Ratio, proportion and rates of change worksheet — GCSE Higher

1.A metal cylinder has a mass of 356.5 g and a volume of 47 cm³. Work out the density of the cylinder, in g/cm³, to 1 decimal place.

2.A runner's speed is 8 m/s. Given that there are 3600 seconds in an hour and 1000 metres in a kilometre, work out the runner's speed in km/h.

3.A hiker's distance from the start of the trail, in kilometres, is plotted against time, in minutes, since she set off. At t = 45 minutes she stops to rest, so her distance from the start is neither increasing nor decreasing at that instant. Which statement about the tangent to the distance–time graph at t = 45 minutes is correct?

4.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.

5.The number of members of a running club increases from 45 to 54. Work out the percentage increase.

6.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.

7.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.

8.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.

9.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.

10.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.

11.In a fruit bowl, the ratio of apples to oranges is 5 : 3. Work out what percentage of the fruit in the bowl is apples.

12.An architect builds a scale model of a staircase before construction. The model is mathematically similar to the real staircase, at a scale of 1 : 10. The model covers a floor area of 0.4 m² on the plan. Work out the floor area the real staircase will cover, giving your answer in m².

13.Noah runs 2 km in 10 minutes. Work out how long he takes to run 5 km at the same speed.

14.A baker uses 450 g of flour and 300 g of butter in a batch of pastry. Write the mass of butter as a fraction of the total mass of flour and butter, in its simplest form.

15.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.