Number worksheet — GCSE Higher

1.Simplify (3a²)² × (2a)³

2.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

3.Round 0.006482 to 2 significant figures.

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.Write 90 as a product of its prime factors.

6.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

7.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

8.Estimate the value of √45, giving your answer to the nearest whole number.

9.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

10.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

11.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.

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

13.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

14.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

15.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?