Science and Engineering Mathematics
Pre-Test Questions
Course Introduction
Science and Engineering Mathematics provides students with a comprehensive foundation in the mathematical principles and techniques essential for solving complex problems in science and engineering fields. The course covers topics such as calculus, linear algebra, differential equations, probability, and numerical methods, emphasizing their practical applications in analyzing physical systems, designing experiments, and interpreting data. By integrating real-world examples and problem-solving exercises, students develop critical thinking and quantitative reasoning skills necessary for advanced studies and professional practice in scientific and engineering disciplines.
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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Page 2
Chapter 1: Functions, graphs, and Limits
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427 Verified Questions
427 Flashcards
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Sample Questions
Q1) How much more interest will be earned if $7,000 is invested for 9 years at an annual rate of 9% compounded continuously,instead of at 9% compounded quarterly? Round your answer to the nearest cent.
A) $47.49
B) $93.15
C) $140.64
D) $2,924.71
E) $3,017.87
Answer: C
Q2) How long (in years)would $800 have to be invested at an annual rate of 11%,compounded continuously,to amount to $1060? Round your answer to two decimal places.
A) 2.95 years
B) 2.70 years
C) 0.56 years
D) 3.38 years
E) 2.56 years
Answer: E
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Chapter 2: Differentiation
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84 Verified Questions
84 Flashcards
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Sample Questions
Q1) 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
Q2) 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
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Page 4
Chapter 3: Applications of the Derivative
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122 Verified Questions
122 Flashcards
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Sample Questions
Q1) The measurement of the circumference of a circle is found to be 54 centimeters,with a possible error of 0.7 centimeters.Approximate the percent error in computing the area of the circle.
A) 3.70 %
B) 1.30 %
C) 2.59 %
D) 5.19 %
E) 1.85 %
Answer: C
Q2) A rectangular page is to contain 144 square inches of print.The margins on each side are 1 inch.Find the dimensions of the page such that the least amount of paper is used.
A) 14, 14
B) 12, 12
C) 10, 10
D) 13, 13
E) 11,11
Answer: A
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Page 5
Chapter 4: Exponential and Logarithmic Functions
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122 Verified Questions
122 Flashcards
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Sample Questions
Q1) What lump sum should be deposited in an account that will earn at an annual rate of 9%,compounded quarterly,to grow to $150,000 for retirement in 20 years? Round your answer to the nearest cent.
A) $147,330.10
B) $18,292.68
C) $53,571.43
D) $24,961.93
E) $25,294.49
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%
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6
Chapter 5: Integration and Its Applications
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88 Verified Questions
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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46 Flashcards
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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 Verified Questions
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 Verified Questions
36 Flashcards
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Sample Questions
Q1) Three people are asked their opinions on a political issue.They can answer Opposed (O)or Undecided (U).Find the sample space S.
A) {OOO, OOU, OUO, UOO, UUU, UUO, UOU}
B) {OOO, OOU, UOO, UUU, UUO, UOU, OUU}
C) {OOO, OOU, OUO, UOO, UUO, UOU, OUU}
D) {OOO, OUO, UOO, UUO, UOU, OUU}
E) {OOO,OOU,OUO,UOO,UUU,UUO,UOU,OUU}
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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11
Chapter 10: Series and Taylor Polynomials
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104 Flashcards
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Sample Questions
Q1) A factory is polluting a river such that at every mile down river from the factory an environmental expert finds 15% less pollutant than at the preceding mile.If the pollutant's concentration is 600 ppm (parts per million)at the factory,what is its concentration 12 miles down river?
A) 180 ppm
B) 90 ppm
C) 85.35 ppm
D) 705.88 ppm
E) 100.41 ppm
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
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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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