Number worksheet — GCSE Higher

1.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

2.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

3.Find the missing number: ▢ ÷ 15 = 24

4.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

5.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

6.Which one of these statements is true?

7.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

8.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

9.Work out (−3) × 4 + 2 × (−5)

10.A cube-shaped storage box has edges of length 7 cm. A shelf can hold a total volume of 2,000 cm³. Work out the greatest number of these boxes that will fit in that volume.

11.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

13.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.

14.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

15.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.