Number worksheet — GCSE Higher

1.Write ∛(x²) as a single power of x.

2.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.

3.Work out (−2)² − 3

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

5.Which one of these statements is true?

6.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.

7.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

8.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

9.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

10.Work out how many factors 36 has.

11.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

12.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

13.Simplify √8 + √18, giving your answer in the form k√2.

14.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

15.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.