Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Solve the
problem.
You have 324
feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize
the enclosed area.
a. | 162 ft by 162
ft | c. | 81 ft by 81
ft | b. | 83 ft by 79
ft | d. | 162 ft by 40.5
ft
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2.
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Which of the following
polynomial functions might have the graph shown in the illustration below?
a. | f(x) =    | c. | f(x) = x (x - 1) | b. | f(x) =  (x - 2)(x -
1) | d. | f(x) = x(x - 2) |
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3.
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Decide which of the rational
functions might have the given graph.
a. | f(x) =  | c. | f(x) =  | b. | f(x) =  | d. | f(x) =  |
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4.
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A surveyor is measuring the
distance across a small lake. He has set up his transit on one side of the lake 90 feet from a
piling that is directly across from a pier on the other side of the lake. From his transit, the angle
between the piling and the pier is 70°. What is the distance between the piling and the
pier to the nearest foot?
a. | 85 ft | c. | 33 ft | b. | 247 ft | d. | 31 ft |
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5.
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Find the exact value under
the given conditions.
sin á = -  ,  < á <
2ð; cos â = -  , ð < â < 
Find sin (á - â).
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6.
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If A denotes the area of the
sector of a circle of radius r formed by the central angle è,
find the missing quantity. If necessary, round the answer to two decimal places.
r = 17
feet, A = 88 square feet, è = ?
a. | 1,457,885.35° | c. | 34.91° | b. | 728,942.68° | d. | 17.46° |
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7.
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Solve the
triangle.
a = 13, b
= 13, c = 11
a. | A = 50°, B = 65°, C =
65° | c. | A =
65°, B = 50°, C = 65° | b. | A = 65°, B = 65°, C =
50° | d. | A = 66°, B = 66°, C
= 48° |
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8.
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Solve the
equation.
= 
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9.
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4 + 5 ln x =
1
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10.
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Solve the
inequality.
- 49  0
a. | (- , -7] or
[ 7,  ) | c. | (- , -49] or [ 49,
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49] | d. | [-7,
7] |
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11.
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Use the information given
about the angle è, 0  è  2ð, to find the exact value of the indicated trigonometric
function.
tan è = 2, cos
è < 0 Find cos  .
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12.
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Two sides and an angle are
given. Determine whether the given information results in one triangle, two triangles, or no triangle
at all. Solve any triangle(s) that results.
B = 35°, b = 6, a = 32
a. | one triangle
A = 31°,
C = 113°, c = 35 | c. | one triangle
A = 34°, C = 112°, c =
39.5 | b. | one triangle
A = 33°, C = 111°, c =
38 | d. | no
triangle
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13.
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Solve the inequality
algebraically. Express the solution in interval notation.
(x + 7)(x + 3)(x - 1) >
0
a. | (- , -7)
 ( -3, 1) | c. | ( -7, -3)  ( 1,  ) | b. | ( 1,  ) | d. | (- ,
-3) |
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14.
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Determine where the function
is increasing and where it is decreasing.
f(x) =  + 2x -
8
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15.
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Write an equation that
expresses the relationship. Use k as the constant of variation.
g varies inversely as the square of
m.
a. | g =  | c. | g =  | b. | g =  | d. | g =  |
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16.
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Find the exact value of the
expression. Do not use a calculator.
tan  - cos 
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17.
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Convert the angle in radians
to degrees.
-  ð
a. | -650° | c. | -11° | b. | -1300ð° | d. | -325° |
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18.
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Solve the system of
equations by elimination.
a. | x = 0, y = 0; (0,
0) | c. | x = 0, y = 10; (0,
10) | b. | x = 10, y = 0; (10, 0) | d. | x = 10, y = 10; (10, 10) |
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19.
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Find the exact value of the
expression.
sin
a. | 0 | c. |  | b. |  | d. | 1 |
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20.
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Convert the angle in degrees
to radians. Express the answer as multiple of ð.
54°
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21.
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Determine algebraically
whether the function is even, odd, or neither.
f(x) = 
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22.
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For the given functions f
and g, find the requested composite function.
f(x) =  ,
g(x) = 8x - 10; Find (f ° g)(x).
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23.
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Find the real solutions of
the equation by factoring.
10 + 70 + 120x
= 0
a. | {-  ,
-4} | c. | {0, 3,
4} | b. | {-3,
-4} | d. | {0, -3,
-4}
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24.
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Determine, without graphing,
whether the given quadratic function has a maximum value or a minimum value and then find that
value.
f(x) = -4 + 12x
a. | minimum;
9 | c. | minimum; -
9 | b. | maximum;
9 | d. | maximum; -
9 |
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25.
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Solve the equation on the
interval 0  è <
2ð.
sec(2è) - 2 = tan(2è)
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26.
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è = 3(1 - sin è)
a. |  | c. |  | b. | {ð} | d. | {0}
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27.
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Find the
function.
Find the function that is finally graphed after the following transformations are
applied to the graph of  The graph is shifted down 3
units, reflected about the x-axis, and finally shifted left 6
units.
a. | y =  -
3 | c. | y = - +
3 | b. | y = - +
3 | d. | y = - -
3 |
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Short Answer
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28.
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If f(x) =  and g(x) = -1 + 5x, find (f
°g)(x) and find the domain of (f °
g)(x).
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29.
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Solve the equation by
factoring.
4x +  = - 14
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