Number worksheet — GCSE Higher

1.Work out (2/3)² + (1/2)². Give your answer as a fraction.

2.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.

3.Which of these statements about −0.7 and −0.25 is true?

4.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.

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

6.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

7.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

8.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

9.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

10.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

11.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

12.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.

13.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

14.Round 592.5 to the nearest 10.

15.Work out 3³ + 2⁴.