Number worksheet — GCSE Higher

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

2.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.

3.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

4.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.

5.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

6.Work out ∛(−27) + ∛8

7.Work out (−3) × 4 + 2 × (−5)

8.Work out how many factors 36 has.

9.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

10.Write ∛(x²) as a single power of x.

11.A triangle has a base of 8 cm and a perpendicular height of 5 cm, each correct to the nearest centimetre. Work out the upper bound of the area.

12.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

13.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

14.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

15.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?