WorksheetsCalculus Semester 1 Review
Total questions: 32
Worksheet time: 2hrs 9mins
Name
Class
Date
1.
Find the critical numbers of
f(x) = 2x4- 4x2 + 1
f(x) = 2x4- 4x2 + 1
a)
x= 0
b)
x = -1, 1
c)
x = -1, 0, 1
d)
no critical points
2.
What are the increasing intervals of the graph for f(x) = 2x4- 4x2 + 1
a)
(-1,0)
b)
(0,1)
c)
(-∞,-1) and (1,∞)
d)
(0,1) and (-1,0)
3.
Which graph is the derivative of the top graph?
a)
A
b)
B
c)
C
d)
D
4.
f' is given, which could be f?
a)
A
b)
B
c)
C
5.
a)
A
b)
B
c)
C
d)
D
6.
What is the derivative of cot(x)?
a)
sec2(x)
b)
-sec2(x)
c)
csc2(x)
d)
-csc2(x)
7.
What is the derivative of -cot(x)?
a)
-sec2(x)
b)
sec2(x)
c)
-csc2(x)
d)
csc2(x)
8.
What is the derivative of csc(x)?
a)
csc(x)cot(x)
b)
-csc(x)cot(x)
c)
-csc2(x)
d)
-cot2(x)
9.
What is the derivative of sin(x)?
a)
-sin(x)
b)
-cos(x)
c)
cos(x)
d)
sin(x)
10.
What is the derivative of -sin(x)?
a)
-sin(x)
b)
-cos(x)
c)
cos(x)
d)
sin(x)
11.
What is the derivative of cos(x)?
a)
sin(x)
b)
-sin(x)
c)
cos(x)
d)
-cos(x)
12.
What is the derivative of xn?
a)
(n-1)xn
b)
nxn+1
c)
(n+1)xn-1
d)
nxn-1
13.
What is the derivative of tan(x)?
a)
-sec2(x)
b)
-csc2(x)
c)
sec2(x)
d)
csc2(x)
14.
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)
15.
Find h'(3)
a)
-2
b)
0
c)
1
d)
3
16.
a)
(3x2-2) cos(x3-2x)
b)
-(3x2-2) cos(x3-2x)
c)
cos(2x2-2)
d)
sin(2x2-2)
17.
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
18.
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
19.
Find the derivative. f(x) = -8x-3 + 5x
a)
f'(x) = -24x-4 + 5
b)
f'(x) = 24x-4 + 5
c)
f'(x) = 24x-2 + 5
d)
f'(x) = 24x-4 - 5
20.
What is the limit?
a)
Infinity
b)
20
c)
DNE
d)
12
21.
Find the second derivative of the function:
f (x) = 2x - 5x6
f (x) = 2x - 5x6
a)
f ''(x)= 2 - 30x
b)
f ''(x) = 2-30x5
c)
f ''(x) = -30x5
d)
f ''(x) = -150x4
22.
Find dy/dx by Implicit Differentiation
x3 +y3 = 36
x3 +y3 = 36
a)
6 -x
b)
3x2 +3y2
c)
−x2/y2
d)
0
23.
Find dy/dx by Implicit Differentiation
2xy3 - x2y = 2
2xy3 - x2y = 2
a)
2xy - 2y3
b)
2y(x-y2)/x(6y2-x)
c)
-2y/x
d)
2
24.
Find dy/dx
sin(y2)=x
sin(y2)=x
a)
1/(2ycos(y2))
b)
cos(y2)
c)
x/(2ycos(y2))
d)
-1/(cos(y2))
25.
Use implicit differentiation to find y' for the following equation: 4x cos(y) = 1
a)
y' = cos(y) / x sin(y)
b)
y' = 4x sin(y)
c)
y' = cot(y)
d)
y' = 4 / sec(y)tan(y)
26.
What is the limit?
a)
5/2
b)
-2/3
c)
Infinity
d)
17/3
27.
What is the limit?
a)
DNE
b)
Infinity
c)
6
d)
12
28.
What is the limit of the function as x approaches -4 from the left?
a)
2
b)
-4
c)
DNE
d)
-2
29.
What is the limit of the function as x approaches 1 from the left?
a)
DNE
b)
1
c)
4
d)
-2
30.
Find the lim as x approaches 4.
(x2-16)/(x-4)
(x2-16)/(x-4)
a)
no way to tell
b)
0
c)
8
d)
infinity
31.
a)
0/0
b)
DNE
c)
-1/4
d)
1/4
32.
a)
0/0
b)
DNE
c)
-1/4
d)
1/4
100 %
