Number worksheet — GCSE Higher

1.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.

2.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

3.Given that 2⁵ = 32, work out 2⁶.

4.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

5.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

6.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

7.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

8.Write 200 as a product of its prime factors, using index notation.

9.Work out the value of 2⁻⁴

10.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.

11.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

12.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

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.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

15.Work out the value of √49 + ∛27