Printable · GCSE Higher · ages 14-16
Ratio, proportion and rates of change worksheet — GCSE Higher
Fifteen questions across the ratio, proportion and rates of change statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Non-calculator
Ratio, proportion and rates of change worksheet — GCSE Higher
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- 1.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
- 2.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.
- 3.A recipe for 8 people needs 320 g of rice. Sanjay scales the recipe down to serve 5 people, then wants to scale his new amount back up to serve 8 people again. Work out the multiplier he should use to scale his amount for 5 people back up to the amount for 8 people.
- 4.A conversion graph between kilometres and miles passes through the origin and the point (50, 31), with the number of kilometres on the horizontal axis and the number of miles on the vertical axis. Work out the number of miles equivalent to 1 kilometre.
- 5.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.
- 6.The price of a games console is reduced by 10%. In a later sale the reduced price is reduced by 10% again. Work out the overall percentage decrease.
- 7.A charity collects donations from adults and children in the ratio 5:2. Altogether, £238 is collected. Work out how much more the adults donate than the children.
- 8.A photo is enlarged so that its new width is 1.4 times its original width. Write the multiplier that would scale the new width back down to the original width, as a fraction in its simplest form.
- 9.An amount of money is shared in the ratio 1:2:3. The largest share is £90 more than the smallest share. Work out the total amount that was shared.
- 10.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.
- 11.A tangent to a curve at the point where x = 3 passes through the points (1, 2) and (5, 14). A candidate says: "The gradient of the tangent at x = 3 is 3, because 14 − 2 = 12 and 12 ÷ 4 = 3." Which statement is correct?
- 12.A room is drawn on a plan with a scale of 1 : 200. On the plan the room has an area of 12 cm². Work out the real area of the room, in square metres.
- 13.An oven is preheating. Its temperature, T °C, is plotted against time, t minutes, on a straight-line graph. The line passes through the points (2, 60) and (6, 140). Work out the gradient of the line.
- 14.A cordial drink is made by mixing cordial concentrate and water in the ratio 1 : 6. Freya says that a 700 ml jug of this drink contains 100 ml of concentrate. Is she correct? Give a reason for your answer.
- 15.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.
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