Number worksheet — GCSE Higher

1.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

2.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.

3.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

4.Work out 3 + 4 × (−2).

5.Work out 100 − 4 × 5²

6.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

7.A café sells ice cream in three flavours: vanilla, mango and pistachio. Isla buys a cone with two scoops, using two different flavours, one for the bottom scoop and one for the top scoop. Work out how many different cones she could buy.

8.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.

9.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

10.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

11.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

12.Work out (−3) × 4 + 2 × (−5)

13.Simplify x⁷ × x⁴, giving your answer as a single power of x.

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

15.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.