Applied Calculus
Pre-Test Questions
Course Introduction
Applied Calculus provides an introduction to the fundamental concepts of calculus with a specific focus on practical applications in business, economics, the social sciences, and the natural sciences. The course covers topics such as functions, limits, derivatives, and integrals, emphasizing their use in real-world problem solving. Students learn to analyze rates of change, optimize functions, and model dynamic systems through hands-on examples and exercises relevant to various professional fields. This course is designed for students seeking a solid understanding of calculus concepts without the theoretical rigor required for advanced mathematics or physical science majors.
Recommended Textbook
Calculus An Applied Approach 10th Edition by Ron Larson
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Chapter 1: Functions, graphs, and Limits
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Sample Questions
Q1) Find a linear equation that expresses the relationship between the temperature in degrees Celsius and degrees Fahrenheit.Use the fact that water freezes at 0° C (32° F)and boils at 100° C (212° F ).Use the equation to convert 82° F to Celsius.Round to the nearest degree.
A) 28°C
B) 14°C
C) 63°C
D) 90°C
E) 116°C
Answer: A
Q2) What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?
A) $4,632.79
B) $4,687.00
C) $6,075.00
D) $6,379.31
E) $8,258.80
Answer: D
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Chapter 2: Differentiation
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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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Sample Questions
Q1) The measurement of the edge of a cube is found to be 18 inches,with a possible error of 0.7 inch.Use differentials to estimate the propagated error in computing (a)the volume of the cube and (b)the surface area of the cube.Give your answers to two decimal places.
A) 816.48, 151.20
B) 544.32, 136.08
C) 612.36, 136.08
D) 544.32, 120.96
E) 680.40,151.20
Answer: E
Q2) 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
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Chapter 4: Exponential and Logarithmic Functions
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Sample Questions
Q1) 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
Q2) What is the resulting balance if $4,500 is invested for 5 years at an annual rate of 7% compounded monthly?
A) $4,632.79
B) $4,687.00
C) $6,075.00
D) $6,379.31
E) $8,258.80
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6
Chapter 5: Integration and Its Applications
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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) 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
Q2) Suppose the mean height of American women between the ages of 30 and 39 is 64.5 inches,and the standard deviation is 2.7 inches.Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 feet 4 inches and 6 feet tall.
A) 0.5734
B) 0.5707
C) 0.8547
D) 0.9522
E) 0.4257
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Page 8
Chapter 7: Functions of Several Variables
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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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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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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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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) 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
Q3) 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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Page 12
Chapter 11: Differential Equations
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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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