Number worksheet — GCSE Higher

1.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

2.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.

3.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

4.Work out 35% of 180.

5.Work out −(−3)⁴ + (−3)³

6.Which of these is written correctly in standard form?

7.A plane flies 2340 km at an average speed of 780 km/h. It departs at 08:20. Work out the arrival time, using the 24-hour clock.

8.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

9.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.

10.Simplify √45.

11.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

12.Work out √25 + 4² − 12 ÷ 3

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

14.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

15.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.