Number worksheet — GCSE Higher

1.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

2.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20

3.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

4.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

5.Simplify (x⁻²)³, giving your answer as a fraction.

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.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

8.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

9.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

10.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

11.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

12.Write down the reciprocal of 0.2

13.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

14.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

15.Work out the value of 2⁻⁴