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.
Ratio, proportion and rates of change worksheet — GCSE Higher
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- 1.The temperature of a chemical reaction, in °C, is modelled by T = 80 − 6t + 0.5t², where t is the time in minutes after the reaction starts. Which of these four statements about the reaction between t = 2 and t = 6 minutes is correct?
- 2.A toy manufacturer makes a model aircraft that is mathematically similar to the real aircraft, at a scale of 1 : 48. The wingspan of the model is 15 cm. Work out the wingspan of the real aircraft, giving your answer in metres.
- 3.In a bag, the ratio of green counters to yellow counters is 3 : 8. There are 24 yellow counters. A student says, 'There must be 9 green counters.' Is the student correct? Choose the correct verdict and reason.
- 4.A savings account starts with £500. Each year, 4% interest is added, and then £30 is withdrawn from the account. Which recurrence correctly models the balance, £S_n, after n years, with S_0 = 500?
- 5.The density of a type of solid plastic is 0.9 g/cm³. Work out the mass of 0.5 m³ of the plastic, in kilograms.
- 6.A pump fills a paddling pool at a rate of 130 litres per hour. Work out the rate in litres per minute, to 2 decimal places.
- 7.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?
- 8.A cyclist rides 17.5 km on Saturday and 12.25 km on Sunday. Write the distance ridden on Saturday as a fraction of the distance ridden on Sunday, giving your answer in its simplest form.
- 9.A population of fish in a lake is modelled by the recurrence P_{n+1} = 1.1P_n − 30, where P_n is the population after n years, 30 fish are removed by fishing each year, and P_0 = 400. After how many complete years does the population first exceed 460?
- 10.On a straight-line graph the volume of water, V litres, in a tank is plotted on the vertical axis and the time, t minutes, on the horizontal axis. The line passes through (2, 50) and (6, 130). Work out the gradient of the line and give its units.
- 11.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.
- 12.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.
- 13.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².
- 14.y is directly proportional to √x. When x = 4, y = 8. Construct the equation connecting x and y, then work out the value of y when x = 9.
- 15.3 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.
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