Printable · GCSE Foundation · ages 14-16
Ratio, proportion and rates of change worksheet — GCSE Foundation
Fifteen questions across the ratio, proportion and rates of change statements at Foundation 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 Foundation
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- 1.Two quantities are connected by the formula y = 0.8x. Write down the ratio y : x in its simplest form.y = 0.8x
- 2.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.
- 3.A block of wood has a mass of 60 g and a volume of 100 cm³. Work out the density of the block, in g/cm³.
- 4.A plan is drawn to a scale of 1 : 25. A real fence is 10 m long. Work out the length of the fence on the plan, in centimetres.
- 5.A coach travels 210 miles at an average speed of 70 mph. Work out how long the journey takes.
- 6.A metal alloy is made from copper and tin in the ratio 7:3. Work out the mass of tin in 250 g of the alloy.
- 7.Write the ratio 5 : 8 in the form 1 : n.
- 8.The ratio of cats to dogs in a shelter is 3:4. There are 18 cats. Work out the total number of animals in the shelter.
- 9.A charity receives £360 in donations in January and £480 in donations in February. Write the amount received in January as a fraction of the amount received in February, giving your answer in its simplest form.
- 10.3 builders put up a fence in 12 days. All the builders work at the same rate, so the number of days is inversely proportional to the number of builders. Work out how long 9 builders take to put up the same fence.
- 11.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.
- 12.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.
- 13.Two mathematically similar rectangles have lengths in the ratio 3 : 5. The area of the smaller rectangle is 27 cm². Work out the area of the larger rectangle.
- 14.A plumber's charge, C pounds, for a job lasting h hours is shown on a straight-line graph. The line passes through the points (1, 45) and (3, 85). Work out what the gradient of this line represents, in context.
- 15.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.
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