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WorksheetsCalculus Final Review
Total questions: 75
Worksheet time: 3hrs 36mins
Name
Class
Date
1.
a)
A
b)
B
c)
C
d)
D
2.
a)
A
b)
B
c)
C
d)
D
3.
a)
A
b)
B
c)
C
d)
D
4.
a)
A
b)
B
c)
C
d)
D
5.
a)
A
b)
B
c)
C
d)
D
6.
a)
A
b)
B
c)
C
d)
D
7.
a)
A
b)
B
c)
C
d)
D
8.
a)
A
b)
B
c)
C
d)
D
9.
a)
A
b)
B
c)
C
d)
D
10.
a)
A
b)
B
c)
C
d)
D
11.
a)
A
b)
B
c)
C
d)
D
12.
a)
A
b)
B
c)
C
d)
D
13.
a)
A
b)
B
c)
C
d)
D
14.
a)
A
b)
B
c)
C
d)
D
15.
a)
A
b)
B
c)
C
d)
D
16.
a)
A
b)
B
c)
C
d)
D
17.
a)
A
b)
B
c)
C
d)
D
18.
a)
A
b)
B
c)
C
d)
D
19.
a)
A
b)
B
c)
C
d)
D
20.
a)
A
b)
B
c)
C
d)
D
21.
a)
0
b)
2
c)
3
d)
4
22.
a)
Does not exist
b)
6
c)
4
d)
3
23.
a)
0
b)
2
c)
3
d)
4
24.
a)
0
b)
3
c)
4
d)
DNE
25.
a)
0
b)
1
c)
2
d)
DNE
26.
Find the slope of the tangent line to f(x) = -3x2-6x at x = 1.
a)
m = 0
b)
f'(x) = -6x - 6
c)
f'(x) = 6x
d)
m = -12
27.
Find the derivative of f(x) = 6x30 -2x15 + 4x3 - 2x + 1
a)
f'(x) = 18x29 + 30x15 + 12x3
b)
f'(x) = 180x29 - 30x14 + 12x2
c)
f'(x) = 180x29 - 30x14 + 12x2 - 2
d)
f'(x) = 180x29 - 30x14 + 12x2 +1
28.
If the position function for a particle is s(t) = -t2 - t, what is the instantaneous velocity function for the particle?
a)
v(t) = -2
b)
v(t) -2t - 1
c)
v(t) = t3
d)
v(t) = -t
29.
Find the derivative. f(x) = -8x-3 + 5x - e2
a)
f'(x) = -24x-4 + 5 - ex-1
b)
f'(x) = 24x-4 + 5
c)
f'(x) = 24x-2 + 5
d)
f'(x) = 24x-4 + 5 - e
30.
Find the derivative. f(x) = 1/(3x2) + 4x3
a)
f'(x) = 6x3 + 12x2
b)
f'(x) = 6x + 12x2
c)
f'(x) = -2/(3x3) + 12x2
d)
f'(x) = -6/x2 + 12x2
31.
f(x)=5x
find f'(x)
find f'(x)
a)
5
b)
1
c)
0
d)
5x
32.
f(x)=x3
f'(x)=
f'(x)=
a)
x2
b)
3x2
c)
6x
d)
3x
33.
g(x)=7x+1
g'(x)=
g'(x)=
a)
7
b)
7x
c)
7x+1
d)
0
34.
y=5x2+ 3x + 9
dy/dx =
dy/dx =
a)
10x
b)
10x+3
c)
10x2+3
d)
10
35.
y=√x
y'=
a)
√x
b)
1/√x
c)
1/(2√x)
d)
-1/(2√x)
36.
f(x)= 9/∛x
f'(x) =
f'(x) =
a)
9x-1/3
b)
-3x-4/3
c)
-9x2/3
d)
-3x2/3
37.
f(x)= 5/x2
f'(x) =
f'(x) =
a)
5x
b)
5/2x
c)
5x-2
d)
-10/x3
38.
y=x
y'=
y'=
a)
x
b)
1
c)
-1
d)
0
39.
y=2/5x3
y'=
y'=
a)
-6/5x4
b)
2/5 x-4
c)
6/5x2
d)
2/5 x2
40.
Find y' if y=e4
a)
0
b)
1
c)
e3
d)
4e3
41.
Derivative means the same thing as
a)
slope of the tangent line
b)
slope of the normal line
c)
exponent
d)
potato
42.
a)
4x9 + 6x7
b)
(2/5)x9 + (3/4)x7
c)
20x9 + 24x7
d)
x9 + x7
43.
a)
(1/2)x-7
b)
(1/2)x-9
c)
-32x-9
d)
-32x-7
44.
a)
A
b)
B
c)
C
d)
D
45.
a)
4
b)
12
c)
12x2
d)
4x3
46.
If the position of a particle is represented by s(t) = -t2 + 1, what is its instantaneous velocity at t = 1?
a)
Velocity = 0
b)
Velocity = 1
c)
Velocity = -1
d)
Velocity = -2
47.
Find the value of the derivative at the indicated x-value.
a)
-4
b)
3
c)
0
d)
24
48.
Find the value of the derivative at the indicated x-value.
a)
-12
b)
5
c)
10
d)
-13
49.
The formal definition of a derivative is:
a)
A
b)
B
c)
C
d)
D
50.
The slope of a function is described by its ____________.
a)
first derivative
b)
second derivative
c)
third derivative
d)
expression
51.
If a function's FIRST derivative is negative at a certain point, what does that tell you?
a)
The function is increasing at that point
b)
The function is decreasing at that point
c)
The concavity of the function is up at that point
d)
The concavity of the function is down at that point
52.
If (a,b) is a local maximum, then what will be true about f'(a)?
a)
It's positive
b)
It's negative
c)
It's zero
d)
Cannot be determined
53.
Find the critical points of f(x) = 2x4- 4x2 + 1
a)
x= 0
b)
x = -1, 1
c)
x = -1, 0, 1
d)
no critical points
54.
If c is a critical number then f(c) is either a local maximum or a local minimum
a)
True (Facts)
b)
False (Not Facts)
55.
The x value where the 2nd derivative is equal to zero is commonly referred to as a "critical point".
a)
True (Facts)
b)
False (Not Facts)
56.
If the 2nd derivative of a function is negative on that interval, then that interval is concave down.
a)
True (Facts)
b)
False (Not Facts)
57.
If the first derivative of a function changes from positive to negative at a certain point, then that point is a known as a relative minimum.
a)
True (Facts)
b)
False (Not Facts)
58.
Find the derivative of f(x)=(x3-2x)2
a)
6x5 - 12x3+8x
b)
6x5 - 16x3+8x
c)
x6-4x4+4x2
d)
6x5 - 16x3-8x
59.
Find the derivative of f(x) = (x6 + 4)5
a)
f '(x) = 5x5(x4 + 4)4
b)
f '(x) = 6x5(x6 + 4)4
c)
f '(x) = 30x5(x6 + 4)4
d)
f '(x) = 30x6(x6 + 4)4
60.
a)
A
b)
B
c)
C
d)
D
61.
a)
A
b)
B
c)
C
d)
D
62.
Find dy/dx if y = cos5x
a)
5cos4x
b)
-5sin4x
c)
5cos4xsinx
d)
-5cos4xsinx
63.
Find y' if y = tan(3x2+2).
a)
sec2(3x2+2)
b)
6xsec2(3x2+2)
c)
6xsec2x(3x2+2)
d)
sec2(6x)
64.
Find y' if y = cos5(4x3)
a)
-5cos4(4x3)sin(12x2)
b)
-60x2sin4(4x3)
c)
-5cos4(4x3)sin(4x3)
d)
-60x2cos4(4x3)sin(4x3)
65.
a)
A
b)
B
c)
C
d)
D
66.
When do you use the chain rule?
a)
anytime you want
b)
when there is a function in a function
c)
where there are multiple layers
d)
when there is division
67.
Find dy/dx if y = sec(8x2).
a)
sec(16x)tan(16x)
b)
16xcos(8x2)
c)
16xsecxtanx(8x2)
d)
16xsec(8x2)tan(8x2)
68.
a)
-135
b)
-5/27
c)
-5/729
d)
-5
69.
Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x5 + 5)2
f(x) = (5x5 + 5)2
a)
y = 500x + 400
b)
y = 100x + 400
c)
y = -500 x - 400
d)
y = 500x - 400
70.
Find dy/dx if y = (cscx + 1)7
a)
-7(cscx + 1)6(cscxcotx)
b)
7(-cscxcotx)6
c)
7(cscx + 1)6(cscxcotx)
d)
-7(cscxcotx)6
71.
Find the derivative f(x) = tanxcosx
a)
f'(x) = sec2xcosx - tanxsinx
b)
f'(x) = sec2xcosx + tanxsinx
c)
f'(x) = sec2xsinx
d)
f'(x) = sec2xcosx - tanxcosx
72.
Find the derivative.
a)
x4 cosx - 4x3sinx
b)
x4 cosx + 4x3sinx
c)
4x3cosx
d)
-4x3cosx
73.
What is the derivative of sec(x)?
a)
sec(x)tan(x)
b)
csc(x)cot(x)
c)
-sec(x)tan(x)
d)
-csc(x)cot(x)
74.
What is the derivative of sin(x)?
a)
sin(x)
b)
cos(x)
c)
-sin(x)
d)
-cos(x)
75.
What is the derivative of ax?
a)
a
b)
x
c)
1
d)
0
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