Number worksheet — GCSE Higher

1.Work out the reciprocal of (2 + 3)

2.Simplify x⁷ × x⁴, giving your answer as a single power of x.

3.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

4.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.

5.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

6.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

7.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

9.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

10.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.

11.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

12.Given that 2⁵ = 32, work out 2⁶.

13.Work out 4368 ÷ 12.

14.Work out 6² − 4².

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