Number worksheet — GCSE Higher

1.2/3 of an amount of money is £30. Work out the amount.

2.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

3.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

4.Write 90 as a product of its prime factors.

5.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

6.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

7.Work out how many factors 100 has.

8.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

9.Work out 3 × (−2)² − 5

10.Simplify √8 + √18, giving your answer in the form k√2.

11.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

12.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

13.4ˣ = 64. Work out the value of x.

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

15.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.