Algebra and Trigonometry Exam Practice Tests
Course Introduction
This course provides a comprehensive foundation in algebra and trigonometry, emphasizing concepts essential for higher-level mathematics and practical applications. Students will explore linear, quadratic, polynomial, rational, exponential, and logarithmic functions, as well as systems of equations and inequalities. The trigonometry portion covers the properties and graphs of trigonometric functions, identities, inverse functions, and solutions of right and oblique triangles. Through problem-solving and real-world examples, students develop critical thinking skills and mathematical proficiency necessary for studies in science, engineering, economics, and related 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) Solve the absolute value inequality. Write solution in interval notation. 3|x + 7| + 9 < 15
A) (-\(\infty\), -15) \(\cup\) (1, \(\infty\))
B) (-\(\infty\), -9) \(\cup\) (-5, \(\infty\))
C) (-15, 1)
D) (-9, -5)
Answer: D
Q2) Simplify using powers of i. i<sup>64</sup>
A) 1
B) -1
C) i
D) -i
Answer: A
Q3) Solve using the zero product property. Be sure each equation is in standard form and factor out any common factors before attempting to solve. Check all answers in the original equation.
-5x<sup>3</sup> = -13x<sup>2</sup> - 6x
Answer: 11ea7f29_4fa9_404c_9ecd_698845ed82c7_TB3307_11
Q4) Solve the quadratic equation. Simplify the result. 5x<sup>2</sup> - 8x + 5 = 0
Answer: 11ea7f29_4fa8_55e6_9ecd_b591c4e04818_TB3307_11
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Chapter 2: Relations, Functions and Graphs
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196 Verified Questions
196 Flashcards
Source URL: https://quizplus.com/quiz/66914
Sample Questions
Q1) Use the slope-intercept formula to find the equation of the line with slope with a slope of -4 if the point (4, -9) is on the line.
Answer: y = -4x + 7
Q2) 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
Q3) 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.)
Q4) Graph using the intercept method.
2x + y = 4
Answer: 11ea7f29_4fb1_2ed6_9ecd_29a8282d57d6_TB3307_00
Q5) Find the product of f and g.
Answer: (f g)(x) = 2x<sup>2</sup> + x - 36
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Chapter 3: Polynomial and Rational Functions
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122 Verified Questions
122 Flashcards
Source URL: https://quizplus.com/quiz/66915
Sample Questions
Q1) Use the direction/approach notation to describe the end behavior of the graph. (This should produce four statements.)
Answer: as x , y -3<sup>-</sup>, as x - , y -3<sup>-</sup>, as x 2<sup>-</sup>, y - , as x 2<sup>+</sup>, y -
Q2) For the complex polynomial below, one of its zeroes is x = 3 - i. Use the given zero to help find all zeroes of the polynomial, then write the polynomial in completely factored form. Hint: synthetic division and the quadratic formula can be applied to all polynomials, even those with complex coefficients. C(x) = x<sup>3</sup>3x<sup>2</sup> + (3 + 3i)x + (-6 + 2i)
A) C(x) = (x - 3 - i)(x + 2i)(x + i); x = -2i, x = -i
B) C(x) = (x - 3 + i)(x - 2i)(x - i); x = 2i, x = i
C) C(x) = (x - 3 + i)(x + 2i)(x - i); x = -2i, x = i
D) C(x) = (x - 3 + i)(x - 2i)(x + i); x = 2i, x = -i
Answer: D
Q3) Find the intercepts. f(x) = x<sup>2</sup> - 10x + 24
Answer: (6, 0), (4, 0), (0, 24)
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Page 5
Chapter 4: Exponential and Logarithmic Functions
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96 Verified Questions
96 Flashcards
Source URL: https://quizplus.com/quiz/66916
Sample Questions
Q1) Compute the average rate of change of y = ln x over the interval [2, 2.0001]. Round your answer to the nearest hundredth
A) \(\approx\) 0.49
B) \(\approx\) 0.50
C) \(\approx\) 0.62
D) \(\approx\) 0.81
Q2) For accounts where interest is compounded continuously, the amount A accumulated or due depends on the principal p, interest rate r and the time t in years according to the formula A = pe<sup>rt</sup>. How long would it take $4000 to double if it were invested at 4.5%? Round your answer to the nearest tenth of a percent.
A) 15.1 years
B) 15.2 years
C) 15.3 years
D) 15.4 years
Q3) Graph the logarithmic function.
f(x) = -ln(x + 1)
Q4) Solve using the method of your choice. Answer in exact form and approximate form rounded to four decimal places.
8<sup>x</sup><sup> + </sup><sup>3 </sup>= 4602
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Chapter 5: Introduction to Trigonometric Functions
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133 Verified Questions
133 Flashcards
Source URL: https://quizplus.com/quiz/66917
Sample Questions
Q1) 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
Q2) Use a calculator to find the value of sec 33°, rounded to four decimal places.
A) 0.5446
B) 1.8361
C) 1.1924
D) 0.8387
Q3) State the exact value of sin \(\pi\) . A diagram may help.
Q4) State the amplitude.
A) 4
B) -4
C) 3
D) -3
Q5) Convert 5.2135 rad to degrees. Round to the nearest tenth.
A) 0.1°
B) 298.7°
C) 597.4°
D) 938.4°
Q6) State the period.
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Chapter 6: Trigonometric Identities, Inverses, and Equations
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97 Verified Questions
97 Flashcards
Source URL: https://quizplus.com/quiz/66918
Sample Questions
Q1) Rewrite in terms of an expression containing only cosines to the power 1. sin<sup>2</sup> x cos<sup>4</sup> x
Q2) Find the exact value using a sum or difference identity. Some simplifications may involve using symmetry and the formulas for negatives. sin(-15°)
Q3) Find all real roots in [0, 2?) using a graphing calculator. State answers in radians rounded to four decimal places. cos(2x) + x<sup>2</sup> = 3
A) x\(\approx\) 1.9131
B) x \(\approx\) 1.9354
C) x \(\approx\) 1.9512
D) x\(\approx\) 1.9726
Q4) Solve the equation in [0, 2 ) by squaring both sides.
sec x - tan x = -1
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.
Page 8
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Chapter 7: Applications of Trigonometry
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86 Verified Questions
86 Flashcards
Source URL: https://quizplus.com/quiz/66919
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) A baby-sitter pulls some kids in a wagon on a level street. How much work is done if she pulls the wagon 200 feet at a constant force of 45 lbs with the wagon handle making an angle of 34° with the street? Round to the nearest whole number.
A) approximately 4808 ft-lbs
B) approximately 5033 ft-lbs
C) approximately 6529 ft-lbs
D) approximately 7461 ft-lbs
Q3) Compute u - 5v.
A) -16i - 17j
B) -15i - 16j
C) -15i - 17j
D) -16i - 16j
Q4) Compute the magnitude of the vector exactly.
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Chapter 8: Systems of Equations and Inequalities
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102 Verified Questions
102 Flashcards
Source URL: https://quizplus.com/quiz/66920
Sample Questions
Q1) 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?
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) Write the system of equations corresponding to the matrix.
Q4) Adult tickets for a play cost $9 and child tickets cost $1. If there were 22 people at a performance and the theatre collected $182 from ticket sales, how many children attended the play?
A) 1 child
B) 2 children
C) 3 children
D) 20 children
Q5) Find any four ordered triples that satisfy the equation.
x - y + z = -3
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Chapter 9: Analytical Geometry
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122 Verified Questions
122 Flashcards
Source URL: https://quizplus.com/quiz/66921
Sample Questions
Q1) Write the equation in standard form and sketch the graph. x<sup>2</sup> + 9y<sup>2</sup> = 36
Q2) Find the focus.
A) (0, -6)
B) (0, -24)
C) (-6, 0)
D) (-24, 0)
Q3) For the conic section 5x<sup>2</sup> - 8xy + 5y<sup>2</sup> = 9 in the xy-plane
(a) Use rotation of axes to find the corresponding equation in the XY-plane (clearly state the angle of rotation \(\beta\) ).
(b) Sketch the graph in xy-plane.
Q4) Use a graphing calculator or computer to draw the graph.
Q5) Identify the graph of the equation using the discriminant. 4x<sup>2</sup> - 10xy + 5y<sup>2</sup> - 4x + 2y - 3 = 0
A) parabola
B) circle or ellipse
C) hyperbola
Q6) Find the vertex.
Q7) Find the vertex.
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Chapter 10: Additional Topics in Algebra
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121 Verified Questions
121 Flashcards
Source URL: https://quizplus.com/quiz/66922
Sample Questions
Q1) Find the probability indicated using the information given. Given P(E<sub>1</sub>) = 0.6, P(E<sub>2</sub>) = 0.5, and P(E<sub>1</sub> \(\cup\) E<sub>2</sub>) = 0.9, compute P(E<sub>1</sub> \(\cap\) E<sub>2</sub>).
Q2) How many distinguishable permutations can be formed from the letters of the word assassin?
Q3) Find the probability indicated using the information given. Given P(E<sub>1</sub>) = 0.5, P(E<sub>2</sub>) = 0.3, and P(E<sub>1</sub> \(\cap\) E<sub>2</sub>) = 0.1, compute P(E<sub>1</sub> \(\cup\) E<sub>2</sub>).
A) 0.9
B) 0.8
C) 0.7
D) 0.2
Q4) Find a<sub>4</sub>.
A) 22
B) 29
C) 36
D) 43
Q5) How many different ways can 6 people stand in line at a cash register?
Q6) Find the sum of the first 20 multiples of 6.
Page 12
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Chapter 12: Review of Basic Concepts and Skills
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112 Verified Questions
112 Flashcards
Source URL: https://quizplus.com/quiz/66912
Sample Questions
Q1) What is the cost of seizing 60% of the drugs?
A) $210
B) $233
C) $350
D) $525
Q2) Compute the product. (x + 4)(x - 4)(x + 1)
Q3) Evaluate (2x - 3y)<sup>2</sup> given x = 3 and y = -1.
A) 81
B) 27
C) 9
D) -9
Q4) Translate the phrase into an algebraic expression. the difference between a number and two is squared
Q5) 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." x<sup>2</sup> + 2x + 3
A) (x + 3)(x + 1)
B) (x - 3)(x - 1)
C) (x + 2)(x + 1)
D) prime
Page 13
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