Number worksheet — GCSE Higher

1.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

2.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

3.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

4.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.

5.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

6.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

7.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

8.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

9.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

10.Work out √(4 × 9)

11.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

12.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

13.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

14.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

15.Simplify x⁶ ÷ x²