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    PracticeAQA GCSEAQA GCSE Maths Higher Tier Paper 3 CalculatorQuestion 10
    Medium3 marksgraphing
    Ratio Proportion and Rates of ChangeHigherRatio Proportion and Rates of ChangeGraphsInverse Proportion

    AQA GCSE · Question 10 · Ratio Proportion and Rates of Change

    Time taken (hours) Average speed (mph) 160 230 3 4 5 610 Time taken (hours) Average speed (mph) 0 10 20 30 40 50 60 0 1 2 3 4 5 6

    A car will travel 60 miles. Draw a graph to show the average speed of the car for times taken between 1 hour and 6 hours. You may use the table to help you.

    How to approach this question

    1. Understand the relationship between speed, distance, and time: Speed = Distance / Time. 2. The distance is constant at 60 miles. The time taken varies from 1 to 6 hours. 3. Use the formula to calculate the average speed for each time value in the table (t=3, 4, 5). 4. For example, when time = 3 hours, speed = 60 / 3 = 20 mph. 5. Once the table is complete, you will have a set of coordinate pairs (Time, Speed). 6. Plot these points on the provided axes. 7. Connect the points with a smooth curve, not straight lines.

    Full Answer

    The relationship between average speed (S), distance (D), and time (T) is given by the formula S = D/T. In this problem, the distance is fixed at D = 60 miles. So the formula is S = 60/T. This is an inverse proportion relationship, which will produce a curve on the graph. First, we complete the table by calculating the speed for each given time: - When T = 1, S = 60/1 = 60 mph. - When T = 2, S = 60/2 = 30 mph. - When T = 3, S = 60/3 = 20 mph. - When T = 4, S = 60/4 = 15 mph. - When T = 5, S = 60/5 = 12 mph. - When T = 6, S = 60/6 = 10 mph. Next, we plot these coordinate pairs (T, S) on the graph: (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10). Finally, we connect these points with a smooth curve. The graph should start high on the left and curve downwards to the right, getting flatter as time increases.

    Common mistakes

    ✗ Joining the points with straight lines instead of a smooth curve. ✗ Incorrectly calculating the speed values. ✗ Plotting the points inaccurately on the graph, for example misinterpreting the scale on the y-axis.
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