Ratio, proportion and rates of change worksheet — GCSE Higher

1.Work out the value of x when 4/x = 2/5.

2.A graph shows y plotted against x. The graph is a curve that gets closer to both axes but never touches them, and y decreases as x increases. Write down whether this graph could show direct proportion, inverse proportion, or neither.

3.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

4.A jumper costs £45 at Shop A, where it is reduced by 20%. The same jumper costs £34 at Shop B, where a further 10% reduction is then applied. Work out the difference between the two reduced prices.

5.Write the ratio 0.75 : 2 as a ratio of whole numbers in its simplest form.

6.A sprinter's distance from the start line, in metres, is plotted against time, in seconds. A tangent to the graph at t = 2 seconds has gradient 6. A tangent at t = 8 seconds has gradient 9.5. Which statement correctly compares the sprinter's speed at these two times?

7.Write 400 g : 1.5 kg as a ratio in its simplest form.

8.Two quantities are connected by the formula y = 0.8x. Write down the ratio y : x in its simplest form.

9.Two mathematically similar cylinders have heights in the ratio 3 : 4. Write the ratio of their volumes in its simplest form.

10.A cyclist's speed, in metres per second, is plotted against time, in seconds, since she sets off. Which statement correctly pairs the gradient of a tangent to this graph, and the area between the graph and the time-axis, with what each one represents?

11.Two mathematically similar rectangles have widths 5 cm and 10 cm. The perimeter of the smaller rectangle is 18 cm. Work out the perimeter of the larger rectangle.

12.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.

13.A shop's profit, P pounds, is in direct proportion to the number of items sold, n. When 15 items are sold, the profit is £45. Write down the ratio n : P in its simplest form for this shop.

14.A rectangular garden has its length and width in the ratio 5:3. Given that the perimeter of the garden is 64 m, work out the width of the garden.

15.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.