Number worksheet — GCSE Foundation

1.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

2.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.

3.Work out ⁴√16

4.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.

5.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

6.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.

7.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

8.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.

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

10.Simplify x⁶ ÷ x²

11.Work out the highest common factor of 12 and 18.

12.A quiz has 50 questions. Freya answers 10% of them incorrectly. Work out how many questions she answers incorrectly.

13.Write down the value of 3⁰

14.Work out √225 ÷ 3.

15.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?