WorksheetsAP Calculus Midterm Review
Total questions: 20
Worksheet time: 39mins
Name
Class
Date
1.
What is the limit?
a)
DNE
b)
Infinity
c)
6
d)
12
2.
Differentiate f(x) =(2/x5) - 5.
a)
x5-3
b)
-10x6
c)
x5-5
d)
-10x-6
3.
Find the derivative.
a)
x4 cosx - 4x3sinx
b)
x4 cosx + 4x3sinx
c)
4x3cosx
d)
-4x3cosx
4.
What is the limit?
a)
Infinity
b)
20
c)
DNE
d)
12
5.
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
6.
Find the Limit
a)
0
b)
-1/4
c)
-5/4
d)
1
e)
DNE
7.
Find the limit as x approaches 1+
a)
1
b)
-1
c)
-3
d)
Infinity
e)
DNE
8.
Select all statements that are TRUE.
a)
b)
c)
d)
e)
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 cos(x)?
a)
sin(x)
b)
-sin(x)
c)
cos(x)
d)
-cos(x)
11.
When we "take the derivative" of a function what are we finding?
a)
What's a derivative?
b)
The rate at which our struggles in Calculus are increasing.
c)
The slope of the secant line
d)
The slope of the tangent line
12.
What is the derivative of tan(x)?
a)
-sec2(x)
b)
-csc2(x)
c)
sec2(x)
d)
csc2(x)
13.
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)
14.
What is the derivative of cot(x)?
a)
sec2(x)
b)
-sec2(x)
c)
csc2(x)
d)
-csc2(x)
15.
What is the derivative of csc(x)?
a)
csc(x)cot(x)
b)
-csc(x)cot(x)
c)
-csc2(x)
d)
-cot2(x)
16.
Note: Not finding derivative, just finding what it's equal to...
a)
cos x
b)
csc x
c)
sec x
d)
cot x
17.
Note: Not finding derivative, just finding what it's equal to...
a)
csc x
b)
sec x
c)
cot x
d)
tan x
18.
Note: Not finding derivative, just finding what it's equal to...
a)
csc x
b)
sec x
c)
cot x
d)
tan x
19.
(3 min) The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100 π square inches, what is the rate of increase, in cubic inches per second, in the volume V? SA = 4 π r2 and V = (4/3) π r3
a)
30π
b)
10π
c)
12π
d)
25π
20.
Find dy/dx by Implicit Differentiation
x3 +y3 = 36
x3 +y3 = 36
a)
6 -x
b)
3x2 +3y2
c)
−x2/y2
d)
0
100 %
