Average rate of change over an interval
9th grade (Year 10 in England) · 16 questions · Common Core: HSF.IF.B.6 · England: GCSE Higher Algebra
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Question 1
A ball is thrown upwards. Its height in metres after t seconds is h(t) = 16t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 1 to t = 2. A negative answer means it is coming down.
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Question 2
f(x) = −2x² − 2. Find the average rate of change of f between x = −1 and x = 3.
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Question 3
x: 0, 1, 2, 3, 4 f(x): 2, 4, 8, 14, 22 Find the average rate of change of f from x = 2 to x = 4.
Answer(as a fraction)
Question 4
A ball is thrown upwards. Its height in metres after t seconds is h(t) = 20t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 2 to t = 3. A negative answer means it is coming down.
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Question 5
f(x) = 3x² − 4x − 4. Find the average rate of change of f between x = 1 and x = 3.
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Question 6
x: 0, 1, 2, 3, 4 f(x): 4, 6, 14, 28, 48 Find the average rate of change of f from x = 1 to x = 3.
Answer(as a fraction)
Question 7
A ball is thrown upwards. Its height in metres after t seconds is h(t) = 27t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 2 to t = 3. A negative answer means it is coming down.
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Question 8
f(x) = 2x² − x − 3. Find the average rate of change of f between x = 2 and x = 6.
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Question 9
x: 0, 1, 2, 3, 4 f(x): 4, 3, 4, 7, 12 Find the average rate of change of f from x = 0 to x = 4.
Answer(as a fraction)
Question 10
A ball is thrown upwards. Its height in metres after t seconds is h(t) = 25t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 0 to t = 1. A negative answer means it is coming down.
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Question 11
f(x) = −x² + 3x. Find the average rate of change of f between x = −1 and x = 3.
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Question 12
x: 0, 1, 2, 3, 4 f(x): −4, −2, 4, 14, 28 Find the average rate of change of f from x = 1 to x = 4.
Answer(as a fraction)
Question 13
A ball is thrown upwards. Its height in metres after t seconds is h(t) = 29t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 1 to t = 3. A negative answer means it is coming down.
Answer
Question 14
f(x) = x² − 2x + 4. Find the average rate of change of f between x = −2 and x = −1.
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Question 15
x: 0, 1, 2, 3, 4 f(x): −2, 1, 6, 13, 22 Find the average rate of change of f from x = 0 to x = 2.
Answer(as a fraction)
Question 16
A ball is thrown upwards. Its height in metres after t seconds is h(t) = 21t − 5t². Find its average speed upwards (rate of change of height, in m/s) from t = 0 to t = 2. A negative answer means it is coming down.
Answer
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