Number worksheet — GCSE Higher

1.Write 0.35 as a fraction in its lowest terms.

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

3.Simplify x⁶ ÷ x²

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

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

6.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

7.Work out −4.5 + 2.8.

8.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

9.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

10.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.

11.Simplify √45.

12.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

13.Write 0.875 as a fraction in its simplest form.

14.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.

15.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.