Number worksheet — GCSE Higher

1.Work out ⁴√16

2.Work out (5 + 2) × 3²

3.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.

4.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?

5.Write 60 as a product of its prime factors, using index notation.

6.Work out (−2)² − 3

7.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.

8.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

9.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

10.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.

11.A car travels 100 km, correct to the nearest km, in a time of 2 hours, correct to the nearest 0.1 hour. Work out the average speed, in km/h, to the greatest degree of accuracy the bounds can guarantee.

12.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

13.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

14.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

15.Work out √144 − 2 × 3 + √25