Number worksheet — GCSE Higher

1.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

2.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

3.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

4.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

5.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.

7.Estimate the value of √45, giving your answer to the nearest whole number.

8.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.

9.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

10.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

11.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

12.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

13.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

15.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.