Number worksheet — GCSE Higher

1.Work out 35% of 180.

2.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

3.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.

4.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.

5.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.

6.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

7.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

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

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

10.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

11.Work out 10% of 30% of £200.

12.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

13.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

14.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

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