Number worksheet — GCSE Higher

1.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

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 sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

4.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

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

6.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

7.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

8.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

9.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

10.Write 0.06 as a fraction in its simplest form.

11.Work out (−36) ÷ (−6) × 2

12.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

13.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.

14.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

15.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.