Number worksheet — GCSE Higher

1.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

2.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

4.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.

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

6.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?

7.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

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

9.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

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

11.Simplify x⁷ × x⁴, giving your answer as a single power of x.

12.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

13.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.

14.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

15.A country has an area of 25,000,000 hectares. Write this area in standard form.