Number worksheet — GCSE Higher

1.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

2.A washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.

3.Write 0.35 as a fraction in its lowest terms.

4.Write 0.325 as a fraction in its simplest form.

5.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

6.Work out the value of (1/3)⁻²

7.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

8.A charity trek covers 830 miles over roughly 19 days. By rounding each number to 1 significant figure, work out an estimate for the number of miles walked per day.

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.Simplify x⁶ ÷ x²

11.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

12.Work out 35% of 180.

13.Simplify x⁷ × x⁴, giving your answer as a single power of x.

14.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

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