Number worksheet — GCSE Higher

1.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.

2.Write down the reciprocal of 0.2

3.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

4.Simplify √8 + √18, giving your answer in the form k√2.

5.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

6.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

7.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

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

9.Write these three numbers in order of size, starting with the smallest: 0.7, 3/4, 0.72

10.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

11.Work out 5⁰ + 5¹ + 5²

12.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

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

14.Write 60 as a product of its prime factors, using index notation.

15.Write 90 as a product of its prime factors.