Number worksheet — GCSE Higher

1.Find the missing number: ▢ ÷ 15 = 24

2.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

3.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

4.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

5.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

6.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.

7.Work out the reciprocal of (2 + 3)

8.Simplify x⁶ ÷ x²

9.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.

10.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.

11.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

12.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

13.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

14.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.