Number worksheet — GCSE Higher

1.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

2.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.

3.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

4.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

5.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.

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

7.Work out 5⁰ + 5¹ + 5²

9.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

10.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.

11.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

12.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.

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

14.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.

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