Number worksheet — GCSE Higher

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

2.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

3.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

4.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

5.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

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

7.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.

8.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

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

10.Round 0.006852 to 2 significant figures.

11.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

12.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

13.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

14.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

15.Work out how many factors 100 has.