Number worksheet — GCSE Higher

1.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

2.Work out the value of √49 + ∛27

3.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.

4.Work out 3³ + 2⁴.

5.Work out −(−3)⁴ + (−3)³

6.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

7.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.

8.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

9.Write 5,000,000 in standard form.

10.Work out (−6) + (−4) × 3

11.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

12.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

13.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

14.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

15.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.