Number worksheet — GCSE Higher

1.Work out the value of √49 + ∛27

2.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

3.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

4.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

5.Work out 3/7 × 14/9. Give your answer as a fraction in its simplest form.

6.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.

7.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

8.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

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

10.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.

11.Work out (5 + 2) × 3²

12.Write 5,000,000 in standard form.

13.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.

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

15.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.