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.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

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

4.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

5.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

6.Simplify (3a²)² × (2a)³

7.Work out 3 + 4 × (−2).

8.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.

9.Work out 4368 ÷ 12.

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

11.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

12.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

13.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.

14.Simplify (x⁻²)³, giving your answer as a fraction.

15.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.