Number worksheet — GCSE Higher

1.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

2.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

3.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

4.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

5.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

6.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

7.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

8.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

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

10.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

11.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

12.Simplify √8 + √18, giving your answer in the form k√2.

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

14.Given that 2⁵ = 32, work out 2⁶.

15.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.