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.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

3.Write 12 as a product of its prime factors.

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

5.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

6.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.

7.Write 7/12 as a decimal, showing clearly which digit is recurring.

8.Work out √144 − 2 × 3 + √25

9.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

10.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

11.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

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

13.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

14.Work out the value of (1/3)⁻²

15.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.