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.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
- 2.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.
- 3.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.
- 4.A model car is built at a scale of 1 : 20 compared with the real car. Work out the factor by which the surface area to be painted on the real car is bigger than the surface area of the model.
- 5.Leah puts £4000 into a savings account paying 3% compound interest each year. At the end of 2 years she takes out all of the money and spends £1500 of it on a laptop. Work out how much of the money she has left.
- 6.The length of ribbon A is 5/12 of the length of ribbon B. Write the length of ribbon B as a fraction of the length of ribbon A.
- 7.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.
- 8.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.
- 9.Noah runs 2 km in 10 minutes. Work out how long he takes to run 5 km at the same speed.
- 10.A train journey takes 2 hours 15 minutes. A bus journey to the same place takes 3 hours 45 minutes. Write the time for the train journey as a fraction of the time for the bus journey, giving your answer in its simplest form.
- 11.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
- 12.Simplify the ratio 45 : 30 : 75 to its simplest form.
- 13.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
- 14.y is directly proportional to x. When x = 5, y = 18. Work out the value of y when x = 15.
- 15.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.
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