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.Square P has sides of length 3 cm. Square Q has sides of length 12 cm. Write the ratio of the area of square P to the area of square Q in its simplest form.
- 2.A rope of length A is 1.5 times as long as a rope of length B. Write the ratio A : B in its simplest form.
- 3.The table shows values of x and y. x: 3, 5, 8. y: 12, 20, 32. Which statement correctly describes the relationship between x and y?
- 4.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.
- 5.A scale drawing of a garden uses a scale of 1 : 20. Write down a formula for the real length, L metres, in terms of the length on the drawing, d centimetres, given that 1 metre = 100 centimetres.
- 6.A beaker holds 500 g of a salt solution of concentration 12%. Pure water is added until the concentration falls to 8%. Work out the mass of water added.
- 7.A parcel has a mass of 2400 g. Given that 1 kg = 1000 g, work out the mass of the parcel in kilograms.
- 8.A spring's extension is directly proportional to the force applied to it. A force of 5 N produces an extension of 12 mm. Work out the extension produced by a force of 20 N.
- 9.Triangle ABC is mathematically similar to triangle PQR, with AB corresponding to PQ and BC corresponding to QR. AB = 6 cm, BC = 8 cm and PQ = 12 cm. Work out the length of QR.
- 10.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.
- 11.Two mathematically similar flags are made in different sizes. The length scale factor from the smaller flag to the larger flag is 5. Work out the area scale factor from the smaller flag to the larger flag.
- 12.A straight-line graph shows the cost, C pounds, of hiring a small van for m miles driven. The line passes through the origin and the point (25, 20). Work out the gradient of the line.
- 13.3 kg of apples cost £6. Work out the cost of 5 kg of the same apples.
- 14.A map's scale is given as '1 cm represents 2 km'. Write this scale in the form 1 : n.
- 15.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.
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