Number worksheet — GCSE Higher

1.Work out 3 × (−2)² − 5

2.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

3.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

4.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

5.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

6.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

7.Work out the value of (1/3)⁻²

8.Work out how many factors 36 has.

9.Work out the value of √49 + ∛27

10.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.

11.Estimate the value of √45, giving your answer to the nearest whole number.

12.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

13.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

14.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

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.