Number worksheet — GCSE Higher

1.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.

2.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

3.Work out (−2)² − 3

4.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

5.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

6.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

7.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

8.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

9.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?

10.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

11.Work out (−2)³ + (−3)² − (−4)

12.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

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

14.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.

15.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.