Number worksheet — GCSE Higher

1.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

2.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

3.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

4.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.

5.Given that 2⁵ = 32, work out 2⁶.

6.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

7.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

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

9.Simplify √45.

10.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

11.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

12.Work out √144 − 2 × 3 + √25

13.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

14.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.

15.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.