Algebra and Trigonometry Solved Exam Questions
Course Introduction
This course provides a comprehensive introduction to the fundamental concepts of algebra and trigonometry, essential for students pursuing studies in mathematics, science, or engineering. Topics covered include linear, quadratic, polynomial, rational, exponential, and logarithmic functions and their properties. The course also explores systems of equations and inequalities, sequences and series, and an in-depth study of trigonometric functions, identities, equations, and applications. Emphasis is placed on problem-solving, real-world applications, and developing the algebraic and graphical skills needed for higher-level mathematics.
Recommended Textbook
Precalculus 2nd Edition by John W. Coburn
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1334 Verified Questions
1334 Flashcards
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Chapter 1: Equations and Inequalities
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107 Verified Questions
107 Flashcards
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Sample Questions
Q1) An arithmetic student needs at least a 70% average to receive credit for the course. If she scored 70%, 64%, and 72% on the first three exams, what score must she get on the fourth exam to receive credit for the course?
A) x 72%
B) x 74%
C) x 76%
D) x 79%
Answer: B
Q2) Compute the special product and write your answer in a + bi form. (3 - 2i)(3 + 2i)
A) 5 - 12i
B) 13 + 12i
C) 5
D) 13
Answer: D
Q3) 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
Q4) 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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Sample Questions
Q1) Determine the domain.
A) x \(\in\) [-3, 1]
B) x \(\in\) (-4, ?)
C) x \(\in\) [-4, ?)
D) x \(\in\) (-?, ?)
Answer: D
Q2) Graph by plotting points or using the intercept method. y = -1
Answer: 11ea7f29_4fb3_2aba_9ecd_2d9359b4d8c5_TB3307_00 (Gridlines are spaced one unit apart.)
Q3) Describe the end behavior.
A) up on left, up on right
B) up on left, down on right
C) down on left, up on right
D) down on left, down on right
Answer: C
Q4) Identify the slope and y-intercept.
Answer: slope = 11ea7f29_4fb4_6343_9ecd_65789875898b_TB3307_11 ; y-intercept (0,-2)
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Chapter 3: Polynomial and Rational Functions
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122 Flashcards
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Sample Questions
Q1) Graph the polynomial function. f(x) = x<sup>3</sup> + 2x<sup>2</sup><sup> </sup>- 5x - 6
Answer: 11ea7f29_4fce_c8f0_9ecd_3f1db19a3ddf_TB3307_00
Q2) State the domain of the function.
A) x \(\in\) (-?, -2) \(\cup\) (-2, ?)
B) x \(\in\) (-?, 2) \(\cup\) (2, ?)
C) x \(\in\) (-?, -3) \(\cup\) (-3, ?)
D) x \(\in\) (-?, 3) \(\cup\) (3, ?)
Answer: B
Q3) 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 -
Q4) Find a cubic polynomial with real coefficients having roots x = -3 and x = -i. Assume a lead coefficient of 1.
Answer: P(x) = x<sup>3</sup> + 3x<sup>2</sup> + x + 3.
Q5) Write the variation equation.
Answer: A = 11ea7f29_4fdb_4c66_9ecd_5d253cf92f09_TB3307_11
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Chapter 4: Exponential and Logarithmic Functions
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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. 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
Q2) 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
Q3) Write the equation in the simplified form log<sub> </sub><sub>b</sub><sub> </sub>x = k (logarithmic term = constant). Do not solve. 5log<sub> 3 </sub>x + log<sub> 3</sub>(x + 8) = -3
Q4) Solve the equation in two ways: by equating bases and using the uniqueness properties and by applying a base-10 or base-e logarithm and using the power property of logarithms. 3<sup>x</sup> = 27
Q5) t = 8.5
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Chapter 5: Introduction to Trigonometric Functions
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Sample Questions
Q1) State the quadrant of the terminal side of \(\theta\) using the information given. csc\(\theta\) < 0,
Tan\(\theta\) > 0
A) QI
B) QII
C) QIII
D) QIV
Q2) 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
Q3) What is the angular velocity of the wheels?
A) 1097\(\pi\) rad/min
B) 1100\(\pi\) rad/min
C) 1105\(\pi\) rad/min
D) 1111\(\pi\) rad/min
Q4) Find an additional value of t (to four decimal places) in [0, 2?) that makes cos t \(\approx\) -0.3379 true, given that cos 1.9155 \(\approx\) -0.3379.
Q5) Graph f(t) = 3 tan t over the interval [-2 , 2 ].
Q6) Give the model for the data.
Page 7
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Chapter 6: Trigonometric Identities, Inverses, and Equations
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Sample Questions
Q1) 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
Q2) Rewrite the product as a sum using a product-to-sum identity. 2sin(2073\9\pi\)t)cos(813\(\pi\)t)
Q3) State the number of roots in [0, 2\(\pi\)].
A) 4
B) 3
C) 2
D) 1
Q4) Rewrite as a single expression. cos(10\(\theta\))cos(6\(\theta\) )sin(10\(\theta\) )sin(6\(\theta\) )
A) cos(16\(\theta\))
B) cos(4\(\theta\) )
C) sin(16\(\theta\) )
D) sin(4\(\theta\) )
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Chapter 7: Applications of Trigonometry
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Sample Questions
Q1) If the maximum range of the ship's radar is 18 miles, approximately how far from port (to the nearest tenth of a mile) is the fleet when it is first detected?
A). \(\approx\) 11.0 mi
B). \(\approx\) 14.6 mi
C).\(\approx\) 23.9 mi
D). \(\approx\) 27.3 mi
Q2) Two planes leave an airport at the same time. One travels due west (bearing 270°) with a cruising speed of 420 mph. The other travels at bearing 235° with a cruising speed of 440 mph. Approximate the distance between the planes after 3 hours of flight.
Q3) 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
Q4) Solve using the nth roots theorem. Approximate answers to four decimal places. x<sup>5</sup> - 1024 = 0
Q5) Find a unit vector pointing in the same direction as the vector v = -2i - 5j.
Q6) Compute the magnitude of the vector exactly.
Q7) Graph the vector.
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Chapter 8: Systems of Equations and Inequalities
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102 Flashcards
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Sample Questions
Q1) Solve the linear inequality by shading the appropriate half plane. 2x + 3y > 6
Q2) Determine whether the ordered pair (0, 0) is a solution. 10x - 3y > 5
A) Yes
B) No
Q3) Model the problem using a system of linear equations. Then solve using the augmented matrix. Suppose $24,000 is invested in three different accounts paying 3%, 4%, and 7%
Annual interest. The interest earned after 1 year is $1270, and the amount Invested at 7% is equal to the sum of the amounts invested at 3% and 4%. Find the amount invested at 3%.
A) $5000
B) $6000
C) $7000
D) $8000
Q4) 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?
Q5) Solve the linear inequality by shading the appropriate half plane. x - y \(\le\) 2
Q6) Write the system of equations corresponding to the matrix.
Page 10
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Chapter 9: Analytical Geometry
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Sample Questions
Q1) 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
Q2) Identify the equation as that of an ellipse or a circle. 5(x - 5)<sup>2</sup> + 5(y + 7)<sup>2</sup> = 80.
A) ellipse
B) circle
Q3) Sketch a complete graph of the equation, including asymptotes. Be sure to identify the center and vertices.
(x - 1)<sup>2</sup> - 9(y - 2)<sup>2</sup> = 9
Q4) A theorem from elementary geometry states: If the diagonals of a quadrilateral have equal length and bisect each other, then the quadrilateral is a rectangle. Verify the points A(-1, 4), B(5, 1), C(3, -3), and D(-3, 0) are the vertices of a rectangle.
Q5) Convert from rectangular coordinates to polar coordinates. A diagram may help. (8, -8)
Q6) Find the focus.
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Chapter 10: Additional Topics in Algebra
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121 Flashcards
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Sample Questions
Q1) Find the first four terms and write them as a list.
A) 1, -2, 3, -4
B) -1, 2, -3, 4
C) 2, -3, 4, -5
D) -2, 3, -4, 5
Q2) Find the number of terms n in an arithmetic sequence if a<sub>1</sub> = 13, a<sub>n</sub> = -95, and d = -6
A) 17
B) 18
C) 19
D) 20
Q3) How long will it take for the number of bacteria to reach 245,760?
A) 5.5 hours
B) 6 hours
C) 6.5 hours
D) 7 hours
Q4) Write the first four terms of the geometric sequence given a<sub>1</sub> = 2 and r = -4.
Q5) Find the sum of the first 20 multiples of 6.
Q6) Find the 11th term of the binomial expansion of (b - 2)<sup>13</sup>.
Page 12
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Chapter 12: Review of Basic Concepts and Skills
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112 Flashcards
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Sample Questions
Q1) Compute the product. -8x(x<sup>2</sup> - 5x - 7)
A) -8x<sup>3</sup> - 40x<sup>2</sup> - 56x
B) -8x<sup>3</sup> + 40x<sup>2</sup> + 56x
C) -8x<sup>2</sup> - 40x - 56
D) -8x<sup>2</sup> + 40x + 56
Q2) Simplify by combining like terms.
-8z - z - 4z
Q3) Evaluate (2x - 3y)<sup>2</sup> given x = 3 and y = -1.
A) 81
B) 27
C) 9
D) -9
Q4) Convert the following number to ordinary notation. The maximum distance from Pluto to the Sun is 7.3 * 10<sup>7</sup> meters.
Q5) 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)
Q6) Factor out the common binomial factor. 10x(x - 5) - 7(x - 5)
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