AP Calculus AB Review

Question 1

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

Accepted Answer

uv' + vu'

Question 2

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

Accepted Answer

-csc2(u)·u'

Question 3

Choose the correct answer.

Accepted Answer

-3

Question 4

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

Accepted Answer

time

Question 5

Choose the correct answer: ∫(1/x)dx

Accepted Answer

ln∣x∣ + C

Question 6

Choose the correct answer.

Accepted Answer

e-1

Question 7

Choose the correct answer.

Accepted Answer

-25/27

Question 8

Choose the correct answer: ∫cos(x)dx

Accepted Answer

sin(x) + C

Question 9

Choose the correct answer: ∫axdx

Accepted Answer

ax / ln(a) + C

Question 10

Choose the correct answer.

Accepted Answer

-6x2sin(x3)cos(x3)

Question 11

Choose the correct answer: ∫exdx

Accepted Answer

ex + C

Question 12

Choose the correct answer.

Accepted Answer

6

Question 13

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

Accepted Answer

(1/u)·u'

Question 14

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

Accepted Answer

sec(x) + C

Question 15

Choose the correct answer.

Accepted Answer

e(t/2) + C

Question 16

Choose the correct answer: ∫sin(x)dx

Accepted Answer

-cos(x) + C

Question 17

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

Accepted Answer

cos(u)·u'

Question 18

Choose the correct answer.

Accepted Answer

32/3

Question 19

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

Accepted Answer

au·ln(a)·u'

Question 20

Choose the correct answer.

Accepted Answer

13

Question 21

Choose the correct answer: ∫sec2(x)dx

Accepted Answer

tan(x) + C

Question 22

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

Accepted Answer

sec(u)tan(u)·u'

Question 23

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

Accepted Answer

slope

Question 24

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

Accepted Answer

∫(top - bottom)dx

Question 25

Choose the correct answer.

Accepted Answer

6

Question 26

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

Accepted Answer

eu·u'

Question 27

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

Accepted Answer

-sin(u)·u'

Question 28

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

Accepted Answer

-csc(u)cot(u)·u'

Question 29

Find the limx→0(sinx / 2x)

Accepted Answer

1/2

Question 30

Choose the correct answer.

Accepted Answer

16π/3

Question 31

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

Accepted Answer

concavity

Question 32

To find position from acceleration, you must...

Accepted Answer

integrate twice

Question 33

Choose the correct answer: ∫csc2(x)dx

Accepted Answer

-cot(x) + C

Question 34

Choose the correct answer.

Accepted Answer

y = -2(x - π/4)

Question 35

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

Accepted Answer

-csc(x) + C

Question 36

To find velocity from position, you must...

Accepted Answer

find the 1st derivative

Question 37

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

Accepted Answer

average slope = instantaneous slope

Question 38

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

Accepted Answer

sec2(u)·u'

Question 39

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

Accepted Answer

(vu' - uv')/(v2)

Question 40

Choose the correct answer.

Accepted Answer

-1 < x < 3

AP Calculus AB Review

Questions 40

AP Calculus AB Review

Questions 40