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 shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.
- 2.Simplify the ratio 45 : 30 : 75 to its simplest form.
- 3.A jumper normally costs £45. In a sale it is reduced by 20%. Work out the sale price, then write the sale price as a fraction of the normal price. Give your answer in its simplest form.
- 4.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.
- 5.The total cost, in pounds, of manufacturing a batch of components is plotted against the number of components produced. A tangent to this graph at a particular point has gradient 3.60. What does the value 3.60 represent?
- 6.In a class, 50% of the students study French, 30% study Spanish and the rest study German. Write down the ratio of French : Spanish : German students, in its simplest form.
- 7.In a fruit drink, 3/8 of the total volume is orange juice and the rest is apple juice. Write down the ratio of orange juice to apple juice, in its simplest form.
- 8.A textbook is reduced from £60 to £45. Work out the percentage reduction.
- 9.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.
- 10.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.
- 11.A shop's number of online orders is proportional to its number of in-store orders. Last month there were 45 in-store orders and 180 online orders. Write the ratio of online orders to in-store orders, in its simplest form.
- 12.An adult cinema ticket costs £15 and a child ticket costs £9. Write the ratio of the adult price to the child price in its simplest form.
- 13.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.
- 14.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.
- 15.Amelia uses 2 kg of flour to bake 5 cakes. Using the same recipe, work out how many cakes she can bake with 6 kg of flour.
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