# Final Exam College Algebra fe_wilma_sp07_main.tst

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"Final Exam College Algebra fe_wilma_sp07_main.tst"

```					Final Exam College Algebra fe_wilma_sp07_main.tst

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ztest_PRE_FINAL_EXAM_v1_pbcc_college_alg_fa09.tst
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the investment problem.
1) Mardi received an inheritance of \$70,000. She invested part at 11% and deposited the remainder in tax-free
bonds at 12%. Her total annual income from the investments was \$7900. Find the amount invested at 11%.
A) \$50,000                    B) \$25,000                   C) \$49,000                 D) \$62,100

Use the square root property to solve the equation.
2) (x + 9)2 = 49
A) {-2}                        B) {-16, -2}               C) {-58}                       D) {16, 2}

Solve the equation.
1  2
3) +     = -6
x 7x
1                              3                          3
A) -                           B) -                       C) -                           D) ∅
2                              2                          14

Solve and graph the inequality. Give answer in interval notation.
4) -2 < 2x + 4 ≤ 6

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

A) (-3, 1]                                                B) [-3, 1)

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7                      -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
C) (-3, 1)                                               D) [-3, 1]

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7                      -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Solve the equation.
5) |7x - 2| = 3
5    1                               1    5                 1    5                       5
A)     ,-                      B) -         ,-            C)       ,-                    D)
7    7                               7    7                 7    7                       7

Find the distance between the pair of points.
6) (5, -7) (3, -3)
A) 2 5                      B) 12 3                       C) 6                           D) 12

Find the center-radius form of the equation of a circle.
7) center (9, -4), radius 3
A) (x + 4)2 + (y - 9)2 = 3                                B) (x - 4)2 + (y + 9)2 = 3
C) (x - 9)2 + (y + 4)2 = 9                               D) (x + 9)2 + (y - 4)2 = 9

1
Solve.
8) A circle has a diameter with endpoints (-2, 1) and (4, 9). Find the radius.
A) 10                         B) 5                           C) 10                            D)   5

Decide whether the relation defines a function.
9) 4x = 10 - 2y
A) Function                                                    B) Not a function

Graph the function.
10)
1,      if x ≥ 1
f(x) =
-4 - x, if x < 1

y
6

4

2

-6    -4   -2              2       4   6 x
-2

-4

-6

A)                                                           B)
y                                                       y
6                                                       6

4                                                       4

2                                                       2

-6   -4        -2            2   4     6 x                   -6   -4   -2            2    4       6 x
-2                                                      -2

-4                                                      -4

-6                                                      -6

C)                                                           D)
y                                                       y
6                                                       6

4                                                       4

2                                                       2

-6   -4        -2            2   4     6 x                   -6   -4   -2            2    4       6 x
-2                                                      -2

-4                                                      -4

-6                                                      -6

2
f(x + h) - f(x)
Compute and simplify the difference quotient                                  , h ≠ 0.
h
11) f(x) = 8x - 7
7
A)                                      B) -7h                              C) 7                         D) 8
8

Solve the problem.
12) Find (f ∘ g)(4) when f(x) = 5x + 9 and g(x) = -5x2 + 3x + 3.
A) -4115                       B) -316                                       C) -55                       D) -16

13) If an object is propelled upward from a height of 96 feet at an initial velocity of 80 feet per second, then its
height h after t seconds is given by the equation h = -16t2 + 80t + 96. After how many seconds does the object hit
the ground?
A) 11                                    B) 6                                C) 5.0                       D) 3.0

For the polynomial, one zero is given. Find all others.
14) P(x) = x3 - 8x2 + 17x - 30; 6
A) -1 + 2i, -1 - 2i                      B) 1 +       5, 1 -   5             C) 1 +   5i, 1 -   5i        D) 1 + 2i, 1 - 2i

Solve the problem.
15) The graph of f(x) = x3 - x2 - 8x + 12 is shown below. Use the graph to factor f(x).

y
20

-5 -4 -3 -2 -1          1   2   3   4   5 x

-20

A) f(x) = (x - 3)(x + 2)2                                                    B) f(x) = x(x + 3)(x - 2)
C) f(x) = (x + 3)(x - 2)2                                                    D) f(x) = -(x + 3)(x - 2)2

Find any vertical asymptotes.
7x + 5
16) f(x) =
5x - 1
7                                        1
A) x =                                   B) x =                              C) x = - 5                   D) x = 5
5                                        5

Find the horizontal asymptote of the given function.
6x2 + 8
17) f(x) =
6x2 - 8
A) y = 8                                 B) None                             C) y = -8                    D) y = 1

3
Solve the problem.
18) The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of
illumination on a screen 5 ft from a light is 2 foot candles, find the intensity on a screen 15 ft from the light.
A) 2 foot-candles              B) 1 2/9 foot-candles          C) 2/9 foot-candle            D) 2/10 foot-candle

Determine whether or not the function is one-to-one.
19) f(x) = x2 + 6
A) Yes                                                       B) No

If f is one-to-one, find an equation for its inverse.
20) f(x) = 3x - 6
x
A) Not a one-to-one function                                 B) f-1 (x) = + 6
3
x-6                                                          x+6
C) f-1(x) =                                                 D) f-1 (x) =
3                                                            3

Solve the equation.
21) 4 (9 - 3x) = 64
A) {-2}                       B) {16}                        C) {3}                        D) {2}

Determine the intervals over which the function is decreasing, increasing, and constant.
22)
y
10

-10      (-1, 0)            10   x

-10

A) Increasing (-∞, 1]; Decreasing [1, ∞)                     B) Increasing (-∞, -1]; Decreasing [-1, ∞)
C) Increasing [-1, ∞); Decreasing (-∞, -1]                   D) Increasing [1, ∞); Decreasing (-∞, 1]

Solve the problem.
23) The decay of 954 mg of an isotope is given by A(t)= 954e-0.018t, where t is time in years since the initial amount
of 954 mg was present. Find the amount left after 8 years.
A) 826                      B) 937                       C) 811                          D) 413

Evaluate the logarithm.
1
24) log
2 2
A) 0                          B) 1                           C) -1                         D) 2

4
Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all
variables represent positive real numbers.
25) log4 13 - log4 a
a                                  13                        13
A) log4                            B) log4                   C) log8                       D) log4 (13 - a)
13                                 a                         a

26) 6 log6 (6x - 1) + 4 log6 (2x - 7)

A) log6 ((6x - 1)6 + (2x - 7)4 )                             B) log6 (6x - 1)6 (2x - 7)4

(6x - 1)6
C) 24 log6 (6x - 1)(2x - 7)                                  D) log6
(2x - 7)4

Solve the problem.
27) How long will it take for \$6000 to grow to \$32,300 at an interest rate of 9.8% if the interest is compounded
continuously? Round the number of years to the nearest hundredth.
A) 17.18                      B) 0.85                       C) 1717.66                       D) 1.72

28) Assume the cost of a gallon of milk is \$2.60. With continuous compounding, find the time it would take the cost
to be 5 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.
A) 0.0 years                 B) 9.9 years                    C) 0.1 years               D) 26.8 years

Solve the system.
29) x + y + z = -10
x - y + 3z = -4
4x + y + z = -25
A) ∅                               B) {(-5, -4, -1)}         C) {(-1, -5, -4)}             D) {(-1, -4, -5)}

Solve the nonlinear system of equations.
30) x2 + y2 = 5
x + y =3
A) {(-2, 1), (-1, 2)}               B) {(2, 1), (1, 2)}       C) {(-2, -1), (-1, -2)}       D) {(2, -1), (1, -2)}

5
Testname: ZTEST_PRE_FINAL_EXAM_V1_PBCC_COLLEGE_ALG_FA09

1) A
2) B
3) C
4) A
5) A
6) A
7) C
8) B
9) A
10) C
11) D
12) B
13) B
14) D
15) C
16) B
17) D
18) C
19) B
20) D
21) D
22) C
23) A
24) C
25) B
26) B
27) A
28) D
29) B
30) B

6

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