USE OF A CALCULATOR :
ACCESS & PROGRESSION DIPLOMA
PART A : Instructions for the CASIO fx-83ES, fx-85GT
ON / OFF
To switch on: Press ON button
To switch off: Press SHIFT
DISPLAY MODES
(a)
DISPLAY
There are two main display modes: 1: MthIO
2: LineIO
AC
Maths Input / output
Line Input / output
Maths Input / output is used for powers, fractions, roots etc, and displays the
results in the way you see them written in maths text books.
Line Input / output is the traditional calculator display and is used for most
calculations where the answer is needed as a decimal number.
To adjust the display mode: SHIFT SETUP then choose 1 or 2
If you choose MthIO on the fx-85 calculator then the input will be in “maths”
mode but you get a choice for the output. Choose 1 for Maths output.
If the answer is displayed as a fraction and you prefer a decimal, use the key
labelled SD. This toggles between the fraction and decimal equivalents.
(b)
ANGLES
SHIFT SETUP 3, 4 and 5 allow users to choose
the way of measuring angles. You will use 3: Degrees.
(c)
NUMBERS
SHIFT SETUP 6, 7 and 8 give a choice of how
you want the numbers displayed.
6: Fix
allows you to fix the number of figures after the decimal point
(often 3). It will round the number correctly for you.
7: Sci
displays the number in Scientific notation (often called Standard
Form or Standard Index Form)
8: Norm this is the usual mode. ( Choose Norm2 rather than Norm1 since
it will display bigger numbers before changing to Standard Form)
CALCULATION
The calculator follows true algebraic logic, i.e. it obeys the rules for the correct
order of calculation: first, brackets; then indices; then multiplication and
division; lastly, addition and subtraction.
 Make use of the bracket keys
 Press the = key to do the calculation
 Do not clear the display and then type in the previous answer; use the
ANS key to re-use the result of the previous calculation (still displayed
on the screen)
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MEMORY KEYS
The calculator has 7 memories: A, B, C, D, X, Y, M, shown in red letters
above the central keys.
To put a number into memory:
Input the number, e.g.
Shift RCL (-)
2
[ STO
2A
A ]
To recall a number from memory:
RCL (-)
[ RCL A ]
Or you can use ALPHA then the letter to recall the number in the memory.
If using memory M, you can add to the memory by pressing M+.
To subtract from memory M, press
Shift M+
[ M- ]
To clear a single memory:
0 Shift RCL (-)
To clear ALL memories:
Shift 9 [CLR ]
[STO
2:Memory
A]
= [yes]
DELETE / CLEAR / REPLAY
DEL
deletes the last input character
AC
clears the screen
REPLAY
allows you to insert a new character
(use  to move to the left;  to move to the right).
PART B
Correct Use of a Calculator :
Some Useful Keys
Powers and roots
Modern calculators will normally have 3 keys for powers:
x2, x3 and x■
The last of these can be used to calculate any power, e.g. to calculate 2 6 you
would input
2 x■ 6 =
(giving the result 64)
Note that the calculator automatically inserts brackets, so to calculate 2 6 + 34
you would need to input 2 x■ 6 ) + 3 x■ 4 =
( answer = 145)
■
■
If you input 2 x 6 + 3 x 4 = without the bracket the calculator would
work out 26+81 = 1.547  1026
3■
■■
There are also 3 keys for roots: ■
(you will need to use the shift key). These give the square root, cube root and
any specified root.
An alternative way to obtain roots is to use the x■ key but with a fractional
index, e.g.
16 x■ ½ = 4
or 16 x■ 0.5 = 4
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Fractions
Either convert to decimals ( remember that any fraction is converted to
5
decimal form by doing
TOP  BOTTOM, e.g.
= 5  8 = 0.625
8
b
Or use the fraction key
a
or
.
c
5
In LineIO, fractions are displayed thus: 5 ┘8 ( ).
8
5
Mixed fractions ( e.g. 2 ) are shown as 2 ┘5 ┘8
8
5
In MathIO, fractions are displayed as they are normally written e.g. , and are
8
input using the arrow keys to fill in the values for the numerator and
denominator. Mixed fractions require the user to press the shift key first.
SD
Converts fractions to decimals and vice versa,
e.g. 5┘6 SD shows 0.8333
Using the shift key and this button converts from top heavy fractions to mixed
fractions and v.v.
The fraction key can also be used to do calculations such as 23.4  17.7
(in MathsIO mode)
2.53 + 32.1
Recurring decimals
A recurring decimal is written with a dot above the decimal to indicate that it
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recurs. E.g.
will be shown as 1.3333333333 or 1. 3 and you can toggle
3
between these using the SD key.
(LOOK OUT FOR THIS DOT!!)
Ans button
This button allows you to use the displayed value in your next calculation.
E.g.
To calculate 23.4  17.7
2.53 + 32.1
You could calculate the denominator first, i.e. 2.53 + 32.1 = 34.63
Now do 23.4  17.7  Ans
(The calculator works out 23.4  17.7
and divides it by the displayed figure of 34.63 to give 11.96…)
The Ans button can also be used to do repeat calculations.
E.g. To keep adding 6 to a number, starting from 12:
Type in 12 =
Ans + 6 =
Then press =
to repeat the calculation (you will get 18, 24, 30 …)
This is a quick way to find all the multiples of a number, i.e. a times table
E.g. to keep doubling a number, starting from 1:
Type in 1 =
Ans  2 =
then press = to repeat
(you will get 2, 4, 8, ….)
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Standard form
To input a number in standard form use the key labelled
56 million = 5.6  107.
E.g.
Input as
5.6
10x
10x
Note that you do not need to input the  sign, simply use the
7.
10x key.
Very large or small answers to calculations will automatically be displayed in
standard form.
1.96  1012
i.e.
and 2.054  10-7
i.e.
E.g.
means 1.96 multiplied by 10 twelve times,
1,960,000,000,000
means 2.054 divided by 10 seven times,
0.000 000 205 4
You can convert the calculator display to be in standard form always by using
the setup facility. (Shift SETUP, choose 7 : Sci, choose the number of
significant figures to be displayed).
You revert back to the normal display by
shift SETUP, choose 8:Norm,
then select option 2.

The value of  is stored in the calculator and should always be used in
preference to 3.14 or 3.14159 since it is more accurate.
PART C
1.
Use of a Calculator:
Some Common Mistakes to avoid
Modern calculators work according to true algebraic logic (BODMAS).
E.g.
To calculate 23.4  17.7
2.53 + 32.1
DO NOT input as
23.4  17.7  2.53 + 32.1
because the calculator will work out 23.4  17.7  2.53 first ( which
equals 163.7075), then add on the 32.1 to give a final result of 195.8075
You should:
(a) Use brackets (23.4  17.7)  (2.53 + 32.1)
= 11.96
or
(b) Use brackets and the equals key 23.4  17.7 =  (2.53 + 32.1)
or
(c) Calculate the numerator and denominator separately, then divide:
23.4  17.7 = 414.18
2.53 + 32.1 = 34.63
414.18  34.63 = 11.96
(This is not a particularly good method as it is easy to make errors in
writing down and inputting the numbers).
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or
(d) Use the memories
(see the instructions on page 2)
23.4  17.7 = 414.18
STO
A
2.53 + 32.1 = 34.63
STO
B
RCL
A
=

RCL
B
=
or
(e) Use the Ans button:
Calculate the denominator first, i.e.
2.53 + 32.1 = 34.63
Now do 23.4  17.7  Ans
(The calculator works out 23.4  17.7 and divides it by the displayed figure of
34.63 to give 11.96…)
2.
Remember to use brackets
E.g.
to calculate  32 + 42
DO NOT input  32 + 42 because this will calculate  32 first (giving 3),
and then add on 42, giving a final result of 19.
You must use brackets:
 ( 32 + 42) =  25 = 5
3.
Be careful with negative numbers,
e.g. -3 squared
Inputting -32 gives the result -9. The calculator assumes that you mean
“put a minus sign in front of 32”, i.e. – (32) = -9
To calculate the square of -3 input as (-3)2. This gives the correct answer
for -3  -3, which is 9.
It is actually easier to remember that the square on any number is
ALWAYS positive, so simply input 32 if you want (-3)2.
4.
Rounding errors
The best way of avoiding rounding errors is to keep all the results in the
calculator rather than writing down a rounded value, then re-using it. You can
make use of the calculator memories and the ANS key.
5.
Common-sense and context
If the data is measurements given to 3 s.f. then the answer should not be
given to more than 3 s.f., and it may be more appropriate to give the answer
to 2 s.f. only.
Always consider the context before deciding on appropriate levels of
accuracy. This includes the accuracy of the data and the purpose of the
calculation.
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If the data relates to a measured component, e.g. a triangular support, side
367mm, 203mm and 387mm then a calculation of area will be in mm 2. It is
meaningless to quote fractions of a mm2 in the answer, and it may be more
appropriate to give the answer to the nearest 100 mm 2 ( = 1 cm2), depending
on the particular context.
Example:
y = 5.9  10
By inputting 5.9  10 =
you should get the answer 18.65743819,
which is 18.66 to 4 s.f.
If you do the calculation in stages i.e. work out 10, write down a rounded
version of this, and then input the rounded value into the calculator your
answer will contain rounding errors.
Rounding 10 to 2 s.f gives 3.2, and y = 5.9  3.2 = 18.88
This is only correct to 2 s.f.; the result can only safely be written as y = 19.
Rounding 10 to 3 s.f gives 3.16, and y = 18.644
This is only correct to 2 s.f., i.e. the result can only safely be written as y = 19.
Rounding 10 to 4 s.f gives 3.162, and y = 18.6558
This is correct to 4 s.f., i.e. the result can only safely be written as y = 18.66
Rounding 10 to 5 s.f. gives 3.1623, and y = 18.65757.
This is correct to 4 s.f., i.e. the result can only safely be written as 18.66
10 rounded
to …..
2 s.f.
3 s.f.
4 s.f.
5 s.f.
6 s.f.
10
3.16227766
3.2
3.16
3.162
3.1623
3.16228
× 5.9
18.65743819
18.88
18.644
18.6558
18.65757
18.657452
Col B
rounded
19
19
18.66
18.66
18.657
Correct answer,
rounded
18.65743819
19
18.7
18.66
18.657
18.6574
Accurate
to …
2 s.f.
2 s.f.
4 s.f.
4 s.f.
5 s.f.
In general, if an intermediate value has been rounded to n significant
figures, then the answer is only correct to (n-1) significant figures.
If you require an answer to be correct to 3 s.f. then you MUST work to at
least 4 s.f. in the preceding calculations.
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