Number worksheet — GCSE Higher

1.A vending machine sells 4 types of crisps, 5 types of chocolate bar and 2 types of drink. Work out how many different combinations of one crisp packet, one chocolate bar and one drink can be bought.

2.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

3.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

4.Work out 3 × (−2)² − 5

5.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

6.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

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.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

9.Work out ⁴√16

10.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

11.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

12.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

13.Which of these statements about −0.7 and −0.25 is true?

14.Write 200 as a product of its prime factors, using index notation.

15.Round 0.006852 to 2 significant figures.