Number worksheet — GCSE Higher

1.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

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

3.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.

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

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.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

7.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

8.Write 7/12 as a decimal, showing clearly which digit is recurring.

9.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

10.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

11.Work out how many factors 100 has.

12.Work out (2/3)² + (1/2)². Give your answer as a fraction.

13.Write 0.875 as a fraction in its simplest form.

14.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.

15.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.