Number worksheet — GCSE Higher

1.Simplify (3a²)² × (2a)³

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

3.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.

5.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

6.Work out (−2)² − 3

7.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

8.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.

9.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

10.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

11.Work out (−3) × 4 + 2 × (−5)

12.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

13.Work out the value of √(16 + 9)

14.Simplify x⁶ ÷ x²

15.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.