Number worksheet — GCSE Higher

1.Work out 6² − 4².

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.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

4.Work out the value of (√5)⁴

5.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

6.Work out ∛64.

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

8.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

9.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.

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

11.Work out (−2)² − 3

12.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?

13.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

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

15.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.