Mathematics for Scientists Exam Practice Tests
Course Introduction
Mathematics for Scientists is designed to equip students with essential mathematical tools and concepts that are foundational to scientific inquiry and analysis. The course emphasizes topics such as algebra, calculus, probability, statistics, and linear algebra, all presented with a focus on practical applications in the natural and physical sciences. Through problem-solving exercises and real-world examples, students develop the quantitative reasoning skills needed to model scientific phenomena, analyze experimental data, and interpret results effectively. This course serves as an essential building block for advanced study and research across various scientific disciplines.
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) Find two consecutive even integers such that the sum of the smaller integer plus twice the larger integer is 148.
Answer: 48, 50
Q2) Solve using the square root property of equality. If there are no real solutions, so state.
(x + 4)<sup>2</sup> = 81
Answer: x = 5, x = -13
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) Graph the inequality on a number line. x > -1
Answer: 11ea7f29_4f9e_b8a6_9ecd_17e8416116c2_TB3307_00
Q5) Solve for y. w = xyz
Answer: 11ea7f29_4f9d_801a_9ecd_6b3d04283d0b_TB3307_11
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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) State the domain and range of the relation. {(5, 8), (6, 9), (7, 10), (8, 11)}
Answer: Domain = {5, 6, 7, 8}
Range = {8, 9, 10, 11}
Q2) Find (f + g)(0).
Answer: 2
Q3) Name the interval(s) where the function is increasing. Write the answer in interval notation. Assume all endpoints have integer values.
A) g(x)\(\uarr\): x \(\in\) (1, ?)
B) g(x)\(\uarr\): x \(\in\) (-1, 4)
C) g(x\(\uarr\): x \(\in\) (-?, -2) \(\cup\) (1, 4)
D) g(x)\(\uarr\): x \(\in\) (-?, -1) \(\cup\) (-1, 4)
Answer: C
Q4) Graph by plotting points or using the intercept method. Choose inputs that will help simplify the calculation.
3x + 5y = -6
Answer: 11ea7f29_4fb2_193f_9ecd_dd4d3cfeb876_TB3307_00
Q5) Write this relationship in equation form.
Answer: c(t) = 14.50t + 21.50
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Chapter 3: Polynomial and Rational Functions
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122 Verified Questions
122 Flashcards
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Sample Questions
Q1) For the complex polynomial below, one of its zeroes is z = 5i. 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(z) = z<sup>3</sup> + (1 - 5i)z<sup>2</sup> + (-6 - 5i)z + 30i.
Answer: C(z) = (z - 5i)(z + 3)(z - 2);
z = -3, z = 2
Q2) State the range of the function.
A) y \(\in\) (-?, -2) \(\cup\) (-2, ?)
B) y \(\in\) (-?, 2) \(\cup\) (2, ?)
C) y \(\in\) (-?, -3)
D) y \(\in\) (-?, 3)
Answer: C
Q3) Use the intermediate value theorem to verify that the polynomial f(x) = -2x<sup>3</sup> - 4x<sup>2</sup> + 3x - 4 has at least one zero "c<sub>i</sub>" in the interval [-3, -1]. Do not find the zeroes.
A) Yes
B) No
Answer: A
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Page 5
Chapter 4: Exponential and Logarithmic Functions
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96 Verified Questions
96 Flashcards
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Sample Questions
Q1) Find the growth rate r. Round your answer to the nearest hundredth.
A) 3.65%
B) 3.77%
C) 3.89%
D) 4.00%
Q2) Use a calculator to evaluate e<sup>3.4</sup>, rounded to six decimal places.
A) 26.962966
B) 27.055977
C) 28.840644
D) 29.964100
Q3) Graph the logarithmic function.
f(x) = -ln(x + 1)
Q4) Solve using any appropriate method. Clearly identify any extraneous roots. If there are no solutions, so state. log(-x - 2) = log(3x) - log x
A) x = 0, -5
B) x = 0, 5
C) x = 5
D) No solution
Q5) t = 8.5
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Chapter 5: Introduction to Trigonometric Functions
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133 Verified Questions
133 Flashcards
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Sample Questions
Q1) Use the formula for arc length to find the value of the unknown quantity: s = r\(\theta\).
\(\theta\)= 2.1; r = 220 ft.
Q2) State the exact value of sin \(\pi\) . A diagram may help.
Q3) A person is standing 250 feet from a building. The angle of elevation to the top of the building is 69.9°. How tall is the building?
A) 681.8 ft
B) 683.2 ft
C) 684.4 ft
D) 685.0 ft
Q4) Use the formula for arc length to find the unknown quantity: s = r\(\theta\). Round your answer to the nearest hundredth of an inch.
\(\theta\) = 280°; s = 68 in.
Q5) Find the value of A.
A) 2.5
B) 3.8
C) 5.7
D) 9.2
Q6) Graph f(t) = 3 tan t over the interval [-2 , 2 ].
Page 7
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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) Solve the equation in [0, 2 ) by squaring both sides. sec x - tan x = -1
Q2) Evaluate without the aid of calculators or tables. Answer in radians. cos<sup>-</sup><sup>1 </sup>1
Q3) Verify the equation is an identity using special products and fundamental identities. (1 + cos x)[1 - cos(-x)] = sin<sup>2</sup> x
Q4) 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
Q5) Rewrite in terms of an expression containing only cosines to the power 1. sin<sup>2</sup> x cos<sup>4</sup> x
Q6) State the number of roots in [0, 2\(\pi\)].
A) 4
B) 3
C) 2
D) 1
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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) Use De Moivre's Theorem to compute (4 + 4i)<sup>4</sup>.
A) 1024
B) -1024
C) 1024i
D) -1024i
Q2) Solve the triangle using the law of sines. Round sides to the nearest tenth. side a = 5 m
\(\angle\)A = 56°
\(\angle\)B = 41°
A). \(\angle\)C = 83° b \(\approx\)3.3 m
C \(\approx\) 5.4 m
B). \(\angle\)C = 83° b \(\approx\) 3.8 m
C \(\approx\) 6.4 m
C). \(\angle\)C = 83° b \(\approx\) 4.0 m
C \(\approx\)6.0 m
D). \(\angle\)C = 83° b \(\approx\) 4.5 m
C \(\approx\) 5.8 m
Q3) Compute the magnitude of the vector exactly.
Q4) 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.
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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) Solve the linear inequality by shading the appropriate half plane. 3x + y \(\le\) 5
Q2) 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?
Q3) Solve the linear inequality by shading the appropriate half plane. -3x + y \(\ge\) 0
Q4) Find any four ordered triples that satisfy the equation. x - y + z = -3
Q5) Solve the linear inequality by shading the appropriate half plane. x - y \(\le\) 2
Q6) Determine if the points (-2, 3), (1, -5), and (-3, 2) are colinear.
A) Yes
B) No
Q7) A stationary store sells rolls of standard gift wrap and deluxe gift wrap. They can stock a total of 110 rolls of gift wrap, of which at least 40 must be standard wrap and at least 20 must be deluxe wrap. The profit on a roll of standard wrap is $4 and the profit on a roll of deluxe wrap is $5. How many rolls of each type of gift wrap should the store stock to maximize their profit?
Q8) Write the system of equations corresponding to the matrix.
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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) Identify the graph of the equation using the discriminant. x<sup>2</sup> - 2xy + y<sup>2</sup> - 5x + 5y - 4 = 0
A) parabola
B) circle or ellipse
C) hyperbola
Q2) Complete the square in both x and y to write the equation in standard form. Then draw a complete graph of the relation and identify all important features. 9x<sup>2</sup> + 4y<sup>2</sup> - 18x + 16y - 11 = 0
Q3) Classify the equation as that of a circle, ellipse, hyperbola, or none of the above. 8y<sup>2</sup> - 4 = 5x<sup>2</sup> + 36
A) Circle
B) Ellipse
C) Hyperbola
D) None of these
Q4) Find the x- and y-intercepts, if they exist.
A) x-intercepts: (2, 0), (4, 0); y-intercept: (0, -8)
B) x-intercept: (2, 0); y-intercepts: (0, -8), (0, 4)
C) x-intercept: (-8, 0); y-intercepts: (0, 2), (0, 4)
D) x-intercepts: none; y-intercept (0, -8)
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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>) = 0.4, P(E<sub>1</sub>\( \cap\)E<sub>2</sub>) = 0.3, and P(E<sub>1</sub> \(\cup\) E<sub>2</sub>) = 0.7, compute P(E<sub>2</sub>).
A) 0.5
B) 0.6
C) 0.7
D) 0.8
Q2) How many codes are possible if no repetitions are allowed?
A) 24
B) 125
C) 60
D) 64
Q3) Find the sum of the first 20 multiples of 6.
Q4) What is the probability that the group consists of exactly two boys? Round your answer to four decimal places.
A) 0.2400
B) 0.1474
C) 0.2947
D) 0.5895
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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) 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>
Q2) Simplify by combining like terms. -8z - z - 4z
Q3) Translate the phrase into an algebraic expression. five times the sum of a number and six, decreased by four
Q4) 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
Q5) Translate the phrase into an algebraic expression. six fewer than a number
A) 6 - n
B) n - 6
C) n / 6
D) n + 6
Page 13
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