Number worksheet — GCSE Higher

1.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

2.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

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

4.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

5.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

6.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

7.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.

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

9.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

10.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

11.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

12.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

13.Write 60 as a product of its prime factors, using index notation.

14.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

15.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.