Number worksheet — GCSE Higher

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

2.Work out the reciprocal of (2 + 3)

3.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

4.Write ∛(x²) as a single power of x.

5.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.

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

7.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

8.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.

9.Work out 5/6 × 2/9, giving your answer in its simplest form.

10.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

11.Which of these is written correctly in standard form?

12.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

13.Work out √144 − 2 × 3 + √25

15.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.