Number worksheet — GCSE Higher

1.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

2.Simplify (y³)⁴, giving your answer as a single power of y.

3.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

4.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

5.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

6.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

7.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.

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

9.Work out 35% of 180.

10.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

11.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

12.Write down the symbol that makes this statement true: −2/3 ___ −5/6

13.Work out √3 × √12, giving your answer as an integer.

14.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

15.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.