Download AP Calculus AB Final

AP Calculus AB Final
First Semester Final – No Calculators!
Name:_________________________________period:_____
1)
Find an equation of the tangent line to the graph of f(x) = -2x2 + 2x + 3 where x = 1.
a)
y = -4x + 2
b)
y = -2x + 1
c)
y = -4x2 + 2x + 1
d)
y = -2x + 5
e)
None of these
2)
Find f’(x) when f(x) = sin34x
a)
4cos34x
b)
3(sin24x)(cos4x)
c)
12(sin24x)(cos4x)
d)
cos34x
e)
None of these
3)
Find the limit:
a)
b)
c)
d)
e)
4)
lim
2x 3  6x 2  5
x 
x3  3
2
½
0
13
Does not exist
What is the x-coordinate of the point of inflection on the graph of y =
a)
b)
c)
d)
e)
1 3
x + 5x2 + 24?
3
5
0
–10/3
–5
There is no point of inflection. Concavity does not change.
5)
Let f(3) = 0, f’(3) = 6, g(3) = 1 and g’(3) = 1/3. Find h’(3) if h(x) = f(x)/g(x).
a)
18
b)
6
c)
–6
d)
–2
e)
0
6)
Find all the intervals on which the graph of the function is concave upward: f(x) = 8x3 – 2x4
a)
b)
c)
d)
e)
7)
(- ∞ , 3)
(- ∞, 0) (2, ∞ )
(0, 2)
(-∞, ∞)
None of these
x 2  2x  15
x5
x 5
Find the limit: lim
a)
b)
c)
d)
e)
2
0
Does not exist
Indeterminate
None of these
8)
What is the value of the y-coordinate of the maximum of f(x) = x2 – 2x + 1 on the interval [0, 3}?
9)
Find all horizontal asymptotes for f(x) =
a)
b)
c)
d)
e)
4x
x2  9
y=+1
y=4
y=+4
y=0
none of these

x 2  2x  4 x  2

x 2
cx
10)
Determine the value of c such that f(x) is continuous on the entire real line if f(x) = 
11)
Find the differential of y = sec3x
a)
(sec3x)(tan3x)dx
b)
3(secx)(tanx)dx
c)
3(sec23x)dx
d)
3(tan23x)dx
e)
None of these
12)
Find the values of x that give relative extrema for the function f(x) = 3x5 – 5x3.
13)
5
a)
relative maximum: x = 0; relative minimum x =
b)
c)
d)
e)
relative maximum: x = +1; relative minimum x = 0
relative maximum: x = 0; relative minimum x = +1
relative maximum: x = -1; relative minimum x = 1
none of these
Given f(x) =
a)
b)
c)
d)
e)
x2  x  2
x2  4
3
, which of the following statements are true? (Multiple answers are possible)
f(x) has a slant asymptote at y = x
f(x) has no horizontal asymptote
f(x) has a horizontal asymptote at y = 1
f(x) has vertical asymptotes at x = 2 and x = -2
f(x) has vertical asymptote at x = -2
14)
The product of two positive numbers is 363. Minimize the sum of the first and three times the second.
a)
33 and 11
b)
11 3 and 11 3
33
c)
22 and
2
d)
30.67 and 12
e)
None of these
15)
As a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4 cubic
inches per second. At what rate is the radius increasing when the radius is 1 inch?
a)
4π in/sec
b)
1
in/sec
16
c) π in/sec
d)
1
in/sec

e) None of these