Number worksheet — GCSE Higher

1.Write 0.325 as a fraction in its simplest form.

2.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

3.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

4.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.

5.Write 5/6 as a decimal, showing clearly which digit recurs.

6.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.

7.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

8.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

9.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.

10.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

11.Expand and simplify √3(2 + √12).

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

13.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

14.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

15.Work out ∛(−27) + ∛8