Number worksheet — GCSE Higher

1.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.

2.Work out ⁴√81

3.Work out the value of 6² − 4³.

4.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.

5.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

6.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

7.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

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

9.Work out 3 + 4 × (−2).

10.Write 0.36 as a fraction in its simplest form.

11.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

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

13.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.

14.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

15.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.