Calculating with a
CASIO ClassPad
First published in 2009.
Questions about this publication should be directed to [email protected]
Copyright © 2009.
StepsInLogic.
ISBN 978-0-646-51770-4
All rights reserved. Except under the conditions specified in the Copyright Act 1968 of Australia
and subsequent amendments, no part of this publication maybe reproduced, stored in a retrieval
system or be broadcast or transmitted in any form or by any means, electronic, mechanical,
photocopying recording or otherwise, without the prior written permission of the copyright
owners.
This publication makes reference to the CASIO ClassPad. This model description is a registered
trademark of CASIO COMPUTER CO., LTD.
CASIO® is a registered trademark of CASIO COMPUTER CO., LTD.
Contents
1. Out of the box
1.1
Straight out of the box
1.2
Not straight out of the box
1.3
Some first steps
1.4
Entry and editing using 2D
1.5
A little about Standard mode
1.6
Fractions and decimal approximations
1.7
A financial calculation
1.8
More about Standard mode
1.9
Checking thinking - expressions
1.10 Symbolic calculations
1.11 A trigonometric calculation
1.12 Basic Format
1.13 A first table of values and a graph
1.14 From function directly to graph
1.15 Checking thinking - equations
1.16 Solving equations
3
4
6
8
11
13
14
18
20
22
24
26
27
28
31
34
36
2. Working with data in Spreadsheet
2.1
From data to boxplot
2.2
From data to summary statistics
2.3
From data to scatter plot
2.4
Least squares line - plus
2.5
Residual plot
38
39
42
43
44
46
3. Keyboards, random numbers, histograms
3.1
Using the soft keyboards
3.2
Random numbers
3.3
Random numbers and the histogram
3.4
Summing two lists
3.5
Leaking bags – binomial distribution
3.6
Square root of a normal distribution
47
48
49
51
55
56
58
4. Working with graphs in Graph & Tab…
4.1
Settings in Graph Format
4.2
Square view – 1:1 aspect
4.3
Make a useable graph - manually
4.4
Make a useable graph – zoom auto
4.5
Working on a graph – G.SOLV
60
61
64
67
70
71
5. Formulae and equations
5.1
Working with a formula
5.2
Solving a cubic equation
5.3
Solving systems of linear equations
75
76
78
80
6. 2D palette, calculus calculations
83
7. Managing my ClassPad
7.1
Touch Panel Alignment
7.2
Naming your ClassPad
7.3
Contrast and Power Properties
7.4
Operating System update
7.5
eActivities and Add-in applications
7.6
Backing up your ClassPad
7.7
Optimizing your ClassPad
7.8
Resetting and initializing
7.9
Screen Capture
86
87
88
89
90
91
92
95
96
98
Index
2
104
1. Out of the box
In this chapter we assume you have just taken the ClassPad out of the
box and have not changed any of the out-of-the-box (aka factory)
settings. If your ClassPad is not out-of-the-box, see section 1.2.
3
1.1 Straight out of the box
When you first take your ClassPad from its box you will need to do a series of things:
1.
Insert the four AAA batteries.
2.
Turn the ClassPad over and see if it has turned on. If it has you will see the Touch Panel
alignment screen. Remove the stylus from the right hand side of the ClassPad and use it to
accurately touch (once), the centre of each of the four target crosses. Once touched, they
will grey-out.
3.
If the above screen does not appear, use a thin blunt object to gently press the P-button on
the back of the calculator. It may take a few seconds for the ClassPad to restart. Do as
instructed in 2.
4.
Now set the screen contrast. Repeatedly tap W or X to make it lighter or darker. Tap Set
when the contrast is as you desire.
5.
Now set the language in which you wish the menus to be displayed.
4
6.
Select the keyboard format you which to be displayed.
7.
Select the style of font you desire. We recommend you use the Bolder font.
8.
Finally, set the Power Save Mode and Auto Power Off settings. To achieve a long battery
life, set the Power Save Mode to 1 hour. Tap Set and the series of tasks is complete.
The ClassPad MENU should now be visible.
You are ready to start!
5
1.2 Not straight out of the box
If your ClassPad is not straight from the box, some of its settings may be different to the factory
(or default) settings. There may also be data saved on the ClassPad that may hinder your progress
if you are a first-time user of the ClassPad.
If you are a first-time user of the ClassPad, we suggest you reset your ClassPad before working
through this book. Note that resetting will erase information saved on the ClassPad by previous
users. If you do not wish to erase the information then do not carry out the steps shown below.
Alternatively, backup the information on the ClassPad first and then reset it. See Section 7 of this
book for details on how to backup your ClassPad’s saved information.
Do the following to reset the ClassPad.
Scroll the MENU to the bottom and launch the
application.
Y
Tap the Reset icon.
Select Variable/Program and tap Reset.
Note that any eActivities saved on the ClassPad will not be
deleted. They will not hamper your progress if you are a first-time
user.
6
Tap OK.
The ClassPad will return to the application MENU.
If the ClassPad does not seem to be responding well to your taps, use a thin blunt object to
gently press the P-button on the back of the ClassPad to restart it. It may take a few seconds for
the ClassPad to restart. Now follow the instructions given in the previous section.
You are ready to start!
7
1.3 Some first steps
Tap the
J
icon to launch the Main application.
Look at the bottom of the screen and make sure you can see the words Alg, Standard, Real
and Rad. If different words are visible, tap each word with the stylus until they reveal those
above.
An almost empty screen awaits you.
Notice that the cursor is flashing to the left of an empty box. This
signifies the calculator is ready for you to enter a calculation.
Let’s calculate 325 ÷ 31.
Enter 325/31
To have a calculation performed and the
result displayed, press the blue E key at
the bottom right corner of the calculator.
The result is shown on the right side of the screen. Not such a helpful
result I hear you thinking!
Note the word Standard at the bottom of the screen. Tap the
word Standard and note it changes to Decimal. Now all
answers will be displayed in decimal form.
Press E again. We now see the result of 10.48387097.
8
Let’s calculate 27435 × 324.
Enter 27435*324 but do
NOT press the EXE button.
Suppose you made an entry error and we wanted 123 not 324.
To delete characters in an input line,
use the blue backspace key.
Press it three times.
Now enter 123 and press the blue E key to
calculate and see the result.
Now calculate 256.12 – 18.28.
Enter 256. etc.
Press E to calculate and see the result.
The decimal 237.84 results.
To see the fractional form of this decimal, tap once on the output
and notice that the entire output is selected.
Now tap u. Now the fractional form is displayed.
9
Suppose we wish to multiple our previous result by 8500.
Press the * key. Look what happened. The calculator
automatically enters ans × .
Enter 8500.
Press E for the result.
Press E again and you will see that the previous operation
( × 8500 ) is applied to the previous answer (2021640) automatically.
Note that 1.718394E+10 means 1.718394 × 1010 . So in this case the
result is 17183940000.
Let’s calculate
32254 .
To enter a square root we must make the ClassPad’s soft-keyboards
visible. Press k and then tap the ) tab.
This reveals the easy-entry templates.
Tap 5 and then 32254.
E to see the result.
10
1.4 Entry and editing using 2D
This section follows on directly from the last section.
To clear the screen of previous working, open the Edit Menu
(by tapping the word Edit) and then tap Clear All
This acts like an eraser and does not clear anything that has
been saved on the ClassPad.
Tap OK and the screen will be cleared.
There are four main soft keyboards, mth, abc, cat and 2D.
Tap each tab in turn to see what the keyboards offer.
From the ) keyboard, tap V. Notice that there is two
entry ‘levels’ denoted with the empty boxes. Use the stylus to
tap the cursor into an empty input box to enter an input.
Alternatively, you can use the W
and X arrows on the mouse to
move the cursor into each of the
possible input positions.
Experiment with both methods.
Calculate the base 2 logarithm of 1024. (What power of 2 is
1024?)
11
Now calculate 12.4 3
And then, 3 1906.624 , which we can enter using the D
function of the ClassPad.
Any of the previous calculations can be edited and recalculated.
To edit a value, drag across it with the stylus to select it, and
then enter the value you desire.
Select 1024 and then enter 511, press E.
Note the new. The cursor is waiting in the lowest entry line
ready for the next calculation.
Now edit each input to achieve the content seen in the screen
to the right, but do not press EXE in between each edit. Note
the answers shown are not correct as we have not recalculated
(i.e. not pressed EXE).
To recalculate each input at once, tap in the first input line so
the cursor is flashing in that line.
Now press E and you will see that all inputs below the
position where the cursor was placed are recalculated. Now we
have correct answers.
12
Suppose we want to delete the second calculation line.
Select the input line by dragging across it with the stylus.
Then open the Edit menu (by tapping Edit) and then tap
Delete.
1.5 A little about Standard mode
Now choose Clear All from the Edit menu to clear all
previous calculations.
Then enter each of the calculations seen in the screen to the right.
Now tap the Decimal setting at the base of the screen to change
the calculation mode to Standard.
Now tap in the first input line so the cursor is flashing beside
20
and press E. Press k to close the soft keyboard.
Notice the different form of the answers. Each value is given in an
exact form as opposed to a decimal approximation.
When set in Standard mode, the ClassPad will try to display values in an exact form,
e.g. using surds, fractions, π , ln and other exact forms.
13
1.6 Fractions & decimal approximations
Fractions show the exact value of a quantity. For example, we know that
1
3
6
5
+
33 33
is exactly equal to
and that the decimal 0.333 (correct to 3 decimal places) is a decimal approximation for
1
.
3
If the application MENU is not visible, tap m from the grey-green toolbar just below the
screen.
Tap the J icon to launch the Main application.
(Alternatively you can launch the Main application from the grey-green toolbar).
Let’s calculate
6
5
+
on the ClassPad.
33 33
Choose Clear All from the Edit menu.
Be sure the ClassPad is set to Standard mode.
Use the fraction template, N, from the ) palette.
Note that the ClassPad automatically reduces fractions to their
lowest terms.
This might make the ClassPad a useful tool for checking our mental
processing.
To see the decimal approximation of the output, use the stylus to
select the output and then tap u.
14
3 2
Calculate, 1 × .
5 5
Using a mental process we find:
Now let’s try this on the ClassPad and check my result.
Oh dear, there seems to be a problem here!
A hint towards the problem can be seen by entering 1
pressing E.
The ClassPad thinks we have entered 1×
3
and
5
3
3
rather than the mixed number 1 .
5
5
3
3
The mixed number, 1 , is actually 1 + , and so when entering mixed numbers into the
5
5
ClassPad we must enter them in this less common form.
Start by entering ( then 1 +and then use N from
the ) palette. Enter the 3 and 5 and then ).
Then complete the entry.
The answer is now consistent with our mental approach.
15
Calculate
12
11
+
.
258415 574803
Maybe I will not try this one using a mental approach! I wonder if the ClassPad can
provide an exact value for this sum? Give it a try.
That is pretty neat! Maybe you should not trust it. Try using a mental approach to verify this is
correct.
Convert the improper fraction,
Using a mental approach:
57
, to a mixed number.
12
Let’s see how the ClassPad can be used to check my result.
57
and then use the stylus to select it by
12
dragging across the screen.
First enter the fraction
Open the Interactive menu by tapping the word Interactive
and then open the Transformation submenu and finally tap
propFac.
And so we agree!
When using commands from the Interactive menu, first enter the input you want the
ClassPad to work on, then select it using the stylus and then choose the command
from the Interactive menu.
16
My notes
17
1.7 A financial calculation
Suppose we wish to calculate the value of an investment of $8000, five years after investing it in
an account that pays interest of 3.4% p.a. compounded monthly. We can use the formula
r ⎞
⎛
A = P⎜ 1 +
⎟
⎝ 100 ⎠
n
.
Therefore we need to calculate 8000 ⎛⎜ 1 +
⎝
Launch the
J
0.034 ⎞
⎟
12 ⎠
60
.
application.
Note that:
1. you can either use the ( buttons on the hard keyboard or
those on the soft keyboard.
2. you can tap on the screen with the stylus and place the
cursor in the correct position for the next entry.
3. this result is not very helpful. A ‘big’ fraction results as we
are in Standard mode.
Because our calculations are associated with financial things, we will
change to Decimal mode. Tap Standard and it will change to
Decimal. In this mode, all results are given as decimal
approximations.
Now tap on the input line so the cursor is flashing in the input line
and press E to recalculate.
Better! But it would be nice if the result was rounded correct to 2
decimal places.
It is possible to set up the ClassPad to display the result correct to two decimal places; a good
idea for many financial calculations. User choice setting like this can be changed within a number
of formats within the ClassPad.
The formats can be found by tapping the settings icon on the grey-green toolbar. Tap s.
18
We need to use the Basic Format in this case. Tap Basic
Format.
Tap the C of the Number Format and choose
Fix 2.
Then tap Set.
Position the cursor in the input line and press E. This
recalculates the answer. The result is now given correct to two
decimal places.
Fix 2 rounds the result correct to 2 decimal places. It does not truncate the result. There are two
Normal settings, Normal 1 and Normal 2. One difference is that Normal 1 displays positive numbers
smaller than 0.01 in scientific notation whereas Normal 2 displays positive numbers smaller than
0.000000001 in scientific notation. For most purposes Normal 2 is the most useful display.
19
1.8 More about Standard mode
Launch the
J
application and set it to calculate in Standard mode.
If you are first-time user of the ClassPad surprising answers may result in the Main application
when set to calculate in Standard mode.
Enter
2
11
and press E.
The ClassPad is programmed to rationalise the denominator in
situations like this. That is, it is able to do the following:
2
2
11
22
=
×
=
11
11
11
11
Selecting the output and tapping u provides a decimal
approximation.
(In Basic Format, set the Number Format to Normal 2 if all the
decimal places are not displayed).
Find a simplified form of 112 + 3 7 .
We again get an exact form for this result.
The ClassPad is able to calculate as follows:
112 + 3 7 = 16 × 7 + 3 7 = 4 7 + 3 7 = 7 7 .
20
Find a simplified form of log 3 19683 .
So we now know that 3 9 = 19683
What do you think would result if we calculated log 3 19682 ?
Wow! I bet you did not expect that. Were you expecting a decimal?
The ClassPad is programmed to use a base change rule. If you do
not know what this is then perform an internet search for “change
of base”.
21
1.9 Checking thinking - expressions.
Suppose you had to calculate
this:
7 5
+ using a mental process. You might produce something like
10 6
The ClassPad has a way that you can check each line of your thinking using an application called
Verify.
Launch the
J
application and set it to calculate in Standard mode.
To launch the Verify application tap C at the end of the tool bar
and then tap W
Enter the first line of your working and press E.
Then enter the second line and press E. Watch closely!
Ah, a happy face, signalling that the first line of thinking is correct.
If you make an error you will get:
Then you can try again.
Now enter the rest of the thinking lines and see if they are correct.
22
Suppose we need to expand and simplify 3( x − 5) − 2(3 − x) .
We could proceed with a mental process as follows:
Verify can also check algebraic work as well as numerical work. So let’s check this thinking.
Opps! What is wrong with that?
Oh yes, that -2x should be a +2x I think.
Ah, that is better.
So the correct thinking lines are:
Verify is a lovely application. But, sometimes, like humans, it can get things wrong. It is not wrong
often, but is sometimes! So beware of this fact and think hard about what it is telling you.
23
1.10 Symbolic calculations
Suppose you had to find a simpler form for − x 2 − (10 − x) 2 − 2 x(10 − x) . We could proceed
using a mental process as follows:
Now let’s see if the ClassPad agrees with me. Instead of using Verify to check each line of
thinking, we will just use the ClassPad to calculate the final line and see if they match.
Launch the
J
application and set it to calculate in Standard mode.
The ClassPad can perform calculations on algebraic expressions.
Enter z x O 2 (now reposition the cursor by tapping
to the right of the power or press : on the mouse button) then
- and so on.
Press E once the entry is complete.
Notice that the ClassPad has only rearranged the order of terms. To
make it simplify this expression we must command it to do so.
Use the stylus to select the whole input by dragging across it.
Then open the Interactive menu and the
Transformation sub-menu and then tap simplify.
Mmm, either it is wrong or there is an error in the working above.
In this case, I have made an error.
Can you find and correct the error in the working above?
24
Suppose we need to factorise x 4 + 5 x 2 + 4 .
Enter the complete expression.
Select it, then open the Interactive menu, then the
Transformation sub-menu and then tap factor.
So this expression is just like the quadratic x 2 + 5 x + 4 but x is
replaced by x 2 .
a b
+ .
b a
We need more variables than the x, y and z that are on the keyboard.
Note the VAR button at the bottom of the 2D keyboard. Tap it and it reveals a set of
Suppose we need a simplified form of
mathematical variables to use. To return to the nice-entry palette tap I.
a b
+ .
b a
Then open the Interactive menu, then the
Transformation sub-menu and then tap combine.
Enter and select
25
1.11 A trigonometric calculation
Suppose you are required to find the length of the currently unknown side in the diagram below.
We could proceed as follows:
We can calculate a simplified form for x in the
M
application.
Trigonometric calculations require us to think about what angle
unit the calculator is set to work in.
Look at the bottom of the screen. Mine is currently set to use
Radians. Tap Rad and it will change to Degree.
To enter the calculation:
k ) N 5 (reposition cursor) 9 r cos
30 q.
Press E.
Select the output and use u to see a decimal approximation.
Note that using the small degree symbol (q) at the end of the 30 ensures the ClassPad will calculate the
result using the degree as the angle unit, regardless of the setting at the bottom of the screen.
26
1.12 Basic Format
There are many settings that the user of a ClassPad can change as they desire. Such things are
arranged in formats that can be accessed by tapping the s icon on the grey-green toolbar when
any application is running. Launch the
M
application and then tap s.
In this section we describe the setting in the Basic Format.
Tap Basic Format.
Current Folder
You can save information in the ClassPad’s memory in folders.
The folder called ‘main’ is a factory made folder. Whatever folder
is current is where things like, functions and the like are stored.
Number Format
Determines the format of a number when displayed as the result
of a calculation. E.g. Fix 2 will round all results correct to 2
decimal places. Normal 2 is the recommended setting for most
applications.
Angle (Deg/Rad/Grad)
Sets the angle unit to be used in calculations. This can be set by
tapping the appropriate word at the base of the Main application
screen.
Complex Format (Cplx/Real)
Sets the ClassPad to be able to work with real numbers only or real
and complex. This can be set by tapping the appropriate word at
the base of the Main application screen.
Decimal Calculation (Decimal/Standard)
Determines whether numerical values will be displayed in decimal
format or ‘exact’ (Standard) format. This can be set by tapping the
appropriate word at the base of the Main application screen.
Assistant (Assist/Alg)
Determines if the ClassPad automatically simplifies answers or
requires the user to add commands to force simplification. This
can be set by tapping the appropriate word at the base of the Main
application screen.
Descending Order
Determines the format of display for polynomial functions. Either
descending or ascending order of powers.
Variable is Real
When checked, the ClassPad treats the values of a and b in a+bi as
real variables. Check this if working with Complex Numbers.
27
1.13 A first table of values and a graph
y = x 2 − 9 is a quadratic function. What does the graph of y = x 2 − 9 look like? We will begin
as follows, calculating each value mentally and then plotting.
Now let’s see if we can replicate this table of values and graph on the ClassPad.
Tap m on the grey-green toolbar and launch the
g
application.
In the y1 location enter x ^ 2 - 9.
Press E.
Pressing E places a tick in the box. This means that this function
is active and ready to be used.
28
To make a table of values, tap #.
The table of values appears in a window in the bottom half of the
screen. Note that the table window is active. It has a thicker window
edging indicating it is active. Therefore the tools and menus at the
top of the screen are associated with the table and not the entry
area.
You can tap any of the values in the table and it is displayed in the
bottom output bar. Note the table starts at 1 (x) and ends at 5.
To change the start, end and step values of the table, tap 8.
Change the start to -5 and then tap OK.
To maximise the active window, tap r. It is located in the centre
of the grey-green toolbar.
29
Now to make a graph similar to that we made by hand, tap !.
Now tap r to maximise the active window.
Not too bad, but the end values of the y axis are not allowing us to
see all of the points we generated.
To change the endpoints of a graph tap 6. Change ymin to -10
and ymax to 16. Press E after each entry. Then tap OK.
We can now trace the along the points of the graph.
Open the Analysis menu and tap Trace.
Use the W and X keys of the mouse
button to move along the points.
The cursor can be seen on the screen
and the coordinates of its position are displayed at the base of the
screen.
30
1.14 From function directly to graph
It is possible to draw a graph of a function without first having made a table of values on the
screen. There is a number of ways to do this. In this section we show to use the Main application
in conjunction with the Graphing application.
We will explore the graphs of the functions y = x 2 − 9 and y = − x 2 − 2
Launch the
M
application.
Enter both functions, pressing E after each complete entry.
To display a graphing area in the bottom half of the screen,
tap $.
To produce a graph, select one of the functions and then drag it
(across the glass) and drop it into the graphing window.
Repeat the process for the second function. You will see the
function right at the bottom of the screen.
Note the graphing window is active. Tap r to maximise the
graphing window.
31
An efficient way to change the section of the Cartesian plane being
viewed is to use the Pan tool. Tap n to activate the Pan tool.
Note the word Pan at the base of the screen. Now place the stylus
on the screen and drag upwards.
The graph view can also be changed using the W, X, S and T
keys on the mouse button.
Note that ‘continuous’ graphs are drawn in this case. The calculator
has actually made a table of lots of values in its ‘head’ - and then
draws all the points. However they are so close together (and there
are so few pixels on the screen) that the illusion of continuity is
achieved.
We can also Zoom in on any features that we might want a closer
look at using the Box zoom option. When activated, the word Box
is seen at the bottom of the screen.
Use the stylus to drag a rectangle around the region you want to
zoom in on and then take the stylus off the screen.
From the Zoom menu, Previous will return the view to the
immediately previous setting.
32
To locate and calculate the coordinates of the intersection points.
Open the Analysis menu, then the G-Solve sub-menu and
tap Intersect.
Use the W, and X keys on the mouse button to move between the
intersection points.
Note that the decimal approximations for the coordinates are
shown at the bottom of the screen.
Tap Q (on the grey-green toolbar) to exit from the Intersect
mode.
Note that if you place the stylus on the Cartesian plane, the
coordinates of the stylus tip will be displayed at the base of the
screen. You can gain a ‘rough’ idea of key values using this method.
Below we have graphed the two functions so that neither of the intersection points are visible on
the screen (use the Pan tool). Note what happens when we try to calculate the intersection points.
Key features of graphs, like maximum values, intersection points and so on will not be calculated by the
ClassPad in a graph window unless they are visible on the screen.
33
1.15 Checking thinking - equations
In the previous section we found the intersection points of the graphs of the functions
y = x 2 − 9 and y = − x 2 − 2 . Note that we found decimal approximations for the points of
intersection. We could have approached this by solving the equation x 2 − 9 = − x 2 − 2 as follows.
This method finds all solutions in exact form.
In doing work like this, you might make the odd mistake here and there. Often, such errors are
hard to notice, and knowing the final answer is wrong (thanks to the back of the book) is often
of little help. Algy 2 is an application that runs on the ClassPad that can check each step of your
working when you are solving equations.
Algy 2 does not come loaded on your ClassPad. You can download a free copy of the application
from www.stepsinlogic.com. An information sheet in your ClassPad box gives you all the details
you need. Once you have installed Algy 2 onto your ClassPad and entered your registration code,
try the following.
Launch the Algy 2 application.
Enter each line of thinking as shown opposite. Press E
between each line.
To check the working, open the Check menu and tap Vs
Previous.
Algy 2 then checks that each line follows correctly from the
previous. The
symbol indicates that this line does follow
correctly from the previous. All correct in this case.
34
Suppose we had to solve the equation 7 x + 5 = 9 x − 3 . We could proceed as follows.
So how did we go? Let’s check out our thinking with Algy 2. Tapping the
previous work so we can enter new thinking. Now check Vs Previous.
rules off the
This result tells us that the second line correctly follows from the first, but the third does not
follow from the second. Hence there must be an error in that line of thinking. After this point
though, each line follows correctly from the previous, albeit giving us the wrong answer.
Rethinking and editing gives us a correct result.
Algy 2 can be used to check the flow of thinking related to most of the numerical and algebraic
work that you will confront at school. You can work with expressions as well as equations. Three
more examples are given below. We have used the Duplicate Zone function (in the Edit menu)
so the flawed attempt remains visible.
Note, like all technology, sometimes Algy 2 makes errors, but not too often!
Expand and simplify
7x 1
Solve 2 x = 625
Simplify
−
2
( x − 2 ) + 5( 2 + x )
5 4x
35
1.16 Solving equations
In the previous section we saw how you can check the steps in your thinking while solving an
equation. The ClassPad can find solutions to equations in a single step, thus giving us a quick way
to check our answers.
Launch the
M
application.
The functions y = x 2 − 9 and y = − x 2 − 2 intersect when x 2 − 9 = − x 2 − 2 . We can solve this
as follows.
Enter the equation to be solved and then use the stylus to select the
equation by dragging across it with the stylus.
Open the Interactive menu, then the Equation sub-menu and then tap solve. Since we
are solving for x leave variable as x. Tap OK.
Note that since the ClassPad is set to calculate in Standard mode, the exact values of all possible
solutions are given.
Selecting the input before tapping on a command in the Interactive menu ensures that it is automatically
inserted into the input line of the wizard boxes that appear when using the Interactive menu. This
means you can enter complex looking inputs using the 2D template and then have them appear in the
wizard box by simply selecting them.
36
My notes
37
2. Working with
data in
Spreadsheet
38
2.1 From data to boxplot
Ali and Ora compete in a challenge to see who can best estimate one quarter of the length of a
strip of paper.
They are each presented with 16 paper strips 210 mm long. Each strip is held in front of them,
one at a time, and they must cut the strip with scissors. They are not allowed to measure or take a
lot of time. Rapid fire cutting and estimating is required.
52.5 mm is exactly one quarter of 210 mm. Not surprisingly, the lengths Ali and Ora cut were not
all this length, they varied.
52.5 mm was subtracted from each length cut by Ali and Ora to determine the error in each
estimate. The data is shown below.
Ali’s
errors
(mm)
Ora’s
errors
(mm)
3
4
2
11
9
9
11
11
8
5
8
9
8
16
7
9
-2
15
11
7
2
9
5
9
15
6
-3
10
-11
-1
6
7
Who do you think is the better estimator of one quarter, based on these data?
To help us decide we will draw some plots and calculate some summary statistics.
Tap m and then launch the
R
application. We start by entering the data.
If data already exists in the Spreadsheet, open the File menu and
tap New and then tap OK.
Press k and then tap 0 to reveal the text keyboard. Tap
the names in cells A1 and B1 respectively and then enter the data.
Press E between each entry.
39
Once the data is entered, we should save the spreadsheet.
From the File menu choose Save.
Tap { to make a new folder on the ClassPad in which you will
save this file.
Name the new folder datasps.
Select the folder datasps. This tells the ClassPad that you want to
save the file into this folder.
In the filename bar, enter the name aliora.
Tap Save to complete the process.
Now make a graphical display to compare the data. We will draw two boxplots, side by side.
Select the two columns of data by dragging the stylus across the
headings for the columns, A and B.
Then tap the last C in the tool bar. This is the chart wizard.
Lastly, tap n.
Tap to select any part of the either boxplot. The column
represented, the statistics name and its value will be displayed at the
bottom of the screen.
40
We can now display and save the five number summary for each variable.
Make sure the boxplot window is active (tap anywhere in the
window) and the boxplot representing Ora’s data is selected.
Now open the Edit menu and choose Copy. This copies all of
the statistics associated with the selected plot.
Tap in cell E1 of the spreadsheet and then from the Edit menu
choose Paste. The 5-number summary for the data set will be
pasted into the spreadsheet.
Repeat for Ali’s data, start the paste in cell C1.
Be sure to save your progress. From the File menu tap Save. Note that the file is already
selected and the file name is entered in the filename bar. Tap Save. You will be asked if you
wish to Overwrite, tap OK.
Write down the 5-number summary for each person’s data.
Do these values help you to decide who is the better estimator of one quarter of the length of a
210 mm paper strip?
41
2.2 From data to summary statistics
In this section we assume you have entered and saved the data from Ali and Ora’s challenge in a
spreadsheet called aliora as shown in section 2.1. If you have not, then please go to section 2.1.
We will now see how to calculate a complete set of summary statistics for Ali’s data.
Select all the data in column A by tapping on the A at the head of
this column.
From the Calc menu tap One-Variable. The summary
statistics are displayed in the lower window.
To paste the summary statistics into the spreadsheet, tap Output.
Choose the labels to be pasted starting at C7 and the Results at D7.
Tap Paste.
Highlighted above are the sample mean ( x ), sample standard deviation (s) and the 5-number
summary.
Repeat this for Ora’s data. Start the paste at E7 and F7 respectively.
Save your progress.
42
2.3 From data to scatter plot
Suppose the following data result from a process where the value of y is partially determined by
the value of x. Therefore, we might assume we could determine a rule for calculating y if given x.
x
1
2
3
4
5
6
7
8
y
12
22.4
26.1
35
46.1
55
59
68
Can you determine a rule from looking at the data? If you think about it you, I bet you can.
Let’s now proceed by making a scatter plot of this data and seeing what it looks like.
Tap m and then launch the
R
application.
Choose New from the File menu. Now enter the data from the table above.
Select both columns of data and then from the chart wizard (C)
tap X. The data certainly seems to be displaying linear features.
To calculate the least squares line of best fit, tap d.
To see the equation of the least squares line of best fit, tap on the
line. The equation will be displayed at the bottom of the screen.
Choose Copy from the edit menu. Now Paste the equation into
M (or anywhere) for further use if required.
43
2.4 Least squares line - plus
In this section we assume you have completed section 2.3. If you have not, go back to section 2.3.
The ClassPad can also calculate other statistics related to the least squares line.
With the graph window active, open the Calc menu and tap the
DispStat option. Be sure a tick appears in the box.
Now close the graph window. To do this, tap in the window to
make it active and then tap the cross in the top right-hand corner
of the screen.
Make the scatter plot (X) again.
Calculate the least squares line (d).
Note that this time, a more complete summary of the least squares
line is given, including the correlation coefficient.
We can paste these statistics into the spreadsheet. Tap Output.
Then tap the Residual checkbox so they are pasted as well. Then
tap Paste.
44
Now tap Close. Also, close the graph window and you will see
the summary statistics and the residuals have been pasted in for
reference and further use.
Note the r 2 value is close to one, suggesting that the least squares line may be a good predictor
for this situation.
However, a line of best fit with a high r 2 value does not necessarily mean is it a good model for
the data. To be a good model, we would want the data to be randomly scattered above and below
the line; no patterns. And we would not want the data points to be too far from the line
(vertically).
To see how these data shape up in this sense, we could look more closely at the residuals by
making a residual plot. We do this in the next section.
45
2.5 Residual plot
In this section we assume you have entered the data from section 2.3 and worked through the
processes illustrated in section 2.3 and 2.4. If you have not, go back to sections 2.3 and 2.4.
Let’s now make a residual plot.
Select all of Column E.
Now from the Edit menu and the Insert sub-menu tap
Columns. An empty column is inserted.
Now copy and paste the data in column A (the x data) into column
E. Then select all of the data in columns E and F (the x data and the
residuals).
Now tap X from the chart wizard menu.
And there it is; a residual plot to consider.
46
3. Keyboards,
random numbers,
histograms
k
47
3.1 Using the soft keyboards.
Launch the
M
application.
Press k.
This reveals the mth keyboard, one of the many variations available.
Tap 0.
This provides access to a qwerty keyboard, useful for entering text.
The lower tabs provide access to further keyboards.
Tap MATH.
This provides access to a range of mathematical symbols.
By tapping the upper tabs and lower buttons you can access a vast
range of symbols and commands.
Explore and see if you can find the commands, templates and
symbols shown below.
48
3.2 Random numbers
Launch the
M
application.
Press k and then 9.
Tap CALC.
This keyboard provides access to a range of computational
tools.
This includes the factorial command, the permutation
command and the combination command
Calculate
a) 12!
b) P26
30
c) C12
Tap 1 2 ! E
Tap nPr 6 , 2 E.
Tap nCr 3 0 , 1 2 E
Tap (.
The catalogue keyboard provides access to every command
that can be entered into the ClassPad. They can be searched
by scrolling down, or by searching alphabetically. We will
search alphabetically to find Random Number commands.
Tap : and then tap on R.
49
Suppose we wish to simulate the rolling of a fair die.
To do this, we will generate pseudo-random integers between 1 and 6 inclusive.
Note that the answers you will receive will be different to ours shown below, due to randomness!
Tap on rand( and then tap INPUT.
Press 1 , 6 and then press E.
Pressing E repeatedly recalculates the previous calculation
and so we can roll the die as many times as we like!
Note that if you know the exact syntax of the command you require,
you can type it in using the qwerty keyboard, rather than using the cat
keyboard.
We can also generate a list of pseudo-random numbers – enabling us to simulating the roll of
many dice at once.
Tap on randList( and tap INPUT.
Press 50 , 1 , 6.and then E.
50 ‘dice’ are ‘rolled’.
Note the small black arrow at the right end of the list. Tap
this arrow to have a look at the outcomes.
Let’s now simulate the production of 20 cans of soft drink. Well, the volumes in the cans at least.
Suppose the volumes are distributed normally with standard deviation 3 ml and mean 380 ml.
Tap on randNorm( and then tap INPUT.
Press 3 , 380 , 20.
and then press E.
20 ‘cans of soft drink’ are ‘filled’.
It would be nice to be able to analyse data like this, maybe
make a histogram or the like of the data. We do this in the
next section.
50
3.3 Random numbers and the histogram
This section follows from the previous so we assume you have completed section 3.2.
Notice that the number generated in the last calculation below has 7 digits after the decimal.
For our purposes (soft drink can volumes), this is a tad extreme!
Tap s and then tap Basic Format.
Change the Number Format setting to Fix 1.
This means that the values produced will only have 1 digit after the
decimal place.
Tap Set to confirm this change and to leave this menu.
Tap back on the randNorm input line and then tap E.
The command is re-calculated (with a different random output).
Note that this time the values are now rounded correct
to 1 decimal place.
We can store and analyse data like that calculated above in the
Tap
m
and launch the
I
I
application.
application.
Let’s ‘roll’, store and analyse 120 die rolls.
Choose Clear All from the Edit menu if data already exist in
the lists, or you cannot see the names list1, list2 and list3.
51
Tap in the Cal row of list1.
We need List 1 to be filled with 120 ‘dice rolls’.
Open the ( keyboard.
Locate and tap on randList( and tap INPUT.
Press 120 , 1 , 6.
and then press E.
Close the keyboard, tap on one of the outcomes and then use the
u and C on the mouse key to have a look at the values in the
list.
Many people believe a six is hardest to roll on a dice. Is it really? How many sixes did you roll?
To find out we will make a histogram of our roll data.
Tap G (or open the SetGraph menu and then tap
Setting…)
We will now set the ClassPad to draw a histogram.
52
For StatGraph 1 make sure that it is On (tap if necessary).
Tap the # of Type: drop down menu and select
Histogram.
This should automatically set the XList as list1 and
the Freq(uency) as 1 – just as we require.
You may want to check that all other StatGraphs are turned off, if
you have previously turned them on.
Tap Set when the settings are as required.
Tap y to draw the graph you just set up.
The ClassPad will ask for the starting value of the first ‘bin’ and
then the ‘bin width’. Set each to 1 since our data are integers from 1
to 6.
Tap OK to draw the Histogram.
But how do we know the number of rolls that were a six?
Tap Analysis:Trace. Use the 2 and 3 keys on the
mouse button to navigate the histogram.
The frequencies for each bin are displayed.
So you can see that we got 24 sixes. You will have ‘rolled’ a
different number though as your pseudo-random numbers will be
different to mine; almost certainly!
53
So do you think a six is the hardest number to roll on a dice?
Now fill List 2 with another 120 ‘dice rolls’. Make a histogram and see if the results are different.
Remember to set up StatGraph 2, not StatGraph1, keep that for List 1.
Mmm, I got 22 this time, not the most frequent.
54
3.4 Summing two lists.
This section assumes that you have carried out the task in section 3.4.
If we rolled two dice 120 times and summed the faces of each roll, what would be the most
frequent sum returned? If you think about it I bet you can work it out.
Let’s see if practice matches the theory.
Launch the
I
application.
Tap into the Cal row of list 3.
Enter the calculation list1+list2.
list1 can be obtained from the cat keyboard.
(or can be typed in using the qwerty keyboard)
Tap E to see the resulting sums.
Open the Set StatGraph (G) window. Set up
StatGraph3 to be a Histogram of the data in list3.
Well, at least in my case, it looks like the practice matches the
theory! Twenty one of my rolls ended in a sum of seven, the
most of any outcome. How did yours turn out?
55
3.5 Leaking bags – binomial distribution
It is claimed that 1 in every 10 plastic bags made by a company are not water tight – they leak.
The bags are sold in packets of 50 bags.
If I was to buy 100 packets, how many ‘leakers’ might I expect in each of my 100 packets?
My guess would be around 5 in each packet. Would yours?
If we assume that the packaging process is a random-like process, then we could use the binomial
distribution to help us think about what might happen.
Let’s simulate the process. We can do this in the
Tap m and launch the
I
I
application.
application.
Find an empty list. We will use List 4.
Tap in the Cal row of list4.
Press k.
Tap ( and then tap 3 and R.
Tap randBin( and then tap INPUT.
Remember bags are sold in packets of 50 (n=50), 1 in 10 are
said to leak (p=0.1) and I decided to buy 100 bags.
So complete the entry with
50 , 0.1 , 100.
E to fill the list.
(be patient it might take a few seconds).
56
Tap G and set up StatGraph 4 to draw a histogram
of the data in list4.
Tap Set.
Finish off by setting the lowest bins start value (0) and the bin width (1).
Your 100 packets will of course be different to ours. But the general shape should look similar.
Note we have one quite ‘bad’ packet with 13 leakers in it! We will send that one back.
57
3.6 Square root of a normal distribution.
If you were to randomly sample 100 data points from a variable that was normally distributed and
then square root each value, what would the distribution of the 100 new values look like?
If you thought about it, I bet you might be able to work it out.
This time, let’s just use the calculator to do this, see what it looks like, and then try to reason why.
We can do this in the
I
Tap m and launch the
application.
I
application.
Open the Edit menu and tap Clear All to clear any
data in the lists.
Press k.
Tap in the Cal row of list1.
Start by entering the square root sign (s).
Tap (.
Tap on the 3 and then on R.
58
Tap randNorm( and then tap INPUT.
We are going to use a normal distribution with standard deviation 20, mean 60 and we will
sample 100 values.
So complete the entry with
20 , 60 , 100
E to fill the list, be patient it might take a few seconds.
Now draw a histogram of the data in List 1.
We see that it is skewed in shape. Can you explain why? Think about what happens when you
square root numbers and what shape a normal distribution is to start with.
59
4. Working with
graphs in
Graph & Tab…
60
4.1 Settings in Graph Format
Launch the
g
application.
Tap s and then tap Graph Format.
There are some critical things you have to set correctly if you are
to have success in producing graphs.
Axes can be set to either Number, meaning that the minimum
and maximum tick marks on the axes are labelled with their
numerical values, On, meaning that the axes are shown without
this labelling, or Off, meaning that the axes are not shown. The
graph of y = 0.2( x + 1)( x − 3)( x − 4) is shown below with
settings Axes:Number and Axes:On.
The recommended setting is Number.
Graph Function can be ticked, which means a function’s
equation is displayed when it is graphed (see below).
It is recommended that this option is ticked.
61
Coordinates can be ticked, which means that while the cursor
is active on a graph, like when tracing or locating points of
intersection (see below), the coordinates of the cursor’s location
are displayed.
It is recommended that this option is ticked.
Derivative/Slope can be ticked, which means that when a
graph is being traced (see below) the derivative of the
function at that point is displayed.
It is recommended that this option is unticked for most
applications.
G-Controller can be ticked, which means that tappable
arrows will appear on graphs, allowing the View Window to be
‘jogged’ left, right, up or down by tapping. They replicate the
behaviour of the arrows on the mouse button.
It is recommended that this option is ticked.
The factory settings for the Graph & Table application are shown right.
These can be restored by tapping Default.
62
My notes
63
4.2 Square view – 1:1 aspect
Launch the g application.
We will begin by drawing the graph of a simple function so we can illustrate certain aspects of
drawing graphs in digital environments (like this ClassPad). In particular, the way graphs appear
depending on how you set the axes.
If you have a function (or more than one function) already
entered, like the screen opposite, tap in the line containing an
unwanted function and then press c
Enter the function
y = x + 1.
The cursor flashing (in y1 for example) indicates the location that
is awaiting your entry of a function.
To enter the variable x for graphing and similar purposes
we use either the x key or the x on the k
Enter:
x+1 and then E to ‘lock it in’.
Note that the box to the left of y1 is ticked, telling us that this
function is active (or selected).
You can select or deselect functions by tapping this box
(just check for the tick!)
Before we draw the graph, set the endpoints of the axes on which the graph will be drawn.
Look in the icon toolbar. You will see 6 , the View Window
icon. Tap it.
Tap Default to set the endpoints of the axes to those set by the
factory.
Study this set of numbers, they may seem a little strange.
They are set this way because the ClassPad uses about half of its
screen to draw a graph, allocating 155 pixels horizontally and 77
pixels vertically.
Using this setup will ensure that 1 unit in the x direction is the
same physical distance as 1 unit in the y direction. Therefore a
graph with a slope of 1, will look like it has a slope of 1. Such a set
up is said to be ‘square’.
Tap OK to leave this screen.
64
Tap $ to draw the graph of the selected function.
Note it makes a 45 degree angle with the x-axis thanks to the
‘square’ View Window settings.
With the graph window active you will see an Analysis menu.
Open it, and then tap Trace.
Use the 2 and 3 on the mouse or on the screen
to travel along the graph.
Note that the trace steps are ‘nice’, 0.1 steps in the x direction.
This is due to the axes endpoints selected as part of the Default
set up.
Tap the Zoom menu and then tap Quick Standard.
This will quickly change the View Window to one of the many
that are pre-set in the ClassPad.
Note that on both axes, the values range from –10 to 10. Given
that the graph area is a rectangle, this means the graph will not be
‘square’.
You can clearly see that the angle this graph makes with the x axis
is less than 45 degrees, even though it has a slope of 1.
Also notice that the trace steps are not at all ‘nice’. This is because
the number of pixels on the screen does not match nicely to the
endpoints chosen.
Tap on 6 to see the View Window menu.
The dot value is in fact the value of the trace step, from one pixel
to the next.
You can change this value, but if you do, the xmax value will
change accordingly as the number of pixels on the screen is fixed.
65
You can see opposite we have changed the dot value to 0.1 and
the xmax value has automatically changed to 5.4. This gives 155
steps (pixels) of 0.1 across the screen.
66
4.3 Make a useable graph - manually
To make a useful graph of a function on paper, or a calculator, you need to focus on the set of x
values that are interesting to study (the domain) and the minimum and maximum y values for
that domain.
Sometimes you will be told what domain to study. Other times you will need to think about it for
yourself.
We will study the function y = x 5 ×
exponential function.
1
2x
, the product of a polynomial function and an
Before starting on the calculator, we should think a little about the function. After all, a graph is
just a picture of lots of y values for a given x. This thinking may also help us to explain the shape
later on.
Launch the
g
application.
Tap on the box to the left of y1 to remove the tick (deselect it).
Enter the function above as y2 and press E.
What we tell you to do next is most likely what NOT to do, but many people probably try it.
Tap $ to graph the function and hope – without any consideration of the View Window
settings.
67
Well, we can see something – but it is hardly helpful, particularly
given the thinking above.
Let’s try something else.
Remember, we think this graph will rise and fall, but exactly how high does it rise before it falls?
One way to find out would be to make a table of values for this function.
Tap on 8 to see the Table Input.
Set the Start, End and Step as shown above.
Choosing the start and end can often require a little bit of trial and
error. But from our previous thinking 20 should be enough.
Tap OK leave the Table Input screen and then tap # to make the table.
Tap in the list of y values so you can see the values in full.
(Set Number Format to Normal 2 if you are not seeing the numbers as shown below).
So from looking at our table it seems the function rises as high as about 131. We cannot be sure
of the value of x for which the function is a maximum, but we can say it seems to be between 6
and 8. This gives us a good idea of the values we could set the axes endpoints too, to produce a
useful graph. Note that for negative x, y is very negative.
Tap 6 to open the View Window menu.
Set the values to those seen opposite (except the dot).
Note we have not worried too much at this point about
negative x region as the y values get very small very quickly.
Tap OK , tap back into the Graph Editor window (to make it
active) and then tap $ to draw the graph.
68
Not bad, but still a lot of wasted space. It would be good to
see more of the positive domain.
Tap the 3 a few times to fine tune the axes.
69
4.4 Make a useable graph – zoom auto
This section follows on direct from section 4.3. If you have not studied section 4.3, do so before
starting this section.
This method offers an alternative to that seen in section 4.3 when drawing a useable graph.
Suppose we have done the prior thinking we did earlier, but had not made the table of values.
We can focus our attention on the positive domain to start with and set the xmin and xmax to
a fairly large domain, say between 0 and 20.
Open the View Window settings by tapping 6.
Tap Default.
Set the xmin and xmax to 0 and 20 respectively.
Do not worry about the y axes endpoints.
Tap OK and then tap $ to draw the graph.
Hardly impressive! But do not panic.
With the Graph window active you will see the Zoom menu.
Tap on it, and then tap Auto.
That’s better!
The Zoom Auto process does not change the domain you set. It
simply searches for the maximum and minimum values of y for
the domain you set and adjusts the ymin and ymax accordingly.
Tap 6 and change xmin to –5 .
Tap OK
From the Zoom menu, tap Auto.
Oh dear, that is not so good. You should think hard about the
domain you are using before trying Zoom Auto.
Note that a Previous option exists in the Zoom menu, to take
you back to the previous View Window setting.
70
4.5 Working on a graph – G–Solve
Here we continue to work with the function from the previous section.
What is the maximum value of the function y = x 5 ×
1
?
2x
To help answer this question, first produce a useable graph of this function.
Open the Analysis menu and then the G-Solve submenu and tap Max to calculate the maximum value.
So we see the maximum value is 131.6
when x = 7.2 (values correct to 1 decimal place).
If y = x 5 ×
1
, find x if y =100.
2x
From the Analysis:G-Solve menu choose x-Cal.
Enter the y -value of 100.
Tap OK to find the value of x .
So if y = 100, x = 5.1 (correct to 1 decimal place).
71
5
Find a decimal approximation for
∫x
2
5
×
1
dx .
2x
Tap 6
Set the View Window as shown opposite.
Tap OK
Tap $ to draw the graph.
From the Analysis:G-Solve menu choose
∫ dx .
Press 2 for the lower limit, note the popup
Appears.
Enter 5 as the upper limit and tap OK.
5
And so
∫x
2
Find the equation of the tangent to y = x 5 ×
5
×
1
dx = 145.9 (correct to 1 decimal place).
2x
1
at x=7.
2x
With the graph drawn, open the Analysis menu and
then the Sketch sub-menu and Tangent.
With flashing cursor and co-ordinates showing, the ClassPad
awaits the location of the desired tangent………
72
With cursor still flashing, press 8. An entry box appears.
Now tap OK.
So the equation is y = −8.725 x + 197.8
(at least approximately).
If you wish to clear a previously sketched object (like this
tangent or a shaded area), tap Analysis: Sketch and
then Cls.
If y = x 5 ×
1
2
x
find the value of
dy
if x = 5 .
dx
Tap s and then tap Graph Format.
Tap on the box to the left of Derivative/Slope to
tick/select this option.
Tap Set.
With this option selected, the value of the derivative of the
function graphed will be shown, whenever the co-ordinates
of a point on the graph are shown, like when we are tracing.
With the graph drawn and the graph window active, open the
Analysis menu and tap Trace. To jump to x = 5 ,
simply type 5.
Tap OK to calculate the value.
So
dy
= 30 when x = 5 (to the nearest whole number).
dx
73
My notes
74
5. Formulae and
equations
75
5.1 Working with a formula
1
The volume of a cone can be calculated using the formula V = πr 2 h .
3
Calculate the base radius of a cone with volume 200 cubic cm and height 30 cm. We could
proceed with a mental approach as follows:
Alternatively, the
N
application is able to efficiently handle calculations associated with
many formulae. Launch the
N
application
An empty working box awaits an input.
Enter the formula.
Make use of the ) and VAR keyboards.
Press E to finish and you will see the variables are laid out
under the equation.
76
Enter the value of each variable.
The Lower and Upper values are the range of values over
which the calculator will search for a solution.
In this case set Lower to 0.
Select the variable that you want to solve for by tapping on
the radio button.
Tap 1 to find calculate the value of r.
We see the same answer as we achieved using the mental
approach.
When using the N application, the result from these calculations will be displayed as a decimal
approximation. This application cannot produce exact values.
77
5.2 Solving a cubic equation
Find the values of x for which 6 x 3 + 7 x 2 + 12 x − 5 = 0 .
It is a good idea to first graph the function y = 6 x 3 + 7 x 2 + 12 x − 5 and note where it cuts the x
axis.
Here it is using the default View-Window settings and then zoom
AUTO.
All cubics have at least one real solution.
Can we confirm in our mind what the graph shows? Some thought tells us that for large positive
x, the function will produce large positive values and for ‘large’ negative x, it will produce ‘large’
negative values. So it seems this cubic has only one real solution (root) and two complex roots.
Let’s find them.
Launch the
J
application.
Make sure this ClassPad is set to calculate in Standard
mode.
Enter the equation and select it by dragging across it with the
stylus.
Open the Interactive menu, then the
Equation/Inequality sub-menu then tap solve.
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The solve wizard appears and offers the opportunity to
Solve (using a CAS algorithm) or Solve numerically.
Choose the Solve option.
If possible, this option will give you all possible solutions, in
exact form (if the ClassPad is set to Standard).
Tap OK.
Note the solution is given in exact form as the ClassPad is in
Standard mode.
But what about the complex roots?
First set the ClassPad to operate in Complex mode.
Tap the word Real on the status bar and you will see it
changes to Cplx.
The ClassPad is now ready to solve for the complex roots.
Tap E to display the solutions. (This will re-calculate the
last entry.)
Note that now we get both the real and complex roots and
each are shown in exact form.
Note that the answers disappear off the screen. Tap the small
black scroll arrow to display the remaining part(s) of the
answers.
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5.3 Solving systems of linear equations
Some systems of linear equations (aka simultaneous equations) can be solved efficiently using
your mind and paper and pen to document your thinking.
For example, solve
5x + 2 y = 7
.
y =8− x
However, other systems, like some with three unknowns, are more efficiently solved using digital
technology.
1.2 x + 3.4 y + 0.8 z = 11
For example, to solve the system 1.8 x + 0.8 y + 1.2 z = 5 we could use the
J
application.
2.1x + 1.8 y + 3.8 z = 12
From the ) palette of the soft keyboard tap the ~
template. Tap it twice to makes three input lines available.
Enter the equations.
Enter the variables being solved for, separated by commas.
E to have the solution set calculated and displayed.
Note the solution set values are given in exact form as the
ClassPad is in Standard mode.
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3x + 2 y + z = 4
Solving the system x + y + 3z = 4
5 x + 3 y − 1z = 4
results in a parametric representation of infinitely many solutions.
This is more conventionally written as:
x = −4 + 5t
y = 8 − 8t
z=t
t∈R
For systems that do not have a unique solution, like that above, a mental approach can be used.
We can apply elementary row operations to an augmented matrix in an attempt to produce
reduced row echelon form.
Reduced row echelon form can be reached efficiently using the M application
From the ) palette of the soft keyboard tap CALC button to
reveal the matrix entry templates.
Tap 8 then 8 again and then 6 to produce a 3 by 4
template.
Then enter the element values and select the matrix by dragging
across it with the stylus.
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Open the Interactive menu and then the MatrixCalculation sub-menu and then tap rref.
So we have:
3x + 2 y + z = 4
Attempting to solve the system x + y + 3z = 5 gives:
5 x + 3 y − 1z = 4
No solution – so what does a row reduction look like in this case?
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6. 2D palette,
calculus
calculations
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Launch the
mode.
J
application and make sure the ClassPad is set to calculate in Standard
Press k and then tap the ) palette.
This soft keyboard allows for natural input of various
mathematical expressions and can be used in most ClassPad
applications.
Tap CALC, ADV and VAR, to view the three other palettes within the ) palette.
To return to the initial template, tap I.
5
Calculate
∫x e
2 −x
dx
3
Tap CALC and then P.
Use default template to enter the power and e functions.
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If y =
3x
dy
find
when x=4.
dx
ln x
Note the use of the ‘for’ or ‘given’ symbol here (|x=4).
It can be found on the 9 keyboard and in the OPTN palette.
Find
∫
2
cos x
4
dx and
∫
2
2
cos x
dx
In the first case, the ClassPad is unable to calculate the integral
requested. Can you?
Given the ClassPad has no analytical result for this integral, then
this is no way it will give an exact value for the second calculation.
Instead, it uses a numerical approach and provides a decimal
approximation, even though the ClassPad is set to calculation in
Standard mode.
When the ClassPad is set in Standard mode, the result of calculations will be displayed, if possible, in
exact form. If it is not possible for the ClassPad to provide an exact value, it will default to providing a
decimal approximation or deliver the input as the output, signalling that the ClassPad cannot currently
calculate what has been asked of it.
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7. Managing my
ClassPad
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7.1 Touch Panel alignment
If you are experiencing inaccurate tapping, i.e. you tap on a certain
icon and the ClassPad does not respond or another icon is
actioned, then it maybe that your touch panel is not properly
aligned. This is not a common occurrence. However, a simple
process exists to realign it.
Tap M on the grey green toolbar. Now tap the
icon and then tap Touch Panel Alignment.
Accurately touch (once), the centre of each of the four target
crosses that appear. Once touched, they will grey-out and then the
Menu will return.
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7.2 Naming your ClassPad
The System application contains the tools you require to manage
your ClassPad.
Tap m and then launch the
Y
application.
Tap System to open the System menu and reveal all the tools.
Here, for example you can name your ClassPad.
Tap ClassPad Name.
We have called our ClassPad User1. It is important that you name
your ClassPad to assist you in the backup process that will be
outlined later in this chapter.
Tap Set when you are done.
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7.3 Contrast and Power Properties
To alter the Contrast of your ClassPad, from within
Y
tap
Z
Repeatedly tap 2 or 3 to alter the contrast of the screen to
suit you.
Tap Set when you are done.
Select Power Properties by tapping X.
To achieve ultimate battery life, set the Power Save Mode to 1
hour.
You can also make changes to the time that passes before the
ClassPad will Auto Power Off.
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7.4 Operating System update
The ClassPad’s operating system is upgradeable. This allows for new features to be developed
and implemented in your ClassPad. New releases of the operating system occur regularly.
To find out which version of software your ClassPad is currently
running, you will need to tap u on the tool bar to reveal the other
options and then tap >.
The version of the operating system currently installed on your
ClassPad will be displayed. OS 03.04.3000 was the latest release at
the time of writing.
For information about the latest operating system
please visit http://edu.casio.com
Operating system upgrades are free, but you must
register as a user on the site above and register the
ClassPad you have purchased.
Instructional movies showing how to carry out the
registration process can be found at
http://edu.casio.com/use/graph01/ or at
http://www.casio.edu.shriro.com.au
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7.5 eActivities and Add-in applications
This calculator has two types of memory storage: Main Memory and Storage Memory.
When you define functions, draw graphs, perform calculations, solve equations and so on, the
calculator is using and storing things in the Main Memory.
Storage Memory serves two functions. Add-in applications (those not loaded at the factory) are
stored and run from here and eActivities (a pre-prepared activities, saved versions of ClassPad
functionality for convenience and other data repositories) are stored and run from this memory
too.
You can find Add-in application at
http://edu.casio.com
You can find eActivites at
http://edu.casio.com or
http://www.casio.edu.shriro.com.au
When you open the
window will appear.
Y
application, the Memory Usage
This window displays the data storage in both the main
memory and storage area.
You can also Delete data in this window.
Remember to check the item box of data you wish to delete
first.
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7.6 Backing up your ClassPad
The more you use your ClassPad the more data you will save to its memory. If you have data
saved on your ClassPad you do not want to lose in the event of a malfunction, you should
regularly backup your ClassPad to a personal computer (PC).
To be able to backup the contents of your ClassPad to your PC, you will need to install the
software called FA-CP1 on your PC.
This software comes on the utilities CD in the
box of your ClassPad.
Alternatively you can download the software
from http://edu.casio.com
You will need to have installed the FA-CP1
program on you computer before proceeding
with this section.
When installing the FA CP1 or the first time you connect your ClassPad to your PC, you may be
asked a question (by Windows) about the installation of the ‘CESG502 USB’ drivers. It may say
they are ‘not signed’. Do not be alarmed by this message and be sure to say ‘Yes” to the
installation. Failure to do this will result in your ClassPad not being able to communicate with the
FA-CP1 via your PC.
Start by checking that your ClassPad is set correctly to talk to your PC.
Open the
B
application.
Open the Setup menu and then tap Open Setup Menu.
Tap Default to configure the settings as displayed right.
Your ClassPad will talk to your PC via the USB cable that came in the box of your calculator.
The Wakeup option needs to be On so that the calculator will automatically go into
communication mode.
92
Launch the FA-CP1 software on your PC.
Connect your ClassPad to your PC via the USB port using the USB cable that came in the box of
your ClassPad. Once connected you will see the ClassPad image appear complete with name, this
one is named User 1.
Open the Backup menu and click Start Auto-backup.
The ClassPad will be backed up onto the computer into the Backups folder. A file will be created
with the name of the ClassPad, date and time attached
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Once back up process is complete, the following window
will be displayed. Another ClassPad can be connected
and backed up or you can exit by clicking Finished.
The reverse of this process can be carried out if you need to restore your data.
Launch the FA-CP1 software on your PC and then connect your calculator to your PC via the
USB port using the USB cable that came in the box of your ClassPad.
Click on the ClassPad icon.
Open the Backup menu and then click Restore to “User 1”.
If you have backed up more than once, you can choose the
back up file you wish to restore too and click OK.
The Handheld Assistant window will open before the data transfer begins.
Select whether to overwrite or erase all existing data and click OK. The
back up file will then be restored to the ClassPad and the window will
close once transfer is complete.
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7.7 Optimizing your ClassPad
Like all computer devices, the memory of your calculator can become fragmented. To keep your
ClassPad in good health and to maximise free space for saving, an optimize option is available.
We suggest you back up your ClassPad before optimizing (see previous section for details).
To optimize your ClassPad, open the
Y
application and tap
u on the tool bar to scroll and view other options.
Tap <. Tap Yes to start the process.
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7.8 Resetting and initializing
You can delete all selected parts of the data saved on your ClassPad’s using the Reset function.
You cannot delete Add-In applications using this function. Be careful with this function as once
data is erased, it is erased!
Tap ; on the toolbar.
You can choose to delete different categories of data: information
stored in the Main Memory, eActivities or both.
You can delete everything from the ClassPad’s memory in one step using the Initialization
function. Be careful with this function as once data is erased, it is erased!
Tap ' on the toolbar.
You can choose to retain any Add-In applications you have
installed or delete everything, which will return all parts of the
ClassPad to factory settings.
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My notes
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7.9 Screen Capture
It is possible to capture an image of the screen of your
ClassPad. You require the software called
Screen Capture.
This software comes on the utilities CD in the box of
your ClassPad.
Alternatively you can download the software from
http://edu.casio.com
Start by checking that your ClassPad is set correctly to talk to your PC.
Open the
B
application.
Open the Setup menu and then tap Open Setup Menu.
Tap Default to configure the settings as displayed right.
Now launch Screen Capture and choose Start from the Capture menu.
The software will now wait patiently for you to send a screen image from the ClassPad.
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Now connect the ClassPad to your PC using the USB cable that came with your ClassPad.
Press c to terminate the Standby state of the ClassPad.
Now carry out whatever task you want to on the ClassPad. When the screen you want to capture
is visible on the ClassPad, tap h (on the grey-green toolbar of the ClassPad) to initiate the
sending of the image.
The image will open in whatever bitmap editor you have installed on your computer. You will
then be able to copy and paste the image as your desire.
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My notes
100
My notes
101
My notes
102
My notes
103
Index
2D Palette
10
5-number summary
41, 42
Add-in application
91
Algebraic expressions
24
Algy 2
34
Analysis
30, 33
Analysis-trace
53
Analytical result
85
Angle
27
Answer function
12
Assistant
27
Auto power off
89
Auto-backup
93
Axes
61
Backup
92
Binomial distribution
56
Bitmap
99
Calculate 2D palette
84
Change of base
21
Chart wizard
40
ClassPad name
88
Clear screen
73
Cls
73
Combination
49
Combine
25
Complex mode
79
Compound interest
18
Contrast
89
Coordinates
62
Correlation coefficient
44
Cplx
79
Cubic equation
78
Current folder
27
Decimal
8, 13
Decimal approx.
13, 14, 20
Decimal calculation
27
Degree
26
Delete
13
Derivative
73
Derivative/slope
62
Descending order
27
Duplicate zone
35
eActivites
91
Editing
11
Elementary row operations 81
End
29
Equations
34, 36, 78
Exact Form
13, 20
Exact value
16
FA-CP1
92
Factorial
49
Factorise
25
File
40
Five number summary 41, 42
Fix 2
19
Folder
40
For
85
Formats
18, 19, 27
basic
19, 27
complex
27
number
19, 27
104
Formula
76
Fractional form
9
Fractions
14
Fragmented
95
Function
31
G-Controller
62
Given
85
Graph
28, 31
Graph format
61
Graph function
61
G-Solve
33, 71
Histogram
51, 53
Improper fraction
16
Inconsistent
82
Infinitely many solutions
81
Initialization
96
Integral
72, 85
Interactive menu
16, 24
equation
24
transformation
24
Intersect
33, 36
Keyboards
11, 48, 49
catalogue
49
qwerty
48
soft
48
Least squares line
43, 44
Line of best fit
43
Logarithm
11
Mathematical symbols
48
Matrix-calculation
82
Max
71
Mean
42
Mixed numbers
15
Normal distribution
58
Num Solve
76
One-Variable
42
Operating system
90
Optimize
95
Overwrite
41
Pan
32
Parametric representation
81
Permutation
49
Power properties
89
Power save mode
89
Quick standard
65
r
44
r2 value
45
Radians
26
rand(
50
randBin(
56
randList(
50, 52
randNorm(
50, 51, 59
Random numbers
50
Randomly scattered
45
Real
79
Reduced row echelon
81
Reset
6, 96
Residual
44
Residual plot
46
Restore
94
Row echelon
81
Row reduction
82
Rref
82
Sample standard deviation 42
Save
40
Scatter plot
43
Scientific notation
10
Screen alignment
87
Screen capture
98
Set graph
52, 55
Simplify
24
Sketch
73
Solving equations
36
Spreadsheet
39, 43
Square root
10
Square view
64
Standard
8, 13
Standard mode
20
Start
29
Stat graph
57
Step
29
Summary statistics
42
Summing two lists
55
Symbolic calculations
24
Systems of equations
80
Tables of values
28, 29
Tangent
72
Trace
30, 65, 73
Trigonometric calculation
26
Two-D palette
10
USB cable
92
Variable is real
27
Verify
22
Wakeup
92
x-Cal
71
xmax
66
ymax
30
ymin
30
Zoom
32, 65, 70
auto
70
box
32
previous
32