Number worksheet — GCSE Higher

1.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

2.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

3.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

4.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.

5.Round 0.006852 to 2 significant figures.

6.Work out the exact value of √(2² + 3²)

7.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

8.A company sells 4 × 10³ items per day, each priced at £2.50. It operates for 3 × 10² days a year. Work out the company's total revenue for the year. Give your answer in standard form.

9.Work out the reciprocal of (2 + 3)

10.Work out −(−3)⁴ + (−3)³

11.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

12.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.

13.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

14.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

15.Write ∛(x²) as a single power of x.