Number worksheet — GCSE Higher

1.Write 90 as a product of its prime factors.

2.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

3.√700 lies between which two consecutive integers?

4.Last year a company made a profit of £5,200,000. Write this amount in standard form.

5.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

6.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

7.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.

8.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

9.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

10.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.

11.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

12.Work out ∛64.

13.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.

14.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

15.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.