Number worksheet — GCSE Higher

1.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.

2.Write 5,000,000 in standard form.

3.A cube-shaped storage tank has a volume of 15,625 cubic centimetres. Work out the length of one edge of the tank.

4.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

5.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

6.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

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

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

9.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

10.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

11.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

12.Work out 3³ + 2⁴.

13.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

14.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.

15.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.