Number worksheet — GCSE Higher

1.Work out 3 + 4 × (−2).

2.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?

3.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

4.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

5.Work out 5⁰ + 5¹ + 5²

6.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

7.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.

8.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

9.Write 7/12 as a decimal, showing clearly which digit is recurring.

10.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

11.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

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

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

14.Simplify (3a²)² × (2a)³

15.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.