Number worksheet — GCSE Higher

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

2.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

3.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

4.Work out 3³ + 2⁴.

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

6.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

7.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

8.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

9.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.

10.Write 5,000,000 in standard form.

11.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.

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

13.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

14.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

15.Work out the value of 2⁻⁴