Number worksheet — GCSE Higher

1.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.

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

3.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

4.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

6.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.

7.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

8.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

9.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

10.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

11.Work out −4.5 + 2.8.

12.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

13.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.

14.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

15.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.