Number worksheet — GCSE Higher

1.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.

2.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

3.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

4.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

5.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

6.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

7.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

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

9.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

10.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

11.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

12.Work out √225 ÷ 3.

13.3/5 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.

14.Work out 6² − 4².

15.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.