Number worksheet — GCSE Higher

1.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

2.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

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

4.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

5.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.

6.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

7.Expand and simplify √3(2 + √12).

8.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

9.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

10.Write ∛(x²) as a single power of x.

11.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

12.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

13.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

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

15.At a book fair the ratio of fiction books to non-fiction books is 4 : 5. Of the non-fiction books, 3/5 are about history. Work out the fraction of all the books at the fair that are history books.