Common Core HSF.BF.B.4 worksheet

Question 1

dy/dx = −2x − 1 and the curve passes through (0, 4). Find y in terms of x.

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Question 2

Find ∫ −16x³ dx. Leave out the + C.

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Question 3

Find ∫ (9x² − 4x − 4) dx. Leave out the + C.

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Question 4

f(x) = 3x + 5 and g(x) = x² + 1. Find f(g(3)).

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Question 5

f(x) = x + 1 and g(x) = 2x − 4. Find g(f(x)) and simplify.

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Question 6

f(x) = 2x − 10. Find the inverse function f⁻¹(x).

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Question 7

Ethan needs ∫ 2/x² dx. Which answer is correct?

• A. −4/x³ + C
• B. 2/x + C
• C. 2/x³ + C
• D. −2/x + C

Question 8

A cyclist's velocity is v = 5 + 2t m/s. Starting from s = 0, how far has she travelled after 4 seconds?

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Question 9

dy/dx = −6x − 3 and the curve passes through (−3, 0). Find y in terms of x.

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Question 10

Find ∫ −8x dx. Leave out the + C.

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Question 11

Find ∫ (−6x² − 8x − 6) dx. Leave out the + C.

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Question 12

f(x) = 3x − 5 and g(x) = x² + 1. Find f(g(3)).

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Question 13

f(x) = x − 5 and g(x) = 4x − 4. Find f(g(x)) and simplify.

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Question 14

f(x) = 5x + 1. Find the inverse function f⁻¹(x).

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Question 15

Kai needs ∫ 2/x² dx. Which answer is correct?

• A. 2/x + C
• B. −4/x³ + C
• C. −2/x + C
• D. 2·ln x + C

Question 16

A cyclist's velocity is v = 4 + 4t m/s. Starting from s = 0, how far has she travelled after 1 seconds?

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