Ratio, proportion and rates of change worksheet — GCSE Higher

1.The ratio of the number of pages Mia has read to the number of pages Leo has read is 7 : 4. Mia has read 84 pages. Work out how many pages they have read altogether.

2.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.

3.Two straight-line graphs represent y = 2x and y = 5x. For the same value of x, where x ≠ 0, write down the ratio of the y-value on the first graph to the y-value on the second graph, in its simplest form.

4.The ratio of the amount Noah has saved to the amount Grace has saved is 4:5. Noah has saved £200. Work out how much they have saved altogether.

5.1 metre = 100 cm. Work out how many square centimetres there are in 1 square metre.

6.A post 2 metres tall casts a shadow 3 metres long. At the same time a nearby tree casts a shadow 12 metres long. Work out the height of the tree.

7.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.

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

9.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.

10.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.

11.The height of a candle, in cm, is measured as it burns: t = 0 min, height = 20.0; t = 3 min, height = 18.7; t = 5 min, height = 17.5; t = 6 min, height = 16.6; t = 7 min, height = 15.4; t = 9 min, height = 13.4. Which pair of readings gives the best estimate of the instantaneous rate of change of the height at t = 6 minutes, and why?

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

13.A cyclist's distance travelled, in metres, is recorded against time, in seconds. From t = 3 to t = 8 the distance increases from 12 m to 32 m. A tangent to the distance–time graph at t = 6 has gradient 3. Work out the average speed of the cyclist over the interval from t = 3 to t = 8.

14.A cyclist rides 17.5 km on Saturday and 12.25 km on Sunday. Write the distance ridden on Saturday as a fraction of the distance ridden on Sunday, giving your answer in its simplest form.

15.The number of euros, e, received is directly proportional to the number of pounds, p, exchanged. Exchanging £40 gives 46 euros. Work out how many euros are received for £65, giving your answer to the nearest euro.