Number worksheet — GCSE Foundation

1.Simplify x⁶ ÷ x²

2.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

3.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

4.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.

5.Four weather stations each recorded their lowest overnight temperature. Which of these readings is the lowest?

6.The mass of a parcel is 3 kg, correct to the nearest kilogram. Which of these masses is not possible for the parcel?

7.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

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

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

11.Which of these numbers is the largest: −9, −7, −4, −2?

12.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

13.Amelia eats 5/8 of a bar of chocolate and Oliver eats 3/4 of an identical bar. Write both amounts as eighths and write down the greater of the two fractions.

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

15.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.