AP Calculus AB Review

Question 1

Choose the correct answer: ∫sin(x)dx

Accepted Answer

-cos(x) + C

Question 2

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

Accepted Answer

sec2(u)·u'

Question 3

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

Accepted Answer

sec(u)tan(u)·u'

Question 4

Choose the correct answer: ∫exdx

Accepted Answer

ex + C

Question 5

Choose the correct answer.

Accepted Answer

e(t/2) + C

Question 6

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

Accepted Answer

-csc(u)cot(u)·u'

Question 7

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

Accepted Answer

sec(x) + C

Question 8

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

Accepted Answer

cos(u)·u'

Question 9

Choose the correct answer.

Accepted Answer

32/3

Question 10

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

Accepted Answer

eu·u'

Question 11

Choose the correct answer.

Accepted Answer

16π/3

Question 12

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

Accepted Answer

au·ln(a)·u'

Question 13

Choose the correct answer: ∫cos(x)dx

Accepted Answer

sin(x) + C

Question 14

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

Accepted Answer

uv' + vu'

Question 15

Choose the correct answer.

Accepted Answer

6

Question 16

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

Accepted Answer

average slope = instantaneous slope

Question 17

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

Accepted Answer

(1/u)·u'

Question 18

Choose the correct answer: ∫(1/x)dx

Accepted Answer

ln∣x∣ + C

Question 19

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

Accepted Answer

time

Question 20

To find velocity from position, you must...

Accepted Answer

find the 1st derivative

Question 21

To find position from acceleration, you must...

Accepted Answer

integrate twice

Question 22

Choose the correct answer.

Accepted Answer

6

Question 23

Choose the correct answer.

Accepted Answer

-1 < x < 3

Question 24

Choose the correct answer: ∫csc2(x)dx

Accepted Answer

-cot(x) + C

Question 25

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

Accepted Answer

-csc(x) + C

Question 26

Choose the correct answer.

Accepted Answer

-1

Question 27

Choose the correct answer.

Accepted Answer

e-1

Question 28

Choose the correct answer.

Accepted Answer

-7/27

Question 29

Choose the correct answer: ∫axdx

Accepted Answer

ax / ln(a) + C

Question 30

What method is used to find volume?

Accepted Answer

Newton's method

Question 31

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

Accepted Answer

concavity

Question 32

Find the limx→0(sinx / 2x)

Accepted Answer

1/2

Question 33

Choose the correct answer.

Accepted Answer

y = -2(x - π/4)

Question 34

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

Accepted Answer

-csc2(u)·u'

Question 35

Choose the correct answer.

Accepted Answer

-6x2sin(x3)cos(x3)

Question 36

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

Accepted Answer

-sin(u)·u'

Question 37

How do you find the area between two functions of x?

Accepted Answer

∫(top - bottom)dx

Question 38

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

Accepted Answer

sec(u)tan(u)·u'

Question 39

Choose the correct answer.

Accepted Answer

13

Question 40

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

Accepted Answer

slope

Question 41

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

Accepted Answer

(vu' - uv')/(v2)

Question 42

Choose the correct answer: ∫sec2(x)dx

Accepted Answer

tan(x) + C

AP Calculus AB Review

Questions 42

AP Calculus AB Review

Questions 42