WorksheetsMaathematical Review
Total questions: 114
Worksheet time: 6hrs 42mins
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)
A
b)
B
c)
C
d)
D
22.
a)
A
b)
B
c)
C
d)
D
23.
a)
A
b)
B
c)
C
d)
D
24.
a)
A
b)
B
c)
C
d)
D
25.
a)
A
b)
B
c)
C
d)
D
26.
a)
cosx
b)
-cosx
c)
-sinx cosx
d)
sinx cosx
27.
a)
sinx
b)
-sinx
c)
-cscx cotx
d)
sec2x
28.
a)
cscx cotx
b)
secx tanx
c)
sec2x
d)
-cscx cotx
29.
a)
secx tanx
b)
sec2x
c)
cscx cotx
d)
-cscx cotx
30.
a)
secx tanx
b)
-secx tanx
c)
tan2x
d)
cscx cotx
31.
a)
-ln |cosx| + C
b)
ln |cosx| + C
c)
ln |sinx| + C
d)
-ln |sinx| + C
32.
a)
sin x + C
b)
-sin x + C
c)
ln |sinx| + C
d)
-ln |sinx| + C
33.
a)
secx tanx + C
b)
-ln |secx + tanx | + C
c)
ln |secx + tanx| + C
d)
-secx tanx + C
34.
a)
-ln |cscx + cotx| + C
b)
ln |cscx + cotx| + C
c)
-cscx cotx + C
d)
cscx cotx + C
35.
a)
-ln |cosx| + C
b)
ln |cosx| + C
c)
-ln |sinx| + C
d)
ln |sinx| + C
36.
a)
-ln |cosx|
b)
ln |cosx|
c)
cosx
d)
-cosx
37.
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
38.
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
39.
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
40.
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
41.
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
42.
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
43.
Find the derivative. f(x) = -8x-3 + 5x - ex
a)
f'(x) = -24x-4 + 5 - ex
b)
f'(x) = 24x-4 + 5 - ex
c)
f'(x) = 24x-2 + 5 - ex
d)
f'(x) = 24x-4 + 5 - ex-1
44.
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
45.
Find the derivative f(x) = (x2 + 2x)5
a)
f'(x) = 5(2x+2)4
b)
f'(x) = 5(x2 + 2x)4
c)
f'(x) = 5(x2 + 2x)4(2x)
d)
f'(x) = 5(x2 + 2x)4(2x + 2)
46.
Find the derivative f(x) = (3x + 5)4
a)
f'(x) = 12(3x)3
b)
f'(x) = 12(3x + 5)3
c)
f'(x) = (3)4
d)
f'(x) = (3x + 5)3
47.
Find the derivative f(x) = secx
a)
f'(x) = tan2x
b)
f'(x) = sec2x
c)
f'(x) = tanx
d)
f'(x) = secxtanx
48.
Find the second derivative of f(x) = x2 + ex - cosx
a)
f"(x) = 2 + ex + cosx
b)
f"(x) = 2x + ex + cosx
c)
f"(x) = 2x + xex - cosx
d)
f"(x) = 2x + ex + sinx
49.
Where does the function, f(x) = 2x3 - 9x2 + 12x -3 have relative max/min?
a)
Rel max x = -1, Rel min x = 2
b)
Rel min x = 1, Rel min x = 2
c)
Rel max x = 1, Rel min x = 2
d)
Rel max x = 2, Rel min x = 1
50.
Find the derivative f(x) = xex
a)
f'(x) = ex
b)
f'(x) = xex + xex
c)
f'(x) = ex - xex
d)
f'(x) = ex + xex
51.
Find the derivative of f(x) = x2sinx
a)
f'(x) = 2xsinx - x2cosx
b)
f'(x) = 2xsinx + x2sinx
c)
f'(x) = 2xsinx + x2cosx
d)
f'(x) = 2xcosx
52.
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
53.
Find the derivative f(x) = x2/ex
a)
f'(x) = (x2ex - 2xex) / (ex)2
b)
f'(x) = (2xex + x2ex) / (ex)2
c)
f'(x) = (2xex - x2ex) / (ex)2
d)
f'(x) = x2ex + 2xex
54.
Disk/Washer Method
a)
B
b)
C
c)
D
d)
E
55.
Disk/Washer Method
a)
B
b)
C
c)
D
d)
E
56.
Disk/Washer Method
a)
A
b)
C
c)
D
d)
E
57.
Disk/Washer Method
a)
A
b)
B
c)
C
d)
D
58.
Disk/Washer Method
a)
A
b)
B
c)
D
d)
E
59.
a)
A
b)
B
c)
C
d)
D
60.
Where does the hole in the graph occur?
a)
∞
b)
Negative Infinity
-∞
-∞
-∞
-∞
c)
x=3
d)
x=-3
61.
What is the limit?
a)
DNE
b)
2
c)
-2
d)
Infinity
62.
What is the limit?
a)
∞
b)
-∞
c)
2
d)
-2
63.
What is the limit?
a)
5/2
b)
-2/3
c)
∞
d)
17/3
64.
What is the limit?
a)
π/2
b)
(-3/4)π
c)
-3/4
d)
DNE
65.
What is the limit?
a)
∞
b)
20
c)
DNE
d)
12
66.
What is the limit?
a)
DNE
b)
∞
c)
6
d)
12
67.
What is the limit?
a)
3
b)
-3
c)
∞
d)
DNE
68.
What is the limit?
a)
DNE
b)
2/3
c)
1/4
d)
∞
69.
What is the limit?
a)
∞
b)
-∞
c)
3
d)
-3
70.
a)
A
b)
B
c)
C
d)
D
71.
If a function has a derivative that is negative, what does that tell you?
a)
The function is increasing
b)
The function is decreasing
72.
What is the limit?
a)
Infinity
b)
20
c)
DNE
d)
12
73.
What is the limit?
a)
5/2
b)
-2/3
c)
Infinity
d)
17/3
74.
a)
A
b)
B
c)
C
d)
D
75.
Do the difference quotient to the following
a)
x2 + 2x + h - 2
b)
2x + h
c)
2x + h - 2
d)
2xh + h2 - 2h
76.
Where is the graph neither continuous nor differentiable?
a)
x = -1, 0, 1, 2
b)
x = -1, 1
c)
x = -1, 0, 1
d)
x = -1, 0, 2
77.
Which graph is the derivative of the top graph?
a)
A
b)
B
c)
C
d)
D
78.
f' is given, which could be f?
a)
A
b)
B
c)
C
79.
At which x-value is f continuous but not differentiable?
a)
a
b)
b
c)
c
d)
d
80.
Where is the graph not differentiable?
a)
x = -2, -1, 0, 1
b)
x = -2, -1, 1
c)
x = -2, -1
d)
x = -1,
81.
Derivative means the same thing as
a)
slope of the tangent line
b)
slope of the normal line
c)
exponent
d)
potato
82.
The derivative of a function is its
a)
Slope
b)
Maximum/Minimum
c)
Instantaneous rate of change
d)
Common Denominator
83.
7
a)
A
b)
B
c)
C
d)
D
84.
a)
a∫c f ( x) dx
b)
a∫b f ( x) dx
c)
b∫c f ( x) dx
d)
c∫a f ( x) dx
85.
a)f ( x)
b)f ( x) + C
c)f '(x)
d)f '(x) +C
86.
a)f ( x)
b)f ( x) + C
c)f '(x)
d)f '(x) +C
87.
a)
Intermediate Value Theorem
b)
Rolle's Theorem
c)
Average Rate of Change
d)
Average Value of f
88.
a)
Average Rate of Change
b)
Average Value of f
c)
Intermediate Value Theorem
d)
Rolle's Theorem
89.
a)
Average Rate of Change
b)
Average Value of f
c)
Intermediate Value Theorem
d)
Rolle's Theorem
90.
a)f ' ( g'( x) )
b)
f '(x)g'(x)
c)f '(g( x)) g'(x)
d)f '(g( x)
91.
a)
Volume using Washers
b)
Volume using Disks
c)
Volume using Shells
d)
Volume using Cross Sections
92.
a)
Volume using Disks
b)
Volume using Washers
c)
Volume using Shells
d)
Volume using Cross-Sections
93.
a)position
b)
acceleration
c)
total distance
d)
displacement
94.
a)f ( u)
b)f ( u) + C
c)f ( u) ⋅( du/dx)
d)f ( t)
95.
What is the derivative?
a)
A
b)
B
c)
C
d)
D
96.
If a function has a derivative that is negative, what does that tell you?
a)
The function is increasing
b)
The function is decreasing
97.
a)
cos x
b)
csc x
c)
sec x
d)
cot x
98.
a)
csc x
b)
sec x
c)
cot x
d)
tan x
99.
Find dy/dx for
y = (x2 + 1)3
y = (x2 + 1)3
a)
dy/dx = 3(x2 + 1)2
b)
dy/dx = 3(2x)2
c)
dy/dx = 3(x2 + 1)2(2x)
d)
dy/dx = 2x(x2 + 1)2
100.
Find the derivative of g(x)=(3x-2)/(x2+2)
a)
9x2+2
b)
3(x2+2)/(x2+2)2
c)
(-3x2+4x +6)/(x2+2)2
d)
(-3x2+10)/(x2+2)2
101.
Find dy/dx for
y = 32x+5
y = 32x+5
a)
dy/dx = 3(2x+4)
b)
dy/dx = (3(2x+4)) ln 3
c)
dy/dx = 3(2x+5) ln3
d)
dy/dx = (3(2x+5)) (ln 3) (2)
102.
Differentiate:
f(x) = x3e4x
*You will need to remove the Greatest Common Factor
f(x) = x3e4x
*You will need to remove the Greatest Common Factor
a)
f '(x) = 3x2e4x
b)
f '(x) = 3x2e4x+3x2e4x
c)
f '(x) = x2e4x(4x+3)
d)
f '(x) = xe4x(4x2+3x)
103.
Differentiate y = √(x² - 1)
a)
√(x² -1)
b)
(1/2x)(x² - 1)^(-1/2)
c)
x(x² - 1)^(-1/2)
d)
x(x² - 1)^(1/2)
104.
Find the derivative:
y=4ex²
y=4ex²
a)
y'=8xe
b)
y'=8xex²
c)
y'=8xe2x
d)
y'=8xe4x²
105.
Find the derivative of f(x) = x2sinx
a)
f'(x) = 2xsinx - x2cosx
b)
f'(x) = 2xsinx + x2sinx
c)
f'(x) = 2xsinx + x2cosx
d)
f'(x) = 2xcosx
106.
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
107.
What is f'(x) if f(x) = cos(5x4)?
a)
f'(x) = sin(20x3)
b)
f'(x) = 20x3 sin(5x4)
c)
f'(x) = -sin(20x3)
d)
f'(x) = -20x3 sin(5x4)
108.
The position function x(t)=t3+6t2+16t-18 is given on the interval of 0<x<9. What is the velocity at t=6?
a)
197
b)
190
c)
18
d)
196
109.
Find the second derivative of f(x) = x2 + ex - cosx
a)
f"(x) = 2 + ex + cosx
b)
f"(x) = 2x + ex + cosx
c)
f"(x) = 2x + xex - cosx
d)
f"(x) = 2x + ex + sinx
110.
Find dy/dx
a)
A
b)
B
c)
C
d)
D
111.
a)
1/(3x2+5)1/4
b)
(3x)/(2(3x2+5))
c)
(2(3x2+5)3/4)/(3x)
d)
(3x2+5)1/4
112.
a)
(5(1-4x))/(12x3)
b)
5(x+1)(3x3-4x2+4x-4)
c)
(5(x3+16))/(x(x3+4))
d)
(5(x+1)(-3x3+4x2-4x+4))/(3x4(x3+4))
113.
a)
((3x2-5)(x2+1))/(10x2(3x4-5))
b)
(2(-3x4-5))/(5x(3x4-5))
c)
(3x2-1)/(60x3)
d)
((3x2-5)(-x2-1))/5
114.
a)
1/(2x5)
b)
1/(10x4)
c)
2x5
d)
5/x
100 %
