Using a Calculator

Why the fuss about using a calculator?

GCSE Mathematics goes beyond using the basic features of a calculator and explores many of the special functions of a scientific calculator
It is important to get to know your calculator, the earlier you get one and learn about the scientific functions the better you will be at using them
It’s not just maths that uses these, some of the scientific functions can be used in science exams too

What do I need to know?

The notes below apply to most if not all scientific calculators but the images are based on the Casio fx-83GTX
The Casio fx-85GTX is the same model but also has solar power. Both are labelled “Classwiz” too but be careful here at there is a more advanced “Classwiz” calculator that is used at A level (fx-991EX)

Calculator, IGCSE & GCSE Maths revision notes

The Casio fx-83GTX Classwiz

Be aware if you have an old or very basic scientific calculator that they may work backwards
For example, if you wanted to find sin (57) you would type 57 then press the sin button
Modern calculators tend to work in the order in which we write things

1. Mode/setup

Make sure you know how to change the mode of your calculator, especially if someone else has used it
The “Angle Unit” needs to be degrees – normally indicated by a “D” symbol across the top of the display
Make sure you can switch between “exact” answers (fractions, surds, in terms of π, etc) and “approximate” answers (decimals)
Most calculators default to “Math” mode with the word Math written across the top of the display or using a symbol
When in “Math” mode you can switch whatever is on the answer line between exact and decimals by pressing the “S-D” button

2. Templates

These are largely the shortcut buttons – the fraction button, the square, cube and power buttons, square roots
You can also use SHIFT and these buttons to access functions including mixed numbers, cube roots, and n^th roots

buttons, IGCSE & GCSE Maths revision notes

Calculator shortcut buttons

3. Trigonometry (sin/cos/tan)

Remember to use SHIFT (sometimes called 2nd or INV button) when finding angles
When using these buttons you will find that before you type the angle the calculator automatically gives you an open bracket "(". You should get into the habit of making sure you use a closed bracket ")" after typing the angle in
This is very important if there is something else to type in that comes after sin/cos/tan

4. Standard Form and π

Find the ×10^x button and know how to use it
Modern calculators display standard form in the way it is written
Older models may use a small capital letter "_E" in place of ×10^xon the display line
π is often near or under SHIFT with the standard form button

5. Memory

The ANS (answer) button is very useful – especially when working with decimals in the middle of solutions that you should avoid rounding until your final answer
ANS recalls the last answer the calculator calculated

6.Table

If your calculator has a table function or mode, use it
This can be extremely useful in those “complete the table of values and draw the graph” type questions

7. Brackets and negative numbers

Use as you would in written mathematics
Remember to use the (-) button for a negative number, not the subtract button

8. Judgement and special features

The rule of thumb is to use your calculator to do one calculation at a time
However, you can also make a judgement call on this as to how many marks are available in the question and whether a question asks you to “write down all the digits on your calculator display”
You are better off writing too much down than not enough!

9. Practice!

This is a long list but we will finish by going back to the start – there is nothing better you can do than getting a calculator early and learning how to use it by practising the varying types of questions you are likely to come across

Exam Tip

Always put negative numbers in brackets
- For a quick example, try using your calculator to work out -3² and then (-3)²
In working out always write down more digits than the final answer requires and don’t round them
- e.g. Write 9.3564… (using the three dots shows you haven’t rounded)
- Use the ANS button when you next need that number on your calculator

Worked example

Use your calculator to work out

$\frac{\sqrt{4.69}}{0 . 34^{3} + \sin (45 °)}$

Give your answer as a decimal.
Write down all the figures on your calculator display.

To show your working write down the top (numerator) and bottom (denominator) separately.
Use " ... " to show you haven't rounded.

$\sqrt{4.69} = 2.165 64 . . .$
$0 . 34^{3} + \sin (45 °) = 0.746 410 . . .$

You can type the whole thing in as a single fraction for the final answer, or use the memory/ANS features of your calculator.

It is best to type the whole thing in in one go, using the fraction button, square root button, cube button and remembering to close the bracket after the sine function.

$2.901 406 085$

$a^{5} = \frac{p + q}{p^{2} q}$

Find the value of a when $p = 1.2 \times 10^{- 4}$ and $q = 7.83 \times 10^{5}$ .
Give your answer to 3 decimal places.

Type the whole of the right-hand side into your calculator in one go if you can, using the button for standard form, brackets and the fraction button.

Show each stage as working.

$p + q = 1.2 \times 10^{- 4} + 7.83 \times 10^{5} = 783 000.000 1$

Use brackets when expressions get long or awkward.

$p^{2} q = {(1.2 \times 10^{- 4})}^{2} \times (7.83 \times 10^{5}) = 0.011 275 2$

Write down all the digits on your calculator display for the working stages.

$a^{5} = \frac{783 000.000 1}{0.011 275 2} = 69 444 444.46$

Write more digits than you need at first, only rounding for the final answer.

Use the ANS button with the button for the 5th root.

$a = \sqrt[5]{69 444 444.46} = 37.010 71 . . .$

$a = 37.011$ (3 d.p.)

Complete the table of values for $y = x^{3} - 6 x + 1$ .

$x$	-3	-2	-1	0	1	2	3
$y$		5					10

Use brackets around negative values and the "(-)" key

${(- 3)}^{3} - 6 \times (- 3) + 1 = - 8$

Use arrow keys to go back to the input line and change the "3"'s to "1"'s

${(- 1)}^{3} - 6 \times (- 1) + 1 = 6$
$0^{3} - 6 \times 0 + 1 = 1 1^{3} - 6 \times 1 + 1 = - 4 2^{3} - 6 \times 2 + 1 = - 3$

You can use the TABLE mode/feature of your calculator instead if it has one
Either way we can now complete the table

$x$	-3	-2	-1	0	1	2	3
$y$	-8	5	6	1	-4	-3	10

Using a Calculator (CIE IGCSE Maths: Core)

Revision Note