Number worksheet — GCSE Higher

1.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

2.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.

3.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.

4.A country has an area of 25,000,000 hectares. Write this area in standard form.

5.Write 90 as a product of its prime factors.

6.Work out the value of 2⁻⁴

7.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

8.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

9.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

10.Work out √(4 × 9)

11.In a science experiment, the temperature of a liquid is recorded as 18.6 °C, correct to the nearest 0.2 °C. Write down the error interval for the actual temperature, T °C.

12.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

13.Write 200 as a product of its prime factors, using index notation.

14.Write 0.06 as a fraction in its simplest form.

15.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.