AP Calculus AB Review

Question 1

What does the mean value theorem state (for continuous, differentiable functions)?

Accepted Answer

average slope = instantaneous slope

Question 2

Choose the correct answer: (d/dx)[sec(u)] =

Accepted Answer

sec(u)tan(u)·u'

Question 3

Choose the correct answer: (d/dx)[vu] =

Accepted Answer

uv' + vu'

Question 4

For all related rates problems, you must derive each term with respect to

Accepted Answer

time

Question 5

Choose the correct answer.

Accepted Answer

-7/27

Question 6

Choose the correct answer.

Accepted Answer

e-1

Question 7

Choose the correct answer: ∫sec(x)tan(x)dx

Accepted Answer

sec(x) + C

Question 8

Choose the correct answer: ∫exdx

Accepted Answer

ex + C

Question 9

Choose the correct answer: (d/dx)[ln(u)] =

Accepted Answer

(1/u)·u'

Question 10

Choose the correct answer: (d/dx)[sec(u)] =

Accepted Answer

sec(u)tan(u)·u'

Question 11

Choose the correct answer: ∫(1/x)dx

Accepted Answer

ln∣x∣ + C

Question 12

Choose the correct answer: (d/dx)[tan(u)] =

Accepted Answer

sec2(u)·u'

Question 13

The second derivative of a function provides information about the _______ of that function.

Accepted Answer

concavity

Question 14

Choose the correct answer.

Accepted Answer

6

Question 15

The first derivative of a function provides information about the _______ of that function.

Accepted Answer

slope

Question 16

Choose the correct answer: ∫csc(x)cot(x)dx

Accepted Answer

-csc(x) + C

Question 17

Choose the correct answer: (d/dx)[u/v] =

Accepted Answer

(vu' - uv')/(v2)

Question 18

Choose the correct answer.

Accepted Answer

16π/3

Question 19

Choose the correct answer.

Accepted Answer

-1

Question 20

Choose the correct answer.

Accepted Answer

y = -2(x - π/4)

Question 21

Choose the correct answer: (d/dx)[cos(u)] =

Accepted Answer

-sin(u)·u'

Question 22

Choose the correct answer: ∫csc2(x)dx

Accepted Answer

-cot(x) + C

Question 23

Choose the correct answer.

Accepted Answer

6

Question 24

Choose the correct answer.

Accepted Answer

-1 < x < 3

Question 25

Choose the correct answer.

Accepted Answer

13

Question 26

Choose the correct answer: ∫sin(x)dx

Accepted Answer

-cos(x) + C

Question 27

Choose the correct answer: ∫sec2(x)dx

Accepted Answer

tan(x) + C

Question 28

Choose the correct answer.

Accepted Answer

-6x2sin(x3)cos(x3)

Question 29

Choose the correct answer.

Accepted Answer

e(t/2) + C

Question 30

Choose the correct answer: (d/dx)[cot(u)] =

Accepted Answer

-csc2(u)·u'

Question 31

Find the limx→0(sinx / 2x)

Accepted Answer

1/2

AP Calculus AB Review

Questions 31

AP Calculus AB Review

Questions 31