Number worksheet — GCSE Higher

1.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

2.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

3.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

4.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

5.Work out √144 − 2 × 3 + √25

6.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

7.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

8.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

9.Work out 3³ + 2⁴.

10.Write 0.325 as a fraction in its simplest form.

11.Write down the exact decimal value of the fraction 1/6.

12.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

13.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

14.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.

15.Simplify (3a²)² × (2a)³