Number worksheet — GCSE Higher

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

2.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

3.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

4.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.

5.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

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

7.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

8.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?

9.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.

10.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

11.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

12.Work out −(−3)⁴ + (−3)³

13.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

14.Work out −4.5 + 2.8.

15.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.