Number worksheet — GCSE Higher

1.Simplify (x⁻²)³, giving your answer as a fraction.

2.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

3.Write 60 as a product of its prime factors, using index notation.

4.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.

5.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

6.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.

7.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

8.Work out (−2)² − 3

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

10.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

11.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

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

13.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.

14.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.

15.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.