Number worksheet — GCSE Higher

1.Write ∛(x²) as a single power of x.

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

3.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

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

5.Work out (5 + 2) × 3²

6.A rectangular plywood panel measures 2.4 m by 0.75 m. Work out the area of the panel in square metres, giving your answer as a fraction in its simplest form.

7.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

8.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

9.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

10.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

11.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

12.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.

13.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

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 supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.