Number worksheet — GCSE Higher

1.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

2.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

3.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

4.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

5.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

6.Work out √(4 × 9)

7.Work out (−2)³ + (−3)² − (−4)

8.Work out (−6) + (−4) × 3

9.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

10.Work out −(−3)⁴ + (−3)³

11.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

12.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

13.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

14.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

15.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.