AP Calculus AB Review

Question 1

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

Accepted Answer

sec2(u)·u'

Question 2

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

Accepted Answer

concavity

Question 3

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

Accepted Answer

-csc(x) + C

Question 4

Choose the correct answer.

Accepted Answer

e-1

Question 5

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

Accepted Answer

eu·u'

Question 6

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

Accepted Answer

(vu' - uv')/(v2)

Question 7

Choose the correct answer: ∫exdx

Accepted Answer

ex + C

Question 8

Choose the correct answer: ∫(1/x)dx

Accepted Answer

ln∣x∣ + C

Question 9

Choose the correct answer: ∫cos(x)dx

Accepted Answer

sin(x) + C

Question 10

Choose the correct answer.

Accepted Answer

13

Question 11

To find position from acceleration, you must...

Accepted Answer

integrate twice

Question 12

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

Accepted Answer

∫(top - bottom)dx

Question 13

Choose the correct answer: ∫sin(x)dx

Accepted Answer

-cos(x) + C

Question 14

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

Accepted Answer

(1/u)·u'

Question 15

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

Accepted Answer

cos(u)·u'

Question 16

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

Accepted Answer

sec(x) + C

Question 17

Choose the correct answer: ∫axdx

Accepted Answer

ax / ln(a) + C

Question 18

Choose the correct answer.

Accepted Answer

-1

Question 19

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

Accepted Answer

-csc(u)cot(u)·u'

Question 20

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

Accepted Answer

slope

Question 21

Choose the correct answer.

Accepted Answer

-7/27

Question 22

Choose the correct answer.

Accepted Answer

-6x2sin(x3)cos(x3)

Question 23

Choose the correct answer.

Accepted Answer

32/3

Question 24

Choose the correct answer.

Accepted Answer

-1 < x < 3

Question 25

Choose the correct answer.

Accepted Answer

6

Question 26

Choose the correct answer.

Accepted Answer

6

Question 27

Choose the correct answer.

Accepted Answer

e(t/2) + C

Question 28

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

Accepted Answer

average slope = instantaneous slope

Question 29

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

Accepted Answer

-csc2(u)·u'

Question 30

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

Accepted Answer

-sin(u)·u'

Question 31

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

Accepted Answer

time

Question 32

What method is used to find volume?

Accepted Answer

Newton's method

Question 33

Choose the correct answer.

Accepted Answer

y = -2(x - π/4)

Question 34

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

Accepted Answer

au·ln(a)·u'

Question 35

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

Accepted Answer

uv' + vu'

Question 36

To find velocity from position, you must...

Accepted Answer

find the 1st derivative

Question 37

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

Accepted Answer

sec(u)tan(u)·u'

Question 38

Choose the correct answer.

Accepted Answer

16π/3

Question 39

Choose the correct answer: ∫csc2(x)dx

Accepted Answer

-cot(x) + C

Question 40

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

Accepted Answer

sec(u)tan(u)·u'

Question 41

Choose the correct answer: ∫sec2(x)dx

Accepted Answer

tan(x) + C

Question 42

Find the limx→0(sinx / 2x)

Accepted Answer

1/2

AP Calculus AB Review

Questions 42

AP Calculus AB Review

Questions 42