Number worksheet — GCSE Higher

1.Ten players enter a chess tournament. Every player plays every other player exactly once. Work out how many games are played in the tournament.

2.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

3.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.

4.Write 0.325 as a fraction in its simplest form.

5.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

6.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

7.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

8.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

10.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

11.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.

12.Work out 36 ÷ (2 × 3)

13.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.

14.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.

15.Write 0.06 as a fraction in its simplest form.