Using a Calculator: Edexcel GCSE Foundation maths revision notes

Using a calculator in the exam

Papers 2 and 3 are calculator papers. The calculator does the arithmetic, but you have to tell it exactly what to work out: where the brackets go, what is on the top and the bottom of a fraction, and what is under a square root.

A common question gives you a calculation with powers, roots or a fraction, and says "Work out … Write down all the figures on your calculator display", for 2 marks. Part (b) then asks you to round your answer, to 2 decimal places or to 2 significant figures, for 1 mark.

Brackets, to group part of a calculation.
The fraction key, for a fraction with a calculation on the top or the bottom.
The x^2 key, the power key and the square root key.
The S⇔D key, which changes a fraction answer into a decimal.
The \pi key, for circles.

Squares, cubes and roots

The x^2 key squares the number before it: 4.5^2=4.5\times4.5=20.25. For a cube, use the power key: 1.5^3=1.5\times1.5\times1.5=3.375

The square root key undoes squaring: \sqrt{20.25}=4.5, because 4.5^2=20.25. The cube root key undoes cubing: \sqrt[3]{3.375}=1.5

To square a negative number, put it in brackets. (-1.5)^2=2.25, but typing -1.5^2 gives -2.25, because the calculator squares the 1.5 first and then puts the minus sign in front.

Worked example 1: A square and a square root

Work out 6.3^2-\sqrt{12.25}

Use the x^2 key: 6.3^2=39.69
Use the square root key: \sqrt{12.25}=3.5
Your turn. Now subtract. What is 39.69-3.5?

Your answer

39.69-3.5=36.19
Answer: 36.19

Brackets and fraction bars

A calculator follows the order of operations: powers first, then multiplying and dividing, then adding and subtracting. So it only gives the right answer if you type the calculation in the right way.

Type brackets wherever the question has them. 2.5\times(7.3-1.8)=2.5\times5.5=13.75, but typing 2.5\times7.3-1.8 gives 16.45

A fraction bar groups the whole top and the whole bottom. For \frac{9.6+4.8}{1.2+0.6}, use the fraction key, or put brackets round the top and the bottom: (9.6+4.8)\div(1.2+0.6)=14.4\div1.8=8. Typing 9.6+4.8\div1.2+0.6 gives 14.2, because only the 4.8 is divided.

Safest of all, work out the top and the bottom separately and write both down before you divide. If the final answer is wrong, you can still get a mark for a correct top or bottom.

Worked example 2: Brackets and a negative number

Work out (-2.4)^2+3\times(5.6-1.85)

Keep the minus sign inside the brackets when you square: (-2.4)^2=5.76
Your turn. Work out the bracket, 5.6-1.85

Your answer

5.6-1.85=3.75
Multiply before adding: 3\times3.75=11.25
Add: 5.76+11.25=17.01. Typing the whole calculation in one go, with every bracket, gives 17.01 too.
Answer: 17.01

Worked example 3: Writing down the calculator display

(a) Work out \frac{18.3+2.6^2}{7.4-2.85}. Give your answer as a decimal. Write down all the figures on your calculator display. (b) Write your answer to part (a) correct to 2 decimal places.

Your turn. Work out the top first. Square before you add: what is 18.3+2.6^2?

Your answer

18.3+2.6^2=18.3+6.76=25.06
Work out the bottom: 7.4-2.85=4.55
(a) Divide: 25.06\div4.55 gives 5.507692308. If the display shows a fraction, press S⇔D to change it to a decimal. Write down every figure.
Typing 25.06\div7.4-2.85 would give 0.5364864865, which is wrong: the calculator divides by 7.4 only, then subtracts 2.85
(b) The 2nd decimal place is 0 and the next digit is 7, so the 0 goes up to 1: 5.51
Answer: (a) 5.507692308 (b) 5.51

Reading the display

When a question says "Write down all the figures on your calculator display", copy every digit, in order. Don't round it yet: part (b) usually asks you to do that.

Many calculators give an answer as a fraction. If the question asks for a decimal, press the S⇔D key, which swaps between the fraction and the decimal. So \frac{7}{16} becomes 0.4375

The reciprocal of a number is 1 divided by that number. The reciprocal of 4 is 1\div4=0.25, and the reciprocal of 0.8 is 1\div0.8=1.25. When you are asked for its value, work it out: don't leave it as \frac{1}{0.8}

A very small or very large answer may be shown in standard form. 6.25\times10^{-4} means 0.000625: move the decimal point 4 places to the left. 3.8\times10^{7} means 38\,000\,000: move it 7 places to the right.

Worked example 4: A reciprocal as a decimal

(a) Work out the reciprocal of 0.48. Give your answer as a decimal. Write down all the figures on your calculator display. (b) Write your answer to part (a) correct to 3 significant figures.

The reciprocal is 1 divided by the number, so work out 1\div0.48
Many calculators show this as the fraction \frac{25}{12}. Press S⇔D to change it to a decimal.
(a) The display shows 2.083333333
Your turn. (b) Write 2.083333333 correct to 3 significant figures.

Your answer

The 3 significant figures are 2, 0 and 8. The next digit is 3, so the 8 stays: 2.08
Answer: (a) 2.083333333 (b) 2.08

A square root over a whole calculation

A square root sign covers everything underneath it. In \sqrt{\frac{40}{2.5}} the root is over the whole fraction, so work out 40\div2.5=16 first, then \sqrt{16}=4

Taking the root of the top only would give \frac{\sqrt{40}}{2.5}=2.529822128, which is a different number.

On a calculator, work out the inside first and press equals. Then take the square root of that answer. Or type the whole calculation inside the root, using the fraction key.

Worked example 5: The square root of a fraction

(a) Work out \sqrt{\frac{40.3-6.85}{2.7}}. Write down all the figures on your calculator display. (b) Write your answer to part (a) correct to 3 significant figures.

Your turn. The root covers the whole fraction, so start inside it. Work out the top, 40.3-6.85

Your answer

40.3-6.85=33.45
Divide by the bottom: 33.45\div2.7=12.38888889. Keep this on the display.
(a) Take the square root of that whole answer. The display shows 3.519785347
(b) The first three significant figures are 3, 5 and 1. The next digit is 9, so the 1 goes up to 2: 3.52
Answer: (a) 3.519785347 (b) 3.52

Round once, at the end

In a longer calculation, keep every figure on the display until the last step, then round once. Rounding part of the way through can make your final answer wrong, and lose the accuracy mark.

For an answer in pounds, to the nearest penny means 2 decimal places. Write money with two figures after the point: 12.3 pounds is written £12.30

For circles, use the \pi key rather than 3.14, unless the question tells you to use 3.14. The \pi key holds many more figures, so your answer is more accurate.

Worked example 6: A problem with pi and money

A circular rug has a radius of 1.35 m. The area of a circle is \pi r^2. The material for the rug costs £18.50 per square metre. Work out the cost of the material for the rug. Give your answer to the nearest penny.

Use the \pi key. The area is \pi\times1.35^2
Your turn. Work out 1.35^2

Your answer

1.35^2=1.8225
Area =\pi\times1.8225=5.725552611 square metres. Keep every figure.
Cost =5.725552611\times18.50=105.9227233 pounds, which is £105.92 to the nearest penny.
Rounding the area to 5.7 first would give 5.7\times18.50=105.45, which is wrong.
Answer: £105.92

Common mistakes

Typing a fraction in one go without brackets. Work out the top and the bottom separately and write them down, or use the fraction key.
Square-rooting only part of the calculation. The root covers everything under it, so work out the inside first.
Leaving a reciprocal as a fraction. Work out 1 divided by the number and write the answer as a decimal.
Rounding to decimal places when the question says significant figures. Read which one is asked for before you round.
Rounding the display too early. Write down every figure, keep them all through the calculation, and round once at the end.
Working it out by hand on a calculator paper. Use your calculator, and write down each value it gives you.