Precalculus Practice Exam
Course Introduction
Precalculus is a foundational mathematics course designed to prepare students for the study of calculus. It covers a wide range of topics, including functions, graphs, polynomial and rational expressions, exponential and logarithmic functions, trigonometry, sequences, and introductory concepts of analytic geometry. Students learn to analyze and solve various types of equations and inequalities, understand the behavior of different types of functions, and apply mathematical reasoning to problem-solving. The course emphasizes the development of algebraic and graphical skills, providing students with the necessary tools and conceptual understanding to succeed in calculus and other advanced mathematics courses.
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) Identify the rules of algebra illustrated from left to right by the following statement. (t - 9) + 9 = t + (-9 + 9) = t + 0 = t
A) commutative property of addition; additive inverse property; additive identity property
B) associative property of addition; additive inverse property; additive identity property
C) commutative property of addition; additive identity property; additive inverse property
D) associative property of addition; additive identity property; additive inverse property
E) distributive property; additive identity property; additive inverse property
Answer: B
Q2) Completely factor the expression. 4u<sup>2</sup> - 64
A) (4u - 16)(u + 4)
B) (4u + 16)(u - 4)
C) (4u + 16)(u + 4)
D) 4(u + 4)(u - 4)
E) 4(u + 16)(u - 16)
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 many liters of a 25% acid solution should be mixed with 3 liters of a 15% acid solution to produce a 23% solution?
A) 4 liters
B) 12 liters
C) 7 liters
D) 2 liters
E) 6 liters
Answer: B
Q2) To determine the height of a tree, you measure its shadow and the shadow of a five-foot lamppost.The shadow of the lamppost is 2 feet and the shadow of the tree is 25 feet.Assuming both the tree and the lamppost are standing next to each other and perpendicular to the ground, how tall is the tree? Round to the nearest tenth of a foot.
A) 62.5 feet
B) 36.3 feet
C) 80.0 feet
D) 10.0 feet
E) 18.8 feet
Answer: A
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4
Chapter 2: Functions and Graphs
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97 Verified Questions
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) 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
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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 Flashcards
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Sample Questions
Q1) 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
Q2) The half-life of <sup>134</sup>Ba is 28.7 hours.How much of a 18.2 g sample of <sup>134</sup>Ba will be left after 24.00 hours? Round to the nearest hundredth of a gram.
A) 20.39 g
B) 7.65 g
C) 10.19 g
D) 32.49 g
E) 14.15 g
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Chapter 5: Systems of Equations and Inequalities
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94 Flashcards
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Sample Questions
Q1) The sales of various types of lawn and garden items vary according to the season.At a certain home improvement store, the monthly sales H of garden hoses (hoses sold per month) declines from July to October whereas the monthly sales of lawn rakes R (rakes sold per month) increase during this same interval.The sales of these two items during the calendar months July-October are modeled by the equations: H(t) = 64 - 6t R(t) = 17t - 97, Where t is the month (t = 7 corresponds to July).In which month does the number of rakes sold equal the number of hoses sold?
A) August
B) September
C) October
D) November
E) July
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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) 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) A computer manufacturer offers a computer system with five different disk drives, two different monitors, and three different keyboards.How many different computer systems could a consumer purchase from this manufacturer?
A) 24
B) 40
C) 30
D) 18
E) 75
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