Number worksheet — GCSE Higher

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

2.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

3.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

4.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

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

6.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

7.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

8.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

9.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

10.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.

11.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

12.Work out the value of √(16 + 9)

13.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

14.Work out (−2)² − 3

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