AQA · Mathematics · 8300
GCSE Maths: Average Rate of Change
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Average Rate of Change (Corbettmaths Video 390), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What does the gradient of a distance–time graph represent?
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Speed — the rate of change of distance with respect to time.
What does the gradient of a velocity–time graph represent?
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Acceleration — the rate of change of velocity with respect to time.
What does the area under a speed–time graph represent?
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The distance travelled.
How do you estimate the gradient of a curve at a single point?
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Draw a tangent to the curve at that point and calculate the tangent's gradient (change in y ÷ change in x).
Why is a gradient found by drawing a tangent to a curve only an estimate?
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The tangent is drawn by eye, so a slightly different tangent would give a different gradient.
How do you find the average rate of change between two points on a curve?
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Draw a chord joining the two points and calculate its gradient: change in y ÷ change in x.
What does the gradient of a volume–time graph of a pool being filled represent?
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The rate at which the volume of water is increasing, e.g. in litres per minute.
On a speed–time graph, when is an object not accelerating?
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Where the graph is horizontal — the gradient is zero, so the speed is constant.
A negative gradient on a velocity–time graph represents ?.
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deceleration
What are the units of acceleration when velocity is in m/s and time in seconds?
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m/s² (metres per second squared).
How do you convert a speed from m/s to km/h?
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Multiply by 3.6 (there are 3600 seconds in an hour and 1000 metres in a kilometre).
On a height–time graph of a thrown ball, when is its speed 0 m/s?
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At the turning point (maximum height), where the gradient of the graph is zero.
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