Math III
Final Exam Review
Unit 1- Statistics
1) On September 1st it was 55o in Williamsville and Bogerville. The mean temperature is 40o and the
standard deviation is 6 for Fisherville on June 1st. The mean temperature is 70o and the standard deviation
is 10o for Mistyville. For which town is the 55o more remarkable? (Explain your answer)
____ 2) 99.7% of the freshman class are between 61 inches and 73 inches tall. Assuming the data is
normally distributed, what is the percentage of students are between the height of 64 inches and 70 inches
in the freshmen class?
A. 68%
B. 50%
C. 86%
D. 95%
____ 3) IQ scores are approximately normally distributed with a mean of 100 and a standard deviation of
15. How many standard deviations below the mean is an IQ score of 85?
A. 0
B. 1
C. 2
D. 3
The officers of a neighborhood association want to know whether the 3000 residents are interested
in how much money they are willing to contribute towards the costs involved in beautifying the
neighborhood. They get valid results from 500 residents who want to spend an average of $25 per
household.
4.
Identify the sample, parameter, statistic, and population
(5-6) Which sampling technique did they use to get their results in the following situations (simple
random, stratified, systemic, cluster):
5.
They randomly placed each family into 4 equal groups. They then chose a random group and then
selected 500 out the 750 from that group.
6.
They placed all of the residents into a hat and selected 500 residents.
7.
Give the name and describe another sampling method (other than 5 and 6) that they could have
used to get an unbiased and random sample
Use the graph given to the right for #10
____10. What cannot change if the maximum value increases?
A.
D only
B.
A only
C.
distance been A and E
D.
C only
Unit 2- Rational Expressions:
_____11) Divide:
c.
d.
a.
b.
_____12) Divide the expressions. Simplify the result:
÷
a.
c.
b.
d.
_____13) The production rate of a small factory is modeled by
another factory is modeled by
. Which is a model for the combined production rate of the two
factories?
a.
c.
b.
d.
_____14) What is the correct factorization of
a.
b.
?
c.
d.
_____15) What is the correct factorization of
a.
b.
, while the production rate of
c.
d.
?
_____16) Determine whether
factorization.
a.
b.
yes;
yes;
is a difference of two squares. If so, choose the correct
c.
d.
yes;
no
_____17) Completely factor
.
a.
c.
b.
d.
cannot be factored
_____18) Which gives the factorization of
?
c.
d.
a.
b.
3
_____19) Factor 54x − 16
c.
d.
a.
b.
(3x+2)
+
_____20) Solve. Simplify completely:
a.
b.
4n + 3
2
n − 2n − 3
n+2
n−3
c.
d.
n2 + 3n + 2
n2 − 2n − 3
n+3
n −1
Unit 3- Quadratic Functions:
_____21) Solve by factoring:
a.
b.
x = 0, x = 3
x = 9, x = 0
3x 2 = 9 x
c.
d.
x=3
x = −3
_____22) Solve using the square root property:
a.
b.
x = 5 ± 5i
x = −5 ± − 5
4( x − 5) 2 + 20 = 0
x =5±i 5
x = −5 ± 5i
c.
d.
_____23) Solve using completing the square:
x 2 − 10 x + 7 = 0
a.
x = −5 ± 2 3
c.
x = 10 ± 4 2
b.
x = 10, x = 0
d.
x = 5±3 2
_____24) Solve completely using the quadratic formula: 2 x 2 − 8 x + 3 = 0
a.
x = 2 ± 10
b.
x=
4 ± i 22
2
c.
x=
8 ± 2 10
4
d.
x=
4 ± 10
2
_____25) What is the discriminant and type of roots for 2 x 2 − 12 x + 5 = 0
a.
104; 2 rational roots
c.
b.
-184; 2 imaginary roots d.
104; 2 irrational roots
-184; 2 irrational roots
_____26) Solve using any method: 3 x 2 − 99 = 0
± 11
3
a.
x = ± 33
c.
x=
b.
x = ±3 11
d.
x = ± 11
_____27) Which is a possible equation for the graph shown:
a.
− x2 − x + 3 = 0
c. x 2 + 4 x + 3 = 0
b.
− 3 x 2 − 12 x − 9 = 0
d. 3 x 2 + 12 x + 9 = 0
_____28) A ball is thrown upwards from an initial height of 3 meter with a velocity of 13 meters per
second. The equation for the path of the ball is given by f (t ) = 3 + 13t − 16t 2 . What is the maximum
height of the ball?
a.
3.0 meters
c.
5.64 meters
b.
4.54 meters
d.
0.41 meters
_____29) A parabola has roots of x = 3 ± 5 . What is the equation of the parabola?
a.
x2 + 4 = 0
c.
x 2 − 6x + 4 = 0
b.
x 2 − 14 = 0
d.
x 2 − 6 x − 16 = 0
_____30) Write the equation of the parabola with vertex at (-3,-2) and directrix of x = 1
a.
x=
−1
( y + 2) − 3
16
c.
y=
b.
x=
−1
( y + 3) − 2
8
d.
y=
1
(x + 3) − 2
16
1
(x − 2) + 3
4
Unit 4- Polynomial Functions
____ 41) Determine whether the binomial (
) is a factor of the polynomial
a. (
) is not a factor of the polynomial
b. (
) is a factor of the polynomial
.
.
c. Cannot determine.
____ 42) Factor
a.
.
(
c.
)
b.
d.
(
)
____ 43) Write the simplest polynomial function with zeros –2, 7, and − 12 .
a.
−
9
2
+
9
2
x−7
c.
−
+
9
2
+
9
2
x+7
d.
–2
7
2
+0
−
+ 7x −
5
2
x−7
1
2
.
____ 44) Computer graphics programs often employ a method called cubic splines regression to
smooth hand-drawn curves. This method involves splitting a hand-drawn curve into regions that
can be modeled by cubic polynomials. A region of a hand-drawn curve is modeled by the function
. Use the graph of
to identify the values of x for which
y
and to factor
.
5
4
3
a.
;
;
b.
;
;
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
c.
;
d.
;
;
–3
–4
–5
;
____ 45) Write the simplest polynomial function with the zeros
,
, and
.
a.
b.
c.
d.
____46)
Identify the leading coefficient, degree, and end behavior of the function
a. The leading coefficient is –5. The degree is 4.
As
,
– and as
+ ,
–
b. The leading coefficient is –5. The degree is 6.
As
,
– and as
+ ,
–
c. The leading coefficient is –5. The degree is 4.
As
,
+ 6 and as
+ ,
+6
d. The leading coefficient is –5. The degree is 6.
As
,
+ 6 and as
+ ,
+6
–5 – 6
+ 6.
____ 47)
Identify whether the function graphed has an odd or even degree and a positive or negative
leading coefficient.
y
a. The degree is odd, and the leading coefficient is negative.
b. The degree is even, and the leading coefficient is negative.
x
c. The degree is even, and the leading coefficient is positive.
d. The degree is odd, and the leading coefficient is positive.
____ 48) Graph
on a calculator, and estimate the local maxima and minima.
a. The local maximum is about –13.627417. The local minimum is about 31.627417.
b. The local maximum is about 31.627417. The local minimum is about –13.627417.
c. The local maximum is about 13.627417. The local minimum is about –31.627417.
d. The local maximum is about 22.627417. The local minimum is about –22.627417.
____49) You want to create a box without a top from an
in. by 11 in. sheet of paper. You will make
the box by cutting squares of equal size from the four corners of the sheet of paper. If you make the box
with the maximum possible volume, what will be the length of the sides of the squares you cut out?
a. About 1.6 in.
c. 66.2 in.
b. About 2.8 in.
d. 61.3 in.
_____50)
Identify the value of k that makes
a solution to
a. -45
c. 9
b. -9
d. 45
.
Unit 5- Exponential and Logarithmic Functions
_____51) Albert opened a savings account at a bank in Chicago. He deposited $5,000 at 3.5% interest
compounded continuously. To the nearest cent, how much will he have in his savings account in
12 years if he makes no additional deposits and no withdrawals?
a. $7,160.00
c. $7,555.34
b. $7,609.81
d. $7,342.71
_____52) At a town with a large convention center, the cost of a hotel room has increased 4.1% annually.
If the average hotel room costs $52.00 in 1990 and this growth continues, what will an average
hotel room cost in 2012?
a. $125.87
c. $126.34
b. $235.79
d. $87.19
_____53) Solve for x:
log 3 39 + log 3 x = log 3 13
a.
b.
x=3
x=
c.
x = −26
d. x = 52
1
3
____54) Simplify using properties of logarithms:
2 log( x) − log( x − 3) = 2 log( −2)
a.
x = −2, x = 6
c.
b. x = −1
b.
x = −2
x=
d. x = 3
log 25 5 = x
____55) Solve for x:
a.
x = 2, x = −6
1
2
c.
d.
x=2
x=
−1
2
_____56) Solve for x:
a.
2 5 x − 4 = 38
x = 2.5677
b. x = 1.0175
c.
x = 1.5430
d. x = 1.0785
_____57) Solve the following natural log: ln ( x + 12 ) = ln x 2
a.
x = 2, x = −6
b. x = −4, x = 3
_____58) Solve the following exponential:
a.
x = 0.4650
b. x = 0.0203
c.
x = −3, x = 4
d. x = −2, x = 6
3 x +1 = 5
c.
x = −0.3174
d. x = 0.6582
(59-60) A certain new car costs $16,750 in the year 2000. Suppose the value of the car depreciates
12% each year.
____59) Which equation models the value of the car x years after 2000?
a. V(x) = 16,750(0.12)x
c. V(x) = 16,750(0.12x)
b. V(x) = 16,750(0.88)x
d. V(x) = 16,750(0.88x)
____60) To the nearest hundred dollars, what will the car’s value be in 2004?
a. $8,700
c. $10,000
b. $8,800
d. $11,400
Unit 6- Nonlinear Functions
_____61) Given the sequence -11, -8, -5, -2…… Find the next three terms.
A)
_____62) Find the sum of the following series:
1 n −1
(3)
n =1 2
5
A)
1845.28
B) 60.5
______63) Find the inverse for the function:
A)
B)
C) 60
D) 20
.
C)
D)
64) Joel was windsurfing at Ocean Isle Beach with the ocean’s current for 3 hours. He covered 12 miles.
When he turned around and went back the same distance it took him twice as long . What was his
speed in still water and what was the rate of the current?
65) Preparing for the summer, a local distributor who produces unique T-shirts and Tanks is
working to figure out how they can get the most profit. In a day they can produce at least 4 T shirts
but no more than 10. They also can make at least 2 Tanks. The time required to make each is one
hour for the T-shirt and two hours for the Tank due to design. They have at most 16 hours
available. If the profit on each T-shirt is $20 and each Tank is $25, how many T-shirts and Tanks
should they make each day for a maximum profit? What is the maximum profit?
Name the constraints:
Name the objective quantity:
(Show all your points for the
Polygon formed and plugged into the
objective quantity.)
Max Profit: ___________________ T-shirts/Tanks: ____________
Unit 7-Angles, Triangles, and Quadrilaterals
Identify the choice that best completes the statement or answers the question.
____ 66.
____ 67.
and
are complementary angles. m
of each angle.
a.
= 47,
= 53
c.
b.
= 47,
= 43
d.
a.
b.
and
are a linear pair.
, and
c.
d.
=
, and m
= 52,
= 52,
=
. Find the measure
= 48
= 38
. Find the measure of each angle.
____ 68. Find the values of x and y.
4y°
112°
7x + 7°
Drawing not to scale
a. x = 15, y = 17
b. x = 112, y = 68
c. x = 68, y = 112
d. x = 17, y = 15
____ 69. Q is equidistant from the sides of
Find
The diagram is not to scale.
T
|
(4
x
|
+
5)
°
Q
(8x – 11)°
S
a. 21
R
b. 42
c. 4
d. 8
____ 70. In
ACE, G is the centroid and BE = 9. Find BG and GE.
C
B
A
a.
D
G
E
F
1
4
BG = 2 , GE = 6
b.
c.
3
4
d.
1
2
BG = 4 , GE = 4
1
2
____ 71. Name a median for
|
A
E
)
|
D
)
C
F B
a.
b.
c.
d.
____ 72. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to
scale.
A
B
4x – 2
y + 14
4y – 7
x + 28
D
a. x = 10, y = 38
C
b. x = 10, y = 21
c. x = 10, y = 7
d. x = 7, y = 10
Find the value of each variable. The
|
|
____ 73. In the rhombus,
diagram is not to scale.
3
1
|
|
2
a. x = 10, y = 85, z = 6
b. x = 5, y = 175, z = 6
____ 74.
and
c. x = 5, y = 85, z = 3
d. x = 10, y = 175, z = 3
Find
The diagram is not to scale.
R
|
S
||
||
|
U
T
a. 65
b. 70
c. 35
d. 80
c. 7.5
d. 10
____ 75. What is the value of x?
x
x+5
x–2
>
x+1
>
a. 5
b. 2.5
____ 76. The surface areas of two similar solids are 384 yd and 1057 yd . The volume of the larger solid is
1795 yd . What is the volume of the smaller solid?
a. 1,795 yd
b. 1,082 yd
c. 393 yd
d. 978 yd
Unit 8 (Trigonometry)
77. Astronomers have observed that sunspots vary sinusoidally. The variation is from a minimum of about
10 sunspots per year to a maximum of about 120 per year. A cycle lasts about 11 years. If a minimum
occurred in 1964, which function could model the number of sunspots, S, as a function of the year, t?
A.
S(t) = -55cos(
(t-1964)) + 65
B. S(t) = -55cos(
t-1964) + 65
C.
S(t) = -65cos(
(t-1964)) + 55
D. S(t) = -65cos(
t-1964) + 55
78. William put the tip of his pencil on the outer edge of a graph of the unit circle at the point (0, -1). He
moved his pencil tip through an angle of radians in the counterclockwise direction along the edge of the
circle. At what angle of the unit circle did William’s pencil tip stop?
B.
A.
79.
C.
D.
Which expression is equivalent to cos( ) tan( ) - 1 sin( )?
A.
sec( )
B. sin( )
C. cos( )
D. csc( )
Use the following function to answer questions 4-7 y = - 4 + 1 cos( 2 π x + π )
2
2
80. What is the period of the function?
A. 4 π
B. π
C. 1
D. 2 π
81. What is the amplitude?
A. 4
B. π
C. 2 π
D. 1
82. What is the phase shift?
A. Left 4
B. Right 2 π C. Left π
D. Right π
83. What is the vertical translation?
A. Up π
B. Down 4
D. Down π
2
2
2
2
2
C. Up 4
2
2
84. Solve sin x = − 1 if 0 ≤ x ≤ 2π
2
A.
7π 11π
,
6 6
85. Solve cos x =
A.
5π 7π
,
4 4
B.
π 5π
,
C.
6 6
π 11π
6
,
D.
6
2
if 0 ≤ x ≤ 2π
2
B.
π 3π
,
4 4
C.
π 7π
4
,
4
D.
3π 5π
,
4 4
86. Solve sin x = 0 if 0 ≤ x ≤ 2π
A. {0}
B. {0 , π }
C. {0 , π , 2 π }
D.
π 3π
2
,
2
5π 7π
,
6 6