Number worksheet — GCSE Higher

1.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.

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

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

4.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.

6.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

7.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

8.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

9.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

10.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

11.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.

12.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

13.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

14.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

15.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.