Number worksheet — GCSE Higher

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

2.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

3.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

4.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.

5.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

6.Work out √144 − 2 × 3 + √25

7.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

8.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

9.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

10.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

11.Simplify √8 + √18, giving your answer in the form k√2.

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

13.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

14.Work out (−6) + (−4) × 3

15.Work out (−2)² − 3