Number worksheet — GCSE Higher

1.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

2.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

3.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

4.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

5.Simplify (3a²)² × (2a)³

6.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

7.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

8.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

9.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

10.Work out 3 × (−2)² − 5

11.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

12.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

14.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

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