Number worksheet — GCSE Higher

1.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

2.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

3.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

4.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

5.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

6.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.

7.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

8.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?

9.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

10.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

11.Work out 3.7 × 24.

12.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

13.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

14.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

15.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.