Number worksheet — GCSE Higher

1.Work out the value of (1/3)⁻²

2.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

3.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.

4.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

5.A red blood cell has a diameter of about 7 × 10⁻⁶ metres. A virus has a diameter about 100 times smaller. Work out the diameter of the virus. Give your answer in standard form.

6.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

7.Work out (5 + 2) × 3²

8.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

9.2/3 of an amount of money is £30. Work out the amount.

10.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.

11.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

12.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

13.Simplify (y³)⁴, giving your answer as a single power of y.

14.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

15.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.