Mathematics for Engineers
Pre-Test Questions
Course Introduction
Mathematics for Engineers provides a comprehensive foundation in the mathematical concepts and techniques essential for engineering disciplines. The course covers topics such as calculus, differential equations, linear algebra, complex numbers, vector analysis, and numerical methods, with an emphasis on their practical applications in solving real-world engineering problems. Students will develop analytical and problem-solving skills through theoretical instruction and practical exercises, preparing them to apply mathematical reasoning in various fields of engineering.
Recommended Textbook
Calculus An Applied Approach 10th Edition by Ron Larson
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11 Chapters
1279 Verified Questions
1279 Flashcards
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Chapter 1: Functions, graphs, and Limits
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427 Verified Questions
427 Flashcards
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Sample Questions
Q1) The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long?
A) 96 ft<sup>2</sup>/min
B) 1,008 ft<sup>2</sup>/min
C) 504 ft<sup>2</sup>/min
D) 2,016 ft<sup>2</sup>/min
E) 84 ft<sup>2</sup>/min
Answer: B
Q2) What is the annual percentage yield (or effective annual rate)for a nominal rate of 8.7% compounded quarterly? Round your answer to two decimal places.
A) 8.70%
B) 9.06%
C) 9.09%
D) 8.99%
E) 8.89%
Answer: D
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Chapter 2: Differentiation
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84 Flashcards
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Sample Questions
Q1) The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long?
A) 96 ft<sup>2</sup>/min
B) 1,008 ft<sup>2</sup>/min
C) 504 ft<sup>2</sup>/min
D) 2,016 ft<sup>2</sup>/min
E) 84 ft<sup>2</sup>/min
Answer: B
Q2) A baseball diamond has the shape of a square with sides 90 feet long.A player running from second base to third base at a speed of 27 feet per second is 60 feet from third base.At what rate is the player's distance s from home plate changing? Round your answer to one decimal place.
A) -24.1 feet/second
B) -0.2 feet/second
C) -0.6 feet/second
D) -15 feet/second
E) -0.9 feet/second
Answer: D
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Chapter 3: Applications of the Derivative
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122 Flashcards
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Sample Questions
Q1) Minimum cost.From a tract of land,a developer plans to fence a rectangular region and then divide it into two identical rectangular lots by putting a fence down the middle.Suppose that the fence for the outside boundary costs $7 per foot and the fence for the middle costs $4 per foot.If each lot contains 5000 square feet,find the dimensions of each lot that yield the minimum cost for the fence.
A) Dimensions are 51.59 ft for the side parallel to the divider and 96.92 ft for the other side.
B) Dimensions are 96.92 ft for the side parallel to the divider and 51.59 ft for the other side.
C) Dimensions are 70.71 ft for the side parallel to the divider and 70.71 ft for the other side.
D) Dimensions are 88.19 ft for the side parallel to the divider and 56.7 ft for the other side.
E) Dimensions are 56.7 ft for the side parallel to the divider and 88.19 ft for the other side.
Answer: D
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Chapter 4: Exponential and Logarithmic Functions
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122 Verified Questions
122 Flashcards
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Sample Questions
Q1) What is the annual percentage yield (or effective annual rate)for a nominal rate of 8.7% compounded quarterly? Round your answer to two decimal places.
A) 8.70%
B) 9.06%
C) 9.09%
D) 8.99%
E) 8.89%
Q2) Find the future value if $4,200 is invested for 6 years at an annual rate of 9% compounded quarterly.
A) $9,072.00
B) $4,799.87
C) $7,043.82
D) $7,122.70
E) $7,164.22
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6
Chapter 5: Integration and Its Applications
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88 Flashcards
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Sample Questions
Q1) A ball is thrown vertically upwards from a height of 6 ft with an initial velocity of 40 ft per second.
How high will the ball go?
A) 29.03 ft
B) 29.34 ft
C) 30.89 ft
D) 25.02 ft
E) 32.12 ft
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Chapter 6: Techniques of Integration
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Sample Questions
Q1) A business is expected to yield a continuous flow of profit at the rate of $200,000 per year.If money will earn interest at the nominal rate of 2% per year compounded continuously,what is the present value of the business forever?
A) $10,100,000
B) $1,000,000
C) $10,000,000
D) $10,010,000
E) $1,100,000
Q2) Present Value of a Continuous Stream of Income.An electronics company generates a continuous stream of 4t income of million dollars per year,where t is the number of years that the company has been in operation.Find the present value of this stream of income over the first 15 years at a continuous interest rate of 10%.Round answer to one decimal place.
A) $407.2 million
B) $176.9 million
C) $497.3 million
D) $1296.3 million
E) $324.1 million
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Chapter 7: Functions of Several Variables
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113 Flashcards
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Sample Questions
Q1) Determine whether the statement is true or false.If it is false,explain why or give an example that shows it is false.
A linear regression model with a positive correlation will have a slope that is greater than 0.
A)True
B)False
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Chapter 8: Trigonometric Functions
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60 Flashcards
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Sample Questions
Q1) A compact disc can have an angular speed up to 3,154 radians per minute.At this angular speed,how many revolutions per minute would the CD make? Round your answer to the nearest integer.
A) 1,004
B) 1,577
C) 402
D) 502
E) 251
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Chapter 9: Probability and Calculus
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36 Flashcards
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Sample Questions
Q1) If x is the net gain to a player in a game of chance,then E(x)is usually negative.This value gives the average amount per game the player can expect to lose over the long run.A service organization is selling $2 raffle tickets as part of a fundraising program.The first prize is a boat valued at $2910,and the second prize is a camping tent valued at $400.In addition to the first and second prizes,there are twenty $24 gift certificates to be awarded.The number of tickets sold is 3000.Find the expected net gain to the player for one play of the game.Round your answer to the nearest cent.
A) $1,109.33
B) $1.34
C) $0.74
D) -$0.74
E) -$1,109.33
Q2) A coin is tossed three times.Describe the event A that at least two tails occur.
A) {TTT, THH, THT, HHT}
B) {HHH, TTH, THT, HTT}
C) {TTT, TTH, THT, HTT}
D) {TTTT, TTHT, THTT, HTTT}
E) {TT,HT,TH}
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Chapter 10: Series and Taylor Polynomials
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104 Flashcards
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Sample Questions
Q1) Bouncing Ball.A ball dropped from a height of 39 feet bounces to 0.6666666667 of its former height with each bounce.Find the total vertical distance that the ball travels.
A) 195 feet
B) 82 feet
C) 234 feet
D) 111 feet
E) 117 feet
Q2) What are the next three terms in the arithmetic sequence -2,-6,-10,....
A) -14, -18, -22
B) 2, 6, 10
C) 56, -224, 896
D) -8, -10, -12
E) -10,-14,-18
Q3) Find the next three terms of the geometric sequence 8,40,200,....
A) 232, 264, 296
B) 1,000, 5,000, 25,000
C) 360, 520, 680
D) 205, 210, 215
E) 200,1,000,5,000
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Page 12
Chapter 11: Differential Equations
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77 Flashcards
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Sample Questions
Q1) The rate of change of the population of a city is proportional to the population P at any time (in years).In 2000,the population was 200,000,and the constant of proportionality was 0.015.Estimate the population of the city in the year 2020.
A) 260,972 people
B) 268,972 people
C) 263,972 people
D) 266,972 people
E) 269,972 people
Q2) A population of eight beavers has been introduced into a new wetlands area.Biologists estimate that the maximum population the wetlands can sustain is 60 beavers.After 3 years,the population is 15 beavers.The population follows a Gompertz growth model.How many beavers will there be in the wetlands after 10 years?
A) 34 beavers
B) 32 beavers
C) 30 beavers
D) 31 beavers
E) 39 beavers
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