Number worksheet — GCSE Higher

1.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

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.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

4.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

5.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

6.Work out 10% of 30% of £200.

7.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

8.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

9.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

10.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.

11.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

12.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

13.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

14.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

15.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.