Number worksheet — GCSE Higher

1.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.

2.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

3.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

4.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

5.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

6.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

7.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.

8.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.

9.Write down the symbol that makes this statement true: −2/3 ___ −5/6

10.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

11.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

12.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

13.Write 90 as a product of its prime factors.

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

15.A quantity surveyor calculates a length as 24.6851 m. Round this length to 2 decimal places.