# Math Homework Multiple Choice

College Algebra

Final Examination—FHSU Math & C.S. Department

Form G Name ____________________________

Multiple Choice:

Mark through (horizontally) the space on the answer card corresponding to the best answer for each

problem.

1. Solve the equation by factoring: 2 9 18 0x x  

[A]  6, 3 [B]  6, 3 [C]  6, 3  [D]  6, 3

2. Write the product in the standard form a + bi: (2 6 )(2 9 )i i 

[A] 58 6i [B] 50 30i  [C] 58 6i [D] 2

54 6 4i i  

3. Find the real solutions of the equation 14 21 2 .x x  

[A]  5 [B]  3 [C]  4 [D]  5

4. Solve the inequality 3 7 2 4x x   . Express your answer using interval notation.

[A]  11,  [B] [3, ) [C]  3, [D] ( , 3]

5. Solve the equation 3 3 18.x  

[A]  3, 9 [B]  3 [C]  9, 3 [D] no solution

6. Solve the inequality 5 1 5x   . Express your answer using interval notation.

[A]  645 5, or ,    [B] 64

5 5 , 

 

[C]  645 5, [D]     64

5 5 , or ,  

7. A bank loaned \$68,000, part of it at a rate of 15% per year and the rest at a rate of 5% per year. If the

interest received was \$6600, how much was loaned at 15%?

[A] \$36, 000 [B] \$33, 000 [C] \$32, 000 [D] \$35, 000

8. Find the distance between the points 1 2(2, 2) and ( 10, 3).PP    

[A] 14 [B] 26 [C] 169 [D] 13

9. List the intercepts for the graph of the equation 2

16 0.x y  

[A] ( 4, 0), (0,16), (4, 0) [B] (4, 0), (0,16), (0, 16)

[C] (0, 4), (16, 0), (0, 4) [D] ( 4, 0), (0, 16), (4, 0) 

2

10. Find the slope-intercept form of the equation of the line that is parallel with the given properties:

( 2, 3); and 9 20y x  

[A] 9 15y x   [B] 9 20y x   [C] 1

20 9

y x  [D] 1

20 9

y x  

11. Write the standard from of the equation of the circle with radius 5 and center (1, 4) .

[A]     2 2

4 1 25x y    [B]     2 2

1 4 5x y   

[C]     2 2

4 1 25x y    [D]     2 2

1 4 5x y   

12. Write a general formula to describe the variation.

The illumination I produced on a surface by a source of light varies directly as the candlepower c of

the source and inversely as the square of the distance d between the source and the surface.

[A] 2

I kcd [B] 2

2

kc I

d  [C]

2

kc I

d  [D]

2 kd

I c

13. For the given functions ( ) 6 3 and ( ) 7 9f x x g x x    , determine ( )( ).f g x

[A] 2

( )( ) 4 27f g x x  [B] 2

( )( ) 13 33 6f g x x x  

[C] 2

( )( ) 42 33 27f g x x x   [D] 2

( )( ) 42 12 27f g x x x  

14. The graph of a function f is given. For what values of x is

( ) 0f x  ?

[A]  15,17.5

[B]  15,17.5, 25

[C]  15

[D]  25, 15,17.5, 25 

15. Determine whether the function 3 2

( ) 4 9f x x  is even, odd, neither, or both.

[A] Even [B] Odd [C] Neither [D] Both

16. Determine the average rate of change for the function 2

( ) 2f x x x  from 5 to 9 using ( ) ( )

. f b f a

b a

[A] 16 [B] 64

9 [C] 11 [D]

99

4

-25 -15 -5 5 15 25

-15

5

15

-5

-25

3

17. The graph of a function f is given. Determine the values

of x at which f has a local minimum.

[A]  3.3, 2.5 

[B]  2.5, 5

[C]  3.3, 5

[D]  2.5, 2.2

18. Determine the function that is graphed after the following transformations are applied to the graph of

y x . The graph is shifted right 4 units, stretched by a factor of 3, and shifted vertically down 2

units.

[A] 3 4 2y x   [B] 3 4 2y x   [C] 3 4 2y x   [D] 3 4 2y x  

19. Find and simplify the difference quotient, ( ) ( )

, 0 f x h f x

h h

   , for the function ( ) 4 5.f x x 

[A] 4 [B] 0 [C] 10

4 h

 [D] 8( 5)

4 x

h

 

20. Suppose that 2

( ) 2 3 and ( ) 2 3f x x x g x x     , solve ( ) ( )f x g x

[A] 1

, 3 2

     

[B] 1

, 3 2

   

  [C]  0, 3 [D]  0, 3

21. Linda needs to have her car towed. Little Town Auto charges a flat fee of \$80 plus \$2 per mile towed.

Write a function expressing Linda’s towing cost, c , in terms of miles towed, x .

[A] ( ) 2c x x [B] ( ) 2 80c x x  [C] ( ) 80 2c x x  [D] ( ) 2 80c x x 

22. Determine the x-intervals where the function graphed at

the right is decreasing.

[A] decreasing on (5, 3.3) and (3.9, 2.5) 

[B] decreasing on ( , 8), ( 2.5, 2.2), and (5, )   

[C] decreasing on ( 8, 2.5) and (2.2,5) 

[D] decreasing on ( 5,0) and (4,5)

4

23. Identify the vertex of the graph of the function 2

( ) 6 5.f x x x  

[A] ( 3, 4) [B] (3, 4) [C] (3, 4) [D] ( 3, 4) 

24. Determine the quadratic function whose graph is given.

[A] 2

( ) ( 2) 1f x x  

[B] 2

( ) ( 1) 2f x x  

[C] 2

( ) ( 1) 2f x x  

[D] 2

( ) ( 2) 1f x x  

25. The number of mosquitos ( )M x , in millions, in a certain area depends on the June rainfall x , in

inches: 2

( ) 10M x x x  . What rainfall produces the maximum number of mosquitos?

[A] 0 inches [B] 5 inches [C] 100 inches [D] 10 inches

26. Solve the inequality 2

3 2x x   .

[A]    ,1 or 2,  [B]  ,1 [C]  2, [D]  1, 2

27. Form a polynomial of degree 3 whose zeros are –5 with multiplicity 2 and 4 with multiplicity 1.

[A] ( ) ( 5)( 5)( 4)P x x x x    [B] ( ) ( 5)( 5)( 4)P x x x x   

[C] ( ) ( 5)( 2)( 4)P x x x x    [D] ( ) ( 5)( 4)( 4)P x x x x   

28. What are the x- and y-intercepts of the function    2

( ) ( 2) 6 1f x x x x     ?

[A] -intercepts are ( 6, 0), (1, 0), (2, 0)

-intercept is (0,12)

x

y

 [B]

-intercepts are ( 2, 0), (1, 0), (6, 0)

-intercept is (0, 12)

x

y

[C] -intercepts are ( 6, 0), (1, 0), (2, 0)

-intercept is (0, 12)

x

y

 [D]

-intercepts are ( 2, 0), (1, 0), (6, 0)

-intercept is (0,12)

x

y

5

29. What is the domain of the rational function 2

2 ( )

16

x f x

x x

 

 ?

[A]  | 0, 16x x x   [B]  | 4, 4x x x  

[C]  | 4, 4, 2x x x x     [D]  | 0, 16x x x 

30. Write the equation of all vertical asymptotes of the rational function 2

2 ( )

16

x f x

x x

 

 .

[A] 16x  [B] 0, 16x x   [C] 4, 4x x   [D] 2x  

31. Write the equation of the horizontal asymptote of the rational function 2

2 ( )

16

x f x

x x

 

 .

[A] 2y   [B] 0y  [C] 1

8 y  [D] 16y 

32. Which of the following displays a graph of a polynomial that has ( 3)x  as a factor with odd

multiplicity?

[A] [B]

[C] [D]

6

33. Which of the following best represents the left and right behaviors of the given graph:

[A] ( ) as

( ) as

f x x

f x x

   

   

[B] ( ) as

( ) as

f x x

f x x

   

   

[C] ( ) as

( ) as

f x x

f x x

   

   

[D] ( ) as

( ) as

f x x

f x x

   

   

34. The function 2 1

( ) 3

x f x

  is one-to-one. Find its inverse.

[A] 3 1

2

x  [B]

3

2 1x  [C]

3

2 1x 

 [D]

2 1

3

x 

35. Solve the exponential equation 7 3 1

4 2

x  .

[A]  1 [B]  3 [C]  3 [D] 1

2

     

36. Using technology, approximate the value of 5

log 20 accurate to four decimal places.

[A] 2.3412 [B] 1.8614 [C] 0.5372 [D] 1.2523

37. Through the properties of logarithms, write 4 3

8 log

x

x

 as the sum and/or difference of logarithms and

powers as factors.

[A] 4 4

log ( 8) logx x  [B] 4 4

3log log ( 8)x x 

[C] 4 4

log ( 8) 3logx x  [D] 4 4 4

log log 8 3logx x 

38. Solve the logarithmic equation: ln( ) ln 3 ln( 4)x x  

[A] 4

3

     

[B]  6 [C]  6 [D] 4

3

     

7

39. Solve the rational inequality, express the solution in interval notation: 4

0 9

x

x

 

[A] ( 9, 4) [B]  ( , 9) or 4,  

[C] ( 9, )  [D] ( , 9) 

40. If        6 6, and 5 4. Then ? f x x g x x g f x    

[A] 30 34x  [B] 30 26x  [C] 30 34x  [D] 30 30x 

41. Find the amount that results from \$1000 being invested at 5% compounded monthly after a period of

8 years. Use  1 . ntr

nA P 

[A] \$1702.09 [B] \$1490.59 [C] \$1400.00 [D] \$400.00

42. How long will it take \$2900 being invested at 7% compounded quarterly to double? Use

 1 ntr

nA P  and round to the nearest tenth of a year.

[A] 10.2 yr [B] 9.8 yr [C] 10.0 yr [D] 10.4 yr

43. Solve the system of equations: 3 5

. 2 3 8

x y

x y

  

   If the system has no solution, choose inconsistent.

[A] (2, 1) [B] ( 1, 2) [C] (1, 2) [D] Inconsistent

44. List all potential rational zeros of the polynomial function 3 2

( ) 2 4 2 8f x x x x     . (Do not find

the zeros.)

[A] 1

, , , 2

1 2 4    [B] 1 1

, , , , , 4 2

1 2 4 8     

[C] 1 1 1

, , , , , , 8 4 2

1 2 4 8       [D] 1

, , , , 2

1 2 4 8    

45. What rate of interest is required to triple an investment in 12 years if the interest is compounded

continuously? Use . r t

A Pe

[A] 3.976% [B] 8.006% [C] 9.155% [D] 12.983%

8

46. Given the piece-wise defined function

2

2

3 if 7 2

( ) 14 if 2

4 3 if 2

x x

f x x

x x

   

 

 

    

, determine the value (5).f

47. It is known that ( 4)x  is a factor of the polynomial 3 2

( ) 4 4 16f x x x x    . Find all the zeros

of ( )f x .

48. Identify the graph the system of inequalities: 3 1 3 1 3y x y x x     

49. The reduced row echelon form of a system of linear equations is

1 2 0 6

0 1 3 5

0 0 1 3

         

. Write the

system of equations corresponding to the given matrix and then give the solution to the system.

50. Given the formula 2

2 2S r rh   . Solve for h .

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