Lesson R15
R15 Average and instantaneous rates of change Quiz: AQA Maths, Unit 3
20 questions
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Lesson R15, Average and instantaneous rates of change: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 3: Ratio, proportion and rates of change, written with Revision Ninja.
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The 20 questions
-
What type of rate of change is given by the gradient of a curve at a single point?
- Average rate
- Instantaneous rate
- Total rate
- Constant rate
-
The average rate of change between two points on a curve is the gradient of which line?
- A chord
- A tangent
- A radius
- A normal
-
(H) What is the gradient of the tangent to y = x² at x = 3?
- 3
- 12
- 9
- 6
-
(H) For y = x², what is the average rate of change between x = 1 and x = 3?
- 4
- 2
- 8
- 5
-
(H) For y = x², what is the gradient of the chord between x = 2 and x = 2.1?
- 4
- 4.1
- 5.2
- 4.01
-
(H) Using a chord between x = 2 and x = 2.01 on y = x², estimate the gradient of the tangent at x = 2.
- 3.99
- 8
- 4.01
- 4.1
-
(H) A distance-time graph has d = t². What is the instantaneous speed at t = 4 seconds?
- 2 m/s
- 16 m/s
- 8 m/s
- 4 m/s
-
(H) For d = t², what is the average speed between t = 0 and t = 4 seconds?
- 16 m/s
- 8 m/s
- 2 m/s
- 4 m/s
-
Which line can be drawn to estimate the gradient of a curve at a given point?
- A normal
- A chord
- A tangent
- An asymptote
-
On a velocity-time graph, what quantity is represented by the gradient at a point?
- Acceleration
- Speed
- Distance
- Displacement
-
(H) Using the derivative of y = x³, find the gradient at x = 2.
- 8
- 24
- 6
- 12
-
(H) What is the average rate of change of y = 2x² + 1 between x = 0 and x = 2?
- 2
- 8
- 4
- 9
-
(H) What is the average rate of change of y = 1/x between x = 1 and x = 1.5?
- −2/3
- −1/2
- −3/2
- 2/3
-
(H) What is the equation of the tangent to y = x² at the point (1, 1)?
- y = 2x − 1
- y = 2x + 1
- y = x² − 1
- y = x − 1
-
(H) The position of an object is s = 5t² metres. What is its velocity at t = 2 seconds?
- 20 m/s
- 25 m/s
- 10 m/s
- 40 m/s
-
If the gradient of a distance-time graph is increasing, what is happening to the speed?
- It is constant
- It is zero
- It is increasing
- It is decreasing
-
(H) What is the average rate of change of y = 1/x between x = 2 and x = 4?
- 0.125
- −0.125
- −0.25
- −0.5
-
A population increases by an average of 50 per year for 10 years. What is the total increase?
- 5
- 500
- 50
- 5000
-
(H) For y = 3x², what is the gradient at x = −1?
- 6
- −3
- 3
- −6
-
What does the gradient of a chord joining two points on a graph represent?
- Instantaneous rate
- Average rate
- Total area
- Maximum value
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