Number worksheet — GCSE Foundation

1.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

2.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

3.Simplify x⁶ ÷ x²

4.4ˣ = 64. Work out the value of x.

5.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.

6.Work out √144

7.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.

8.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

9.Work out an estimate for 37 × 84, by rounding each number to 1 significant figure.

10.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

11.Freya types 4² + 3² into her calculator and writes down 49. Work out the correct value of 4² + 3².

12.Work out the value of √49 + ∛27

14.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

15.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.