Paper Together: sit a paper in a room with your friends.See how it works
A second set of gradient of a curve questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.
A car is 40 m from a post after 5 s and 100 m from the post after 10 s. Work out its average speed in m/s.
Answer: 12
A curve passes through (2, 8) and (4, 8). What is the average gradient between the points?
Answer: 0
A tangent to a speed-time graph passes through (2, 6) and (8, 24), with speed in m/s and time in s. What is the acceleration at the point of contact, in m/s squared?
Answer: 3
A curve passes through (3, 9) and (5, 25). Work out the average gradient between them.
Answer: 8
A ball is 5 m high after 1 s and 15 m high after 3 s. Work out its average speed in m/s over this time.
Answer: 5
A tank holds 20 litres after 2 minutes and 56 litres after 8 minutes. Work out the average rate of filling in litres per minute.
Answer: 6
A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.
A tangent to a distance-time graph passes through (1, 3) and (4, 12), with distance in metres and time in seconds. Estimate the speed at the point of contact.
Answer: 3 m/s
Short one-step questions. Pick an option before you open the answer.
What is the average gradient between two points on a curve?
The change in y divided by the change in x, which is the gradient of the chord joining them. The change in y divided by the change in x, which is the gradient of the chord joining them.
What is a chord?
A straight line joining two points on a curve. A straight line joining two points on a curve.
What is a tangent to a curve?
A straight line that touches the curve at one point without crossing it there. A straight line that touches the curve at one point without crossing it there.
How do you estimate the gradient of a curve at a point?
Draw a tangent at the point and work out the gradient of the tangent. Draw a tangent at the point and work out the gradient of the tangent.
Why choose two points far apart on a tangent?
A small reading error then changes the answer much less. A small reading error then changes the answer much less.
Why is a gradient drawn from a tangent only an estimate?
The tangent is drawn by eye, so it may be slightly off the true tangent. The tangent is drawn by eye, so it may be slightly off the true tangent.
What does the gradient of a distance-time graph represent?
Speed. The unit is distance per time, such as m/s. Speed. The unit is distance per time, such as m/s.
What does the gradient of a speed-time graph represent?
Acceleration. The unit is m/s squared. Acceleration. The unit is m/s squared.
A question says between two points. Chord or tangent?
Chord. Between two points means an average gradient. Chord. Between two points means an average gradient.
A question says at a point. Chord or tangent?
Tangent. At a point means the gradient of the tangent there. Tangent. At a point means the gradient of the tangent there.
What happens to chord gradients as the second point moves closer?
They settle towards the gradient of the tangent at the starting point. They settle towards the gradient of the tangent at the starting point.
Why must you subtract in the same order on the top and the bottom?
Reversing one of them changes the sign of the answer. Reversing one of them changes the sign of the answer.
What unit does a gradient have?
The vertical unit per the horizontal unit, such as litres per minute. The vertical unit per the horizontal unit, such as litres per minute.
What does a negative gradient mean on a distance-time graph?
The distance is falling, so the object is moving back towards the start. The distance is falling, so the object is moving back towards the start.
A curve is steeper at one point than another. How do the gradients compare?
The steeper point has the larger gradient, ignoring the sign. The steeper point has the larger gradient, ignoring the sign.
AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.