AP Calculus AB Review 1

Question 1

Choose the correct answer: ∫exdx

Accepted Answer

ex + C

Question 2

Choose the correct answer: ∫csc2(x)dx

Accepted Answer

-cot(x) + C

Question 3

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

Accepted Answer

concavity

Question 4

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

Accepted Answer

average slope = instantaneous slope

Question 5

Find the limx→0(sinx / 2x)

Accepted Answer

1/2

Question 6

Choose the correct answer.

Accepted Answer

16π/3

Question 7

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

Accepted Answer

(1/u)·u'

Question 8

Choose the correct answer.

Accepted Answer

y = -2(x - π/4)

Question 9

Choose the correct answer.

Accepted Answer

e(t/2) + C

Question 10

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

Accepted Answer

-csc(x) + C

Question 11

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

Accepted Answer

sec(x) + C

Question 12

Choose the correct answer: ∫sin(x)dx

Accepted Answer

-cos(x) + C

Question 13

Choose the correct answer.

Accepted Answer

-6x2sin(x3)cos(x3)

Question 14

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

Accepted Answer

-sin(u)·u'

Question 15

To find position from acceleration, you must...

Accepted Answer

integrate twice

Question 16

To find velocity from position, you must...

Accepted Answer

find the 1st derivative

Question 17

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

Accepted Answer

(vu' - uv')/(v2)

Question 18

Choose the correct answer.

Accepted Answer

e-1

Question 19

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

Accepted Answer

uv' + vu'

Question 20

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

Accepted Answer

sec2(u)·u'

Question 21

Choose the correct answer.

Accepted Answer

-1

Question 22

What method is used to find volume?

Accepted Answer

Newton's method

Question 23

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

Accepted Answer

∫(top - bottom)dx

Question 24

Choose the correct answer: ∫sec2(x)dx

Accepted Answer

tan(x) + C

Question 25

Choose the correct answer: ∫(1/x)dx

Accepted Answer

ln∣x∣ + C

Question 26

Choose the correct answer.

Accepted Answer

6

Question 27

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

Accepted Answer

cos(u)·u'

Question 28

Choose the correct answer: ∫axdx

Accepted Answer

ax / ln(a) + C

Question 29

Choose the correct answer: ∫cos(x)dx

Accepted Answer

sin(x) + C

Question 30

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

Accepted Answer

time

Question 31

Choose the correct answer.

Accepted Answer

32/3

Question 32

Choose the correct answer.

Accepted Answer

6

Question 33

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

Accepted Answer

sec(u)tan(u)·u'

Question 34

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

Accepted Answer

-csc(u)cot(u)·u'

Question 35

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

Accepted Answer

au·ln(a)·u'

Question 36

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

Accepted Answer

eu·u'

Question 37

Choose the correct answer.

Accepted Answer

-1 < x < 3

Question 38

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

Accepted Answer

-csc2(u)·u'

Question 39

Choose the correct answer.

Accepted Answer

-7/27

Question 40

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

Accepted Answer

sec(u)tan(u)·u'

Question 41

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

Accepted Answer

slope

Question 42

Choose the correct answer.

Accepted Answer

13

AP Calculus AB Review 1

Questions 42

AP Calculus AB Review 1

Questions 42