Number worksheet — GCSE Higher

1.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.

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

3.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

4.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

5.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

6.Simplify (y³)⁴, giving your answer as a single power of y.

7.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

8.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

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

10.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

11.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

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

13.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

14.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

15.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.