Number worksheet — GCSE Higher

1.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

2.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

3.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

4.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

5.Work out (3 × 10²) × (2 × 10⁵). Give your answer in standard form.

6.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.

7.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

8.Work out 3³ + 2⁴.

9.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

10.A café buys 18 boxes of teabags at £3.45 each, and sells all the teabags for £108 in total. Work out the café's profit.

11.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

12.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

13.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

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

15.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.