AP Calculus AB Review

Question 1

Choose the correct answer.

Accepted Answer

6

Question 2

Choose the correct answer.

Accepted Answer

-1 < x < 3

Question 3

Choose the correct answer: (d/dx)[h(x)*m(x)] =

Accepted Answer

h(x)m'(x) + h(x)m'(x)

Question 4

Choose the correct answer.

Accepted Answer

-3

Question 5

Choose the correct answer.

Accepted Answer

e-1

Question 6

Choose the correct answer: (d/dx)[g(h(x))] =

Accepted Answer

g'(h(x))h'(x)

Question 7

To find velocity from position, you must...

Accepted Answer

find the 1st derivative

Question 8

Choose the correct answer.

Accepted Answer

-6x2sin(x3)cos(x3)

Question 9

Choose the correct answer.

Accepted Answer

-7/27

Question 10

Choose the correct answer: (d/dx)[e2x] =

Accepted Answer

2e2x

Question 11

Find the limx→0(sinx / 2x)

Accepted Answer

1/2

Question 12

Choose the correct answer: ∫sin(x)dx

Accepted Answer

-cos(x) + C

Question 13

Choose the correct answer.

Accepted Answer

16π/3

Question 14

Choose the correct answer: ∫sec2(x)dx

Accepted Answer

tan(x) + C

Question 15

Choose the correct answer: ∫(1/x)dx

Accepted Answer

ln∣x∣ + C

Question 16

Choose the correct answer.

Accepted Answer

6

Question 17

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

Accepted Answer

sec(x) + C

Question 18

To find position from acceleration, you must...

Accepted Answer

integrate twice

Question 19

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

Accepted Answer

(vu' - uv')/(v2)

Question 20

Choose the correct answer: ∫cos(2x)dx

Accepted Answer

(1/2)sin(2x) + C

Question 21

Choose the correct answer: ∫(1/x3)dx

Accepted Answer

(-1/2)x-2 + C

Question 22

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

Accepted Answer

concavity

Question 23

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

Accepted Answer

cos(u)·u'

Question 24

Choose the correct answer.

Accepted Answer

13

Question 25

What method is used to find volume?

Accepted Answer

Newton's method

Question 26

Choose the correct answer.

Accepted Answer

32/3

Question 27

Choose the correct answer: ∫exdx

Accepted Answer

ex + C

Question 28

Choose the correct answer: ∫cos(x)dx

Accepted Answer

sin(x) + C

Question 29

Choose the correct answer.

Accepted Answer

e(t/2) + C

Question 30

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

Accepted Answer

average slope = instantaneous slope

Question 31

Choose the correct answer.

Accepted Answer

y = -2(x - π/4)

Question 32

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

Accepted Answer

sec(u)tan(u)·u'

Question 33

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

Accepted Answer

sec2(u)·u'

Question 34

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

Accepted Answer

slope

Question 35

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

Accepted Answer

time

Question 36

Choose the correct answer: ∫e4xdx =

Accepted Answer

e4x

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)[cos(u)] =

Accepted Answer

-sin(u)·u'

Question 39

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

Accepted Answer

(1/u)·u'

AP Calculus AB Review

Questions 39

AP Calculus AB Review

Questions 39