Number worksheet — GCSE Higher

1.Simplify √45.

2.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

3.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

4.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

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

6.Round 592.5 to the nearest 10.

7.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

8.Simplify (y³)⁴, giving your answer as a single power of y.

9.Which of these statements about −0.7 and −0.25 is true?

10.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

11.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

12.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.

13.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

14.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

15.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.