Number worksheet — GCSE Higher

1.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

2.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.

3.Simplify ⁴√(16a⁸b¹²)

4.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?

5.Work out √225 ÷ 3.

6.Write these numbers in order, starting with the smallest: −1.4, 5/4, −6/5, 1.3, 0

7.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

8.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

9.Work out the value of 2⁻²

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.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

12.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.

13.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

14.Simplify (x⁻²)³, giving your answer as a fraction.

15.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.