Number worksheet — GCSE Higher

1.Work out √144 − 2 × 3 + √25

2.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

3.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.

4.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

5.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

6.Work out the value of 2⁻⁴

7.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.

8.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

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

10.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

11.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

12.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.

13.Write 200 as a product of its prime factors, using index notation.

14.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

15.Round 0.006852 to 2 significant figures.