Number worksheet — GCSE Higher

1.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.

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

3.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.

4.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.

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

6.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

7.Write 0.35 as a fraction in its lowest terms.

9.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

10.Work out (−2)² − 3

11.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

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

13.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

14.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

15.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?