Number worksheet — GCSE Higher

1.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

2.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.

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

4.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

5.Work out (−6) + (−4) × 3

6.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

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

8.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.

9.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.

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

11.Work out how many factors 100 has.

12.Work out the value of 2⁻²

13.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

14.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.

15.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.