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AP Calculus Formula Review

Total questions: 40

Worksheet time: 19mins

Name
Class
Date
1.

The equation y−y1=m(x−x1)y-y_1=m\left(x-x_1\right)  represents all of the following

a)

The point-slope equation of a line

b)

The equation of a line that contains the point  (x1,y1)\left(x_1,y_1\right)  

c)

The slope of a line passing the point  (x1,y1)\left(x_1,y_1\right)  

d)

The slope of a line perpendicular to a function at the point  (x1,y1)\left(x_1,y_1\right)  

2.

Equals

a)

a∫c f(x)dx

b)

a∫b f(x)dx

c)

b∫c f(x)dx

d)

c∫a f(x)dx

3.

Equals

a)

a∫c f(x)dx

b)

a∫b f(x)dx

c)

b∫c f(x)dx

d)

c∫a f(x)dx

4.

Equals

a)

∫ f(x)dx

b)

cx∫ f(x)dx

c)

c∫f(x)dx

d)

(1/c)∫f(x)dx

5.

equals

a)

f(x)

b)

f(x) + C

c)

f '(x)

d)

f '(x) +C

6.
a)
Intermediate Value Theorem
b)
Rolle's Theorem
c)
Average Rate of Change
d)
Average Value of f
7.

Equals

a)

a∫c f(x)dx

b)

a∫b f(x)dx

c)

b∫c f(x)dx

d)

c∫a f(x)dx

8.
a)
Average Rate of Change
b)
Average Value of f
c)
Intermediate Value Theorem
d)
Rolle's Theorem
9.

Equals

a)

d∫cf(x)dx

b)

- d∫cf(x)dx

c)

f(d) - f(c)

d)

f(c) - f(d)

10.
a)
f '(g'(x))
b)
f '(x)g'(x)
c)
f '(g(x))g'(x)
d)
f '(g(x)
11.
a)
Volume using Washers
b)
Volume using Disks
c)
Volume using Shells
d)
Volume using Cross Sections
12.
a)
c⋅f(x)
b)
c⋅f '(x)
c)
c⋅f '(x) + c⋅f(x)
d)
c⋅f '(x) - c⋅f(x)
13.
a)
Volume using Disks
b)
Volume using Washers
c)
Volume using Shells
d)
Volume using Cross-Sections
14.
a)
position
b)
acceleration
c)
total distance
d)
displacement
15.
a)
f '(x)
b)
0
c)
∞
d)
f(x)
16.
a)
f(u)
b)
f(u) + C
c)
f(u)⋅(du/dx)
d)
f(t)
17.
a)
Volume using Shells
b)
Volume using Disks
c)
Volume using Washers
d)
Volume using Cross Sections
18.

If y = f(x)/g(x), then dy/dx =

a)

f '(x)⋅g(x) + f(x)⋅g'(x)

b)

f '(x)⋅g(x) - f(x)⋅g'(x)

c)

[f '(x)⋅g(x) + f(x)⋅g'(x)] / [g(x)]2

d)

[f '(x)⋅g(x) - f(x)⋅g'(x)] / [g(x)]2

19.
a)
f '(x)⋅g(x) + f(x)⋅g'(x)
b)
f '(x)⋅g(x) - f(x)⋅g'(x)
c)
[f '(x)⋅g(x) + f(x)⋅g'(x)] / [g(x)]2
d)
[f '(x)⋅g(x) - f(x)⋅g'(x)] / [g(x)]2
20.
a)
(1/n) ⋅xn-1
b)
(1/n) ⋅xn+1
c)
n ⋅xn-1
d)
n ⋅xn+1
21.
a)
(1/n)⋅un-1(du/dx)
b)
n⋅un+1(du/dx)
c)
n⋅un-1(du/dx)
d)
(1/n)⋅un+1(du/dx)
22.
a)
Mean value theorem
b)
Rolle's theorem
c)
Intermediate Value Theorem
d)
Fundamental Theorem of Calculus
23.
a)
linear approximation
b)
integration by parts
c)
average rate of change
d)
product rule
24.
a)
f(a) - f(b)
b)
f(b) - f(a)
c)
f '(b) - f '(a)
d)
f '(a) - f '(b)
25.
What is the limit?
a)
Infinity
b)
20
c)
DNE
d)
12
26.
Find the second derivative of the function:
f (x) =  2x - 5x6
a)
f ''(x)= 2 - 30x
b)
f ''(x) =  2-30x5
c)
f ''(x) = -30x5
d)
f ''(x) = -150x4
27.
If the position of a particle is represented by s(t) = -t2 + 1, what is its position at t = 1? 
a)
Position = 0
b)
Position = 1
c)
Position = 2
d)
Position = -1 
28.
a)
position
b)
acceleration
c)
total distance
d)
speed
29.
a)
position
b)
velocity
c)
acceleration
d)
total distance
30.
a)
position 
b)
velocity
c)
acceleration
d)
total distance
31.

What is the derivative of y= 1 - x2 + x - 3x4

a)

y/=x+-2x+1-12x3

b)

y/=x-x3/3+x2/2-3x5/5

c)

y/=-2x+1-12x3

d)

y/=2x+1-12x3

32.

what is the derivative of y= sin(2x)?

a)

y/=cos(2x)

b)

y/=2sin(2x)

c)

y/=2sin(x)+cos(2x)

d)

y/=2cos(2x)

33.

when is the function f(x)=x2+6x+9 increasing?

a)

(3,∞)

b)

(-∞,3)

c)

(-3,-∞)

d)

(-3,∞)

34.

What is the speed of the position function f(x)=-3x2-6x-6 at x=2

a)

-18

b)

18

c)

-6

d)

6

35.

What is the integral of f(x)=sin(2x)+1/x

a)

-2cos(2x)+ln(x)+c

b)

ln(|x|)−cos(2x)/2+C

c)

ln(|x|)−cos(2x)/2

d)

ln(|x|)+cos(2x)/2+C

36.

Let f be the function defined by f(x)=4x3-10x+5. Find the equation of the tangent line to the graph of f at the point where x = 1

a)

y+1=2(x-1)

b)

y-1=2(x-1)

c)

y+1=2(x+1)

d)

y+1=-2(x-1)

37.

If g is the inverse function of F and f(2)=3, find the value of g'(3) for F(x)=6x2+2x-1

a)

1/24

b)

1/25

c)

1/26

d)

26

38.

what is the limit as x approaches infinity of the function f(x)= (3x-5)/(5x2+4)

a)

infinity

b)

negative infinity

c)

0

d)

1

39.

What are the vertical asymptotes of the function f(x)=(x2-9)/(x2+6x+9)

a)

x=3

b)

x=-3

c)

x=3,-3

d)

no vertical asymptote

40.

what is the limit when x approaches infinity of the function f(x)=ex

a)

negative infinity

b)

e

c)

infinity

d)

0

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