Number worksheet — GCSE Higher

1.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

2.A car travels 180 km using 6 litres of fuel. Work out the car's fuel consumption in kilometres per litre, then work out how many kilometres it can travel on a full tank of 12 litres at this rate.

3.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.

4.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

5.Write 200 as a product of its prime factors, using index notation.

6.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

7.4ˣ = 64. Work out the value of x.

8.Write 0.36 as a fraction in its simplest form.

9.Simplify x⁶ ÷ x²

10.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.

11.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.

12.√700 lies between which two consecutive integers?

13.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.

14.Write 7/12 as a decimal, showing clearly which digit is recurring.

15.Last year a company made a profit of £5,200,000. Write this amount in standard form.