Number worksheet — GCSE Higher

1.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

2.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.

3.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

4.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

5.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

6.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.

7.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

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

9.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

10.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

11.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

12.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

13.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

14.Round 0.006482 to 2 significant figures.

15.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.