Course Introduction
College Algebra
Exam Materials
College Algebra introduces students to the fundamental concepts of algebra, focusing on the development of skills necessary for problem-solving and critical thinking. Topics covered include linear, quadratic, polynomial, rational, and exponential functions, as well as systems of equations and inequalities. The course emphasizes the application of algebraic techniques to real-world problems and provides a strong foundation for advanced studies in mathematics, science, and related disciplines. Students will engage with graphing, analysis, and interpretation of mathematical models, fostering both analytical proficiency and mathematical confidence.
Recommended Textbook
Precalculus 2nd Edition by John W. Coburn
Available Study Resources on Quizplus
12 Chapters
1334 Verified Questions
1334 Flashcards
Source URL: https://quizplus.com/study-set/3371
Page 2
Chapter 1: Equations and Inequalities
Available Study Resources on Quizplus for this Chatper
107 Verified Questions
107 Flashcards
Source URL: https://quizplus.com/quiz/66913
Sample Questions
Q1) Solve by completing the square. Write your answer in exact form. 4x<sup>2</sup> + 2x - 3 = 0
Answer: 11ea7f29_4fa7_9292_9ecd_81c71ec5d742_TB3307_11
Q2) Solve using the most efficient method. 2x<sup>2</sup> + 6x - 11 = 0
Answer: x = 11ea7f29_4fa7_b9a3_9ecd_ebf76a431ce0_TB3307_11
Q3) At 9:00 a.m. a truck leaves the truck yard and travels west at a rate of 35 mph. At 11:00 a.m., a second truck leaves along the same route, traveling at 70 mph. When will the second truck catch up to the first?
A) 1:00 p.m.
B) 4:00 p.m.
C) 3:00 p.m.
D) 2:00 p.m.
Answer: A
Q4) Name the complex conjugate, then find the product. 5 - i
A) 5 + i; 26
B) -5 + i; 26
C) 5 + i; 24
D) -5 + i; 24
Answer: A
To view all questions and flashcards with answers, click on the resource link above. Page 3
Chapter 2: Relations, Functions and Graphs
Available Study Resources on Quizplus for this Chatper
196 Verified Questions
196 Flashcards
Source URL: https://quizplus.com/quiz/66914
Sample Questions
Q1) Sketch the graph using transformations of a parent function (without a table of values).
f(x) = -3|x|
Answer: 11ea7f29_4fb8_f748_9ecd_bf83a1bfbb24_TB3307_00 (Gridlines are spaced one unit apart.)
Q2) State the domain of the function.
A) (0, ?)
B) (-?, 4)
C) (-?, -1) \(\cup\) (-1, 4)
D) (-?, 0] \(\cup\) (1, ?)
Answer: B
Q3) Determine whether the function is odd using x = k. f(x) = 6x<sup>3</sup>10x<sup>2</sup> - 8
A) odd
B) not odd
Answer: B
Q4) Graph by plotting points or using the intercept method.
x = -2
Answer: 11ea7f29_4fb2_8e74_9ecd_852cd61328d6_TB3307_00 (Gridlines are spaced one unit apart.)
Page 4
To view all questions and flashcards with answers, click on the resource link above.
Chapter 3: Polynomial and Rational Functions
Available Study Resources on Quizplus for this Chatper
122 Verified Questions
122 Flashcards
Source URL: https://quizplus.com/quiz/66915
Sample Questions
Q1) Use the information gathered, testing for 1 and -1, synthetic division, and the factor theorem to factor p completely.
A) p(x) = (x + 1)(x - 1)(x + 2)(x + 3)
B) p(x) = (x + 1)(x - 1)(x - 2)(x + 3)
C) p(x) = (x + 1)(x - 1)(x + 2)(x - 3)
D) p(x) = (x + 1)(x - 1)(x - 2)(x - 3)
Answer: D
Q2) Find the y-intercept and explain what it means in this context.
Answer: (0, -22,000); when no cars are produced, there is a loss of $22,000
Q3) State whether the degree of the function is even or odd.
A) even
B) odd
Answer: B
Q4) Use synthetic division and the remainder theorem to show that x = -2 is a zero of P(x) = x<sup>3</sup> - 4x<sup>2</sup> - 4x + 16.
Answer: 11ea7f29_4fc9_bfb9_9ecd_6f73501b6fd2_TB3307_00 Since the remainder is 0, -2 is a zero of x<sup>3</sup> - 4x<sup>2</sup> - 4x + 16.
Q5) Write the variation equation.
Answer: A = 11ea7f29_4fdb_4c66_9ecd_5d253cf92f09_TB3307_11
To view all questions and flashcards with answers, click on the resource link above. Page 5
Chapter 4: Exponential and Logarithmic Functions
Available Study Resources on Quizplus for this Chatper
96 Verified Questions
96 Flashcards
Source URL: https://quizplus.com/quiz/66916
Sample Questions
Q1) Use a calculator to evaluate ln 401, rounded to six decimal places.
A) 4.992827
B) 5.993961
C) 7.117417
D) 8.184048
Q2) Stanley borrowed $4200 for 4 years. The total amount repaid is $4452.00. Find the annual simple interest rate on this loan.
Q3) Solve the equation by writing it in exponential form. Answer in exact form and approximate form using a calculator (round to thousandths). ln x = 1.587
Q4) t = 8.5
Q5) Graph by the following function by translating the basic function y = b<sup>x</sup>, sketching the asymptote, and strategically plotting a few points to round out the graph. Clearly state what shifts are applied. y = 4<sup>-</sup><sup>x</sup>
Q6) Determine the value without using a calculator. log<sub> 17 </sub>17
Q7) Solve the exponential equation. 100<sup>x</sup><sup> - 3 </sup> = 1000<sup>x</sup>
To view all questions and flashcards with answers, click on the resource link above. Page 6
Chapter 5: Introduction to Trigonometric Functions
Available Study Resources on Quizplus for this Chatper
133 Verified Questions
133 Flashcards
Source URL: https://quizplus.com/quiz/66917
Sample Questions
Q1) Name the reference angle \(\theta\)<sub>r</sub> for \(\theta\) = 225°.
A) 15°
B) 25°
C) 35°
D) 45°
Q2) Use a calculator to find the acute angle A whose corresponding ratio is given. Round to the nearest tenth of a degree. cot A = 0.7456
A) 76.8°
B) 13.2°
C) 1.6°
D) 53.3°
Q3) Find the value of the six trigonometric functions given P(4, -12) is on the terminal side of angle \(\theta\), with \(\theta\)in standard position.
Q4) State the amplitude.
A) 4
B) -4
C) 3
D) -3
Q5) Give the model for the data.
To view all questions and flashcards with answers, click on the resource link above. Page 7
Chapter 6: Trigonometric Identities, Inverses, and Equations
Available Study Resources on Quizplus for this Chatper
97 Verified Questions
97 Flashcards
Source URL: https://quizplus.com/quiz/66918
Sample Questions
Q1) Find the exact value using a sum or difference identity. Some simplifications may involve using symmetry and the formulas for negatives. sin(-15°)
Q2) Rewrite as a single expression. cos(6\(\theta\) )cos(2\(\theta\) ) + sin(6\(\theta\) )sin(2\(\theta\) )
A) cos(8\(\theta\) )
B) cos(4\(\theta\) )
C) sin(8\(\theta\) )
D) sin(4\(\theta\) )
Q3) Solve the equation in [0, 2 ) by squaring both sides. sec x - tan x = -1
Q4) Rewrite the product as a sum using a product-to-sum identity. 2sin(2073\9\pi\)t)cos(813\(\pi\)t)
Q5) Rewrite as a single expression. sin(6\(\theta\) )cos(3\(\theta\) )cos(6\(\theta\))sin(3\(\theta\) )
A) cos(9\(\theta\) )
B) cos(3\(\theta\) )
C) sin(9\(\theta\) )
D) sin(3\(\theta\) )
To view all questions and flashcards with answers, click on the resource link above. Page 8
Chapter 7: Applications of Trigonometry
Available Study Resources on Quizplus for this Chatper
86 Verified Questions
86 Flashcards
Source URL: https://quizplus.com/quiz/66919
Sample Questions
Q1) If the maximum range of the ship's radar is 16.0 miles, will the departing fleet be detected?
A) yes
B) no
Q2) Use De Moivre's Theorem to verify z = -1 + i is a solution to z<sup>4</sup>2z<sup>3</sup> - z<sup>2</sup> + 2z + 10 = 0.
Q3) Compute u - 5v.
A) -16i - 17j
B) -15i - 16j
C) -15i - 17j
D) -16i - 16j
Q4) Solve using the law of cosines (if possible). Round to tenths.
side a = 153 yd
side b = 168 yd
side c = 103 yd
Q5) Compute 2u + 5v.
A) -17i + 7j
B) -16i + 8j
C) -17i + 8j
D) -16i + 7j
Page 9
To view all questions and flashcards with answers, click on the resource link above.
Chapter 8: Systems of Equations and Inequalities
Available Study Resources on Quizplus for this Chatper
102 Verified Questions
102 Flashcards
Source URL: https://quizplus.com/quiz/66920
Sample Questions
Q1) Solve the linear inequality by shading the appropriate half plane. -3x + y \(\ge\) 0
Q2) Determine whether the ordered pair (0, 0) is a solution. 10x - 3y > 5
A) Yes
B) No
Q3) Solve the linear inequality by shading the appropriate half plane. 2x + 3y > 6
Q4) A coin jar contains nickels, dimes, and quarters. There are 38 coins in all. There are 2 more nickels than quarters. The value of the dimes is $2.70 less than the value of the quarters. How many coins of each type are in the jar?
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) The length of a rectangle is 9 in. more than twice its width. If the perimeter of the rectangle is 54 in., find the width of the rectangle.
A) 5 in.
B) 6 in.
C) 7 in.
D) 8 in.
To view all questions and flashcards with answers, click on the resource link above. Page 10
Chapter 9: Analytical Geometry
Available Study Resources on Quizplus for this Chatper
122 Verified Questions
122 Flashcards
Source URL: https://quizplus.com/quiz/66921
Sample Questions
Q1) Graph the curve defined by the parametric equations using the specified interval.
Q2) Find the eccentricity of Mercury's orbit.
A) 0.1938
B) 0.2029
C) 0.2055
D) 0.2110
Q3) Sketch the polar graph using an r-value analysis (a table may help), symmetry, and any convenient points. r = 3sin\(\theta\)
Q4) Sketch the polar graph using an r-value analysis (a table may help), symmetry, and any convenient points. r = 3 - 5sin\(\theta\)
Q5) Write the equation in standard form and sketch the graph. x<sup>2</sup> + 9y<sup>2</sup> = 36
Q6) Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices. 25y<sup>2</sup> - 4x<sup>2</sup> = 100
Q7) Convert from rectangular coordinates to polar coordinates. A diagram may help. (8, -8)
Page 11
To view all questions and flashcards with answers, click on the resource link above.
Chapter 10: Additional Topics in Algebra
Available Study Resources on Quizplus for this Chatper
121 Verified Questions
121 Flashcards
Source URL: https://quizplus.com/quiz/66922
Sample Questions
Q1) How many codes are possible if repetitions are not allowed and the code must be less than 200 and divisible by 10?
A) 2
B) 24
C) 12
D) 3
Q2) 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
Q3) How many different ways can 6 people stand in line at a cash register?
Q4) Alex has 6 shirts, 6 pairs of pants, and 5 pairs of shoes. How many outfits can he wear?
Q5) Predict the next term for the sequence.
Q6) List Felicia's hourly wage for the first 5 years.
Q7) For S<sub>n</sub> = n(5n - 3), find S<sub>4</sub>, S<sub>5</sub>, S<sub>k</sub>, and S<sub>k</sub><sub> + 1</sub>.
Page 12
To view all questions and flashcards with answers, click on the resource link above.
Chapter 12: Review of Basic Concepts and Skills
Available Study Resources on Quizplus for this Chatper
112 Verified Questions
112 Flashcards
Source URL: https://quizplus.com/quiz/66912
Sample Questions
Q1) Create a mathematical model using descriptive variables. The speed of the truck was three miles per hour more than the speed of the car.
Q2) Factor using u-substitution. 36 + x<sup>4</sup> - 13x<sup>2</sup>
Q3) Simplify the expression using the product to a power property. (-10ab<sup>7</sup>)<sup>2</sup>
A) 100ab<sup>14</sup>
B) -100ab<sup>14</sup>
C) 100a<sup>2</sup>b<sup>14</sup>
D) -100a<sup>2</sup>b<sup>14</sup>
Q4) Compute the product. (x + 4)(x - 4)(x + 1)
Q5) Factor the trinomial completely. x<sup>2</sup> - 18x + 80
A) (x + 8)(x + 10)
B) (x - 8)(x + 10)
C) (x + 1)(x + 80)
D) (x - 8)(x - 10)
Q6) Factor the trinomial completely. 9x<sup>2</sup> - 30x + 25
A) (3x - 5)(3x - 5)
B) (3x + 5)(3x + 5)
C) (9x - 5)(x - 5)
D) (3x + 1)(3x + 25)
Page 13
To view all questions and flashcards with answers, click on the resource link above.