Casio Calculator FX 82AU PLUS User Manual

Using the Casio fx-82AU PLUS  
Scientific Calculator  
Techniques and activities  
© Sue Thomson and Shriro Australia PTY Limited Casio Education division  
The pages and activities included in this publication may be copied for classroom  
use.  
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Contents  
Page  
Getting started ……………………………………………………………………. 4  
MathIO display ……………………………………………………………………. 4  
LineIO display ………………………………………………………………………. 4  
Setting degrees or radians ………………………………………………… 5  
Fixing decimal places ……………………………………………………………. 5  
Scientific notation ……………………………………………………………… 5  
Normal display ……………………………………………………………………… 5  
Fractions and decimals ……………………………………………………… 6, 7  
Fractional indices ………………………………………………………………… 7  
Negative, fractional indices ……………………………………………… 8  
Powers and roots ……………………………………………………………………9  
Trigonometry ………………………………………………………………………10, 11  
Changing degrees radians ……………………………………………… 11  
Statistics …………………………………………………………………………… 12 – 15  
Using the random number function …………………………………. 15  
Using the memories ……………………………………………………………. 16  
Tips and hints ………………………………………………………………………. 17  
Trouble shooting …………………………………………………………………18, 19  
Developing calculator skills practice sheets  
Fractions and decimals……………………………………………… 20  
Percentages ……………………………………………………………….. 21  
Working with fractions …………………………………………… 22  
Fix, scientific notation and norm …………………………… 23  
Roots and exponents ………………………………………………… 24  
Trigonometry ……………………………………………………………… 25  
Statistics ……………………………………………………………………… 26  
Using the memories ………………………………………………….. 27  
Degree Radians ……………………………………………………… 28  
Logs, natural logs and e ……………………………………………… 29  
Activities and worksheets for students  
Gallipoli Australia and New Zealand join WWI 30, 31  
Waiting time investigation ……………………………………. 32  
Playing dice simulation …………………………………………….. 33  
Subtracting dice bingo …………………………………………… 34  
Should you require further information refer to the booklet of instructions  
that was supplied with the calculator. Watch the Casio website  
www.casioed.net.au or contact [email protected] for more classroom  
activities with the fx-82AU PLUS.  
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Getting started  
After you have turned the calculator on the first step is to choose whether you  
want to do a calculation or to work in statistics. Press the MODE key to enter your  
choice of calculations (i.e. computation) or statistics.  
Press 1 for calculation or 2 for statistics.  
The Comp (calculations) menus  
The calculations menu offers you the choice of how you would like the maths  
displayed. The choices are MthIO, the way we write maths or Line IO the way  
calculators have traditionally displayed maths. The following screens show an  
example of the two options.  
MthIO mode  
LineIO mode  
Selecting Math (MthIO) or LineIO  
When you are in the comp mode press SHIFT MODE (SET UP) and the following  
screen will be displayed. Enter the Math mode by pressing 1 and Line mode by  
pressing 2.  
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Set up information  
Setting the calculator to degrees or radians  
When you are in the comp mode press SHIFT MODE (SET UP) and the following  
screen will be displayed.  
Press 3 for degrees or 4 for radians.  
Setting decimal places and scientific notation  
To fix the number of decimal places  
When you are in the comp mode press SHIFT MODE (SET UP) and the above  
screen will be displayed. Press 6.  
The screen then asks for the number of decimal places required. Press the number  
you want and the calculator will continue to display all numbers in this form until you  
instruct it to do otherwise. Refer to information on page 6 about toggling between  
fractions and decimals for answers in different forms.  
Answers expressed in scientific notation  
When you are in the comp mode press SHIFT MODE (SET UP) and the above  
screen will be displayed. Press 7.  
The screen then asks for the number of significant figures required. Press the  
number you want and the calculator will continue to display all numbers in this form  
until you instruct it to do otherwise.  
Setting the calculator back to ‘normal‛  
When you are in the comp mode press SHIFT MODE (SET UP) and the above  
screen will be displayed. Press 8.  
The screen then asks whether you would like Norm 1 or Norm 2.  
The difference between Norm 1 and Norm 2 is the value when the calculator swaps  
from a display as a decimal to a decimal in scientific notation.  
In norm 1, the answer to 1P200 is displayed as 5 × 10 -3.  
In norm 2, the answer to 1P200 is displayed as 0.005.  
Norm 2 doesn‛t use scientific notation until the display is of the order of 5 × 10 -9.  
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Fractions and decimals  
The key strokes for fractions are slightly different in the Math mode than in the  
Line mode.  
Fractions in the Line mode  
Use the a button to enter any expression involving fractions in the same way as  
the z button was used in the past.  
To enter 1½ + 3¾ press 1a1a2+3a3a4p.  
Answers in different forms  
The calculator can display the answer as an improper fraction, mixed numeral or  
decimal and it can toggle between all three.  
To change 5E1E4 to a decimal press n.  
To change either 5.25 or 5E1E4 into an improper fraction press SHIFT nN.  
Fractions in the Math mode  
To enter a traditional fraction, for example ½, press a1 then use the bottom  
of the replay button to position the cursor on the denominator and press 2.  
To enter a mixed numeral, for example 5¾ press SHIFT a then  
5$3R4p.  
To enter 1½ + 3¾ press  
SHIFT a1$1R2$+ SHIFT a 3$3R4p.  
The picture of the screen for this calculation is on the following page.  
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Remember you can toggle between the answer displayed as an improper fraction,  
mixed numeral and decimal. Refer to the section ‘answers in different forms‛ on the  
previous page.  
Simplifying fractions  
In either mode the calculator will express a fraction in its simplest form. Enter the  
fraction followed by p.  
OR  
Reciprocals  
The u button will find the reciprocal of a fraction. To find the reciprocal of 1½  
enter the fraction and press p, then up.  
OR  
Fractional indices  
The fraction button can be used as an index.  
OR  
In the Math mode the button pressing is 32fa3R5p.  
In the line mode the button pressing is 32f3a5p. Note! The first  
bracket is supplied by the calculator and the second bracket can be omitted if it is  
the last entry before p.  
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Negative, fractional indices  
The calculator can execute an impressive range of calculations with negative and  
positive fractional indices.  
or  
Occasionally the whole screen can‛t be displayed in the math mode, but the  
calculation remains possible. Naturally the following calculations can be executed in  
the line mode.  
Powers, math mode and brackets  
Provided the cursor is placed appropriately brackets can be omitted. Observe the  
above calculations in the math mode entered without brackets.  
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Powers and roots  
Determining powers  
Both screens show the value of 1.53. The button pressing is the same in both modes.  
1.5f3p.  
OR  
Determining roots  
The F button is used to determine roots. The screens show the value of the 5th  
root of 1024. The button pressing in each mode is shown below the screens.  
OR  
In the maths mode: SHIFT f5$1024p.  
In the line mode: SHIFT f1024!!!!!5.  
Using the M feature  
The M button allows a calculation to proceed using the previous answer. In both  
modes the button pressing used to produce the following screens was:  
sMp.  
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Trigonometry  
Before starting any calculations involving trigonometry always check the angle  
measure for degrees, radians or gradients. If the angle measure isn‛t consistent  
with the type of angle being used, all answers will be wrong. A D at the top of the  
screen indicates that the calculator is set to degrees. An R indicates radians and G  
gradients. Gradients are NEVER used in trigonometry in Australian schools.  
Set in degrees  
Set in radians  
Instructions to change the calculator from degrees to radians or radians to  
degrees are on page 5.  
Entering trigonometric expressions  
Enter the trigonometric ratio followed by the angle. The calculator will insert a left  
hand bracket but entering a ‘close brackets‛ is not required.  
Degrees, minutes and seconds  
The x button is used for entering degrees, minutes and seconds. The button  
sequence for entering 52o 36‛ 14” is 52x36x14xp.  
Using inverse trig  
The following button sequence is required to solve the equation tanθ = 1.56.  
SHIFT l1.56. If the 1.56 is the result of the previous calculation the  
sequence SHIFT lM can be used.  
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Changing a decimal to degrees, minutes and seconds  
Press SHIFT x to express 57.33908o in degrees, minutes and seconds.  
Changing radians into degrees or degrees into radians  
When you are converting angle types you MUST have the calculator set to the type  
of angle you are converting INTO.  
Radians to degrees  
The calculator is set in degrees. In the Maths mode the button sequence used was:  
aSHIFTKR2$SHIFTM2p.  
In the line mode the sequence is:  
(SHIFTKa2)SHIFTM2p.  
Degrees to radians  
The calculator is set in radians. In Maths or line mode the button sequence is:  
50SHIFTM1p.  
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The statistics menu  
Hint! When you are going to work in statistics start with the calculator turned off.  
Then you know all the statistics memories are empty. The data is cleared  
automatically when the calculator is turned off or the statistics menu is exited.  
Turn the calculator on. After you have selected MODE 2 for statistics the  
following screen will be displayed.  
The only thing that is relevant is 1-VAR, or 1 variable statistics. When you press 1  
for 1 variable statistics, one of two different screens will appear. The screen  
displayed will depend on whether frequency ‘on‛ or ‘off‛ was selected the previous  
time the calculator used statistics.  
OR  
The first screen allows you to enter scores one after the other. The second allows  
you to enter scores with their frequencies.  
Turning frequency on or off  
You can turn the frequency on or off in the SET UP menu, which is the second  
function on the MODE button. When you press SHIFT MODE (SET UP) the  
following screen will be displayed.  
The little black arrow head, R above LineI0, indicates that there are further  
options below. Press the bottom edge of the round REPLAY button to bring up the  
next screen.  
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The options for statistics are in 3. Press 3 to view the options.  
Press 1 if you want to have a separate list for frequencies and 2 if you want to  
enter scores without frequencies.  
Example  
Let‛s find the summary statistics for the following set of scores.  
4, 6, 2, 8, 3, 9, 12, 6, 4, and 5.  
Step 1  
Start with the calculator turned off. Turn the calculator on then set the calculator  
to statistics (MODE 2) and press 1 for 1 variable statistics. If the calculator has  
a frequency column showing turn the frequency off by pressing SHIFT, MODE  
(SET UP), REPLAY down, 3 for statistics then 2 for ‘off‛.  
Step 2  
Press 4 then p6p2p and so on until you have pressed 5p. If you  
make a mistake, don‛t worry! Simply scroll up to the wrong score and type the  
correct value over it. If you‛ve left a value out just put it at the end. If you‛ve put  
in an additional score that you don‛t require, highlight the score and press o. The  
incorrect score will be removed and the following scores moved up one position.  
Step 3  
After you have finished entering the scores, press C to indicate the completion  
of the data entering stage. Don‛t panic when the scores disappear! The data  
entering screen will disappear but can be brought back if required.  
Step 4  
The summary statistics are the second function on the number 1. Press SHIFT  
1.  
A summary of what each option does is on the following page.  
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1 : Type takes you back to the first screen in this section of the notes.  
2 : Data takes you back to the entered data. This is ideal for checking student data  
entries. Data also allows you to insert a score or delete all the scores. Caution! If  
you edit or change the data make sure that you press AC to indicate the changes  
are complete before you go to any data calculations.  
3 : Sum gives the sum of the squares of the scores or the sum of the scores.  
4 : Var gives the number of scores, mean, standard deviation and sample standard  
deviation.  
5 : MinMax gives the smallest and largest score.  
You can move backwards and forwards between these options using SHIFT, 1.  
Continuing with the example from the previous page  
The mean  
The screen should be the same as at the bottom of page 13. Press 4 (Var), 2  
(for mean) then you must press p to bring up the value of the mean.  
The standard deviation  
To find the standard deviation, press SHIFT, 1, 4 (Var), 3 for standard  
deviation then you must press p to bring up the value.  
The mean is 5.9 and the standard deviation is 2.8792 to 4 decimal places.  
Entering scores with their frequency  
Turn the calculator off to clear then memories. Turn it on then press MODE, select  
2 for statistics and 1 for 1-VAR. If there is no frequency column press SHIFT,  
SET UP, replay down, 3 (for statistics) then 1 to turn the frequency on.  
Example  
Scores  
Frequency  
4
5
6
7
8
9
12  
5
2
1
Enter all the scores by pressing the value then p. The calculator automatically  
makes the frequencies 1. Use the replay button to highlight the frequencies one at  
a time then type the appropriate number followed by p.  
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Press Cwhen you have completed the data entry stage. Don‛t panic when the  
scores disappear. The process for finding the mean and standard deviation is the  
same as outlined in the example using scores without frequencies. In the scores  
with frequencies example the mean is 5.1 and the standard deviation is 1.03.  
The random number function  
The calculator has two random number features. Ran# generates 3-digit pseudo  
random numbers between 0 and 1. RanInt generates random integers in a specified  
domain.  
Using Ran#  
If you want the number to be displayed as a decimal set the calculator to work in  
LineIO. In MathIO the random numbers are displayed as fractions. Press  
q.p and a random decimal will be displayed. Each time you press p another  
random number will be displayed.  
Random number formulas  
Random numbers can be incorporated into calculations.  
For example, the formula 1 + 2 × Ran# will generate random numbers between 1 and  
3. Each press of p will generate another random value between 1 and 3.  
The RanInt function  
To simulate the result of rolling a normal 6-sided die the formula RanInt#(1,6) is  
required. Enter this formula as Q.1q)6)p. Each time you press  
p another die simulation will be displayed.  
The formula RanInt#(1,6) + RanInt#(1,6) simulates the results of rolling a pair of  
dice and adding the numbers showing.  
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Using the memories  
The calculator has an independent memory that can store the result of a calculation.  
In addition there are six pronumerals A, B, C, D, X and Y which may be assigned  
values.  
The independent memory M  
Before you start using the memory, check that there is nothing in the memory. In  
the following screen shot the small M in the top left hand corner of the screen  
indicates that a value is stored in the memory. The contents of the memory can be  
cleared by pressing 0q J (STO) m.  
Store the result of a calculation by pressing m.  
In the above screen 15 is stored in the M memory. The button sequence to add the  
memory to 12 is: 12+Jmp.  
Caution! The calculator ‘remembers‛ the values stored in the memories even after  
the machine has been turned off. If you place a value in the memory without first  
clearing the memory, the calculator will add the new value to the value already in  
the memory.  
Storing values in A, B, C, D, X or Y  
In the above screen the result of 3 + 5 is being stored in A. The button sequence is:  
3+5SHIFT J (STO) z.  
Using values stored in A, B, C, D, X or Y  
The button sequence for the above screen is:  
3d+Jzdp  
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Tips and hints!  
Using brackets  
It is not necessary to enter the final bracket.  
Scrolling through previous entries  
When there is a small up E or down R arrow displayed in the window you can  
review previous entries and answers by scrolling up or down using the top or bottom  
of the replay button.  
Setting the calculator back to the factory settings  
The second function on 9 allows you to clear memories and reset the calculator if  
required. When you press SHIFT9 the following screen will be displayed.  
Press the number corresponding to your required action then follow the screen  
prompts.  
Editing a calculation  
Use the left or right side of the replay button to position the cursor. Pressing the  
o key will delete the entry immediately to the left of the cursor. If you want to  
insert a digit or operation, use the round replay button to position the cursor then  
press the required button. An ‘insert‛ function is available as the second function on  
o should it be required.  
Order of operations  
This calculator ‘knows‛ sophisticated order of operations. In addition to the usual  
order of operations this calculator ‘knows‛ that in expressions like 8 ÷ 2π or 8 ÷ 22  
the correct order is 8 ÷ (2π) and 8 ÷ (22). It is not necessary to include the  
brackets in the key strokes.  
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Trouble shooting  
The calculator is using a comma in place of a decimal point  
Solution: In ‘display‛, ‘comma‛ has been selected instead of ‘dot‛. In the calculations  
menu press SHIFT MODE (SET UP) then arrow down by pressing the bottom of the  
round replay button.  
Press 4(for display).  
Then press 1for dot.  
Answers to fractions calculations are improper fractions  
There are several ways to deal with this issue. You can set the calculator to always  
display answers as a mixed numeral (see instructions below), or you can make use of  
N, the second function of the n button to toggle between mixed numerals and  
improper fractions and decimals.  
If you want to set the calculator to answer as a mixed numeral  
Solution: In the calculations menu press SHIFT MODE (SET UP) then arrow down  
by pressing the bottom of the round replay button.  
Press 1 for mixed numeral or 2 if you want to change to improper fractions.  
The calculator is set to Maths mode but the fractions show the old way  
You are working in the statistics menu rather than in calculations. Press MODE 1.  
The calculator gives the wrong answer for calculations involving  
trigonometry.  
Most likely the calculator is set to radians and the input is intended to be degrees.  
See the instructions on page 5 for changing from radians to degrees.  
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The calculator is recalling the wrong value for a value in the memory  
You must clear the memory before placing a new value in the memory. The clear  
function is the second function on 9. Press SHIFT 9 then follow the  
instructions on the screen.  
The calculator is frozen  
In the middle of the back of the calculator there is a small hole. Press in the middle  
of the hole with a fine tipped biro.  
In statistics the calculator is pasting the value of the mean in place of a  
score in the data list.  
You haven‛t pressed C to indicate that you have finished entering the scores. The  
calculator is treating the mean as a score.  
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Fractions and Decimals  
Remember!  
When you have a fraction or a decimal displayed on the screen pressing the nbutton  
will allow you to toggle between decimal and fractional representation. Pressing SHIFT  
n will toggle between an improper fraction and mixed numeral representation for  
expressions with a value greater than 1. Instructions for entering fractions in MathIO and  
LineIO are on pages 6 and 7.  
Practice your skills with the following questions.  
1. Express 134 as a decimal.  
2 87  
2. Express  
as an improper fraction.  
3. Change 0.135 to a fraction.  
4. Write 2.65 as an improper fraction.  
5. What is 11 as a mixed numeral?  
5
6. Enter 5% into your calculator by pressing 5 SHIFT(. Press pand n to  
express 5% as a decimal and as a fraction.  
7. Express 36% as a fraction.  
8. What is 8% as a decimal?  
9. What number is equivalent to 125%?  
10. Express 45% as a fraction.  
11. Write 8.5% as a decimal.  
12. What decimal is equivalent to 83 ?  
13. What improper fraction is equivalent to 4 25 ?  
8
14. Express  
15. Express  
as a fraction in its simplest form. (Enter the fraction then press p.)  
12  
85  
25  
as a mixed numeral expressed in simplest form.  
Answers  
23  
8
27  
53  
20  
1
9
2 51  
1 1.75  
2
3
4
5
6 0.05,  
7
8 0.08  
9 1.25  
200  
20  
25  
9
22  
2
17  
5
10  
11 0.085 12 0.375 13  
14  
15  
20  
5
3
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Percentages  
1
The screen shot shows the calculator converting 25% to a fraction.  
Enter 25% by pressing 25SHIFT(followed by pto check the value of  
25% as a fraction.  
2
3
Express each percentage as a fraction.  
A 50%  
B 75%  
C 40%  
D 5%  
E 100%  
J 35%  
1
1
F 200%  
G
%
H 1.5%  
I
%
2
4
Express each percentage as a decimal.  
Hint! Express the percentage as a fraction then press the nbutton.  
1
2
A 45%  
B 79%  
C 5%  
D 7.5%  
E
%
2
1
2
F 245%  
G 1000%  
H 1%  
I 120.5%  
J
%
11  
4
The screen shot shows the solution to the problem ‘Increase 40 by 10%’.  
Check the calculation by pressing 40+10SHIFT(O40p.  
Determine the following amounts.  
A Increase 60 by 10%.  
B Increase 75 by 25%.  
C Decrease 80 by 20%. (Hint! Remember decrease means make smaller.)  
D Decrease $120 by 30%.  
E Increase $90 by 25% then decrease the result by 25%.  
5
The local sports store is having a ‘15% off sale’. Gillian is going to buy a pair of  
running shoes that normally cost $165. How much will the running shoes cost in  
the ‘15% off sale’?  
Answers  
3
4
3
200  
7
20  
1
2
5
1
20  
1
200  
1
400  
2A  
B
C
D
E 1 F 2  
G
H
I
J
2
3A 0.45 B 0.79 C 0.05 D 0.075 E 0.025 F 2.45 G 10 H 0.01 I 1.205 J 0.115  
4A 66 B 93.75 C 64 D $84 E 84.375  
5 $140.25  
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Working with fractions  
Practise the calculator fractions skills outlined on pages 6 and 7 with the following  
questions that involve fractions. Remember to use the round replay button to position the  
cursor correctly when you are using MathIO.  
1
2
3
4
1. Evaluate  
and express your answer as a mixed numeral, improper fraction  
+
and a decimal.  
7
8
2
5
2. Express  
as a fraction.  
×
1
4
3. Write the value of  
as a fraction.  
13 5  
9
4. Evaluate 10 ×135 and express your answer as an improper fraction.  
3
1
5. Write the answer to  
as a mixed numeral.  
18 ×2 4  
1
3
6. Find the value of  
and express the value as an improper fraction.  
3 2 ÷ 2 5  
7. Calculate3170 + 5 53 . Write your answer as a mixed numeral.  
2 . Write your answer as a fraction and as a decimal.  
3
8. Find the value of  
(5)  
9. Calculate the value of 1196 and express your answer as an improper fraction.  
3
1
10. Evaluate  
1 . Express your answer as a mixed numeral.  
2 4 + 2 ×12  
145 + 5 25 ÷ 45  
11. Find a decimal value for  
.
2
12. The u button produces the reciprocal of a fraction. Enter uand record the  
5
2
reciprocal of as an improper fraction and a mixed numeral.  
5
13. What is the reciprocal of 5 ? Express your answer as a mixed numeral.  
9
1
14. Write the reciprocal of  
as a fraction.  
3 2  
3
3
5
15. What is the value of multiplied by the reciprocal of  
?
5
Answers  
14  
1
7
20  
8
15  
36  
25  
3
35  
26  
3
9
5
4
1
,
54 , 1.25  
2
3
4
5
6
7
8
25 , 0.36  
9
3 32  
910  
1
5
2
1
2
7
154  
10  
11 8.55 12  
,
13  
14  
15 1  
3 2  
2 2  
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Fix, scientific notation and norm  
Remember!  
When you want to cancel fix or scientific notation choose Norm2. Refer to page 5 for fix  
and scientific notation procedures.  
1. Express 65 123 in scientific notation with 2 significant figures.  
6.8×103  
2. Express  
without using scientific notation. (Hint! Press 6.8 OK3  
then set the calculator to Norm2.)  
3.25×106  
3. Express  
4. Write 4.6349 correct to 2 decimal places.  
without using scientific notation.  
5. Determine the value of 16.8731 correct to 1 decimal place.  
6. Find the value of  
correct to 2 decimal places.  
175  
2
3
7. Calculate the value of  
in scientific notation with two  
8.61×10 × 9.356×10  
significant figures.  
8. What is the value of  
? Express your answer as a decimal.  
8.3× 2.5  
2
9. Find the value of  
correct to two decimal places.  
11.75  
(
)
5
4
10. What is the value of  
correct to the nearest whole number?  
4.1×10 ÷ (8.75×10 )  
3
11. The calculation 1.07 ×$1260 gives the value of an investment in 3 years time.  
(
)
Calculate the value of the investment in 3 years time correct to the nearest cent.  
12. Calculate the value of when r = 17.6 and h = 11.8. Express your answer  
2π rh  
correct to 1 decimal place.  
13. The screen capture shows a calculation.  
A How do you know the calculator is set in scientific notation, not Norm1 or 2?  
B How many significant figures is the calculator set to display?  
C Express the answer without any rounding or scientific notation.  
Answers  
6.5×104  
8 20.75  
8.1×106  
1
2 6800  
9 138.06 10 5  
13 A SCI is at the top of the screen B 2 C 31 102 015  
3 3 250 000  
4 4.63  
5 16.9  
6 13.23  
7
11 $1543.55 12 1304.9  
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Roots and exponents  
Button procedures for roots and exponents are on pages 7 to 9. Remember that you can  
use the nbutton to toggle between fractions and decimals if you want your answer in a  
different form.  
1. Use the dbutton to find the value of the following squares.  
52  
2.62  
4.32  
A
B 112  
C
D
2. Use the button to calculate the value of the following cubes.  
23  
3. Use the fbutton to calculate the following quantities.  
63  
1.23  
4.13  
A
B
C
D
2
3
A 27  
B
F
C
D
161.5  
160.5  
8
2
1
2
1
2
5  
3
3
27  
8
1
E
G 111  
H
16 ×2  
( 2 )  
( )  
(
)
25  
4. Use the s button to find the following roots.  
482 + 552  
432 4×6×55  
652 562  
A
E
B
C
F
D
2809  
23104  
62 4×1×8  
5. Use the SHIFT then fbuttons to find the value of the following roots. Express  
each answer correct to one decimal place.  
4 32 + 53  
5
4 700  
620  
8 11  
A
B
C
D
6. Express the following values as whole numbers or mixed numerals.  
3
2
5
2  
A 11  
B
2 97  
C
D
1
4
(
)
( 5 )  
( 9 )  
2
Answers  
1A 25 B 121 C 6.76 D 18.49  
2A 8 B 216 C 1.728 D 68.921  
1
5
3A 128 B 64 C  
D 4 E 32 F 9  
G
H 2  
4
4
6
4A 53 B 152 C 73 D 33 E 2 F 23 5A 5.1 B 3.6 C 1.3 D 3.4  
19  
2
3
6A  
B
C 25  
D
7 32  
13  
3 8  
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Trigonometry  
The instructions for working with trigonometry are on pages 10 and 11.  
Check your calculator settings!  
0
The statement  
is correct. Explain why both of the following calculator  
sin30 = 0.5  
0
screens are displaying the wrong value for  
.
sin30  
Set your calculator to degrees before you start the following practice questions.  
1
Find the value of the following expressions correct to 2 decimal places.  
43.6sin 520  
28.9 tan380  
11cos610  
A
B
C
2
Determine the value of correct to the nearest degree.  
θ
A
D
B
C
F
cosθ = 0.743  
5
tanθ =  
4
tanθ =1.628  
2
cosθ =  
5
sinθ = 0.463  
16.3  
sinθ =  
21.5  
E
3
4
5
Use the xbutton twice each time to enter the degrees and minutes in the  
following expressions. Express each answer correct to 2 decimal places.  
8sin 41028'  
12.3cos62050'  
7.4tan 42013'  
A
B
C
Enter each angle, press pthen SHIFT followed by xto express each of the  
following angles in degrees and minutes and seconds.  
73.650  
44.780  
25.640  
A
B
C
Determine the value of  
30 seconds to the minute.  
correct to the nearest minute. Remember that there are  
α
A
B
C
tanα =1.26  
sinα = 0.634  
cosα = 0.25  
12sin360 25'  
5sin 280 32'  
6
Determine the value of  
. Express your answer to 2 decimal places.  
Answers  
The first screen is set in radians and the second in gradients. Change the calculator to  
work in degrees by pressing SHIFTw3.  
2A 420 B  
C
D
E
F
580  
280  
440 46' 48''  
510  
660  
250 38' 24''  
490  
1A 34.36 B 22.58 C 5.33  
3A 5.30 B 5.62 C 6.71  
730 39' 0''  
4A  
B
C
0
'
'
510 34'  
39 21  
750 31  
5A  
B
C
6 2.98  
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Statistics  
The button pressing sequence for statistics is on pages 12 to 15.  
Remember!  
When you have finished entering the data you must press Cto tell the calculator  
that you have completed entering the scores.  
When you press SHIFT14 then 2to bring up the value of the mean you  
must press pto display the value. This is particularly important when you  
proceed to find the second piece of information, e.g. the standard deviation.  
Practise your statistics skills with the following questions.  
1
Set your calculator to statistics and turn the frequency list off.  
A Enter the scores 16, 19, 5, 11, 15, 12 and 9.  
B Determine the value of the mean, ( ) to 2 decimal places.  
x
C What is the value of the standard deviation ( n ) to 3 decimal places?  
σ
D Determine the sample standard deviation ( n1 ) correct to 3 decimal  
σ
places.  
2
3
Clear the data in the statistics list. The easiest way to clear the data is to turn the  
calculator off. Alternatively, set the calculator to comp then back to statistics.  
Set the calculator to statistics with the frequency on.  
A Enter the data in the table into the calculator.  
Scores  
Frequency  
5
6
4
9
7
8
9
15  
11  
7
10  
4
B Determine the size of n, the number of scores.  
C What is the value of the mean?  
D Determine the size of the standard deviation correct to 3 decimal  
places.  
4
Determine the mean and standard deviation of the scores in the following table.  
10  
11  
12  
13  
14  
15  
16  
Scores  
Frequencies  
15  
12  
5
8
10  
13  
6
Answers  
1B  
,
,
= 4.685  
3B n = 50 C  
D
x =12.43 σn = 4.338 σn1  
x = 7.4  
σn =1.356  
4
,
x =12.7 σn = 2.079  
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Using the memories  
Remember!  
You must clear the memory before you place anything in the memory. If you forget to  
clear the memory the calculator will add the new value to the value that is already in the  
memory. The instructions for clearing the memory are on page 16.  
1
In which of the following calculators is a number stored in the memory?  
or  
2
3
Clear the memory on your calculator and place the value of π in the memory. Use  
the Jmpbuttons to determine the value of the following expressions.  
Express each answer correct to 2 decimal places.  
A 2 + π  
B 2π  
C 12 − π  
D π ÷ 2  
E 2 × π × 4.32  
Store the result of the calculation 3 + 8.1 in the memory, then determine the value  
of each expression.  
A (3 + 8.1) × 4.5  
B 12.7 + 3 + 8.1  
C (3 + 8.1) ÷ 4.3  
Hint! If you are not getting the answers at the bottom of the page, you may not  
have cleared the memory properly before you started.  
4
5
In Australia a 10% GST is added to prices to determine the final selling price.  
Increasing an amount by 10% is the same as multiplying the amount by 1.1. Place  
1.1 in the calculator’s memory then determine the final price of each item.  
A $32 book  
D $260 camera  
B $3.20 ice cream  
D $33 000 car  
C $20 hair cut  
If you want to determine the amount of GST included in a price, divide the price  
by 11. Use the calculator memory to determine the amount of GST in each price.  
A $132 pair of jeans  
B $38.50 movie ticket  
C $5.72 bus ticket  
D $11.55 take-away lunch  
Answers  
1
2
3
4
5
The right hand screen has a value stored in the memory.  
A 5.14  
B 6.28  
B 23.8  
B $3.52  
B $3.50  
C 8.86  
D 1.57  
E 116.18  
A 49.95  
A $35.20  
A $12  
C 2.85 to 2 decimal places  
C $22  
C 52c  
D $286  
D $1.05  
E $36 300  
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Degrees Radians  
Remember!  
The small c in the expression  
c
means radians. When you want to change from  
1.4  
degrees to radians, or the reverse, you must have the calculator set on the measure you  
are changing into. The button pressing sequence for degrees radians and changing  
degrees into degrees and minutes is on page 11.  
Note!The only times when the degrees or radians setting is relevant is when you are  
converting between degrees and radians or when you are going to press one of the j  
kor lbuttons.  
π
1
Express 4 radians in degrees.  
2
3
Convert 0 into radians, correct to 3 decimal places.  
30  
π
5
Express radians in degrees.  
0
'
4
Convert  
Express  
into radians. Express your answer correct to 3 decimal places.  
55 30  
c
5
6
in degrees, correct to the nearest minute.  
1.8  
Determine the following values correct to 3 decimal places.  
tan1.6c  
cos1.2c  
12 r2θ  
sin540 28'  
A
B
C
c
7
8
Determine the value of  
when r = 6.4 and  
.
θ =1.9  
1 r2 θ sinθ  
Evaluate  
when r = 11.7 and  
c . Express your answer correct  
θ = 0.8  
(
)
2
to 2 decimal places.  
Solve the equations for  
places.  
π
2
9
,
. Express each answer correct to 3 decimal  
θ 0 θ ≤  
A
B
C
sinθ = 0.4  
cosθ = 0.128  
tanθ =1.7  
5 +6.2 10  
2×5×6.2  
2
2
10 Determine the value of  
,
for  
2 . Express your answer  
θ 0 <θ < π  
correct to 3 decimal places.  
11 Calculate the value of  
cosθ =  
9sin 0.7c  
π
2
,
, in the equation sinα =  
. Express  
α 0 < α <  
10  
your answer correct to 4 decimal places.  
12 Determine the positive solution for p in the equation  
p2 = 4.82 + 7.32 2× 4.8×7.3×cos1.9c  
. Answer correct to 1 decimal place.  
Answers  
2 0.524c 3 360 4 0.969c  
7 38.912 8 5.66  
9A 0.412c B 1.442c C 1.039c 10 2.20c 11 0.6185c 12 9.9  
450  
1030 8'  
1
5
6A  
34.233  
B 0.362 C 0.814  
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Logs, natural logs and e  
The calculator uses gfor log base 10 and hfor log base e. You don’t have to  
remember which button is which. All you need to do is look at the second function above  
each button. The gbutton has Gabove it reminding you that the gbutton is base  
10. Similarly the hbutton has Habove it. his base e.  
1
Use your calculator to evaluate each expression correct to 3 decimal places.  
A
B
C
log10 105  
loge 8  
log10 0.6  
D
E
F
loge 0.5  
log10 4.3× 2.5  
4loge 209  
(
)
2
3
A Enter  
into your calculator.  
log 1  
(
)
e
B Explain why your calculator displays the message “Math ERROR”.  
Your calculator has two e buttons. You can find the value of e as the alpha  
function on K. The value of ex can be determined by using the second function  
on h.  
A Determine the value of e using Q K p. Answer to 4 decimal places.  
B Find the value of 3 to 2 decimal places by pressing SHIFTh3.  
e
1. Determine the following values correct to 2 decimal places.  
e2.5  
e1  
e
A
B
C
4
Calculate the values of the following expressions.  
loge e2  
loge e3  
loge e  
A
B
C
loge e1  
log10 100  
log10 101  
D
F
G
5
What is the value of  
n ? (You’ll have to use your brain for this one!)  
loge e  
12k  
6
7
Evaluate  
when k = 0.4. Express your answer to the nearest hundred.  
800e  
10k  
Determine the value of  
when k = 1.4.Express your answer in scientific  
950e  
notation with 3 significant figures.  
8
What is the value of  
? Express your answer to 2 decimal places.  
πe  
Answers  
1A 2.021 B 2.079 C  
D
E 1.031 F 21.369  
0.222  
0.693  
2 log x only exists for x > 0. 3A 2.7183 B 20.09 4A 12.18 B 0.37 C 2.72  
7.90×104  
5A 2 B 3 C 1 D 1 E 2 F 1 6 n 7 97 200 9 8.54  
8
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Gallipoli  
Australia and New Zealand joined the First World War1  
In 1915 soldiers from Australia and New Zealand joined allies from Britain, France and India to  
fight against soldiers from Turkey in the Gallipoli Campaign. As you work through this set of  
questions you will learn about some of the tragedy of war and of Gallipoli in particular.  
1. The youngest ANZAC soldier to die in the Gallipoli Campaign was James Martin. He  
was a 14-year-old Australian. In which of the school years, Year 7, Year 9 or Year 11,  
would a 14-year-old boy be included today?  
2. Major Frank Chapman from New Zealand was the oldest ANZAC to die in Gallipoli. He  
was 57 years old. What was the range in ages of ANZAC soldiers who died in the  
Gallipoli Campaign?  
3. This table shows a random sample of the ages of 520 ANZAC soldiers who died in  
Gallipoli.  
Ages  
(class)  
16 - 20  
21 - 25  
26 - 30  
31 - 35  
36 - 40  
41 - 45  
46 - 50  
Class  
centres  
18  
Frequency  
78  
226  
110  
58  
36  
9
23  
28  
33  
38  
43  
48  
3
Use the information in the table to answer these questions.  
What is the modal class?  
A
B
C
In this context, what does the mode represent?  
What fraction of the soldiers in the sample were 25 years old or less when they  
were killed? Use your calculator to express this fraction in its simplest form.  
D
Set your calculator to statistics and enter the class centres in the score column  
and the frequencies in the frequency column. Remember to press pafter you  
enter each value. If you want to change a value, highlight the value and type  
over it. When you’ve finished entering all the values press C. Then press  
SHIFT 1(STAT) and 4(Var). Press 2pto find the mean age of the  
sample of soldiers killed in the Gallipoli Campaign.  
1 The random sample information used in this activity was obtained from information on the Australian  
War Memorial, Canberra website.  
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E
F
In 1915 the average age of Australian and New Zealand soldiers was 28 years.  
(i)  
How many years younger than 28 was the average age of the sample of ANZAC  
soldiers killed in Gallipoli?  
(ii)  
Calculate this age difference as a percentage of 28.  
No one is sure exactly how many men died in action or as a result of wounds  
in Gallipoli. The number is somewhere between 8160 and 8710.  
(i)  
Assuming the number is 8710, use the sample information to estimate the  
number of ANZAC soldiers killed in the Gallipoli Campaign who were less than  
21 years old.  
(ii)  
How many maths classes with 25 students in each class could have been made  
from the ANZAC soldiers who were less than 21 years old when they were killed  
in the Gallipoli Campaign?  
4. The first ANZAC Division contained 30 000 men. Of these men, 631 were officers and  
29 369 were enlisted men.  
A
Of the 631 officers only about one-sixth had previous war experience.  
How many of the officers had no previous war experience?  
B
C
Calculate the percentage of the first Division who were officers.  
In the random sample of 520 ANZAC soldiers killed in the Gallipoli  
Campaign only 1 man was an officer, the remaining 519 men were enlisted.  
What percentage of the sample killed in Gallipoli was an officer?  
D
One T.V. commentator said: “If you are going to fight in a war, make sure you  
are an officer. Officers are less likely to be killed.”  
Use your answer to parts (B) and (C) to determine whether the T.V.  
commentator’s statement is correct. Give a reason for your opinion.  
Want to know more?  
Log onto these sites to find out more information about the ANZACs at war  
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Waiting time investigation  
On average, how long do customers wait in your school canteen queue before they have  
completed their purchases? In this activity you will be investigating this question and evaluating  
the results.  
Equipment required  
A watch that measures time in minutes and seconds  
Pen and paper for recording results  
A Casio fx-82AU PLUS calculator  
What you have to do  
In groups of 3 assign each person one of the roles of timer, recorder or customer selector.  
Arrange for different groups to measure customer-waiting times at the beginning, middle  
and end of buying times.  
To make sure your results are valid it is important to choose a random sample of  
customers to time. The ‘customer selector’ will use the calculator’s random number  
generator to choose customers. Set the calculator to Line10 and fix the display to show 2  
decimal places. When you press SHIFT . pthe calculator will show a decimal  
number. If the random number is less than 0.50 select the next customer that joins the line  
to time. Each time you press panother random number will be displayed.  
The ‘timer’ measures the time from when the selected customer joins the queue until they  
move away from the counter.  
Record the time for at least 10 randomly selected customers.  
Calculating the mean (average) time  
Set the calculator to statistics by pressing MODE then 2(for stats) then 1(for 1-  
VAR).  
Use the xbutton to enter the waiting times in minutes and seconds. e.g. enter 2 minutes  
and 35 seconds by pressing 2x35x and the calculator will display the  
amount automatically as 2.5833 minutes. After you have entered all the times press C.  
Then press SHIFT 1(stats) 4(Var). The screen options show that pressing 2will  
give the mean. Press 2then pto find the mean of the times. The calculator will show  
the time as a decimal. Press SHIFT x to show the time in minutes and seconds.  
Evaluating your results  
Compare the results from different groups. Are they the same? If they are different  
suggest a reason for the difference.  
Use the information to determine whether customers have to wait too long. If the times  
are too long, can you suggest a way to shorten the time?  
Who is interested in your results?  
Write a report of your investigation and your findings. Give the report to someone who can  
implement any suggestions you can make.  
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Playing dice simulation  
Simulation 1  
When you roll a pair of normal, 6-sided dice together and add the numbers showing, what is the  
most likely total?  
What you have to do  
Enter the formula RanInt#(1,6) + RanInt#(1,6) into your calculator. Each time you press  
p the calculator will simulate another roll of the dice.  
Record the number displayed by your calculator each time you press p in the table.  
Simulate the dice rolls at least 40 times.  
Total of the dice  
Tally  
Frequency  
2
3
4
5
6
7
8
9
10  
11  
12  
Discussion questions  
What is the most common total when the numbers on a pair of dice are added?  
Why does this number occur more than other numbers?  
What are the two rarest totals?  
Simulation 2  
Andrew and Imran are rolling a pair of normal, 6-sided dice. Andrew thinks that a sum of 7 will  
occur twice before a sum of 6 and a sum of 8 happens. Imran doesn’t agree. He thinks that a sum  
of 6 and a sum of 8 before two sums of 7.  
Your task is to determine who is right!  
What you have to do  
Enter the formula RanInt#(1,6) + RanInt#(1,6) into your calculator. When you press p ignore  
any values that are not 6, 7 or 8. Record whether two sums of 7 or a sum of 6 and a sum of 8  
happens first. Carry out at least 20 simulations and show your results in the table.  
Two sums of 7  
A sum of 6 and a sum of 8  
(or a sum of 8 and a sum of 6)  
Which event occurs first most often; two sums of 7 or a sum of 6 and a sum of 8? Why?  
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Subtracting dice Bingo  
The game rules  
The values called in this game of bingo will be determined by subtracting the numbers  
showing on a pair of normal 6-sided dice. The subtraction will always be the bigger value  
subtract the smaller value. There will be no negative values.  
Players choose 9 numbers. They can be all the same, mostly the same or mostly different.  
However, if a player chooses to have all nine numbers the same, that number must be  
called 9 times for the player to win. Players can only cross out one of their numbers each  
time a number is called.  
The first player to have all their numbers crossed out is the winner.  
Your challenge is to determine the best set of 9 numbers to use in this game.  
What you have to do  
Enter the formula “the absolute value of [RanInt#(1,6) RanInt#(1,6)]” into your calculator by  
pressing the following sequence of buttons:  
eQ.1SHIFT)6)‐Q.1SHIFT)6)p  
Each time you press p another simulation value will be displayed.  
Simulate the roll of the dice at least 50 times and record your results in the table.  
Number rolled  
Tally  
Frequency  
0
1
2
3
4
5
What set of 9 numbers do you think are the best set for winning this game?  
Write a paragraph to explain the reason for your choice.  
In your group, play the game with a real pair of dice. Which group member’s set of numbers wins  
the most frequently?  
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