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.
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Ratio, proportion and rates of change worksheet — GCSE Higher
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- 1.A delivery driver travels 45 km in the first 30 minutes of a journey, and then a further 75 km in the next 1 hour. Work out her average speed for the whole journey, in km/h.
- 2.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.
- 3.The volume of water in a paddling pool, in litres, is plotted against the time since the tap was turned on, in minutes. What are the units of the gradient of a tangent to this graph?
- 4.Noah runs 2 km in 10 minutes. Work out how long he takes to run 5 km at the same speed.
- 5.Two mathematically similar polygons have perimeters in the ratio 2 : 5. Write the ratio of their areas in its simplest form.
- 6.A furniture designer makes a scale model of a wardrobe using a scale of 1 : 8. The real wardrobe is 2.4 m tall and 1.2 m wide. Work out the perimeter of the front face of the model wardrobe, in centimetres.
- 7.Two mathematically similar triangular flags have areas in the ratio 4 : 25. The height of the smaller flag is 6 cm. Work out the height of the larger flag.
- 8.There are 84 passengers on a double-decker bus. 35 of the passengers are adults and the rest are children. Write the number of adults as a fraction of the number of children. Give your answer in its simplest form.
- 9.The speed of a car is given by v = d ÷ t. A car travels 180 km in 3 hours. Work out the average speed of the car in km/h.
- 10.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.
- 11.1 metre = 100 cm. Work out how many square centimetres there are in 1 square metre.
- 12.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
- 13.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.
- 14.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.
- 15.5 decorators paint 3 rooms in 6 hours. All the decorators work at the same rate. Work out how long it takes 10 decorators to paint 5 rooms.
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