AQA · Mathematics · 8300
GCSE Maths: Area under a Graph
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions and answers for Area under a Graph (Corbettmaths Video 389), 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 area under a speed-time graph represent?
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The distance travelled.
On a speed-time graph, when is the acceleration zero?
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Where the graph is horizontal — the speed is constant.
How is the distance under a curved speed-time graph estimated?
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Split the area into strips of equal width (a triangle and trapezia), find each area and add them up.
What is the formula for the area of a trapezium?
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½ × (a + b) × h, where a and b are the parallel sides and h is the distance between them.
Why can trapezium strips underestimate the area under a curve?
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When the curve bends above the straight tops of the strips, some area between the curve and the chords is missed.
How is average speed found from a speed-time graph?
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Total distance (area under the graph) divided by total time.
How is the rate of deceleration read from a speed-time graph?
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It is the gradient of the downward-sloping section: decrease in speed ÷ time taken (in m/s²).
A runner accelerates uniformly from rest to 6 m/s in 4 s, then keeps 6 m/s. How long does a 300 m race take?
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52 seconds. First 4 s: ½ × 4 × 6 = 12 m; remaining 288 m at 6 m/s takes 48 s.
Estimate the area under y = 4 − x² from x = −2 to 2 using strips of width 1.
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10 square units (heights 0, 3, 4, 3, 0; trapezia give 1.5 + 3.5 + 3.5 + 1.5).
On a speed-time graph, a straight sloping line represents ? acceleration.
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uniform
What does the gradient of a speed–time graph represent?
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Acceleration (a negative gradient is deceleration).
How does uniform acceleration from rest appear on a speed–time graph?
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As a straight line starting at the origin; the area beneath it is a triangle, ½ × time × final speed.
How does constant speed appear on a speed–time graph?
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As a horizontal line; the area beneath it is a rectangle, speed × time.
What does the area under a flow-rate (cm³/s) against time graph give?
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The volume of liquid that has flowed, in cm³.
Before using a speed–time graph in m/s with a distance given in km, the distance must be converted to ?.
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metres
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