Number worksheet — GCSE Higher

1.Work out √144 − 2 × 3 + √25

2.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.

3.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

4.Work out the value of (1/3)⁻²

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

6.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

7.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

8.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?

9.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

10.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

11.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.

12.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

13.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.

14.Write 0.06 as a fraction in its simplest form.

15.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.