Number worksheet — GCSE Higher

1.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

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

3.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.

4.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

5.Work out the reciprocal of (2 + 3)

6.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

7.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.

8.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

9.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

10.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

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

12.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

13.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

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.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?