Number worksheet — GCSE Higher

1.Work out (−2)³ + (−3)² − (−4)

2.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.

3.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

4.Work out 3.7 × 24.

5.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

6.Write 12 as a product of its prime factors.

7.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

8.Work out −4.5 + 2.8.

9.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

10.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

11.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

12.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

13.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

14.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

15.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%