Number worksheet — GCSE Higher

1.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?

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

3.Write 0.875 as a fraction in its simplest form.

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

5.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

6.Work out an estimate for 2.9² + 3.1², by rounding each number to the nearest whole number.

7.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.

8.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

9.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

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

11.Write down the reciprocal of 0.2

12.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

13.Work out (−2)² − 3

14.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.

15.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.