Number worksheet — GCSE Higher

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

2.Write 12 as a product of its prime factors.

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.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

5.Work out (5 + 2) × 3²

6.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

7.Write 200 as a product of its prime factors, using index notation.

8.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

9.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

10.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

11.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.

12.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.

13.Simplify x⁶ ÷ x²

14.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

15.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.