Number worksheet — GCSE Higher

1.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

2.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

3.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

4.4ˣ = 64. Work out the value of x.

5.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

6.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.

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

8.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

9.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

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

11.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

12.Work out 3 + 4 × (−2).

13.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

14.Work out ⁴√16

15.Work out √(4 × 9)