
f ( x) = x 2 + 2 x + 2 at x = 3.
Demonstration
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).
Page 58
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.
Page 59
5.3 Derivatives
Example
Find
a. the derivative of
f ( x) = x 2 + 2 x + 2
b. f ′(2)
c. f ′(−3)
Demonstration
Method for part (a):
1. Define the function,
press E.
2. Key in the problem,
using the derivative
, on the
feature,
) soft keyboard
(choose the
option).
1.
2.
Alternative method for part
(a) See screen captures 1 &
2.:
1. Key in and select the
function.
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.)
Page 60
Alternative method for part
(c):
1. Key in and select the
function.
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.
Page 61
Using the W
application, find f ′(2)
where f ( x) = x 2 + 2 x + 2 .
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.
Page 62
5.3.1 Sketching the derivative function
Example
Sketch f ( x) = x 2 + 2 x + 2
and its derivative, f ' ( x) .
Demonstration
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.
3. Key in the derivative
function, using the
derivative template,
, on the )
palette of the soft
keyboard (choose the
option). Press
Graph line style
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
.
Page 63
5.3.2 Tangent to a curve.
Example
Sketch f ( x) = x 2 + 2 x + 2
and the tangent at x = −2 .
Find the equation of the
tangent.
Demonstration
Method:
1. In this example the
function has been
defined as f(x).
2. Key in the function into
the graph editor
window. Press E.
Tap $ to graph.
3. With the graph view
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.
Page 64
5.4 Integration
5.4.1 Indefinite integrals
Example
Find the integral of
f ( x) = 10 x 4 + 6 x 3 + 2 .
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.
Demonstration
When working with
indefinite integrals,
don’t forget you will
need to include the
constant of
integration, c, when
writing down your
answer.
Alternative method:
1. Key in and select the
function.
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
.
Page 65
5.4.2 Definite integrals (without a graphical display)
Example
Demonstration
4
Calculate
5
∫ x +e
x
2
dx .
1
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:
1. Key in and select the
function.
2. Tap Interactive,
then Calculation,
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.
Page 66
5.4.3 Definite integrals (with a graphical display)
Using the W
application, compute and
display and interpretation of
x
4
5
2
∫1 x + e dx .
Method:
1. Key the function into
the graph editor. Press
E. Tap $ to graph.
2. With the graph view
window active, tap
Analysis, then GSolve, 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.
Page 67
Section 6 – Statistical Calculations
In this section we use the I application.
6.1 Univariate data
6.1.1 Working with ungrouped univariate data
Example
Demonstration
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).
2. Select Calc then
One-Variable.
3. Select the XList
using the drop down
menu. Tap
.
4. The Stat
Calculation
screen will appear
containing a basic
statistical summary
of the selected listed
data.
To draw a histogram of
these data use the
SetGraph then
Setting ...menu.
Page 68
6.1.2 Working with grouped univariate data
Example
The following table shows
the number of “Smarties” in
each of 50 packets .
# of Smarties
Demonstration
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).
2. Select Calc then OneVariable.
3. Select list1 for the
XList and list2 for
the Freq using the drop
down menu. Tap
.
4. The Stat
Calculation screen
will appear containing a
basic statistical
summary of the selected
listed data.
Note: Name the list before
entering your data. Once
named, the list is
considered to be a
variable.
Page 69
6.1.3 Histogram
Example
The frequency table shows
the length (l) of 80 fish
caught in a fishing
competition.
Length (mm)
295 ≤ l<305
305 ≤ l<315
315 ≤ l<325
325 ≤ l<335
335 ≤ l<345
345 ≤ l<355
355 ≤ l<365
365 ≤ l<375
Demonstration
Frequency
8
17
19
13
10
6
4
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.)
Page 70
6.1.4 Box plot
Example
Demonstration
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).
2. Tap G on the tool
bar. (Or, select
SetGraph from the
menu bar, then
Setting.)
3. Adjust the Set
StatGraphs
options. Type:
MedBox. Make sure
you do not tick the
Show 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.
Page 71
Box plot with outliers
(Modified box plot)
- utilises the 1.5 × IQR rule,
which defines limits for
“outliers”.
To make modified box plot,
make sure you tick the
Show Outliers box.
We have set up StatGraph 2
as a modified box plot and
then drawn both StatGraph
1 and StatGraph 2.
Page 72
6.2 Cumulative frequency curves (or ogives)
Example
The frequency table shows
the length of 80 fish caught
in a fishing competition.
Length (mm)
300 – 309
310 – 319
320 – 329
330 – 339
340 – 349
350 – 359
360 – 369
370 - 379
Demonstration
Frequency
8
17
19
13
10
6
4
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.
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.
Page 73
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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Max. temp
18
17
30
16
20
22
16
12
14
15
16
17
15
15
18
19
23
21
19
21
25
29
26
24
30
°C
Attendance
870
819
2168
714
1435
1458
819
406
231
572
603
839
572
806
1218
1007
931
1215
995
275
1894
2301
2207
2109
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 23°C and compare
your result to Day 17.
Page 74
Example
Task:
a) Calculate the summary
statistics for the two
variables.
Demonstration
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.
Page 75
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
bar. (Or, select
SetGraph from the
menu bar, then
Setting.)
2. Adjust the Set
StatGraphs options.
Press
.
3. Tap y on the tool bar
to view the scatter plot.
Page 76
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.
Page 77
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.
Page 78
6.4.5 Using the Least-squares line
g) Use your equation to
predict the attendance on a
day of maximum
temperature at 23°C 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.
Page 79
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
Example
Demonstration
The volume of a cone,
radius r cm and height h
πr 2 h
cm, is given by: V =
.
3
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.
Page 80
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.
Page 81
Section 8 – Matrices
8.1 Inputting matrix data
The examples below use the ) soft keyboard to enter the matrix using natural
input.
Example
Define the following
matrices.
 2 1
A=

4 3
Demonstration
2 1 − 1 
B=

0 − 4 2 
 − 1
C = − 2
− 2
 2 1
D=

− 1 2
Method:
Key in the matrix, using the
features,
, on
the ) soft keyboard
(choose the
option).
Page 82
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:
 2 1
A=

4 3
2 1 − 1 
B=

0 − 4 2 
 − 1
C = − 2
− 2
 2 1
D=

− 1 2
Calculate the following:
a) A + D
b) 2 A − D
c) BC
d) A 2
e) A −1
f) det A
Addition
a) A + D
Subtraction
b) 2 A − D
Page 83
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) A 2
Inverse
e) A −1
Page 84
Determinant
f) det A
Method:
1. Enter A.
2. From the menu bar,
tap Interactive,
then MatrixCalculation,
followed by det.
8.2 Solving simultaneous equations using matrices
Example
Using matrices, solve
3 x − y = 10 and 2 x + 5 y = 1 .
Demonstration
Method:
We can express the
simultaneous equations in
matrix form:
3 − 1  x  10
2 5   y  =  1 

   
x
And so   = A −1 × B
 y
3 − 1
Enter 
 as A and
2 5 
10
 1  as B and then compute
 
A −1 × B
Page 85
8.3 Geometric transformations using matrices
Example
a) Determine the
transformation matrix,
D x , y , 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
Dx , y .
Demonstration
Note that we know that each
point ( x, y ) is mapped onto
its image ( x′, y ′) by:
x′ = ax + by
y ′ = cx + dy
Therefore, in matrix form:
 x′ a b   x 
 y ′ =  c d   y 
  
 
Page 86
8.4 Transition matrices (Markov chains)
Example
Demonstration
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.
Parts a) and b).
a) Determine a transition
matrix, T that models
this situation.
b) Determine the initial
state matrix, S 0 .
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?
Part c)
Part d).
Page 87
Section 9 – Sequences
When you open the H application, the following will be displayed:
Page 88
9.1 Define, tabulate & plot a sequence.
Example
Consider the sequence
a n = n 2 + 3n, n > 1 .
a) Enter the sequence
into the ClassPad.
b) Tabulate the
sequence.
c) Plot the sequence.
Demonstration
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.
a)
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.)
b)
c)
Page 89
9.2 Summing of a sequence
Example
Consider the arithmetic
series: 13 + 26 + 39 + ...
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?
Demonstration
Part a) and b)
Method:
We note that, a = 13, d = 13.
Therefore,
a n = 13 + 13(n − 1) .
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.
Part c)
Recall, to use the solve
function:
Select the equation.
Tap
Interactive menu, then
tap
Equation/Inequality,
and then
solve.
Page 90
9.3 Difference equations
Example
Demonstration
Part a)
Consider the sequence
defined by the difference
equation:
t n + 1 = t n + 2, t 0 = 1 .
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.
Part b)
Part c)
3. To plot the sequence,
the table window must
be active. Tap ! to
plot. (Or, select
Graph, then G-Plot
on the menu bar.)
Page 91
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
Example
Sketch the graph of
 x, x ≥ 0

f ( x) =  x + 2, − 2 < x < 0

2
( x + 2) , x ≤ −2
Method:
Key in the function, then
Demonstration
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(x≤-2,(x+2)^2,piecewise(2<x<0,x+2,x)
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
x = 0.
Page 92
10.2 Graphing reciprocal functions
Example
Sketch the graph of
f ( x) = x + 1 and the
reciprocal function,
Demonstration
1
.
f ( x)
Method:
Key in the function into y1
and the reciprocal function
into y2.
Tap $ on the tool bar.
You could also define the
function f ( x) = x + 1 in the
Main application. Then go
to the Graph & Table
application to graph the
defined function
Page 93
10.3 Graphing rational functions
Example
Sketch the graph of
x 2 − 5x + 6
f ( x) =
,
x−4
showing axial intercepts
and asymptotes.
Demonstration
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.
Page 94
10.4 Graphing sum and difference functions
Example
Sketch the graph of
1
y = x+ .
x
Demonstration
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
1
y3 =
x
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 ycoordinate value of the sum
function, in this case y1.
Graph (and view the table
of) all three functions to
check your answers.
Page 95
10.5 Graphing absolute value (modulus) functions
Example
Sketch the graph of
y = 2 sin 2 x over the
Demonstration
domain [0, 2π ] .
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
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.
Page 96
10.6 Graphing product functions
Example
Sketch the graphs of
i) f ( x) = x
ii) g ( x) = sin x
iii) f ( x) g ( x) .
Demonstration
Method:
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.
Page 97
10.7 Graphing composite functions
Example
For the functions
f ( x) = sin x and
Demonstration
g ( x) = x :
Sketch and state the domain
of
i) f ( g ( x))
ii) g ( f ( x))
Method:
1. Define the functions first.
This way you can easily key
in calculations and/or graph
the functions.
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.
Page 98
Section 11 – More on Calculus.
11.1 Area between two curves
Example
Find the area between the
two curves over the given
interval [0, 1]
f ( x) = 1 − x 2
g ( x) = 1 − x .
Demonstration
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.
6. Key in and select the
function.
7. Tap Interactive,
then Calculation,
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
.
Page 99
11.2 Mean value of a function
Example
Find the mean value of the
function f ( x) = 6 x 2 over
the interval [0, 4].
Demonstration
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.
Page 100
11.3 Second derivative
Example
Find f ′′(x) if
Demonstration
5
f ( x) = x 2 + 2 x
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
.
Page 101
11.4 Volumes of solids of revolution
Example
Consider the region
bounded by the x-axis and
the given lines for:
y = sin x; x = 0 and x =
π
2
Find the volume of solid of
revolution generated when
the region is rotated about
the x-axis.
Demonstration
.
Method:
1. Define the function in
the Main application.
2. Tap ! to show the
graph editor window.
Enter the function and
tap $ to graph.
3. With the graph view
window active, tap
Analysis, then GSolve, followed by
π ∫ f ( x) 2 dx .
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.
Page 102
11.5 Direction fields for a differential equation.
Enter the
application. Enter the DE y ′ = 2 y . 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.
Page 103
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.
Page 104
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.
Example
Suppose a random variable X
has distribution:
x
p(x)
0
k2
8
1
4 − k3
8
Demonstration
2
2−k2
2
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.
Page 105
Example
Demonstration
Note:
If the distribution is given in
the form:
p(x) = kx(14 − x), x = 1,3,5
proceed as shown opposite to
find P(X>1).
Page 106
Example
Find the mean, variance and
standard deviation of the
discrete random variable with
distribution:
x(14 − x)
, x = 1,3,5
p(x) =
91
Method:
1. Define p(x).
2. Compute the mean using
the mean formula. Note
that two ways are
illustrated opposite.
Demonstration
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.
Page 107
Example
Find the mean, variance and
standard deviation of the
discrete random variable with
distribution:
Demonstration
x
1
p ( x) =   , x = 1,2,3,.......
4
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.
Page 108
12.1.2 Finding probabilities, the expected value, the variance & the
standard deviation associated with the binomial distribution.
Example
Suppose a random variable X
has binomial distribution with
n = 10 and p = 0.4.
Demonstration
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.
and the
Tap
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.
Page 109
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.
Page 110
Example
Suppose a random variable X
has binomial distribution with
n = 10 and p = 0.4.
Demonstration
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.
and the
Tap
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.
Page 111
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.
2. Define the function
Bin(n,r,p) as the
‘binomial formula’.
3. We can use the
(‘sum’ function) to
compute the cumulative
probability required. Note
the two different ways to
achieve the result.
Page 112
Example
Suppose a random variable X
has binomial distribution with
n = 10 and p = 0.4. Find the
mean, variance and standard
deviation of X.
Demonstration
Method:
1. Enter the Main application,
J.
2. Define the function
Bin(n,r,p) as the
‘binomial formula’.
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
n × p × (1 − p ) .
Page 113
12.2 Continuous probability distributions.
12.2.1 Finding k, graphing and finding the mean and variance.
Example
A continuous random variable,
X, has distribution described
by f ( x) = ke −2 x , x ≥ 0 . Find k,
draw the distribution and then
find the mean, variance and
standard deviation.
Demonstration
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.
Page 114
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.
Page 115
12.2.2 Standard normal distribution.
Example
Find Pr( Z < 2) using the
cumulative normal
distribution.
Demonstration
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.
Page 116
12.2.3 Inverse cumulative normal distribution
Example
Find the value of c if
Pr(−c < Z < c) = 0.9370 .
Method:
Demonstration
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.
Page 117
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:
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.
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.
Page 118
Example
Sketch the graph of the
circle with centre (2, 2) and
radius 1.
Demonstration
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.
Page 119
Example
Sketch the graph of the
ellipse:
(x − 1)2 + ( y − 2)2 = 1 .
4
9
Demonstration
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.
Page 120
Section 14 - Complex Numbers
To work with complex number calculations, the ClassPad needs to operate in
Complex mode.
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.
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.
Page 121
Example
For z = 1 + 3i , find the
following:
a) argument of z over
[0, 2π ].
b) conjugate of z.
c) real part of z.
d) imaginary part of z.
Demonstration
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.
Page 122
Section 15 - Financial Calculations - TVM
Enter the TVM application
; you will see it has an amazing array of abilities
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.
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.
Page 123
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.
Page 124
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.
Page 125
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.
Page 126
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.
Page 127
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 r = i cos t + 2 j sin t where t is time. What path does this describe?
~
~
~
This path can be plotted by considering this as a function in parametric form, namely:
x = cos t
y = 2 sin t
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.
Page 128
Note that the settings for the values for t can be found in the View Window setting
window (scroll to the bottom).
Page 129
Appendices - Text-book cross referencing
Units 1 & 2
A.01 Cambridge Essential Advanced General Mathematics
Text Page
8
8
15
16
33
46
47
48
48
49
49
49
49
70
70
109
110
132
144
145
151
154
156
157
199
200
250
251
255
256
260
260
280
282
285
288
297
482
How do I
How
do I … …
Section Page
Description
Matrix calculation
8.1
82
Matrix calculation
8.1
82
Determinant & inverses for 2x2 matrices
8.1.1
84
Determinant & inverses for 2x2 matrices
8.1.1
84
Intersection point
2.4
45
Solve application
1.9/7.1
32/80
Factorise
1.9
32
Expand
1.9
32
zeros/roots/x-intercepts
2.3.1
41
Approximate
1.1
13
Common denominator
1.9
32
Proper fraction
1.9
32
solve
1.7
27
Highest common factor
1.1
11
Factor
1.1
11
Sequence
9.1
89
Sequence
9.1
89
Fixed point iteration
9.1
89
Solve application
1.9/7.1
32/80
Solve application
1.9/7.1
32/80
Expand – partial fractions
1.9
32
Expand – improper fractions
1.9
32
Simultaneous equations
2.4
45
Simultaneous equations
2.4
45
Transformations
4.3
52
Transformations
4.3
52
Sketch function over a specific domain
4.5
55
Sketch function over a specific domain
4.5
55
E.g. 12 solving circular function equations 2.4
45
E.g. 12 solving circular function equations 1.9
32
E.g. 15 find axis intercepts
2.3.1
41
E.g. 15 find axis intercepts
1.9
32
Addition of ordinates
4.3
52
Solve circular function equations
1.9
32
Graphing reciprocal trig functions
2.2/2.4
38/45
Addition & double angle formulae
1.9
32
Solve circular function equations
1.9
32
Construct a histogram
6.1.3
70
Page 130
503
508
510
514
515
516
529
539
549
552
553
554
Summary statistics
Construct a boxplot
Construct a boxplot with outliers
Construct a histogram
Construct a boxplot with outliers
Summary statistics
Scatterplot
Pearson's correlation coefficient, r
Least squares regression
Scatterplot
Pearson's correlation coefficient, r
Least squares regression
1.7
6.1.4
6.1.4
6.1.3
6.1.4
1.7
6.4.1
6.4.2
6.4.3
6.4.1
6.4.2
6.4.3
27
71
72
70
72
27
76
77
78
76
77
78
Page 131
A.02 Cambridge Essential Mathematical Methods 1 & 2 CAS
Text Page
4
5
10
10
15
18
30
30
68
68
72
75
79
87
91
103
106
108
114
117
158
159
169
178
197
201
204
207
207
212
212
220
220
221
221
221
232
235
236
307
314
Description
Solve
Solve
simultaneous equations - solve
simultaneous equations - intersection
point
solve inequality
solve
solve
plot
inputting matrix data
matrix calculations/+/-/scalar x
matrix calculations/x
matrix calculations/inverse/det
simultaneous equations - matrices
expand
factor
enter & plot
solve
iteration/sequence
simultaneous equations - solve
simultaneous equations - solve
define function
restrict domain
inverse function
define function
division polynomials
Factor
Solve
plot cubic
Stationary points
define function
Solve
intersection point
Maximum
define function
Solve
Stationary points
simultaneous equations - solve
simultaneous equations - solve
simultaneous equations - solve
matrix multiplication
transition matrix
How do How do I
I…
…
Section Page
1.9/7.1
32/80
1.9
32
1.9
32
2.4
45
1.9
1.9
1.9
2.2
8.1
8.1.1
8.1.1
8.1.1
8.2
1.9
1.9
2.2
1.9
9.1
1.9/2.4
1.9/2.4
1.4
4.5
4.4
1.4
1.9
1.9
1.9
2.2
2.3.3
1.4
1.9
2.4
2.3.3
1.4
1.9
2.3.3
1.9/2.4
1.9/2.4
1.9/2.4
8.1.1
8.4
32
32
32
38
82
83
84
84/85
85
32
32
38
32
89
32/45
32/45
19
55
53
18\9
32
32
32
38
42
19
32
45
42
19
32
42
32/45
32/45
32/45
84
86
Page 132
333
385
389
396
407
419
430
439
440
452
507
510
511
514
536
539
552
603
615
640
642
642
643
644
645
645
645
645
645
646
646
648
649
649
650
650
650
651
651
nCr
intersection point
exp calculation
solve
define & solve
degree, radian mode
restrict domain
solve/ intersection point
solve/ intersection point
trig
limits
derivative
derivative
derivative
tangent
derivative
f'(x)=0
indefinite integral
definite integral
Introduction
Using Algebra menu
solve
factor
expand
zeros
approx
common denominator
propFrac
(nSolve)
Trig & A:Complex
Graphing
Defining functions
Probability & Counting
Trigonometric functions
Using the calculus menu
Differentiate
Integrate
Limit
min/max
1.8
2.4
1.9
1.9/7.1
1.4/1.9
1.5.1
4.5
1.9/2.4
1.9/2.4
1.6
5.1
5.3
5.3
5.3
5.3.2
5.3
5.3
5.4.1
5.4.2
A, B, C
1
1.9/7.1
1.9
1.9
2.3.1
1.1
1.9
1.9
1.9
1.6
2.0/3.0
1.4
1.8
1.6
5
5.3
5.4
5.1
2.3.3
29
45
32
32/80
19/32
20
55
32/45
32/45
25
56
60
60
60
64
60
60
65
66
7
11
32/80
32
32
41
13
32
32
32
25
37/46
19
29
25
56
60
65
56
42
Page 133
A.03 Cambridge Essential Mathematical Methods 1 & 2
Text Page
5
5
10
67
82
89
116
133
145
148
152
170
183
185
185
192
199
199
271
294
322
322
332
356
367
387
420
482
484
486
486
488
490
541
565
567
567
568
569
570
570
Description
Graph Application – intersection point
Solver
Graph Application – intersection point
Solve – find x-intercepts
Iteration – sequence
Graph Application – intersection point
Draw Circle – method 1 (graph app)
Y for domain after defining y1
Draw inverse
Translation
Dilation
Plot y1, y2 in terms of y1 etc
Create a table of values
Maximum
Minimum
Graph quartics
Maximum
intersection point
nCr
Create a table of values
Find y given x
Find x given y
Solver
DEG – RAD mode
Trigonometric function graph
Graph Application – intersection point
plot/trace/zoom
Stationary points
Finding a tangent to a curve at a given
point
Maximum
Minimum
intersection point
intersection point
Integration
Introduction
Using Algebra menu
solve
factor
expand
zeros
approx
How
do I …
Section
2.4
7.1
2.4
2.3.1
9.1
2.4
2.2
1.4
4.4
4.3
4.3
4.3
2.1
2.3.3
2.3.3
2.3
2.3.3
2.4
1.8
2.1
2.3.4
2.3.5
7.1
1.5.1
4.5
2.4
2.2.1/3
2.3
How do I
…
Page
45
80
45
41
89
45
38
19
53
52
52
52
40
42
42
41
42
45
29
37
44
44
80
20
55
45
40/46
41
5.3.2
2.3.3
2.3.3
2.4
2.4
5.4.2
A, B, C
1
1.9/7.1
1.9
1.9
2.3.1
1.1
64
42
43
45
45
66
7
11
32/80
32
32
41
13
Page 134
570
470
570
571
571
575
577
579
580
580
580
581
581
common denominator
propFrac
(nSolve)
Trig & A:Complex
Graphing
Defining functions
Probability & Counting
Trigonometric functions
Using the calculus menu
Differentiate
Integration
Limit
Stationary points
1.9
1.9
1.9
1.6
2, 3
1.4
1.8
1.6/1.9
5
5.3
5.4
5.1
2.3.3
32
32
32
25
37/46
19
29
25/32
56
60
65
56
42
Page 135
A.04 Cambridge Essential Standard General Mathematics
Text Page
12
33
38
44
61
76
81
86
97
97
109
128
139
215
215
224
224
230
230
234
234
248
263
304
305
321
321
340
364
422
431
437
444
448
466
467
468
468
469
Description
Histogram
Summary statistics
Box plot
Box plot with outliers
Table of values
sequence
intersection point
Simultaneous equations
straight line graph
Table of values
Equation of a line from 2 points/linear
regression
Scatterplot
Linear regression/ least squares regression
simple interest/plot
simple interest/table of values
compound interest/plot
compound interest/table of values
Flat rate depreciation & book value/ plot
Flat rate depreciation & book value/ table
of values
Reducing balance depreciation & book
value/plot
Reducing balance depreciation & book
value/table
Degree mode
Calculator tip/define variables
Generate arithmetic sequence
Position counter arithmetic sequence
Generate geometric sequence
Position counter geometric sequence
Difference equations
graph feasible region
inputting matrix data
matrix calculations/+/-/scalar x
matrix calculations/x
matrix calculations/det/inverse
simultaneous equations/matrix
calculate/basic
straight line graph
table of values
Simultaneous equations/solve
Histogram
How
do I …
Section
6.1.3
1.7/6.1
6.1.4
6.1.4
2.1
9.1
2.4
1.9/2.4
2.2
2.1
6.4.3
How do I
…
Page
70
27/68
71
72
37
88
45
32/45
38
37
78
6.4.1
6.4.3
2.2
2.1
2.2
2.1
2.2
2.1
76
78
38
37
38
37
38
37
2.2
38
2.1
37
1.5.1
1.2
9.1
9.1
9.1
9.1
9.3
4.2
8.1
8.1.1
8.1.1
8.1.1
8.2
1.1
2.2
2.1
1.9/2.4
6.1.3
20
16
88
88
88
88
91
51
82
83
84
85/84
85
11
37\8
37
32/45
70
Page 136
471
472
473
474
475
476
476
476
477
477
478
479
479
480
Boxplot
Boxplot with outliers
Mean & standard deviation
Scatterplot
sequence generate
simple interest/plot
simple interest/table
compound interest/plot
compound interest/table of values
inputting matrix data
matrix calculations/+/-/scalar x
matrix calculations/x
matrix calculations/det/inverse
simultaneous equations/matrix
6.1.4
6.1.4
1.7
6.4.1
9.1
2.2
2.1
2.2
2.1
8.1
8.1.1
8.1.1
8.1.1
8.2
71
72
27
76
89
38
37
38
37
82
83
84
85/84
85
Page 137
A.05 Heinemann VCE Zone General Mathematics
Text Page
8
25
62
63
63
64
66
67
70
94
96
103
103
104
130
131
132
132
137
140
141
142
142
143
148
171
193
193
198
199
210
210
211
211
212
216
248
263
263
265
266
Description
basic arithmetic
solver
finding x-intercepts
intersection point
zoom
table of values
table of values
table of values
simultaneous equations - intersection
point
simultaneous equations - solve
simultaneous equations - intersection
point
scatterplot
linear regression
coefficient of determination, r^2
inputting matrix data
matrix +
matrix matrix multiplication
matrix multiplication
determinant
inverse
decimal to fraction
simultaneous equations - matrices
simultaneous equations - matrices
transition matrix
scatterplot
enter & plot
intersection point
inequality
inequality
enter & plot
trace
enter & plot
functions in terms of functions
scatterplot
log graph
cumulative frequency curve
five figure summary
boxplot
modified boxplot
modified boxplot
How
How do I
do I … …
Section Page
1.1
11
7.1
80
2.3.1
41
2.4
45
3.2
47
2.1
37
2.1
37
2.1
37
2.4
45
1.9/2.4
2.4
6.4.1
6.4.3
6.4.2
8.1
8.1.1
8.1.1
8.1.1
8.1.1
8.1.1
8.1.1
1.1
8.2
8.2
8.4
6.4.1
2.2
2.4
4.2
4.2
2.2
2.2.1
2.2
4.3
6.4.1
4.3
6.2
1.7
6.1.4
6.1.4
6.1.4
32/45
45
76
78
77
82
83
83
84
84
85
84
13
85
85
87
76
38
45
51
51
38
40
38
52
76
52
73
27
71
72
72
Page 138
267
272
280
293
301
301
302
309
309
318
384
384
389
394
508
521
522
523
603
mean &standard deviation
statistics
random numbers
scatterplot
scatterplot
Correlation coefficient, r
Coefficient of determination, r2
linear regression
linear regression - sketch
linear regression
Degree/radian mode
Trigonometric calculations
Trigonometric calculations
Trigonometric calculations
table of values
generate sequence
plot sequence
sum of a series
definite integral
1.7
1.7
1.8.1
6.4.1
6.4.1
6.4.2
6.4.2
6.4.3
6.4.4
6.4.3
1.5.1
1.6
1.6
1.6
2.1
9.1
9.1
9.2
5.4.2
27
27
29
76
76
77
77
78
78
78
20
25
25
25
37
89
89
90
66
Page 139
A.06 Heinemann VCE Zone Mathematical Methods 1 & 2
Text Page
12
14
14
21
52
66
74
78
79
82
89
89
90
90
92
94
107
108
116
117
119
119
120
123
129
130
151
151
151
151
155
155
158
165
166
191
192
245
247
270
Description
enter & plot
table of values
Trace
simultaneous equations - intersection
point
define function
Solver
enter & plot
enter & plot fn with parameters
enter & plot fn with parameters
functions in terms of functions
x intercepts
Maximum and minimum points
x intercepts
Maximum and minimum points
simultaneous equations - intersection
point
simultaneous equations - intersection
point
define function
table of values
enter & plot
Maximum and minimum points
enter & plot
x intercepts
intersection point
functions in terms of functions
restrict domain
restrict domain
enter & plot
x intercepts
y intercept
Maximum and minimum points
enter & plot
x intercepts
enter & plot
enter & plot
enter & plot
random numbers
random numbers
find y given x
Tangent to a curve
enter & plot
How do How do I
I…
…
Section Page
2.2
38
2.1
37
2.2.1
40
2.4
1.4
7.1
2.2
4.1
4.1
4.3
2.3.1
2.3.3
2.3.1
2.3.3
45
19
80
38
50
50
52
41
42
41
42
2.4
45
2.4
1.4
2.1
2.2
2.3.3
2.2
2.3.1
2.4
4.3
4.5
4.5
2.2
2.3.1
2.3.2
2.3.3
2.2
2.3.1
2.2
2.2
2.2
1.8.1
1.8.1
2.3.5
5.3.2
2.2
45
19
37
38
42
38
41
45
52
55
55
38
41
42
42
38
41
38
38
38
29
29
44
64
38
Page 140
270
272
275
275
277
277
277
278
278
291
301
307
307
341
341
345
345
345
353
353
354
355
358
360
364
387
393
393
394
394
397
397
404
408
412
412
419
436
438
451
table of values
piecewise/restrict domain
enter & plot
table of values
enter & plot
table of values
Limits
piecewise/restrict domain
table of values
Derivative
Tangent
Trace
sketch derivative
deg to dms
Degree/radian mode
Degree/radian mode
convert degrees to radians
convert radians to degrees
enter & plot
functions in terms of functions
functions in terms of functions
functions in terms of functions
functions in terms of functions
enter & plot
intersection point
enter exponential function
enter & plot
table of values
enter & plot
table of values
enter & plot
table of values
log calculation
intersection point
enter & plot
table of values
find y given x
factorial
nPr
nCr
2.1
4.5
2.2
2.1
2.2
2.1
5.1
4.5
2.1
5.3
5.3.2
2.2.1
5.3.1
1.5.2
1.5.1
1.5.1
1.5.4
1.5.5
2.2
4.3
4.3
4.3
4.3
2.2
2.4
1.1
2.2
2.1
2.2
2.1
2.2
2.1
1.1
2.4
2.2
2.1
2.3.5
1.8
1.8
1.8
37
55
38
37
38
37
56
55
37
60
64
40
63
21
20
20
23
24
38
52
52
52
52
38
45
11
38
37
38
37
38
37
11
45
38
37
44
29
29
29
Page 141
A.07 Jacaranda Maths Quest 11 General Mathematics A
Text Page
24
28
53
103
107
112
116
146
162
171
184
212
239
264
265
280
308
319
358
363
364
365
386
387
388
389
391
407
421
434
490
499
539
548
580
651
741
Description
Solving matrix equations
Matrix multiplication
Converting decimals to fractions
Listing the terms of an arithmetic
sequence
Sum of an arithmetic sequence
Listing the terms of a geometric sequence
Sum of a geometric sequence
histogram
Finding statistical information
Measures of variability
Box plot
Scatterplot
linear regression – line of best fit
Random number generation
histogram
matrix calculations
Solving linear equations
Generating a table of values/sequence
Generating a table of values
Graphs of non-linear equations
Find x intercepts (roots)
Solving non-linear equations using tables
Zoom functions/window settings
simultaneous equations – graphical
simultaneous equations – graphical
simultaneous equations - iteration
simultaneous equations - solver
simultaneous equations – table of values
Plot linear functions
Point of intersection
Line of best fit (linear regression)
Graphing linear inequations
Simultaneous linear inequations
Compound interest
Simple and compound interest functions
Straight line depreciation using solver
Ratios
Viewing perpendicular lines
How
How do I
do I … …
Section Page
8
82
8.1.1
84
1.1
12
9.1
89
9.2
90
9.1
89
9.2
90
6.1.3
70
1.7/6.1
27/68
1.7/6.1
27/68
6.1.4
71
6.4.1
76
6.4.3
78
1.8.1
29
6.1.3
70
8.1.1
83
1.9/7.1
32/80
2.1/9.1
37/88
2.1
37
2.2
38
2.3.1
41
2.1
37
3
46
2.4
45
2.4
45
9.1
89
7.1
80
2.1
37
2.2
38
2.4
45
6.4.4
78
4.2
51
4.2
51
6.4
74
2
37
7.1
80
1.1
12
3
46
Page 142
A.08 Jacaranda Maths Quest 11 General Mathematics B
Text Page
24
28
46
129
133
138
142
168
169
185
212
223
262
267
268
269
290
291
292
293
295
365
379
392
453
470
540
545
560
569
669
Description
Solving matrix equations
Matrix multiplication
Cube and nth root
Listing the terms of an arithmetic
sequence
Sum of an arithmetic sequence
Listing the terms of a geometric sequence
Sum of a geometric sequence
Random number generation
histogram
matrix calculations
Solving linear equations
Generating a table of values/sequence
Generating a table of values
Graphs of non-linear equations
Find x intercepts (roots)
Solving non-linear equations using tables
Zoom functions/window settings
simultaneous equations – graphical
simultaneous equations – graphical
simultaneous equations - iteration
simultaneous equations - solver
simultaneous equations – table of values
Plot linear functions
Point of intersection
Line of best fit (linear regression)
Direct variation using plots
Inverse variation using plots
Graphing functions
Finding distance using sequences
Graphing linear inequations
Simultaneous linear inequations
Viewing perpendicular lines
How
How do I
do I … …
Section Page
8
82
8.1.1
84
1.1
12
9.1
89
9.2
9.1
9.2
1.8.1
6.1.3
8.1.1
1.9/7.1
2.1/9.1
2.1
2.2
2.3.1
2.1
3
2.4
2.4
9.1
7.1
2.1
2.2
2.4
6.4.4
2.2
2.2
2.2
9.1/9.2
4.2
4.2
3
90
89
90
29
70
83
32/80
37/88
37
38
41
37
46
45
45
89
80
37
38
45
78
38
38
37
89/90
51
51
46
Page 143
A.09 Jacaranda Maths Quest 11 Mathematical Methods
Text Page
4
4
9
27
28
32
38
46
81
92
95
98
125
137
153
154
159
188
210
244
248
289
357
410
437
499
522
528
537
Description
Solving linear equations with solver
Solving linear equations graphically
Using the Solve function
Finding x and y intercepts
simultaneous equations – graphical
simultaneous equations – matrices
Distance between two points
Intersection point
Repeated calculations
Finding significant points on a graph
Finding significant points on a graph
Solving quadratic equations - graphs
Calculating functions using parameters
Sketching cubic functions
Finding significant points on a graph
Maximum and minimum points
Finding significant points on a graph
Modelling
Plotting points
Piecewise defined functions
Indicial equations - solver
Intersection point
Working with angles
Degrees to radians
Radians to degrees
Drawing a tangent to a curve
Plotting the derivative function
Finding stationary points
Random number generation
Factorials
Permutations
Combinations
How
How do I
do I … …
Section Page
7.1
80
2.2/2.3
38/21
1.9/7.1
36/80
2.3.1
41
2.4
45
8.2
85
2.5
45
2.3.3
43
1.2
16
2.3
41
2.3
41
2.3.1
41
4.1
50
2.2
38
2.3
41
2.3.3
42
2.3
41
6.4
74
6.4.1
76
4.5
55
1.9/7.1
35/80
2.3.3
43
1.5
20
1.5.4
23
1.5.5
24
5.3.2
64
5.3.1
63
2.3.3
42
1.8.1
29
1.8
29
1.8
29
1.8
29
Page 144
A.10 Macmillan MathsWorld Technology Toolkit (TI-89)
Description
1.1 How to perform simple arithmetic calculations
1.2 How to store and use numerical values
1.3 How to store and use lists
1.4 How to perform simple function calculations
1.5 How to work with angles
1.6 How to perform simple trigonometric calculations
1.7 How to perform simple statistical calculations
1.8 How to perform simple probability calculations
1.9 How to perform simple symbolic calculations
2.1 How to enter and plot functions
2.2 How to create a table of values
2.3 How to ‘jump to’ significant points on a graph
2.4 How to find the intersection point of two graphs
3.1 How to change the viewing window
3.2 How to zoom options
4.1 How to enter and plot a function using parameters
4.2 How to shade above/below a function graph
4.3 How to graph functions defined in terms of other
functions
4.4 How to draw the inverse of a function
4.5 How to restrict the domain of a function
5.1 How to calculate average & instantaneous rates of
change
5.2 How to calculate the numeric derivative
5.3 How to calculate and plot derivative functions
5.4 How to draw tangent lines
5.5 How to calculate the definite integral
6.1 How to store and summarise ungrouped univariate
data
6.2 How to store and summarise grouped univariate
data
6.3 How to construct cumulative frequency curves
6.4 How to construct a histogram
6.5 How to construct a box plot
6.6 How to store and summarise bivariate data
6.7 How to construct a scatter plot
6.8 How to calculate correlation coefficients
6.9 How to calculate the least-squares regression line
7.1 How to use the numeric solver APP
8.1 How to store and use matrices
8.2 How to solve equations with matrices
How do I …
Section
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.2
2.1
2.3
2.4
3.1
3.2
4.1
4.2
4.3
4.4
4.5
5.2.1/5.5.2.2
5.3
5.3.1
5.3.2
5.4.2
How do
I…
Page
11
16
17
19
20
25
27
29
32
38
37
41
45
46
47
50
51
52
53
55
57/58
60
63
64
66
6.1.1
68
6.1.2
6.2
6.1.3
6.1.4
6.4
6.4.1
6.4.2
6.4.3
7.1
8.1
8.2
69
73
70
71
74
76
77
78
80
82
85
Page 145
8.3 How to transform points and equations with
matrices
8.4 How to work with transition matrices
9.1 How to define, plot and tabulate a sequence rule
9.2 How to sum a sequence
9.3 How to work with difference equations
10.1 How to define and use functions
10.2 How to use the symbolic solve command
10.3 How to work with general solutions
10.4 How to rearrange equations and expressions
10.5 How to work with limits
10.6 How to find the symbolic derivative
10.7 How to calculate indefinite integrals
8.3
8.4
9.1
9.2
9.3
1.4
1.9
1.9
1.9
5.1
5.3
5.4.1
86
87
89
90
91
19
32
32
32
56
60
65
Page 146
A.11 Pearson Longman General Maths Dimensions (An advanced
course) 1 & 2
Text Page
13
25
27
28
87
110
122
122
150
150
179
228
238
241
252
267
269
273
273
292/3
297
304
308
320 – 323
335/6
350
383
385
464
Description
Basic calculations/operations
Convert degrees to radians
Rational numbers (exact answers)
Fraction (recurring decimal)
Logarithms
Finding equation of a straight line
Convert degrees to radians
Input degrees, minutes and seconds
Convert degrees to radians
Convert radians to degrees
Solving trig equations(using
graph/intersection)
Create histogram (enter data to list)
Boxplot
Basic statistical calculations (summary
statistics)
Least squares regression line
(Addition &) Subtraction of matrices
Matrix multiplication
Inverse of a matrix
Determinant
Sequences – define, tabulate and plot
Define arithmetic sequence
Summing of a sequence
Define geometric sequence
Difference equations
Linear regression
Linear regression
Convert into polar coordinates
Plotting polar curves
Complex number mode
How
How do I
do I … …
Section Page
1.1
11
1.5.4
23
1.1
11
1.1
11
1.1
11
2
37
1.5.4
23
1.5
20
1.5.4
23
1.5.5
24
2.4
6.1.3
6.1.4
45
70
71
6.1.1
6.4.3
8.1.1
8.1.1
8.1.1
8.1.1
9.1
9.1
9.2
9.1
9.3
6.4.3
6.4.3
13
13
14
68
78
83
84
84
85
89
89
90
89
91
78
78
119
119
122
Page 147
A.12 Pearson Longman Mathematical Methods Dimensions 1 & 2
Text Page
11
13
13
14
15
17
18
27
48
48
52
73
73
85
89
92
122
122
125
125
148
148
148
148
148
149
151
151
151
153
153
153
153
153
153
153
155
155
155
156
Description
Solve linear equations
Simultaneous equations – graphically plot
Simultaneous equations – graphically
intersection point
Simultaneous equations – solve
Simultaneous equations – matrices
Linear inequations
Transpose equations
Sketch linear graph
Expand
Factorise
Solve quadratic equations
- matrices
- define & solve
Division of polynomials
Factorise polynomials
Solve cubics
Define functions f(x) =
Solve f(x)=0
Inverse functions – graphically
Inverse functions – defined f(y)=x
Intersecting lines – sketch
Find x intercept
Find y intercept
Intersection point
Intersection point – using matrices
Solve with matrices
Equation of polynomial function – plot
values
Simultaneous equations
Matrices
Inverse functions – (expand/simultaneous)
Turning point
Inverse functions – solve
Inverse functions – graph
Coordinate geometry – sketch
Maximum
Distance between 2 points
Matrix transformations – translation
Matrix transformations – reflection
Matrix transformations – dilation
Relations & functions – sketch circle
How do I
…
Section
1.9
2.2
2.4
How do I
…
Page
32
38
45
1.9/2.4
8.2
1.9
1.9
2.2/4.1
1.9
1.9
1.9/7.1
8.2
1.4
1.9
1.9
1.9
1.4
1.9
4.4
4.4
2.2
2.3.1
2.3.2
2.4
8.2
8.2
6.4.1
32/45
85
32
32
38/50
32
32
32/80
85
19
32
32
32
19
32
53
53
38
41
42
45
85
85
76
1.9/7.1
8.2
1.9
2.3.3
4.4
4.4
2.2
2.3.3
2.5
8.3
8.3
8.3
2.2
32/80
85
32
42
53
53
38
42
45
86
86
86
38
Page 148
156
156
184
184
184
184
184
186
186
227
232
232
247
247
250
261
261
265
265
266
267
269
270
270
286
286
286
286
301
302
306
306
306
315
319
329
330
333
333
348
353
363
Circle inequality
Trigonometry (sohcahtoa)
Average & instantaneous rates – define
function
Sketch
Draw tangent
Calculate gradient
Equation of tangent
Rate of change application – graph
specific domain
Find x-value given a specific y-value
Generate random numbers
Probability distribution – quadratic
regression
Define function p(x)/solve
Radian mode
Solve sin/cos angles
Solve sin/cos angles
Learning task 7F – radian
Learning task 7F – plot/window settings
Solve trigonometric equations
Solve trigonometric equations
Solve trigonometric equations over
specific domain
Solve trigonometric equations over
specific domain
Sketch y=tan(x) [0,2pi]
Radian mode
plot/window settings
E.g. 2&3 different tan graphs/domain
Sketch trig graph
Find y-value given a specific x-value
Find x-value given a specific y-value
Intersection point
Solve exponential equations
Solve indicial equations
Exponential function graph – domain
Find y-value given a specific x-value
Find x-value given a specific y-value
Solve exponential equations
Solve exponential equations
Euler's number – limits
Solve exponential equations
Solve logarithmic equations
Average rates of change
Limits
Positive & negative limits
Derivative of a function with respect to x
at a specific point
4.2
1.6
5.2.1/5.2.2
51
25
57/58
4.5
5.3.2
5.3
5.3.2
5.2.1/4.5
55
64
60
64
57/55
2.3.4
1.8.1
44
29
6.1.2
1.4/1.9
1.5.1
1.6
1.6
1.5.1
2.2
2.2
2.4
1.9/4.5
69
19/32
20
25
25
20
38
38
45
32/55
1.9/4.5
32/55
4.5
1.5.1
2.2
4.5
2.2
2.3.5
2.3.4
2.4
1.9/7.1
7.1
4.5
2.3.5
2.3.4
1.9/7.1
7.1
5.1
7.1
7.1/1.4
5.2.1
5.1
5.1
5.3
55
20
38
55
38
44
44
45
32/80
80
55
44
44
32/80
80
56
80
80/19
57
56
56
60
Page 149
366
379
386
387
387
388
388
388
394
400
400
400
401
401
401
415
415
428
428
428
429
429
436
438
444
451
455
466
466
467
467
467
488
490
490
490
491
491
498
508
518
528
529
531
534
[tangents & normals]
Sketch f'(x) from f(x)
Rates of change – plot points/table
Polynomial models of growth – plot
Predict y given x
Average rates of change
Limits
Differentiation
Instantaneous rate of change
Solve f'(x)=0
Maximum
Minimum
Find constants
Define function
Solve given conditions
Maximum
Minimum
Derivative of a function
Sketch over specific domain
Stationary points **
Define function
Find derivative (operation at same time)
Antiderivative – indefinite integrals
Definite integrals
Definite integrals
Area under a curve [bounded]
Area between two curves
Integral
Gradient at specific points/values
Integral
Solve function through a point (constant)
Maximum
Gradient of tangent
Gradient of tangent
Equation of tangent
Find x-value given a specific y-value
Derivative of a function
Sketch over specific domain
Permutations
Combinations
Markov sequences/matrices
CAS to find first 6 rows of Pascal's
triangle
Define probability function p(x)
Probability involving combinations
Transition matrices – matrix calculations
5.3.2
5.3.1
6.4.1
4.5
2.3.5/1.4
5.2.1
5.1
5.3
5.3
1.9
2.3.3
2.3.3
1.9
1.4
1.9
2.3.3
2.3.3
5.3
4.5
2.3.3
1.4
5.3
5.4.1
5.4.2
5.4.2
5.4.3
5.4.3
5.4
5.3
5.4.1
1.9/7.1
2.3.3
5.3.2
5.3.2
5.3.2
2.3.4
5.3
4.5
1.8
1.8
8.4
1.8
1.4
1.8
8.4
64
63
76
55
44/19
57
56
60
60
32
42
42
32
19
32
42
42
60
55
42
19
60
65
66
66
67
67
67
60
65
32/80
42
64
64
64
44
60
55
29
29
87
29
19
29
87
Page 150
Units 3 & 4
A.13 Cambridge Essential Further Mathematics 3 & 4
Text Page
13
43
62
75
95
103
121
183
237
242
249
254
273
282
302
414
415
437
488
493
495
527
529
532
639
646
654
669
674
717
719
720
721
722
723
724
Description
Histogram
Boxplot with outliers
Summary statistics – mean & standard
deviation
Random number generation
Scatterplot
Correlation coefficient
Equation of least squares regression line
Time series plot
Generate terms of arithmetic sequence
Generate terms of arithmetic sequence
Sum of arithmetic sequence
Generate terms of geometric sequence
Generate terms of geometric sequence
Generate sequence defined by difference
equation
Generate /graph terms of Fibonacci
sequence
Simultaneous equations
Simultaneous equations – graphical
Scatterplot /linear regression
Simple interest – Financial solver
Compound interest – Financial solver
Financial solver
Financial solver
Financial solver
Financial solver
Entering a matrix
Add, subtract & scalar multiply matrices
Matrix multiplication
Determinant and inverse of a matrix
Simultaneous equations – matrices
Appendix
Name a list
Basic calculations
Histogram
Boxplot with outliers
Summary statistics
Scatterplot
Correlation coefficient
How
How do I
do I … …
Section Page
6.1.3
70
6.1.4
72
6.1.1
1.8.1
6.4.1
6.4.2
6.4.3
2.2
9.1
9.1
9.2
9.1
9.1
68
29
76
77
78
38
89
89
90
89
89
9.3
91
9.1
1.9
2.4
6.4
15
15
15
15
15
15
8.1
8.1.1
8.1.1
8.1.1
8.2
89
35
45
74
124
124
124
124
124
124
82
83
84
85/84
85
1.3
1.1
6.1.3
6.1.4
6.1.1
6.4.1
6.4.2
17
11
70
72
68
76
77
Page 151
725
731
732
733
734
735
736
737
738
738
740
741
Least squared regression line
Time series plot
Generate terms of a sequence
Generate sequence defined by difference
equation
Simple interest – Financial Solver
Compound interest – Financial Solver
Financial Solver
Financial Solver
Enter a matrix
Matrix calculations
Determinant and inverse of a matrix
Simultaneous equations – matrices
6.4.3
2.2
9.1
78
38
89
9.3
15
15
15
15
8.1
8.1.1
8.1.1
8.2
91
124
124
124
124
82
83
85/84
85
Page 152
A.14 Cambridge Essential Mathematical Methods 3 & 4 CAS
Text Page
8
19
24
28
54
59
88
104
120
122
140
144
149
150
172
178
184
216
222
226
243
247
247
281
283
292
311
312
324
336
339
384
423
425
515
567
613
614
616
Description
Define & evaluate functions
Absolute value/modulus
Composite functions – sketch
Inverse functions
Matrix operations
Simultaneous equations – matrices
Defining functions
Inverse Functions
Division of polynomials
Factor and solve
Graph – maximum /minimum
Solve
Solve
Solve
Solving log equations
Solving exponential functions
Solving exponential functions
Finding axes intercepts
Solve trig equations
Solution of circular function equations
Define and sketch functions
Inverse function
Solve function
Limits
Derivative at a point
Define & differentiate
Derivative – graph
Derivative – graph
Tangent to the curve
Stationary points
Stationary points
Limits
Indefinite integral
Indefinite integral
Binomial cdf
Definite integral
Normal cdf
Inverse normal
Normal area curves
How
How do I
do I … …
Section Page
1.4
19
10.5
96
10.7
98
4.4
53
8.1.1
83
8.2
85
1.4
19
4.4
53
1.9
34
1.9
34
1.9
32
1.9/7.1
32/80
1.9/7.1
32/80
1.9/7.1
32/80
7.1
80
7.1
80
7.1
80
2.3
41
1.9/7.1
32/80
1.9/7.1
32/80
1.4/2.2
19/38
4.4
53
1.9/7.1
32/80
5.1
56
5.3
60
5.3
60
5.3.1
63
5.3.1
63
5.3.2
64
2.3.3
42
2.3.3
42
5.1
56
5.4.1
65
5.4.1
65
12.1.2
109
5.4.3
67
12.2
115
12.2.3
118
12.2.2
117
Page 153
669
671
672
672
673
674
674
674
674
675
675
675
677
678
679
681
Appendix
Introduction
Using Algebra menu
solve
factor
expand
zeros
approx
common denominator
propFrac
(nSolve)
Trig & A:Complex
Graphing
Defining functions
Circular functions
Using the calculus menu
Probability
1.1
1.1
1.9/7.1
1.9
1.9
2.3.1
1.1
1.9
1.9
1.9
1.6/14
2/3
1.4
1.6/1.9
5/10
1.8
11
11
32/80
32
32
41
13
32
32
32
24/122
7/46
19
25/32
56/99
29
Page 154
A.15 Cambridge Essential Mathematical Methods 3 & 4
Text Page
8
19
25
28
98
116
116
152
179
181
215
215
219
226
227
260
278
299
314
401
402
402
481
486
492
506
549
549
550
551
551
553
Description
Define & evaluate functions
Absolute value/modulus
Composite functions – sketch
Inverse functions
Table application
Eg 16 minimum
Eg 16 maximum
Intersection point
Sketch trig function over specific domain
Sketch trig function over specific domain
Eg 6 inverse functions
Eg 7 inverse functions
Linear regression
Linear regression
Linear regression
Derivative of a function at a specific point
Graph of function & derivative
Tangent to the curve
Stationary points
Area under the curve – bounded
Definite integrals
Plot antiderivative function
Binomial distribution
Plot of binomial pdf
Solve for n – sample size
Calculate probability/ area under curve
Normal distribution
Eg 4 normal distribution
Eg 5 normal distribution
Eg 6 inverse normal
Eg 7 inverse normal
Eg 8 normal distribution
How
How do I
do I … …
Section Page
1.4
19
10.5
96
10.7
98
4.4
53
2.1
37
2.3.3
42
2.3.3
42
2.4
45
4.5
55
4.5
55
4.4
53
4.4
53
6.4
74
6.4
74
6.4
74
5.3
60
5.3.1
63
5.3.2
64
2.3.3
42
5.4.3
67
5.4.2
66
5.4
65
12.1.2
109
12.1.2
109
12.2.1
115
5.4.3
67
12.2.2
117
12.2.2
117
12.2.2
117
12.2.3
118
12.2.3
118
12.2.2
117
Page 155
603
605
606
606
607
608
608
608
608
609
609
609
611
614
616
621
Appendix
Introduction
Using Algebra menu
solve
factor
expand
zeros
approx
common denominator
propFrac
(nSolve)
Trig & A:Complex
Graphing
Defining functions
Trigonometric functions
Using the calculus menu
Probability
1.1
1.1
1.9/7.1
1.9
1.9
2.3.1
1.1
1.9
1.9
1.9
1.6/14
2/3
1.4
1.6/1.9
5/10
1.8
11
11
32/80
32
32
41
13
32
32
32
24/122
7/46
19
25/32
56/99
29
Page 156
A.16 Cambridge Essential Specialist Mathematics 3 & 4
Text Page
7
8
10
27
28
28
43
44
104
105
108
108
112
113
125
125
125
138
139
140
142
145
146
149
149
158
159
160
163
164
199
204
206
206
211
220
220
220
220
How
How do I
do I … …
Description
Section Page
Intersection point
2.4
45
Solve application
7.1
80
Tan graph
2.2
38
Eg 24 sequence
9.1
89
Eg 25 sequence
9.1
89
Sequence
9.1
89
Parametric equations
16
126
Parametric equations/conics
16
126
Graph cosec(x)
2.2
38
Graph cot(x)
2.2
38
Eg 4 simplifying trigonometric functions
1.9
32
Eg 5 solving trigonometric functions
1.9/7.1
32/80
Eg 6 Exact solutions
1.1
11
Eg 7 solve/expand trigonometric functions 1.9/7.1
32/80
Eg 18a maximum
2.3.3
42
Eg 18a minimum
2.3.3
42
Eg 18b y2=1/y1
10.2
93
Eg 1 complex mode/application
14
122
Eg 2b simplify complex expressions
14
122
Define/store complex expressions
14
122
Eg 7
14
122
Eg 8 complex conjugate
14
122
Eg 9a
10.5
96
Eg 10a absolute/angle
[modulus/argument]
10.5
96
Eg 10b
10.5
96
Eg 15 Factorisation of quadratics
1.9
32
Eg 16 Factorisation of cubics
1.9
32
Eg 17 Factorisation of higher degree
polynomials
1.9
32
Eg 19 solutions of quadratics
2.3
41
Solutions of quadratics = 0
2.3
41
Gradient at a specific point
5.3
60
Derivatives of x=f(y)
5.3
60
Graph inverse trigonometric functions
4.4
53
Derivative of inverse trigonometric
functions
5.3/4.4
60/53
Eg 9b second derivative
11.3
101
(using eg 9b) derivative
5.3
60
(using eg 9b) second derivative
11.3
101
(using eg 9b) f'(x)=0
5.3
60
(using eg 9b) f''(x)=0
11.3
101
Page 157
220
240
241
269
298
303
346
349
352
354
439
439
444
(using eg 9b) stationary points
Eg 28 implicit differentiation
[eg 29 implicit differentiation]
Eg 12c integration by substitution
Section 8.3 Integration using graphics
calculator
[section 8.4 Volume of solids/revolution]
Section 9.6 Differential equations
Differential equations
Program for Euler's method
Section 9.8 Direction(slope) field for
differential eqn
Eg 6 Parametric equations-plot eqns
simultaneously
Eg 6 Parametric equations-intersection
point
Vector Calculus (eg 12)
2.3.3
5.4
5.4
5.4
42
65
65
65
5.4
11.4
11.5
11.5
11.5
65
102
103
103
103
11.5
103
16
126
16
16
126
126
Page 158
A.17 Heinemann VCE Zone Further Mathematics
Text Page
13
14
17
25
26
37
42
49
58
111
117
121
122
127
130
141
146
164
167
175
179
228
237
241
260
265
266
296
300
300
314
319
320
389
391
394
399
403
404
Description
Basic statistical calculations
Summary statistics
Boxplots
Random number generation
Random numbers & basic statistical
calculations
Boxplots
Scatterplot
Correlation coefficient
Least squares regression line
Plotting a sequence
Summing a sequence
Calculating nth roots
Tabulating sequence
Tabulating sequence
Recurring decimal (fraction)
Difference equations
Define, tabulate & plot a sequence
Define variables to have a numerical
value
Exact answer (fraction)
Basic trig calculations (answers → DMS)
Basic trig calculations
Solving simultaneous equations
graphically
Break-even analysis
Graphing linear inequations
Graphs of y = kx x
Graphs of non-linear relations
Plot points (regression)
Plot points (interest)
Graph/ table
Financial solver
Financial solver
Graph/ table
Financial solver
Inputting matrix data
Matrix addition & subtraction
Scalar multiplication
Matrix multiplication
Inverse & determinant of a matrix
Solve simultaneous equations – matrices
How
How do I
do I … …
Section Page
1.7
27
1.7
27
6.1.4
71
1.8.1
29
1.8.1
6.1.4
6.4.1
6.4.2
6.4.3
9.1
9.2
9
9.1
9.1
9.1
9.3
9.1
29
71
76
77
78
89
90
88
89
89
89
91
89
1.2
1.1
1.6
1.6
16
11
25
25
2.4
2.4
4.2
45
45
51
2.2
13
6.4
6.4
2.1
15
15
2.1
15
8.1
8.1.1
8.1.1
8.1.1
8.1.1
8.2
38
119
74
74
37
124
124
37
124
82
83
83
84
84/85
85
Page 159
412
417
Solve simultaneous equations – matrices
Transition matrices
8.2
8.4
85
87
Page 160
A.18 Heinemann VCE Zone Mathematical Methods 3 & 4
Text Page
6
11
22
29
35
39
41
42
64
68
69
71
98
99
100
109
124
128
144
151
158
169
182
183
190
198
206
209
237
249
254
268
302
307
311
351
352
363
374
380
386
394
Description
Graphing polynomials
Graphing functions with restricted domain
Graph (graph view window settings)
Turning points (maximum /minimum)
Graph /table – hyperbola
Graph – truncus
Graph – negative powers
Graph /square root function
Graph – exponential functions
Reflection in x/y axis
x-intercept
Graph – logarithmic functions
Covert radians to degrees
Parametric mode
Graph – parametric
Graph – trig functions
Solve trig equations – intersection point
Graph – trig func. with restricted domains
Addition (& subtraction) of ordinates
Product of functions
Inverse functions
Plotting data
Hybrid /piecewise functions
Limits (graph /table)
Derivative
Derivative – chain rule
Derivative – log functions
Derivative – trig functions
Derivative – stationary points
Sketch gradient function
Maximum /minimum
Equation of tangents & normals
Definite integrals – graph & algebraic
Integral – signed area
Area between two curves
Binomial pdf
Binomial cdf
Markov sequences – transition matrices
Integral (pdf)
Normal distribution
Standard normal distribution
Inverse standard normal distribution
How
How do I
do I … …
Section Page
2.2
38
4.5
55
2
37
2.3.3
42
10.2
93
10.2
93
10.2
93
10.2
93
2
37
4.4
53
2.3.1
41
2
37
1.5.5
24
16
126
16
126
2.2
38
2.4
45
4.5
55
10.4
95
10.6
97
4.4
53
6
68
10.1
92
5.1
56
5.3
60
5.3
60
5.3
60
5.3
60
5.3
60
5.3.1
63
2.3.3
42
5.3.2
64
5.4.3/2
67/66
5.4.3
67
11.1
99
12.1.2
109
12.1.2
109
8.4
87
5.4.3
67
12.2
115
12.2.2
117
12.2.3
118
Page 161
A.19 Heinemann VCE Zone Specialist Mathematics
Text Page
37
39
42
47
48
50
99
100
113
120
135
160
166
177
202
216
225
232
247
287
302
304
328
340
395
Description
Complex numbers
Complex addition & subtraction
Complex multiplication
Complex conjugate
Complex division
Powers of complex numbers
b
Sketch graph – f ( x) = ax 2 + 2
x
Solve function
Sketch circles & ellipses
Sketch hyperbolas
Reciprocal circular functions
Graph – inverse circular functions
Derivative – inverse circular functions
Indefinite integrals
Partial fractions (define & expand)
Definite integrals
Area between two curves
Volumes of solids of revolution
Second derivative
Numerical solution of differential
equations
Non-constant velocity – graph derivative,
solve for given value
Sketch function /derivative function
Area under curve
Parametric mode
Graph & table
How
How do I
do I … …
Section Page
14
122
14
122
14
122
14
122
14
122
14
122
10.4
7.1
13
10.2
10.2
10.2
5.3
5.4.1
1.9
5.4.2
11.1
11.4
11.3
95
80
119
93
93
93
60
65
32
66
99
102
101
11.5
103
5.3.1
5.3.1
5.4.3
16
2.1
63
63
67
126
37
Page 162
A.20 Jacaranda Maths Quest 12 Further Mathematics 2nd ed
Text Page
10
23
30
32
35
41
56
80
93
101
122
128
136
167
210
216
219
225
237
238
245
294
298
438
438
500
515
528
549
586
600
608
616
619
622
625
639
Description
Histogram
Summary statistics
Boxplot
Boxplot with outliers
Summary statistics – mean
Summary statistics – standard deviation
Random number generation
Parallel boxplots
Scatterplot
Correlation coefficient & coefficient of
determination
Three median method
Least-squares regression
Interpretation, interpolation &
extrapolation
Time series
Equation solver
Equation solver – arithmetic sequence
Listing terms of arithmetic sequence
Summing sequence
Equation solver – geometric sequence
Listing terms of geometric sequence
Summing a given number of terms of a
geometric sequence
Difference equations
Difference equations – graphical
representation
Entering angles in degrees & minutes
Changing angles from degrees to DMS
Sketching straight line graphs
Solve simultaneous equations – graphical
Non-linear relations and graphs
Graphing linear inequations
Simple interest calculations – Financial
solver
Compound interest – Financial Solver
Financial solver
Financial solver
Financial solver
Financial solver
Financial solver
Financial solver
How
How do I
do I … …
Section Page
6.1.3
70
6.1.1
68
6.1.4
71
6.1.4
72
6.1.1
68
6.1.1
68
1.8.1
29
6.1.4
71
6.4.1
76
6.4.2
77
6.4.3
78
6.4.5
2.2
7.1
9.1
9.1
9.2
9.1
9.1
79
38
80
89
89
90
89
89
9.2
9.3
90
91
9.3
1.5
1.5.2
2.2
2.4
2.2
4.2
91
20
21
38
45
38
51
15
15
15
15
15
15
15
15
124
124
124
124
124
124
124
124
Page 163
649
655
705
711
842
852
860
868
876
Financial solver
Financial solver
Financial solver
Graph & table
Matrix operations – addition, subtraction,
scalar
Matrix multiplication
Inverse & determinant of a matrix
Simultaneous equations – matrices
Transition matrices
15
15
15
2.1
8.1.1
8.1.1
8.1.1
8.2
8.4
124
124
124
37
83
84
84/85
85
87
Page 164
A.21 Jacaranda Maths Quest 12 Mathematical Methods 2nd ed
Text Page
12
86
98
103
179
218
322
426
432
438
529
532
542
584
614
618
625
627
Description
Listing several values of a function
Graph – asymptotes
Graph – absolute value
Modeling – Plotting data
Graph – exponential function
Graphing inverse relations
Gradient of a function at a particular point
Definite integrals
Integrals – Signed area
Area bound by graph & x-axis
Binomial pdf
Binomial pdf
Binomial cdf
Definite integrals
Standard normal distribution
Normal cdf
Normal curve areas
Inverse normal distribution
How
How do I
do I … …
Section Page
1.4
19
2.2
38
10.5
96
6.4
74
2.2
38
4.4
53
5.3
60
5.4.2
66
5.4.3
67
5.4.3
67
12.1.2
109
12.1.2
109
12.1.2
109
5.4.3
67
12.2.2
117
12.2.2
117
12.2.2
117
12.2.3
118
Page 165
A.22 Jacaranda Maths Quest 12 Specialist Mathematics 2nd ed
Text Page
28
53
71
123
146
224
265
277
283
286
292
328
377
384
392
434
440
469
484
Description
Graphing ellipses
Graph – window settings
Graphs – reciprocal trig functions
Simple algebra of complex numbers
Roots of complex numbers
Finding numerical derivatives
Graph – function and antiderivative
Definite integrals
Definite integrals – graph
Area bounded by two curves
Volume of a solid of revolution
Solving first order differential equations
Graphing x-t graph & v-t
Graphing x-t graph & v-t
Numerical solver
Parametric plots
Magnitude & direction of vectors
Parametric plots
Derivatives – vector functions
How
How do I
do I … …
Section Page
13
119
2.1
38
10.2
93
14
122
14
122
5.3
60
5.4
65
5.4.2
66
5.4.3
67
11.1
99
11.4
102
11.5
103
16.3
129
16.3
129
7.1
80
16
126
16
126
16
126
16
126
Page 166
A.23 Pearson Longman Mathematical Methods Dimensions 3 & 4
Text Page
24
36
47
56
63
66
72
78
84
87
94
95
96
97
97
99
100
101
102
103
103
105
105
105
106
106
122
124
139
141
157
159
176
192
220
222
Description
Inverse functions
Addition (& subtraction) of ordinates
Sketch graphs – find intercepts
Solve equation – quadratic
Solve simultaneous equations
Factorise cubics
Factorise/sketch polynomials
Sketch/graph
Sketch/graph
Define/solve functions
Graphing polynomials
Graphing polynomials – turning point/
point of inflection/ intercepts
Graphing polynomials
Factor
Define/solve functions
Eg. 4 define
Graph/point of inflection
Inverse functions – define/solve/sketch
point of intersection
Define
Eg.6 Graph absolute value function
Define function over specific domain and
solve
Eg. 7 Define matrix
Solving simultaneous equations with
matrices.
Graph domain/restrictions
Define and solve functions
Define/solve/graph composite functions
Solve exponential equations (using
numerical solver & solve function)
Sketch exponential functions
Solve logarithmic equations
Sketch logarithmic equations
Solve/graph
Eg. 2 Modelling with logarithmic
functions. Define/solve/graph
Basic trig calculations
Solve trig equations
Limits
Limits
How do
I…
Section
4.4
10
2.3
7.1
1.9
1.9
1.9/2.2
2.2
2.2
1.4/1.9
2.2
2.3
2.2
1.9
1.4/1.9
1.4
2.3.3
How do I
…
Page
53
92
41
80
35
32
32/38
38
38
19/32
38
41
38
32
19/32
19
43
4.4
1.4
10.5
53
19
96
4.5
8.1
55
82
8.2
4.5
1.4/1.9
10.7
85
55
19/32
98
7.1
2.2
7.1
2.2
7.1/2.2
80
38
80
38
80/38
7.1
1.6
1.9/7.1
5.1
5.1
80
25
32/80
56
56
Page 167
Define functions lim (Differentiation
h →0
224
236
237
241
289
297
300
309
322
323
325
326
327
328
329
330
331
332
341
342
346
347
383
384
392
399
422
423
424
425
425
426
427
427
429
448
452
from first principles)
Derivative
Derivative (& expand)
Derivative – chain rule
Stationary points.
Maximum value/graph
Minimum value/graph
Instantaneous rate of change
Stationary points. Limit/
intercept/maximum
Eg. 2 Stationary points with parameters
Intersection
Eg. 4 Average & instantaneous rates of
change
Graph with restricted domain
Eg. 6 Circular functions & rates of
change.
Maximum/average & instantaneous rates
of change
Eg. 7 Circular functions & graphs
Maximum/minimum. Graph with
restricted domain
Eg. 9 Stationary points
Integration – indefinite
Integration – indefinite
Integration – indefinite
Integration – indefinite
Definite integrals
Definite integrals (& finding limit)
Calculating area (with & without
graphical display)
Area bounded by two curves
Eg. 1 Areas & graphs. Define/ integrate
with & with out graphical display
Eg. 2 Rules of differentiation
Define/ solve/ derivative/ graph
Area between two curves
Eg. 3 f ′(x) / ∫ f (x) graphs with
parameters
Integral – solve with restrictions
Eg. 5 Find areas under curves
Eg. 6 Equation of tangent to a curve. Area
between curves
Average value of a function
Combinations (nCr)
Markov sequences
5.1
5.3
5.3
5.3
2.3.3
2.3.3
2.3.3
5.2.2
56
60
60
60
42
42
42
58
2.3.3
2.3.3
2.4
42
42
45
5.2
4.5
57
55
5.2
57
5.2
2.2
57
38
2.3.3/4.5
2.3.3
5.4.1
5.4.1
5.4.1
5.4.1
5.4.2
5.4.2
42/55
42
65
65
65
65
66
66
5.4.3
11.1
67
99
11.1
5.3
99
60
11.1
99
5.3.1/
5.4.3
5.4
5.4.3
63/67
65
67
5.3.2
64
1.8
8.4
29
87
Page 168
461
462
486
489
500
501
509
513
514
522
524
536
537
538
540
542
543
544
Markov sequences
Markov sequences
Binomial distribution
List/plot binomial distribution
Eg. 1 defining a binomial distribution
Eg. 2 Calculating probabilities
Basic statistical calculations
Calculate probabilities/ definite integral
Mean/ standard deviation
Normal pdf
Inverse normal
Eg. 1 defining a pdf
Eg. 2 calculating probabilities
Eg. 3 Infinity & pdf. (Define/ definite
integral/ graph)
Eg. 4 Measures of central tendancy &
spread
Rule for defining normal distribution
Normal distribution
Eg. 6 Mean & standard deviation. Find z
value.
8.4
8.4
12.1.2
12.1.2
12.1.2
12.1.1
1.7
5.4.3
12.2.1
12.2.2
12.2.3
12.2
12.2
87
87
109
109
109
105
27
67
115
117
118
115
115
12.2
115
12.2
12.2
12.2
115
115
115
12.2
115
Page 169
A.24 Pearson Longman Specialist Maths Dimensions 3 & 4
Text Page
11
12
12
12
13
14
14
14
25
27
32
54
55
58
61
61
65
67
68
79
95
102
103
104
111
113
129
140
141
143
144
144
144
158
159
162
163
185
186
Description
Graph (including asymptotes)
Derivative
Second derivative
Solve f ′( x) = 0
Graph
Derivative
Second derivative
Graph
Graphing relations
Graph - ellipse
Graph - hyprerbola
Basic trigonometric calculations (radians)
Basic trigonometric calculations
Basic trigonometric calculations (exact
value)
Trig expressions with restricted domain
Solve trig equations
Inverse trig calculations
Graph trig functions
Graph trig functions
Simplify complex expressions
De Moivre’s Theorem
Solving complex equations (quadratic)
Solving complex equations (cubic)
Solving complex equations
Graph – ellipse
Graph relations – hyperbola/circle
Derivative
Derivative of inverse circular functions
Derivative of inverse circular functions
Derivative of inverse circular functions
Derivative of inverse circular functions
Find equation of a tangent
Find equation of the normal
Second derivative/point of inflection
(stationary points) with graph
Second derivative/point of inflection
(stationary points) with graph
Solve f ′′( x) = 0 to find turning points
Sketch
Indefinite integrals
Indefinite integrals (& factor)
How
How do I
do I … …
Section Page
2.2
38
5.3
60
11.3
101
5.3
60
2.2
38
5.3
60
11.3
101
2.2
38
13
119
13
119
13
119
1.6
25
1.6
25
1.6
1.9
1.9/7.1
4.4
2.2
2.2
14
14
14
14
14
13
13
5.3
5.3
5.3
5.3
5.3
5.3.2
5.3.2
25
32
32/80
53
38
38
122
122
122
122
122
119
119
60
60
60
60
60
64
64
11.3
101
11.3
11.3
2.2
5.4.1
5.4.1
101
101
38
65
65
Page 170
187
188
190
194
200
208
228
232
248
260
270
272
273
305
309
310
311
352 – 354
445
Indefinite integrals
Indefinite integrals
Indefinite integrals
Indefinite integrals
Indefinite integrals (inverse trig functions)
Indefinite integrals (trig functions)
Indefinite integrals
Definite integrals
Area under curve
Areas bounded by two curves
Volumes of solids of revolutions
Regions bounded by two curves
Regions bounded by two curves
Differential equations
Definite integral
Definite integral
Solve equations
Direction fields
Parametric forms (graph)
5.4.1
5.4.1
5.4.1
5.4.1
5.4.1
5.4.1
5.4.1
5.4.2
5.4.3
11.1
11.4
11.1
11.1
11.5
5.4.2
5.4.2
7.1
11.5
16
65
65
65
65
65
65
65
66
67
99
102
99
99
103
66
66
80
103
126
Page 171