Number worksheet — GCSE Higher

1.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?

2.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

3.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

4.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

5.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

6.Find the missing number: ▢ ÷ 15 = 24

7.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

8.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

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.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

11.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

12.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

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

14.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

15.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.