College Algebra
Exam Preparation Guide
Course Introduction
College Algebra is designed to provide students with a solid foundation in algebraic concepts and techniques necessary for success in higher-level mathematics and various applied fields. The course covers topics such as linear, quadratic, polynomial, rational, exponential, and logarithmic functions; systems of equations and inequalities; matrices; sequences and series; and basic probability. Emphasis is placed on problem-solving skills, analytical reasoning, and the effective use of graphing technology. By the end of the course, students will be able to model and solve real-world problems using algebraic methods and demonstrate proficiency in manipulating mathematical expressions and equations.
Recommended Textbook
College Algebra with Applications for Business and Life Sciences 2nd Edition by Ron Larson
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8 Chapters
787 Verified Questions
787 Flashcards
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Chapter 1: Fundamental Concepts of Algebra
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119 Verified Questions
119 Flashcards
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Sample Questions
Q1) Factor the difference of two squares. 49 - (m + 4) <sup>2</sup>
A) (m + 11)(3 - m)
B) (m + 11)(19 - m)
C) (19 - m)<sup>2</sup>
D) (3 - m)<sup>2</sup>
E) (m + 11)<sup>2</sup>
Answer: A
Q2) Identify the degree and leading coefficient of the polynomial. 5 - 6x<sup>2</sup> + 4x
A) degree: 3 leading coefficient: 4
B) degree: 2 leading coefficient: 6
C) degree: 3 leading coefficient: 6
D) degree: 2 leading coefficient: -6
E) degree: 2 leading coefficient: 5
Answer: D
Q3) Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them. 2, -3
A) 2 < -3
B) 2 > -3
Answer: B
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Chapter 1: Equations and Inequalities
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94 Verified Questions
94 Flashcards
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Sample Questions
Q1) The price of a home theater system has been discounted 18%.The sale price is $289.Find the original price of the system.
A) $341.02
B) $356.25
C) $363.86
D) $352.44
E) $348.63
Answer: D
Q2) Two friends fly from from one city to another (a distance apart of 2417 miles).It takes 2 hours and 25 minutes to fly the first 860 miles.At this rate, how long is the entire flight? Round to the nearest hundredth of an hour.
A) 8.15 hours
B) 6.79 hours
C) 6.34 hours
D) 5.89 hours
E) 7.24 hours
Answer: B
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Chapter 2: Functions and Graphs
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97 Flashcards
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Sample Questions
Q1) Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-1, 1, 3}
A) {(5, -1), (10, 1), (10, 3), (15, 1), (20, -1)}
B) {(15, -1), (15, 1), (15, 3)}
C) {(15, 1), (10, -1), (5, 1), (10, 3), (15, -1)}
D) {(10, 1), (15, 3), (20, 1)}
E) {(5, 3), (15, 1), (5, -1), (15, 3)}
Answer: D
Q2) After opening the parachute, the descent of a parachutist follows a linear model.At 7:28 P.M., the height of the parachutist is 6150 feet.At 7:31 P.M., the height is 3450 feet.Use a linear equation that gives the height of the parachutist in terms of the time to find the time when the parachutist will reach the ground.
A) 7:33:30 P.M.
B) 7:34:50 P.M.
C) 7:32:00 P.M.
D) 7:37:30 P.M.
E) 7:31:00 P.M.
Answer: B
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Chapter 3: Polynomial and Rational Functions
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105 Flashcards
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Sample Questions
Q1) A farmer wants to enlarge an existing rectangular pig pen such that the total area of the new pen is twice as large as the original pen.The current pen's dimensions are 25' × 27'.The farmer wants to add 13 feet more to the long side than to the the short side.Find the dimensions of the new pen.
A) 5 feet × 18 feet
B) 30 feet × 45 feet
C) 30 feet × 32 feet
D) 30 feet × 43 feet
E) 30 feet × 40 feet
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Chapter 4: Exponential and Logarithmic Functions
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92 Flashcards
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Sample Questions
Q1) An initial investment of $6000 grows at an annual interest rate of 3% compounded continuously.How long will it take to double the investment?
A) 23.10 years
B) 24.10 years
C) 24.00 years
D) 23.00 years
E) 1 year
Q2) An investment is expected to pay 11% per year compounded continuously.If you want the value of the investment to be $900,000 after 25 years, how much should you invest initially? Round to the nearest dollar.
A) $14,384
B) $28,768
C) $57,535
D) $115,070
E) $368,953
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Chapter 5: Systems of Equations and Inequalities
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Sample Questions
Q1) A total of $50,000 is invested in two funds paying 6.5% and 7.5% simple interest.The total yearly interest is $3600.How much is invested at the 6.5% rate?
A) $28,000
B) $12,000
C) $26,000
D) $15,000
E) $20,000
Q2) You are offered two different jobs.Company A offers an annual salary of $34,000 plus a year-end bonus of 3.5% of your total sales.Company B offers a salary of $28,000 plus a year-end bonus of 7.5% of your total sales.What is the amount you must sell in one year to earn the same salary working for either company?
A) $170,000
B) $120,000
C) $150,000
D) $90,000
E) $130,000
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Chapter 6: Matrices and Determinants
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Sample Questions
Q1) A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility.Some of the money was borrowed at 9%, some at 11%, and some at 14%.Use a system of equations to determine how much was borrowed at 9% if the total annual interest was $216,000 and the amount borrowed at 9% was twice the amount borrowed at 14%.Solve the system using matrices.
A) $400,000 was borrowed at 9%
B) $800,000 was borrowed at 9%
C) $300,000 was borrowed at 9%
D) $1,600,000 was borrowed at 9%
E) $1,700,000 was borrowed at 9%
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9
Chapter 7: Sequences, Series, and Probability
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Sample Questions
Q1) Twenty-four students are selected as semifinalists for a literary award.Of the twenty-four students, fourteen finalists will be selected.In how many ways can fourteen finalists be selected from the twenty-four students?
A) 38,760
B) 319,770
C) 4,457,400
D) 1,961,256
E) 116,280
Q2) Find the indicated nth partial sum of the arithmetic sequence. 2.5, 3.8, 5.1, 6.4, ..., n = 100
A) 12,505
B) 6815
C) 6685
D) 6683.8
E) 6686.2
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