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MULTIPLE CHOICE REVIEW WORKSHEET
FOR
COLLEGE ALGEBRA FINAL EXAM
The multiple choice questions included in this review worksheet are intended to be a
sampling of questions and concepts that could be asked on the College Algebra Final
Exam.
There are many mathematical ideas that you have learned throughout the semester that
are NOT included in this worksheet review. Because there may be College Algebra
material discussed in class yet not included on this review worksheet, you should also
study your textbook, homework, quizzes, and exams to adequately prepare for the
College Algebra Final Exam.
You will notice that this review worksheet includes about 80 questions. The actual
College Algebra Final Exam contains approximately40 questions pertaining to
information included in Chapters 1 through 4, and Section 5.1 and 5.5 of your textbook.
The actual final exam includes at least one question from each section and no more
than four questions from each section.
After you have completed the Multiple Choice Review Worksheet, you may check your
answers. The answers are located on the last page of this Review.
MULTIPLE CHOICE REVIEW WORKSHEET FOR COLLEGE ALGEBRA FINAL EXAM
- Which one of the following is true?
[A] The point (1, 4 ) lies in Quadrant II. [B] The graph of an equation is the set of all points whose coordinates satisfy the equation. [C] Every graph has at least one intercept. [D] The graph of 4 is a line. 2 y x
2. Solve the equation for x : 5 3 x 6 2 x 6
[A] 7 [B]
[C] 1 [D] 7
- Solve the equation for x : 3
x
[A]
[B]
[C] 10 [D]
- Solve the equation for x :
x
x x
[A] 0 [B] 3 [C]
[D]
- Solve the equation for x :
x x
x x
[A]
[B]
[C] 1 [D]
- You inherit $2500 with the stipulation that for the first year the money must be invested into two
stocks paying 10% and 6% annual interest, respectively. How much should be invested at the 10% rate if the total interest earned for the year is to be $221.92? [A] $449.50 [B] $702 [C] $1798 [D] $2219.
- After a 7% increase in salary, Laurie makes $1016.50 per month. How much did she earn per
month before the increase? [A] $871.29 [B] $ 945.35 [C] $950 [D] $1087.
- Solve the formula for the specified variable: A P P rt for P.
[A] P A P rt [B] 1
A
P
rt
[C] P A (1 rt ) [D] 2
A
P
rt
- Find the slope of the line containing the pair of points: (5, 2) and ( 3 , 7)
[A]
[B]
[C]
[D]
20. Which one of the following is an equation of a line that passes through the point 2, 3 with a
slope of 4?
[A] y 4 x 11 [B] y 4 x 5 [C]
y x [D] y 4 x 11
- Find the slope of the line described: A line perpendicular to 3 x 2 y 5 0
[A]
[B]
[C]
[D]
22. Find the exact distance between the two ordered pairs 0 , 5 and 7 , 9 .
[A] 65 [B] 33 [C] 7 [D] 5
23. Find the midpoint of the line segment joining the ordered pairs 5 , 20 and 16 , 4 .
[A]
[B] 5 , 12 [C]
[D]
- The center of the circle with the following equation is: ( 4 ) ( 9 ) 25
2 2 x y
[A] 4 , 9 [B] ( 4 , 9 ) [C] ( 2 ,3) [D] (2, 3 )
- Which one of the following is the standard form of the equation of the circle whose center is at the
point 5 , 1 and whose radius is 4?
[A] 5 1 2 [B]
2 2
x y 5 1 16
2 2 x y
[C] 5 1 2 [D]
2 2
x y 5 1 16
2 2 x y
- Which one of the following does not define y as a function of x?
[A] [B] [C] 2 x y 16 ( 3 ) 1 2 y x x y 3 [D] 2 x y
- If ( ) 3 then find g ( 4 ). 2 g x x
[A] 19 [B] 13 [C] 5 [D] 11
- If f ( x ) x 2 x , then find 2 f ( a h ) f a ( ).
[A] [B] [C] 2 h 2 a 2 h h h 2 h 4 a 2 2 h 2 ah 2 [D] h 2 h 2
- If , then evaluate f ( 3)
1 for 1 ( ) 2 for 1
x x f x x x
^ ^ ^
[A] 8 [B] 6 [C] 3 [D] 4
- State the domain of the following function: y 3 x 4
[A]
[B]
[C]
[D]
- State the domain of the following function in interval notation: 7
x
f x
[A] 7 , [B] 7 , [C] , [D] , 7 7 ,
- Use the graph below to determine the function’s range. Tick marks along the axes represent one
unit each. y
[A] 3, 2 [B] 3,
[C] 3, 2 [D] 2 , 3
x
- If f ( x )for every value of x in the domain of the function f , then which one of the
following is true about f?
f ( x )
[A] f is called an odd function and its graph is symmetric about the y -axis.
[B] f is called an even function and its graph is symmetric about the y -axis.
[C] f is called an odd function and its graph is symmetric about the origin.
[D] f is called an even function and its graph is symmetric about the origin.
- The graph of 3 x 5 can be obtained by doing which of the following transformations of the
graph of
y
y x?
[A] reflect about the x -axis, stretch by a factor of 3, shift up 5 units. [B] shift down 5 units, reflect about the y -axis, stretch by a factor of 3. [C] reflect about the x- axis, stretch by a factor of 3, shift down 5 units. [D] reflect about the x -axis, shrink by a factor of 3, shift down 5 units.
- If 2
f ( ) x x 9 and g x ( ) x 3 , then 5
f
g
[A] 5( x 3) [B] x 3 [C]
[D] 8
36. If f ( ) x 2 x 4 and g x ( ) 3 x 1 , then f g ( ) x
[A] x 3 [B] 5 2 x 3 x [C] x 3 [D] 5 x 3
- If 1 2 f ( x ) x and g ( x ) x 2 , then ( f g )( x )
[A] [B] x [C] x [D] 2 4 5 x 2 x x 3 2 1 2 2 x 5
- If 7 x 3 and 4
2 f ( x ) g ( x ) x , what is ( f g )( 2 )?
[A] 53 [B] 59 [C] 125 [D] 292
- Find the quotient and remainder for the following:
4 3 2 x x x x x
[A] 5 2 9 14 ; 17 [B] 3 2 x x x 5 2 4 13 ; 53 3 2 x x x
[C] 5 2 4 1 ; 17 [D] 3 2 x x x 5 32 106 331 ; 979 3 2 x x x
- If the number 3 is a zero of a polynomial function f ( ) x , then which of the following is true?
[A] x 3 is a factor of f ( ) x [B] x 3 is a factor of f ( ) x
[C] 3 is a zero of f ( ) x [D] f ( 0 3)
- Use the rational zero theorem to find all possible rational zeros for the polynomial function.
f ( ) x 9 x 5 x 7 x 1 7 3 0
[A]
1 , 3 , 9 , [B] 1 2 5 10, , ,
[C]
1 , 2 , 5 , 10 , [D] 1 3 9 , ,
- Find the remaining zeros of 75 0 , given –5 is a double root.
What is the sum of these remaining roots?
4 3 2 f x x x x x
[A] 2 [B] 4 [C] 2 [D] 4
- Which one of the following equations have the given roots, 3 and 4 i?
[A] 3 16 48 [B] 3 2 x x x 48
48
3 2 x x x
[C] 3 16 48 [D]
3 2 x x x 3 16
3 2 x x x
- Write the following as a product of linear factors given that 1 and 3 are zeros: 4 3 2 f ( ) x x 2 x x 8 x 12
[A] ( x 1 )( x 3)( x 2 )( i x 2 i ) [B] ( x 1)( x 3)( x 2 )( i x 2 ) i
[C] ( x 1)( x 3)( x 2 )( i x 2 i ) [D] ( x 2)( x 2)( x 3)( x 1)
- State the domain of the following function in interval notation:
2 4 ( ) 2
x f x x
[A] , 2 or 2, [B] , 2 or 2,
[C] , [D] , 2 or 2, 2 or 2,
- Find the horizontal asymptote:
x f x x
[A]
y [B] y 0 [C]
x [D]
y
- Find the vertical asymptote(s): (^2)
x f x x x
[A]
x x
[B] x x
, 5 [C] x
[D] y 0
- Find the y intercept: 3
2
x
x f x
[A] ( 0, 3) [B]
^
[C]^
[D] ( 3, 0)
- Find the x intercept: 5
x
x f x
[A] (0, 1) [B] (5, 0) [C] (1, 0) [D] (–1, 0)
- If P varies inversely as w , and 3
P when 4
w , then what is P when 6
w ?
[A] 1 [B] 16 [C]
[D] 4
- Which one of the following is true?
[A] If y varies inversely as x , then for x 0 , we get y 0.
[B] The area of a rectangle varies directly as its length and inversely as its width. [C] The number can be a constant of variation. [D] If y varies directly as x , then y is not a linear function.
- If y varies directly as u and varies inversely as the square of v , and y 7 when u 9 and v 6 ,
then find the constant of variation.
[A]
[B]
[C]
[D] 28
- The number of spiders, S t ( ) , remaining within a 10-foot radius of their birthplace t days after birth
is given by the formula:
0.
. Find the number of spiders present within this radius
10 days after their birth.
S t ( ) 200 2 t
[A] 0 [B] 5 [C] 50 [D] 800
- If $4500 is invested at a rate of 8% compounded quarterly, then how much interest will be earned
at the end of 6 years? Hint:
nt
n
r A P
[A] $353,235.81 [B] $24,035.31 [C] $7237.97 [D] $2737.
- The growth in the population of a biology experiment fits t e where t is the number of
years since 1987. Estimate the population in the year 2000.
A t
. 013 ( ) 445
[A] 527 [B] 451 [C] 264 [D] 534
- The spread of a flu virus through a particular population is modeled by (^) 0.
y (^) t e
where y is
the total number of people infected after t days. In how many days will 530 people be infected with the virus? (Round your answer to the nearest whole number.) [A] 8 days [B] 9 days [C] 10 days [D] 11 days
- When the system of linear equations is solved, what is the x- value of the solution?
x y
x y
[A]
[B]
[C]
[D] 4
Solutions for the Multiple Choice Review Worksheet
- A 32. D 48. C 64. A
- B 17. C 33. C 49. A 65. B
- D 18. D 34. C 50. C 66. B
- B 19. C 35. D 51. A 67. A
- D 20. D 36. D 52. A 68. C
- B 21. B 37. A 53. C 69. D
- C 22. A 38. A 54. B 70. C
- C 23. A 39. C 55. D 71. C
- B 24. B 40. D 56. B 72. A
- A 25. D 41. A 57. B 73. D
- B 26. D 42. B 58. B 74. D
- C 27. B 43. C 59. A 75. D
- D 28. C 44. D 60. C 76. C
- A 29. D 45. C 61. D 77. D
- A 30. D 46. B 62. C
- B 31. A 47. C 63. D
