Number worksheet — GCSE Higher

1.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

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

3.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

4.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.

5.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

6.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

7.Work out 5⁰ + 5¹ + 5²

8.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

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 numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

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

12.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

13.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

14.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

15.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³