Number worksheet — GCSE Higher

1.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

2.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

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

4.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.

5.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

6.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

7.Round 0.006482 to 2 significant figures.

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

9.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

10.Work out (−2)³ + (−3)² − (−4)

11.Work out ⁴√81

12.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

13.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

14.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

15.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.