Number worksheet — GCSE Higher

1.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

2.Simplify x⁶ ÷ x²

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.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

5.Work out ⁴√16

6.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.

7.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.

8.Work out √144 − 2 × 3 + √25

9.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

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

11.Work out −(−3)⁴ + (−3)³

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

13.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.

14.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

15.Write 0.36 as a fraction in its simplest form.