Algebra and Trigonometry Test Preparation - 1334 Verified Questions

Algebra and Trigonometry Test Preparation

Course

Introduction

Algebra and Trigonometry is a foundational mathematics course designed to equip students with essential skills in algebraic manipulation, equation solving, and the understanding of functions, as well as an in-depth knowledge of trigonometric concepts. The course covers topics such as linear, quadratic, and polynomial equations; inequalities; systems of equations; complex numbers; exponential and logarithmic functions; and the properties and graphs of trigonometric functions. Emphasis is placed on problem-solving techniques, real-world applications, and preparation for more advanced mathematical studies in calculus and related disciplines.

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

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107 Verified Questions

107 Flashcards

Source URL: https://quizplus.com/quiz/66913

Sample Questions

Q1) 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. (m + 5)(m + 6) = 6

A) m = -5, m = -6

B) m = 1, m = 0

C) m = -8, m = -3

D) m = 8, m = 3

Answer: C

Q2) Simplify using powers of i. i⁴⁶

A) 1

B) -1

C) i

D) -i

Answer: B

Q3) Solve using the most efficient method. 4x² - 19x - 5 = 0

Answer: x = 11ea7f29_4fa7_e0b4_9ecd_09c4b2c284ca_TB3307_11 , x = 5

Q4) Solve. 0.2(5 - 2.4x) - 3.4 = 0

Answer: -5

Q5) Graph the inequality on a number line. x > -1

Answer: 11ea7f29_4f9e_b8a6_9ecd_17e8416116c2_TB3307_00

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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 h(a - 2).

Answer: 11ea7f29_4fb0_e0b5_9ecd_0362b1c9b3d2_TB3307_00

Q2) Identify the center and radius of the circle. (x + 6)² + (y4)² = 16.

A) center (-6, 4) and radius 4

B) center (6, -4) and radius 4

C) center (-6, 4) and radius 16

D) center (6, -4) and radius 16

Answer: A

Q3) Write the equation in factored form to find the center and radius of the circle. x² + y² + 14x - 2y + 3 = 0

Answer: (x + 7)² + (y - 1)² = 47; center (-7, 1), radius 11ea7f29_4fad_5e22_9ecd_9fc2d39a5f25_TB3307_11

Q4) Determine the equations of asymptotes (if any).

A) x = 0, y = -1

B) x = -5, x = 1, x = 5

C) x = 1

D) none

Answer: D

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Chapter 3: Polynomial and Rational Functions

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122 Flashcards

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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 2⁺, as x - , y 2^-, as x 4^-, y - , as x 4⁺, y

Q2) Find the constant of variation.

A) 1.125

B) 11.25

C) 112.5

D) 0.1125

Answer: B

Q3) Use synthetic division and the remainder theorem to evaluate P(4) if P(x) = x³ - 5x² - 4x + 20. Verify using a second method.

Answer: 11ea7f29_4fc9_98a8_9ecd_8d2ca986cce7_TB3307_00 Since the remainder is -12, P(4) = -12.

Verification: P(4) = (4)³ - 5(4)² - 4(4) + 20 = -12

Q4) 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

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Chapter 4: Exponential and Logarithmic Functions

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96 Verified Questions

96 Flashcards

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Sample Questions

Q1) 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. Paul deposited $8400 in a savings account that pays 7.5% simple interest. How long will it take the account balance to reach $11,172.00 at this rate of interest, if no more deposits are made? (Hint: How much interest will be paid?)

Q2) Graph the function using transformations of y = log_bx and strategically plotting a few points. f(x) = -log₃(x + 2)

Q3) Graph the logarithmic function. f(x) = -ln(x + 1)

Q4) Solve the equation using the uniqueness property of logarithms. log(10x + 10) = log 20

Q5) Write the equation in exponential form. 2 = log₅25

Q6) Use the properties of logarithms to write the expression as a single term. ln(x + 7) + ln(7x)

Q7) Find the inverse function of the one-to-one function given. {(-1, 1), (-3, 4), (4, 0), (-5, 3), (-2, 2)}

Page 6

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Chapter 5: Introduction to Trigonometric Functions

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133 Flashcards

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Sample Questions

Q1) _______ angles measure greater than 90°.

Q2) Identify the amplitude (A).

A) |A| = 8

B) |A| = -8

C) |A| = 70

D) |A| = -70

Q3) Use a calculator to find the acute angle A whose corresponding ratio is given. Round to the nearest tenth of a degree.

sin A = 0.9746

Q4) How tall is the factory across the street? Round to the nearest tenth of a foot.

A) approx. 122.5 ft

B) approx. 130.7 ft

C) approx. 138.3 ft

D) approx. 145.9 ft

Q5) Complementary angles sum to _____.

A) 45°

B) 90°

C) 180°

D) 360°

Q6) 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) Find the volume of a cone with radius 8 ft, slant height 4 ft, and angle of deflection \(\alpha\)= 15°. Round to four decimal places.

A) 174.3308 ft³

B) 268.0826 ft³

C) 69.3849 ft³

D) 258.9479 ft³

Q2) Rewrite in terms of an expression containing only cosines to the power 1. sin² x cos⁴ x

Q3) Solve the equation in [0, 2 ) by squaring both sides. sec x - tan x = -1

Q4) Evaluate without the aid of calculators or tables. Answer in radians. cos^-¹1

Q5) State the quadrant of the principal root.

A) QI

B) QII

C) QIII

D) QIV

Q6) Evaluate using a calculator. Answer to the nearest tenth of a degree. sec^-1 5.593

Q7) 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) Hal pushes a box full of books 40 ft. If he uses a constant force of 75 pounds, how much work did he do?

Q2) If the maximum range of the ship's radar is 16.0 miles, will the departing fleet be detected?

A) yes

B) no

Q3) How many triangles can be formed if side a = 23 ft?

A) 0

B) 1

C) 2

D) 3

Q4) Solve using the law of sines and a scaled drawing. Round to the nearest tenth. If two triangles exist, solve both completely.

side c = 27.5 mi

\(\angle\)A = 44°

side a = 10.1 mi

Q5) Find a unit vector pointing in the same direction as the vector v = -2i - 5j.

Q6) Use the nth roots theorem to find the three cube roots of -64i. Answer in exact form.

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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. 2x + 3y > 6

Q2) Solve the linear inequality by shading the appropriate half plane. -3x + y \(\ge\) 0

Q3) Write the system of equations corresponding to the matrix.

Q4) Solve the linear inequality by shading the appropriate half plane. 3x + y \(\le\) 5

Q5) Solve the linear inequality by shading the appropriate half plane. x - y \(\le\) 2

Q6) Find the area of the triangle with vertices (-1, -2), (4, 2), and (1, -2). Assume area units are cm².

A) 16 cm²

B) 4 cm²

C) 8 cm²

D) 12 cm²

Q7) Determine if the points (-2, 3), (1, -5), and (-3, 2) are colinear.

A) Yes

B) No

Page 10

Q8) 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

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Sample Questions

Q1) Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.

x² - 9y² - 6x - 36y - 36 = 0

Q2) Sketch the polar graph using an r-value analysis (a table may help), symmetry, and any convenient points. r = 3sin\(\theta\)

Q3) Sketch the polar graph using an r-value analysis (a table may help), symmetry, and any convenient points. r = 5sin(2\(\theta\) )

Q4) Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 4x² + 9y² - 40x - 18y = -73

A) Circle

B) Ellipse

C) Hyperbola

D) None of these

Q5) Use the graph to approximate all x- and y-intercepts, and maximum and minimum values to one decimal place.

Q6) Find the x- and y-intercepts, if they exist.

Q7) Find the focus.

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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) Write the sum using sigma notation. Answers are not necessarily unique. 10 + 20 + 30 + 40 + 50 + 60

Q2) Write the first four terms of the geometric sequence given a₁ = 2 and r = -4.

Q3) Jim deposits $15,000 in an account on January 1. Starting on January 2, he withdraws $100 each morning. Find the amount in his account on the evening of January 27. (Hint: For a₁ = 15,000, the amount remaining 26 days later will be what term of the sequence?)

A) $12,700

B) $12,600

C) $12500

D) $12,400

Q4) What is the population after 5 hours?

A) 100

B) 200

C) 640

D) 20,480

Q5) A coin is flipped three times. Draw a tree diagram illustrating all possible outcomes. How many elements are in the sample space?

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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) Translate the phrase into an algebraic expression. six fewer than a number

A) 6 - n

B) n - 6

C) n / 6

D) n + 6

Q2) Translate the phrase into an algebraic expression. the difference between a number and two is squared

Q3) Find the binomial square. (x + 2)²

Q4) Create a mathematical model using descriptive variables. The speed of the truck was three miles per hour more than the speed of the car.

Q5) What is the cost of seizing 60% of the drugs?

A) $210

B) $233

C) $350

D) $525

Q6) Factor using u-substitution. 36 + x⁴ - 13x²

Q7) List all the numbers in the set that are elements of W.

Q8) Factor the trinomial completely. 3x² + 20x + 25

Q9) Evaluate/simplify the expression. | -2.5 |

Q10) Factor by grouping. x⁵+ 3x³ - 5x² - 15 Page 13

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