Number worksheet — GCSE Higher

1.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

2.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

3.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

4.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.

5.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

6.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.

7.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

8.Write 5/6 as a decimal, showing clearly which digit recurs.

9.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?

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

11.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

12.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

13.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

14.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

15.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%