AQA · Mathematics · 8300
GCSE Maths: Instantaneous Rate of Change
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Instantaneous 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.
How do you estimate the instantaneous rate of change at a point on a curved graph?
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Draw a tangent to the curve at that point and calculate the tangent's gradient.
How do you find the average rate of change between two points on a curved graph?
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Draw a chord joining the two points and calculate the chord's gradient (change in y ÷ change in x).
Why is a gradient found by drawing a tangent only an estimate?
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The tangent is drawn by eye, so its position and gradient are approximate rather than exact.
What does the area under a speed-time graph represent?
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The distance travelled.
What is the gradient of a curve at a turning point?
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Zero — the tangent at a turning point is horizontal.
When is an object's acceleration zero on a speed-time graph?
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Where the graph is horizontal (constant speed), so its gradient is zero.
On a depth-time graph measured in cm and seconds, the gradient has units of ?.
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cm/s
Acceleration found from a velocity-time graph in m/s and seconds has units of ?.
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m/s²
How do you convert a speed from m/s to km/h?
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Multiply by 3.6 (×3600 seconds per hour, ÷1000 metres per kilometre).
On a distance-time graph, where is the speed highest?
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Where the graph is steepest, i.e. the gradient is greatest.
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