Mathematics for Business and Economics
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Course Introduction
Mathematics for Business and Economics introduces students to essential mathematical concepts and techniques used in solving real-world business and economic problems. Topics include algebra, systems of equations, functions, mathematics of finance, introductory calculus, and optimization. The course emphasizes practical applications such as cost analysis, revenue and profit maximization, supply and demand modeling, and investment decision-making. Students will also develop problem-solving skills and the ability to interpret mathematical results within a business and economic context, preparing them for further studies and professional challenges in these fields.
Recommended Textbook
Precalculus 2nd Edition by John W. Coburn
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12 Chapters
1334 Verified Questions
1334 Flashcards
Source URL: https://quizplus.com/study-set/3371
Page 2
Chapter 1: Equations and Inequalities
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107 Verified Questions
107 Flashcards
Source URL: https://quizplus.com/quiz/66913
Sample Questions
Q1) Compute the special product and write your answer in a + bi form. (5 + 6i)<sup>2</sup>
Answer: -11 + 60i
Q2) Solve. 0.2(5 - 2.4x) - 3.4 = 0
Answer: -5
Q3) Solve using u-substitution.
(x<sup>2</sup> - x)<sup>2 </sup> - 14(x<sup>2</sup> - x) + 24 = 0
Answer: x = -3, x = -1, x = 2, x = 4
Q4) Solve using the most efficient method. x<sup>2</sup> - 9x = -14
A) x = -7, x = -2
B) x = 7, x = -2
C) x = -7, x = 2
D) x = 7, x = 2
Answer: D
Q5) Solve for y. w = xyz
Answer: 11ea7f29_4f9d_801a_9ecd_6b3d04283d0b_TB3307_11
Q6) Fill in the blank so the result is a perfect square trinomial, then factor into a binomial square.
x<sup>2</sup> - 20x + _____
Answer: 100; (x - 10)<sup>2</sup>
Page 3
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Chapter 2: Relations, Functions and Graphs
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196 Verified Questions
196 Flashcards
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Sample Questions
Q1) Determine the value of f(-6) if f(x) = -x<sup>2</sup> - 4x.
A) 30
B) -12
C) 36
D) -40
Answer: B
Q2) Find h(x) = f(x) - g(x).
Answer: h(x) = -x<sup>2</sup> - 7x - 5
Q3) Find (f - g)(-1).
Answer: -1
Q4) Determine the domain of the difference of f and g.
A) x \(\in\) (-5, 2)
B) x \(\in\) (-?, -5) \(\cup\) (2, ?)
C) x \(\in\) (-?, -5) \(\cup\) (-5, 2) \(\cup\) (2, ?)
D) x \(\in\) (-?, ?)
Answer: C
Q5) Find the equation of a circle with center (0, 0) and radius 10.
Answer: x<sup>2</sup> + y<sup>2</sup>= 100
Q6) Graph the line.
Answer: 11ea7f29_4fb6_d459_9ecd_1bbf062cea8c_TB3307_00
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Chapter 3: Polynomial and Rational Functions
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122 Verified Questions
122 Flashcards
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Sample Questions
Q1) Use the graph to estimate the zeroes of the function, then state whether their multiplicity is even or odd.
A) -1, even; 2 odd
B) -1, odd; 2 even
C) -1, even; 2 even
D) -1, odd; 2 odd
Answer: A
Q2) Use synthetic division and the remainder theorem to show x = 1 - 3i is a zero of P(x) = -x<sup>3</sup> - x<sup>2</sup> - 4x - 30.
Answer: 11ea7f29_4fcb_4664_9ecd_4354b793d423_TB3307_00
Q3) Find all zeroes (real and complex) of the polynomial. p(x) = 6x<sup>3</sup> + 29x<sup>2</sup> - 149x + 24
Answer: x = 3, -8, 11ea7f29_4fcd_6957_9ecd_d596869fde1d_TB3307_00
Q4) State the end behavior and y-intercept of the function. Do not graph. f(x) = -2x<sup>4</sup> - 2x<sup>3</sup> + x<sup>2 </sup>- 2x + 5
Answer: down/down; (0, 5)
Q5) Graph the polynomial function. f(x) = x<sup>4</sup> + 3x<sup>3</sup> - 3x<sup>2</sup><sup> </sup>- 11x - 6
Answer: 11ea7f29_4fd2_9981_9ecd_6b6d1c3c82c7_TB3307_00
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Chapter 4: Exponential and Logarithmic Functions
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96 Flashcards
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Sample Questions
Q1) Solve using any appropriate method. Clearly identify any extraneous roots. If there are no solutions, so state. log(-x - 2) = log(3x) - log x
A) x = 0, -5
B) x = 0, 5
C) x = 5
D) No solution
Q2) For simple interest accounts the interest earned or due depends on the principal p, interest rate r, and the time t in years according to the formula I = prt. Find p given I = $50.14, r = 10.5%, and t = 6 months. Round your answer to the nearest dollar.
A) $955
B) $960
C) $965
D) $970
Q3) Use a calculator to evaluate ln 401, rounded to six decimal places.
A) 4.992827
B) 5.993961
C) 7.117417
D) 8.184048
Q4) t = 8.5
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Chapter 5: Introduction to Trigonometric Functions
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133 Verified Questions
133 Flashcards
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Sample Questions
Q1) Convert 5.2135 rad to degrees. Round to the nearest tenth.
A) 0.1°
B) 298.7°
C) 597.4°
D) 938.4°
Q2) Graph f(t) = 3 tan t over the interval [-2 , 2 ].
Q3) Use a calculator to find the value of tan 34°, rounded to four decimal places.
Q4) Use a reference rectangle and the rule of fourths to draw an accurate sketch through at least one complete cycle where t > 0. y = -2 sin t
Q5) Find the exact value of sin\(\theta\), cos\(\theta\), and tan\(\theta\) using reference angles. \(\theta\)= 225°
Q6) Fill in the blank so that the functions given are equal. cos _____, sin 10°
A) 10°
B) 80°
C) -10°
D) 100°
Q7) Graph f(t) = cot(2t) over the interval [- , ].
Q8) Find two positive and two negative angles that are coterminal with 270°.
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Chapter 6: Trigonometric Identities, Inverses, and Equations
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97 Verified Questions
97 Flashcards
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Sample Questions
Q1) Rewrite the product as a sum using a product-to-sum identity. 2sin(2073\9\pi\)t)cos(813\(\pi\)t)
Q2) Use a cofunction identity to write an equivalent expression. cos 13°
Q3) Verify the equation is an identity using special products and fundamental identities. (1 + cos x)[1 - cos(-x)] = sin<sup>2</sup> x
Q4) Rewrite as a single expression. sin(7\(\theta\) )cos(3\(\theta\)) + cos(7\(\theta\))sin(3\(\theta\) )
A) cos(10\(\theta\) )
B) cos(4\(\theta\) )
C) sin(10\(\theta\) )
D) sin(4\(\theta\) )
Q5) State the number of roots in [0, 2\(\pi\)].
A) 4
B) 3
C) 2
D) 1
Q6) Write cot x entirely in terms of cos x.
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Chapter 7: Applications of Trigonometry
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86 Verified Questions
86 Flashcards
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Sample Questions
Q1) Find the time(s) required to reach a height of 200 feet? Round to the nearest hundredth.
A) approximately 0.65 sec.
B) approximately 20.30 sec.
C) approximately 0.65 sec. and 19.17 sec.
D) approximately 0.65 sec. and 20.30 sec.
Q2) Write the complex number in trigonometric form. Answer in radians using both an exact form and an approximate form, rounding to four decimal places.
-4 + 6i
Q3) For the vector below, \(\theta\)represents the acute angle formed by the vector and the x-axis. Write the vector in i, j form. Round to the nearest tenth. v in QIV, |v| = 29, \(\theta\)= 80°
A) v = 28.6i + 5j
B) v = 28.6i - 5j
C) v = 5i + 28.6j
D) v = 5i - 28.6j
Q4) Graph the vector.
Q5) Find the acute angle \(\theta\) formed by the vector and the nearest x-axis. Round to the nearest tenth of a degree.
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Chapter 8: Systems of Equations and Inequalities
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102 Verified Questions
102 Flashcards
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Sample Questions
Q1) Solve the linear inequality by shading the appropriate half plane. 3x + y \(\le\) 5
Q2) Determine which of the ordered pairs given produces the maximum value of P(x, y).
P(x, y) = 20x + 50y; (0, 0), (5, 2), (4, 0), (0, 6)
A) (0, 0)
B) (5, 2)
C) (4, 0)
D) (0, 6)
Q3) Determine if the points (-2, 3), (1, -5), and (-3, 2) are colinear.
A) Yes
B) No
Q4) Solve the linear inequality by shading the appropriate half plane. -3x + y \(\ge\) 0
Q5) Whitney invested $8,000, part at 14% and part at 8%. If the total interest at the end of the year is $940, how much did she invest at each rate?
Q6) Determine if the points (-2, 1), (-1, 1), and (0, 1) are colinear.
A) Yes
B) No
Q7) Write the system of equations corresponding to the matrix.
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Chapter 9: Analytical Geometry
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122 Verified Questions
122 Flashcards
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Sample Questions
Q1) Complete the square in both x and y to write the equation in standard form. Then draw a complete graph of the relation and identify all important features. 9x<sup>2</sup> + 4y<sup>2</sup> - 18x + 16y - 11 = 0
Q2) Find the vertex.
Q3) Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 8y<sup>2</sup> - 4 = 5x<sup>2</sup> + 36
A) Circle
B) Ellipse
C) Hyperbola
D) None of these
Q4) Write the equation in standard form and identify the center and the values of a and b. x<sup>2</sup> + 9y<sup>2</sup> = 36
Q5) Convert from rectangular coordinates to polar coordinates. A diagram may help. (8, -8)
Q6) Sketch the polar graph using an r-value analysis (a table may help), symmetry, and any convenient points. r = 3 - 5sin\(\theta\)
Q7) Find the directrix.
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Chapter 10: Additional Topics in Algebra
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121 Verified Questions
121 Flashcards
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Sample Questions
Q1) Determine whether the infinite geometric series has a finite sum. If so, find the limiting value. 112 + 56 + 28 + . . .
A) S<sub> </sub> = 224
B) S<sub> </sub> = -224
C) S<sub> </sub> = 56
D) no finite sum
Q2) A Scrabble player has the six letters (A, A, E, E, N, N) in her rack. How many distinguishable, six-letter permutations can be formed?
A) 90
B) 240
C) 360
D) 720
Q3) Two fair dice are rolled. What is the probability of rolling a sum of 3 or a sum of 8?
Q4) Find the 11th term of the binomial expansion of (b - 2)<sup>13</sup>.
Q5) Write the first four terms of the arithmetic sequence with the given first term and common difference.
a<sub>1</sub> = 3, d = 3
Q6) What is the probability the student answered "No" and is a boy?
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Chapter 12: Review of Basic Concepts and Skills
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112 Verified Questions
112 Flashcards
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Sample Questions
Q1) Find the binomial square. (4x - 3)<sup>2</sup>
A) 4x<sup>2</sup> - 12x + 9
B) 16x<sup>2</sup> - 12x + 9
C) 16x<sup>2</sup> + 9
D) 16x<sup>2</sup> - 24x + 9
Q2) Why does the cost increase dramatically the closer you get to 100%?
Q3) List all the numbers in the set that are elements of N.
Q4) Perform the operation indicated mentally or using pencil/paper. -16 - (-20)
A) 36
B) -4
C) 4
D) -36
Q5) Simplify by combining like terms.
-8z - z - 4z
Q6) Factor the expression completely, if possible. Rewrite the expression in standard form and factor out "-1" if needed. If you believe the trinomial will not factor, answer "prime."
-21x<sup>2</sup> + 6x + 15x<sup>3</sup>
Q7) Graph the elements of the set on a number line.
Q8) List all the numbers in the set that are elements of W.
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