Number worksheet — GCSE Higher

1.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

2.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

3.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

4.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.

5.Work out 35% of 180.

6.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.

7.Work out ∛64.

8.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

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

10.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

11.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

12.Work out 3.7 × 24.

13.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

14.Which statement about the number 91 is correct?

15.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.