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WorksheetsAP Calculus Unit 2 Review
Total questions: 20
Worksheet time: 20mins
Name
Class
Date
1.
Find dy/dx by Implicit Differentiation
x3 +y3 = 36
x3 +y3 = 36
a)
6 -x
b)
3x2 +3y2
c)
−x2/y2
d)
0
2.
Find dy/dx
xy+y2=2
xy+y2=2
a)
-y/(x+2y)
b)
y/(x+2y)
c)
-3y/x
d)
-3x/y
3.
Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?
a)
3 ft/sec
b)
-7.2 ft/sec
c)
7.2 ft/sec
d)
12
4.
Brandon is starting to clean up after a birthday party. He begins deflating each spherical balloon by puncturing a hole in each. The air leaves the balloon at a constant rate of 2 cm3/sec. How fast is the diameter changing when the diameter is 8 cm?
a)
-1/(16pi) cm/sec
b)
-1/16 cm/sec
c)
-1/(4pi) cm/sec
d)
1/(4pi) cm/sec
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.
Set up the derivative of y=(3x4 - 7)*(5x2 + 1)
a)
(12x3)*(10x)
b)
(3x4 - 7)*(10x) + (12x3)*(5x2 + 1)
c)
(3x4 - 7)*(10x) - (12x3)*(5x2 + 1)
d)
(3x4 - 7)/(10x) + (12x3)/(5x2 + 1)
7.
Find the derivative of the given equation
f(x) = x4 + 4x3 - 2x2
f(x) = x4 + 4x3 - 2x2
a)
x3 + x2 - x
b)
4x3 + 12x2 + 4x
c)
4x + 12x - 4x
d)
4x3 + 12x2 - 4x
8.
Find the derivative.
a)
x4 cosx - 4x3sinx
b)
x4 cosx + 4x3sinx
c)
4x3cosx
d)
-4x3cosx
9.
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
10.
.
a)
(3x2-2)cos(x3-2x)
b)
-(3x2-2)cos(x3-2x)
c)
cos(2x2-2)
d)
sin(2x2-2)
11.
Find y' if y=e3x
a)
e3x
b)
e2x
c)
0
d)
3e3x
12.
Calculate the average rate of change from 20 to 40 minutes.
a)
-2 minutes per gallon
b)
-20 minutes per gallon
c)
-2 gallons per minute
d)
-20 gallons per minute
13.
Find the average rate of change over the given interval.
a)
4
b)
7
c)
7/3
d)
3/7
14.
Find the slope of the line that passes through the points (2, 4) and (6, 12)
a)
1/2
b)
-1/2
c)
2
d)
-2
15.
What does "m" represent in y=mx+b?
a)
y-intercept
b)
slope
c)
macaroni
d)
nothing
16.
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
17.
If a function has a derivative that is negative, what does that tell you?
a)
The function is increasing
b)
The function is decreasing
18.
f(x) = ln x
a)
f '(x) = x
b)
f '(x) =ex
c)
f '(x) =lnx
d)
f '(x) = 1/x
19.
d/dx ln(x3)
a)
3/x
b)
1/x3
c)
ln(3x2)
d)
1 / 3x2
20.
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
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