Number worksheet — GCSE Higher

1.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

2.Which statement about the number 91 is correct?

3.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

4.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

5.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

6.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

7.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

8.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

9.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

10.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

11.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

12.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

13.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

14.Write 7/12 as a decimal, showing clearly which digit is recurring.

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