Algebra for Business and Economics
Midterm Exam
Course Introduction
This course introduces the fundamental concepts and techniques of algebra with a focus on applications relevant to business and economics. Topics include linear equations and inequalities, functions and graphs, systems of equations, matrices, quadratic equations, and exponential and logarithmic functions. Emphasis is placed on developing problem-solving skills and utilizing algebraic methods to analyze and solve practical problems encountered in business and economic contexts, such as cost-benefit analysis, revenue and profit maximization, and financial modeling. The course is designed to build a strong mathematical foundation for students pursuing careers in business, economics, and related fields.
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) Write the polynomial in standard form.
9 + 7x<sup>2</sup> + 8x
Answer: 7x<sup>2</sup> + 8x + 9
Q2) Factor the sum or difference of cubes. r<sup>3</sup> - 125
A) (r - 5)(r<sup>2</sup> + 5r + 25)
B) (r + 5)(r<sup>2</sup> - 5r + 25)
C) (r - 5)(r<sup>2</sup> - 5r + 25)
D) (r + 5)<sup>3</sup>
E) (r - 5)<sup>3</sup>
Answer: A
Q3) Give a verbal description of the subset of real numbers represented by the inequality. 6 < x \(\le\) 9
A) all real numbers less than 6 and greater than 9
B) all real numbers between 6 and 9 not including 6 or 9
C) all real numbers between 6 and 9, including 6 but not including 9
D) all real numbers between 6 and 9, including 9 but not including 6
E) all real numbers between 6 and 9, including 6 and 9
Answer: D
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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) How much water must be added to 8 liters of a 51% saline solution to dilute it to a 36% saline solution? Round answer to nearest tenth of a liter.
A) 3.1 liters
B) 3.3 liters
C) 3.5 liters
D) 3.7 liters
E) 3.9 liters
Answer: B
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) Determine whether lines L<sub>1</sub> and L<sub>2</sub> passing through the pairs of points are parallel, perpendicular, or neither. L<sub>1 </sub>: (-1, 8), (9, -4)
L<sub>2 </sub>: (0, 9), (1, -1)
A) parallel
B) perpendicular
C) neither
Answer: C
Q2) Find the slope and y-intercept of the equation of the line. -y - 8x = -2
A) slope: 8; y-intercept: -2
B) slope: -2; y-intercept: 8
C) slope: 8; y-intercept: -1
D) slope: 2; y-intercept: -8
E) slope: -8; y-intercept: 2
Answer: E
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Chapter 3: Polynomial and Rational Functions
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105 Verified Questions
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 Verified Questions
92 Flashcards
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Sample Questions
Q1) 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
Q2) What is the half-life of a radioactive substance if 2.9 g decays to 1.80 g in 64 hours? Round to the nearest tenth of an hour.
A) 93.0 hours
B) 69.8 hours
C) 46.5 hours
D) 23.3 hours
E) 13.8 hours
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Chapter 5: Systems of Equations and Inequalities
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94 Flashcards
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Sample Questions
Q1) 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
Q2) An airplane flying into a headwind travels 280 miles in 2 hours and 48 minutes.On the return flight, the distance is traveled in 2 hours.Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.
A) plane speed = 135 mph; wind speed = 27 mph
B) plane speed = 135 mph; wind speed = 20 mph
C) plane speed = 97 mph; wind speed = 9 mph
D) plane speed = 97 mph; wind speed = 20 mph
E) plane speed = 120 mph; wind speed = 20 mph
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Page 8
Chapter 6: Matrices and Determinants
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94 Flashcards
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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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92 Flashcards
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Sample Questions
Q1) In a certain state, each automobile license plate number consists of two letters followed by a five-digit number.To avoid confusion between "O" and "zero" and "I" and "one", the letters "O" and "I" are not used.How many distinct license plate numbers can be formed?
A) 13,824,000
B) 57,600,000
C) 331,776,000
D) 5,760,000
E) 138,240,000
Q2) Consider a job offer with a starting salary of $37,700 and a given annual raise of $2325.Determine the total compensation from the company through three full years of employment.
A) $366,700
B) $312,725
C) $77,725
D) $423,000
E) $120,075
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