Number worksheet — GCSE Higher

1.Work out (−2)² − 3

2.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.

3.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

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

5.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.

6.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.

7.Simplify x⁶ ÷ x²

8.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

9.A country has an area of 25,000,000 hectares. Write this area in standard form.

10.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

11.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

12.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

13.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

14.Work out (−36) ÷ (−6) × 2

15.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.