Number worksheet — GCSE Higher

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

2.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

3.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

4.Simplify x⁷ × x⁴, giving your answer as a single power of x.

5.Write down the exact decimal value of the fraction 1/6.

6.Simplify (3a²)² × (2a)³

8.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.

9.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

10.Write ∛(x²) as a single power of x.

11.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.

12.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?

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

14.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

15.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.