Number worksheet — GCSE Higher

1.4ˣ = 64. Work out the value of x.

2.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

3.Write 90 as a product of its prime factors.

4.Simplify ⁴√(16a⁸b¹²)

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

6.Work out (−6) + (−4) × 3

7.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

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

9.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

10.Work out √225 ÷ 3.

11.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.

12.Find the missing number: 17 × ▢ = 391

13.Write 60 as a product of its prime factors, using index notation.

14.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

15.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.