Number worksheet — GCSE Higher

1.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.

2.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

3.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

4.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

5.Write ∛(x²) as a single power of x.

6.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

7.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

8.A country has an area of 25,000,000 hectares. Write this area in standard form.

9.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.

10.Which of these statements about −0.7 and −0.25 is true?

11.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

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

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

14.Which statement about the number 91 is correct?

15.Round 0.006852 to 2 significant figures.