1
FE Practice Material
Josh McCurley
2
Mathematics and Statistics:
1. The roots of F =
a.
b.
c.
d.
𝑥 3 +6𝑥 2 +11𝑥+6
𝑥+1
are most nearly:
-1, -2, -3
2, -3
-2, -3
2, 3
2. The equation of a sphere with its center at (0,1,-2) and a radius of 9 is:
a. x2 + (y-1)2 + (z+2)2 = 81
b. x2 + (y+1)2 + (z-2)2 = 81
c. (x+1)2 + (y+1)2 + (z+2)2 = 81
d. (x+1)2 + (y+1)2 + (z+2)2 = 9
(1−𝑖)2
3. The term
a.
b.
c.
d.
(1+𝑖)2
, where i =√−1, is most nearly:
-1
-1 + i
0
1+i
4. Which of the following is a unit vector perpendicular to the plane determined by the
vectors A = 2i + 4j and B = i + j - k
a. -2i + j – k
1
b.
(i + 2j)
c.
d.
√5
1
(-2i + j - k)
√6
1
(-2i -j -k)
√6
3
5. The following data has been collected:
Test
1
2
3
4
5
6
7
8
9
Average Score
85
87
95
90
85
88
90
90
91
Which of the following statements is true?
a.
b.
c.
d.
The median and mode are equal.
The mean and median are equal.
The mean and the mode are equal.
The mean is larger than both the mode and the median.
6. You have a fair coin that you toss ten times. The probability of getting exactly four heads
in ten tosses is most nearly:
a. 0.1
b. 0.2
c. 0.4
d. 0.5
7. You throw two 6-sided fair dice. The probability that the sum will be less than 12 is most
nearly.
a. 0.028
b. 0.083
c. 0.333
d. 0.972
4
8. The only point of inflection on the curve representing the equation y = x3 + x2 -3 is at:
2
a. x = 3
1
b. x = -
3
c. 0
1
d. x =
3
9. A spreadsheet display shows the following values in column A:
1
2
3
4
5
A
-2
-1
0
1
2
B
Cell B1 contains the formula $A1^3 + A$1^2 – 3. The formula in Cell B1 is copied down in
Column B with automatic cell referencing. The formula in Cell B5 will be:
a.
b.
c.
d.
$A1^3 + A$5^2 – 3
A5^3 + B$1^2 – 3
$A5^3 + A$1^2 – 3
A5^3 + A5^2 – 3
10. The area of the shaded portion of the figure shown below is most nearly:
a.
b.
c.
d.
18
39
117
133
5
11. The indefinite integral of x3 – x + 1 is:
a. 3x2 -1 + C
b.
c.
d.
𝑥4
3
𝑥4
3
𝑥4
4
-
𝑥2
2
𝑥2
2
𝑥2
2
+1+C
+1
+x+C
4 1
12. The integral ∫2
a.
b.
1
𝑑𝑥 equals:
4
3
4
c. d.
𝑥2
3
16
5
16
𝜕2 𝑦
13. If y = 4x3 +3x2z +5xz2 +6z3 +20, then (
a.
b.
c.
d.
𝜕𝑥 2
)=
12x + 6z
24x + 6z
12x2 +6xz +5z2
24x2 + 6xz + 5z2
14. The water content of a soil volume is measured four times gravimetrically by oven
drying. The mean value of the water content is 23.2%. If the standard deviation of the
four measurements is 1.0%, the 99% confidence interval for the soil water content is most
nearly:
a. (18.6%, 27.8%)
b. (19.5%, 26.9%)
c. (20.6%, 25.8%)
d. (20.9%, 25.5%)
15. What is the sample variance of the following numbers: 2,4,6,8,10,12,14?
a. 4.32
b. 5.29
c. 8.00
d. 18.70
6
16. You collect 10 observations from an experiment. The sample average is 14.0, and the
standard deviation is 5.8. The 90% confidence interval on the mean is:
a. 11.57 < µ > 16.43
b. 10.68 < µ > 17.32
c. 8.20 < µ > 19.80
d. 8.78 < µ > 19.22
17. Two students are working independently on a problem. Their respective probabilities of
solving that problem are 1/3 and ¾. What is the probability that at least one of them will
solve the problem?
a. 0.5
b. 0.625
c. 0.4
d. 0.833
18. A coin is flipped, and a 6-sided die thrown. What is the probability of getting heads and a
5 at the same time?
a. 0.5
b. 0.33
c. 0.167
d. 0.083
19. What is the length of a line segment with a slope of 4/3, measured from the y-axis to a
point (6,4)?
a. 10
b. 25
c. 50
d. 75
20. What is the general form of the equation for a line whose x-intercept is 4 and y-intercept
is -6?
a. 2x – 3y -18 = 0
b. 2x + 3y +18 = 0
c. 3x – 2y -12 = 0
d. 3x + 2y + 12 = 0
7
21. Simplify and evaluate the following expression:
a.
b.
c.
d.
0.95
1.33
2.00
2.20
22. For some angle ө, csc(ө) = -8/5. What is cos(2ө)?
a.
b.
c.
d.
7/32
1/4
3/8
5/8
23. The expression…
… is equivalent to which of the following?
a.
b.
c.
d.
Sin(x)
Cos(x)
1 – sin^2(x)
1 + sin^2(x)
24. What is the value of x (less than 3600) that will satisfy the following equation?
a.
b.
c.
d.
450
900
1800
2700
8
25. If the rectangular coordinates of a point are (-3, -5.2), what are its polar coordinates?
a.
b.
c.
d.
(-6, -1200)
(6, -1200)
(6, 1200)
(6, -1500)
26. Determine the (x,y) coordinates of the center of the circle defined by the following
equation?
a.
b.
c.
d.
(3, 2)
(3, 4)
(4, 5)
(5, 4)
27. What is the slope of the following curve when it crosses the positive part of the x-axis?
a.
b.
c.
d.
3/20
1/5
1/3
7
28. What is the maximum value of the following function on the interval x < 0?
a.
b.
c.
d.
-210
-36
-5
210
9
29. What is the value of the following limit?
a.
b.
c.
d.
0
0.87
1
5
30. What is the partial derivative with respect to “x” of the following function?
31. What is the result of the following indefinite integral?
10
32. What is the result of the following indefinite integral?
33. For the three vectors, what is the value of the following product?
a.
b.
c.
d.
0
64
80
216
11
34. What is the angle between the two given vectors?
35. What is the determinate of the following matrix?
a.
b.
c.
d.
-8
-4
0
4
36. The second and sixth terms of a geometric progression are 3/10 and 243/160,
respectively. What is the first term of this sequence?
a.
b.
c.
d.
1/10
1/5
3/5
3/2
12
Engineering Ethics and Professional Practice:
(Study Without Using FE Manual)
1. According to the Model Rules, Section 240.15, Rules of Professional Conduct, licensed
professional engineers are obligated to:
a. Ensure that design documents and surveys are reviewed by a panel of licensed
engineers prior to affixing a seal of approval.
b. Express public opinions under the direction of an employer or client regardless of
knowledge of subject matter.
c. Practice by preforming services only in areas of their competence and in
accordance with the current standards of technical competence.
d. Offer, give, or solicit services directly or indirectly in order to secure work or
other valuable or political considerations.
2. As a professional engineer originally licensed 30 years ago, you are asked to evaluate a
newly developed computerized control system for a public transportation system. The
owner requires a currently licensed engineer to evaluate the system. You may accept this
project if: Select all that apply.
a. You are competent in the area of computerized control systems.
b. You professional engineering license has lapsed, but you have two FE interns
working for you.
c. You took a transportation course in college.
d. You have regularly attended meetings of a professional engineering society.
e. You have another licensed engineer work for you who is competent in this area,
and he/she will conduct all related work and stamp the related design.
3. An engineer testifying as an expert witness in a product liability case should:
a. Answer as briefly as possible only those questions posed by the attorney’s.
b. Provide an evaluation of the character of the defendant.
c. Provide a complete and objective analysis within his or her area of competence.
d. Provide information on the professional background of the dependent.
4. A lien is a:
a. Claim on property for a payment of debt.
b. Requirement that a contractor secure a performance bond for a contract.
c. Requirement that a contractor secure a payment bond for a project.
d. Claim for damages for a lack of specific performance.
13
5. One of the responsibilities of the principal contractor in construction projects before
commencing with work is to have risk assessments performed. Which one of the
following constitutes a risk assessment?
a. Appointment of a full or part-time construction health and safety officer.
b. Plan to mitigate or reduce risks.
c. Appoint a full-time competent employee.
d. Appoint construction supervisors.
6. A recently finalized regulation impacts a design contract that you have already signed
with a company for the construction of a new copper smelter. In order to comply with the
regulation, the cost on the project would need to be increased. What are you ethically
obligated to do?
a. Nothing, as the design for the facility is fluid.
b. File an amendment to the bid detailing the impact of the regulation and
subsequent cost increase after notifying the company.
c. Add in cost increase to the final invoice.
d. Consider the smelter grandfathered in to previous regulations, and a redesign
should not be necessary.
7. A civil engineer with 10 years of experience reads a story in his local newspaper about
the planned construction of a landfill in an area where be believes significant damage will
be caused to a nearby wetland. What would be an acceptable course of action?
a. The engineer should form a grassroots environmental movement to stop the
project.
b. The engineer should start a petition to try and delay the project.
c. The engineer is not directly involved in the project, so it is none of his concern.
d. The engineer should contact the appropriate agencies to gather more information
and data on the project before making a decision on what to do.
8. When may professional engineers make political donations?
a. At no time.
b. Only if it is for current, past, or future influence.
c. Only if all donations are made as an individual and do not represent a firm or
entity.
d. Only below specified amounts.
9. Which of the following is not an ethics violation?
a. Signing plans/blueprints without having first designed and/or checked the plans.
b. Revealing confidential information about a product without first obtaining
permission.
c. Granting a contract to a company for which the professional is an officer while
concurrently serving on the board issuing the grants.
d. Any individual accepting fees from contractors hired for a project.
14
10. In the event of an ethical content, to whom does the engineer hold the least ethical
responsibility:
a.
b.
c.
d.
The employer
The client
The consumer
Society
11. Who owns the rights to inventions that arise during work for a client if no prior
specifications regarding inventions are made?
a.
b.
c.
d.
The inventor
The inventor’s company.
The client
The state
12. Which of the following is not an ethical violation?
a. Designing a product to fail in a specified number of years.
b. Charging a premium for a superior product.
c. Using proceeds from one product in order to sell another product below fair
market price.
d. All of the above are ethical violations.
13. A professional engineer is the principal at an engineering company and has multiple
designers and engineers working on a project. Based on the Model Code of Ethics, select
all of the instances where it is appropriate for the engineer to sign and seals plans
associated with this project
a. The engineer may sign and seal plans which he personally prepared and did the
design.
b. The engineer may sign and seal plans if the design was developed by employee of
his firm, if a general review is preformed.
c. The engineer may sign, and seal drawings prepared by other professional
engineers that are working under his direct supervision and responsible charge,
and are reviewed in detail.
d. The engineer may sign, and seal plans prepared by other unlicensed designers that
are working under his direct supervision and responsible charge, and are reviewed
in detail.
e. The engineer may sign and seal drawings for coordination of multiple disciplines
if each technical segment is signed and sealed by a licensee responsible for the
respective technical segments.
f. The engineer may sign, and seal designs prepared by other licensed engineers as
the design engineer in responsible charge.
15
14. An engineer is retained to preform an inspection of asphalt on a bridge. During the
inspection, the engineer notices a potential defect in structural wall that may have
contributed to a fatal accident that occurred on the bridge in the past year. The engineer
notes that this information in his field notes and then notifies his client of the potential
defect. The client then notifies the public agency that owns the bridge. At the request of
the public agency, the engineer does not include the information about the wall in his
final report on the asphalt inspection, but the engineer does retain the information in his
field notes.
Which of the following statements best captures the ethical considerations presented?
a. The engineer acted ethically as the potential defect was raised to the appropriate
parties for further consideration but was not included in the report since it was
speculation and not based on actual design calculations, testing our evaluation by
a competent professional.
b. The engineer acted ethically to notify the agencies, but acted unethically in not
including the potential wall defect in the final report as this information should be
documented to ensure further evaluation is performed.
c. The engineer acted unethically by not preforming further analysis of the potential
defect to determine the adequacy of the bridge.
d. The engineer acted unethically, since ignoring the potential defect and leaving it
out of the final report could jeopardize the health, safety, or welfare of the public
and the engineer has an obligation to document the potential defect to appropriate
legal authorities.
16
15. An engineer is retained to preform a routine mine inspection. Upon arriving at the site,
the engineer realized he forgot his safety boots and will be unable to enter the mine to
preform the inspection. Due to the remote nature of the site, the mine company routinely
provides visitors to the site with required personal protective equipment including boots
for use at the site. The engineer recognizes that accepting the boots will violate his
company’s code of ethics since the company prohibits accepting gifts that have value of
more than $100:
Select all of the following approaches that would be considered ethical:
a. The engineer may accept the boots and is not obligated to notify his employer as
the boots are nominally more than $100. By accepting the boots, the engineer will
avoid costs associated with delaying the inspection, resulting in a net savings to
the company.
b. The engineer may accept the boots and is obligated to notify his employer since
the boots are more than $100 threshold set by the employer.
c. The engineer may use the boots and return them after the inspection. The engineer
is not obligated to notify his employer since the boots were used and returned.
d. The engineer may decline the boots and request that the inspection be postponed.
e. The engineer is not obligated to disclose his forgetting his boots and should
postpone the inspection without the need for further explanation.
f. The engineer should proceed with the inspection and forego the safety boot
requirement since a personal impact and does not affect the safety of others.
16. Engineer A was the primary engineer with direct control for a design of a project at Firm
X. When the project was in final review, i.e., essentially complete, Engineer A left to
work at Firm Y. prior to leaving, Engineer A did not sign or seal the drawings as the
design was not fully complete. A principal from Firm X asks Engineer A to sign and seal
the drawings.
An ethical response for Engineer A would be:
a. To ignore the request as he has no obligation to the former employer.
b. To refuse to sign and seal the drawings as he no longer works at Firm X and is no
longer in direct control of the design.
c. To request a nominal fee to review the final changes and to sign and seal the
drawings.
d. To request that the contract be transferred to his new firm due to professional
liability concerns.
17
17. Experience requirements that must be satisfied for individuals seeking professional
licensure typically include all the following except:
a. Eights years of progressive experience for students that graduated from an
EAC/ABET-accredited engineering program with a qualifying associates degree.
b. Four years of progressive experience for students that graduated from an
EAC/ABET-accredited engineering program with a qualified bachelor’s degree.
c. Three years of progressive experience for students that graduated from an
EAC/ABET-accredited engineering program with a qualifying master’s degree.
d. Two years of progressive experience for students that graduated with a qualifying
doctoral degree in engineering.
18. The profession of engineering requires all of the following except:
a.
b.
c.
d.
Special Knowledge
Special Privileges
Special Responsibilities
Special Powers
19. Obtaining a professional engineering license in a given state indicates which of the
following:
a. The licensee is minimally qualified to practice engineering.
b. The licensee is an expert in their respective field of examination.
c. The licensee may accept professional services contracts only for which they are
insured.
d. The licensee is qualified to preform each assignment provided by his employer.
20. A state licensing board could revoke a professional engineer’s license for which the
following:
a.
b.
c.
d.
Evidence of alcoholism.
Defaulting on a home mortgage.
Issuing public opinions based on facts.
Running for a political office.
18
21. The three main requirements necessary for a valid contract are typically:
a.
b.
c.
d.
Design, Bid, Build
Offer, Acceptance, Consideration
Design, Solicitation, Bid
Solicitation, Offer, Build
22. Engineering Firm X holds professional services contracts with private companies Y and
Z. The project work at Firm X has exceeded the budget for Company Y and supervisor A
directs Engineer B to charge future time to the budget of Company Z, which is well under
budget.
a. Charge time as directed to Company Z.
b. Charge time to Company Y and ignore Supervisor A’s directive.
c. Charge time to Company Y ad communicate concerns with incorrectly charging
time to Supervisor A and firm principals if the directive does not change.
d. If convinced that Supervisor A and Firm X is acting unethically, document the
process, resign from Firm X and report the unethical practices.
e. Contact Company Y and Z to suggest transferring the contracts from Firm X
directly to Engineer B due to internal ethical concerns with billing and
misappropriation of funds.
f. Notify the press.
19
Engineering Economics:
1. A company borrows $100,000 today at 12% nominal annual interest. The monthly
payment of a 5-year loan is most nearly:
a. $1,667
b. $2,200
c. $3,100
d. $12,000
2. You must choose between four pieces of comparable equipment based on the costs and
salvage values given below. All four pieces have a life of 8 years.
Parameter
First Cost
Annual Cost
Salvage Value
A
$25,000
$8,000
$2,500
B
$35,000
$6,000
$3,500
C
$20,000
$9,000
$2,000
D
$40,000
$5,000
$4,000
The discount rate is 12%. Ignore taxes. The two most preferable equipment pieces and
the approximant difference between their present worth values based upon least cost are:
a.
b.
c.
d.
A and C, $170
B and D, $170
A and C, $234
B and D, $234
3. A company can manufacture a product using hand tools. Tools will cost $1,000, and the
manufacturing cost per unit will be $1.50. As an alternative, an automated system will
cost $15,000 with a manufacturing cost per unit of $0.50. With an anticipated annual
volume of 5,000 units and neglecting interest, the payback period (years) to invest in the
automated system is most nearly:
a. 2.0
b. 2.8
c. 3.6
d. 15.0
20
4. A construction company bought a new rubber-tire loader and is preforming a risk analysis about
whether to purchase insurance. The construction company paid $100,000 for the loader. The
annual cost for the insurance premium is $2,000, and the deductible is $1,000. The risk options
to purchase or to not purchase insurance are as follows:
•
•
•
0.88 probability of no accident
0.11 probability of a small accident at a cost of $800
0.01 probability of a total loss of the loader
The best option and projected cost savings are:
a.
b.
c.
d.
Purchase insurance and save $990.
Purchase insurance and save $1,088.
Do not purchase insurance and save $1,010.
Do not purchase insurance and save $2,098.
5. A tractor cost $7,500. After 10 years it has a salvage value of $5,000. Maintenance cost
are $500 per year. If the interest rate is 10%, the equivalent uniform annual cost is most
nearly:
a. $500
b. $750
c. $1,400
d. $2,000
6. If the sum of $12,000 is borrowed and the debtor is obligated to pay the creditor $900 for
each year the loan is in existence, then, the simple interest is most nearly:
a. 2.0%
b. 5.0%
c. 7.5%
d. 12.5%
7. If a one-time amount of $500 is invested at an interest rate of 8% per year, what is the
future worth at the end of 30 years?
8. If you need to have $800 in savings at the end of 4 years, how much do you need to
deposit today, assuming 5% annual interest?
9. A company borrows $100,000 today on a 5-year loan at 12% nominal annual interest,
compounded monthly. What would the monthly payment be?
21
10. The Powerball was won by a single individual. The individual was given two choices:
receive 26 payments of $7 million each year, with the first payment to be made now; or
receive a single equivalent lump-sum payment. If the state uses an interest rate of 4% per
year, the amount of the lump sum payment closest to:
a.
b.
c.
d.
$72 million
$109 million
$116 million
$135 million
11. If $10,000 is borrowed now at 10% per year interest, the balance at the end of year 2 after
payments of $3,000 in years 1 and 2 will be closest to:
a.
b.
c.
d.
$4,100
$5,800
$6,100
$7,300
12. If a company wants to have $100,000 in a contingency fund 10 years from now, the
amount the company must deposit each year in years 6 through 9, at an interest rate of
10% per year, is closest to:
a.
b.
c.
d.
$19,591
$20,614
$21,547
$22,389
22
13. The present worth of machine “X” (assuming 10% annual interest) is closest to:
a.
b.
c.
d.
$-65,270
-$87,840
-$103,910
-$114,310
14. An interest rate of 12% per year, compounded monthly, is closest to an effective rate per
year of:
a.
b.
c.
d.
12.08%
12.28%
12.48%
12.68%
15. A machine with a 5-yar life has a first cost of $50,000 and a $10,000 salvage value. Using
straight-line depreciation, the book value at the end of year 3 will closest to:
a.
b.
c.
d.
$8,000
$12,000
$24,000
$26,000
16. A machine with a 5-year life has a first cost of $50,000 and a $20,000 salvage value.
Using MACRS depreciation, the book value at the end of year 2 will be closest to:
a.
b.
c.
d.
$10,000
$16,000
$24,000
$30,000
23
17. A new engineer decides to invest $6,000 each year into a retirement savings account. The
engineer continues this practice for a 30-year period and earns on average 10% a year.
The amount at the end of 30 years is most nearly:
a.
b.
c.
d.
$200,000
$990,000
$1,620,000
$3,140,000
18. A new engineer has a goal of investing enough money into a retirement account to have
the equivalent of $1,000,000 in today’s dollars at retirement in 30 years. Assume a rate of
return on the investment of 10% per year and average inflation of 2.0% a year, the
amount that should be invested annually is most nearly:
a.
b.
c.
d.
$7,000
$9,000
$11,000
$13,000
19. A piece of equipment will have an initial cost of $125,000 to purchase. It is assumed that
maintenance costs will begin at a base level of $2,000 in the first year, increase to $2,500
in year two, and to continue to increase at $500 each year through year 10. The
equipment will have a salvage value of $12,000 after 10 years. Using an interest rate of
8%, the present worth of the equipment cost is most nearly:
a.
b.
c.
d.
$138,000
$142,000
$146,000
$157,000
24
20. Interest on a loan is 8% per year compounded each month. The effective annualized
interest rate is most nearly:
a.
b.
c.
d.
8%
8.1%
8.3%
8.7%
21. A piece of equipment with an initial cost of $120,000 is expected to have a salvage value
of $15,000 after its 5-year service life is depreciated using the straight-line method. The
equipment’s book value at the end of year three is most nearly:
a.
b.
c.
d.
$52,000
$55,000
$57,000
$60,000
22. A solar project is expected to have an initial cost of $2 million, with an annual operations
and maintenance cost $50,000. Profits for the project have been estimated at $250,000
per year over a 25-year lifespan. Using an interest rate of 8% per year, the benefit to cost
ratio for this project is most nearly:
a.
b.
c.
d.
0.95
1.00
1.05
1.10
23. A piece of equipment with an initial cost of $120,000 is expected to have a salvage value
of $15,000 after its 5-year service life is depreciated using the MACRS method. The
deprecation charge for year three is most nearly:
a.
b.
c.
d.
$20,000
$21,000
$23,000
$24,000
25
24. Two alternatives are being considered for procuring a part. An interest rate of 8% will be
used for each alternative. These alternatives are presented as follows:
Method A: Involves purchasing equipment at an initial cost of $100,000, with a 5-year
equipment life, $5,000 equipment salvage value, and an operating cost of $15,000 per
year. In addition, each part will cost $18 to make.
Method B: Involves purchasing parts from a supplier for $32 a part.
a.
b.
c.
d.
2800
2950
3100
3250
25. Four levels of quality are being considered for equipment to produce a part. The initial
cost and repair cost ad probability of equipment failure in any given year I presented in
the table below. If this equipment must be used for 10 years and an interest rate of 6% is
used, the most economical option is most likely:
a.
b.
c.
d.
Option A
Option B
Option C
Option D
26
Statics:
1. The magnitude (N) of the resultant of the three coplanar forces A, B, and C, is most
nearly:
a.
b.
c.
d.
7.0
7.8
9.2
10.3
2. A heavy roller is held in equilibrium on a frictionless plane AB by the force F, as
shown. Which diagram correctly shows a vector polygon of the forces acting on the
roller?
a.
b.
c.
d.
Option A
Option B
Option C
Option D
27
3. Select the location on the x-axis where an additional load must be placed in order to
achieve equilibrium of the L-shaped bar.
4. The figure below shows a simple truss. Which members in the truss have no (zero)
force in them?
a.
b.
c.
d.
BG, CG, CF, CE
BG, CE
CG, CF
CF
28
5. Consider the following graph:
Which of the following expressions gives the distance from the y-axis to the centroid of
the shaded area?
31
a.
b.
c.
3
∫0 3𝑥 3 𝑑𝑥
1
∫0 (𝑥+3𝑥 2 )𝑑𝑥
3
1
3
1
3
1
3
1
∫0 (𝑥 2 −3𝑥 3 )𝑑𝑥
∫0 (𝑥−3𝑥 2 )𝑑𝑥
∫0 (𝑥−3𝑥 2 )𝑑𝑥
∫0 (𝑥−3𝑥 2 )𝑑𝑥
3 1
d.
1
∫0 (2𝑥 2 +3𝑥 3 )𝑑𝑥
3
1
∫0 (𝑥−3𝑥 2 )𝑑𝑥
29
6. The moment of inertia (in4) of the area about the x’ axis (Ix’) is most nearly:
a.
b.
c.
d.
78.0
78.6
118.5
138.8
7. In the figure below, the coefficient of static friction between the block and the
inclined plane is 0.25. The block is in equilibrium. As the inclined plane is raised, the
block will begin to slide when:
a.
b.
c.
d.
Sin ɵ = 1.0
Cos ɵ = 1.0
Cos ɵ = 0.25
Tan ɵ = 0.25
30
8. Three forces act as shown below. The magnitude of the resultant of the three forces
(N) is most nearly:
a.
b.
c.
d.
140
191
370
396
9. What is most nearly the magnitude of the resultant of these forces on the eyebolt?
a.
b.
c.
d.
2.5 lbs
11.3 lbs
19.9 lbs
22.6 lbs
31
10. A sign has a mass of 150 kg. The sign is attached to the wall by a pin at point B and is
supported by a cable between points A and C. Determine the tension in the cable.
a.
b.
c.
d.
1875 N
2450 N
3750 N
5000 N
11. What are the x- and y- coordinates of the centroid of the area?
a.
b.
c.
d.
3.40 cm; 5.60 cm
3.50 cm; 5.50 cm
3.93 cm; 4.79 cm
4.00 cm; 5.00 cm
32
12. Forces F1 = 220 kN and F2 = 240 kN act at the angles given below. When these
forces are added together, the magnitude of their resultant (not shown) is most nearly:
a.
b.
c.
d.
190 kN
360 kN
380 kN
440 kN
13. The magnitude of force F at distance x as shown below that will cause vertical and
rotational equilibrium for the system is most nearly:
a.
b.
c.
d.
F = 121 kN, x = 3.9 m
F = 121 kN, x = 4.2 m
F = 154 kN, x = 3.9 m
F = 154 kN, x = 4.2 m
33
14. The forces shown below can be replaced by a single equivalent moment. The
magnitude of an equivalent moment is most nearly:
a.
b.
c.
d.
50 kN-m
110 kN-m
380 kN-m
440 kN-m
15. A rigid body with mass of 1000 kg and applied loads is shown below. The magnitude
of the resultant force at support A to maintain equilibrium of the rigid body below is
most nearly:
a.
b.
c.
d.
60 kN
70 kN
130 kN
140 kN
34
16. Consider the cable system below that supports the hung load indicated. Ignore selfweight. The magnitude of the force P to maintain equilibrium with the geometry
indicated is most nearly:
a.
b.
c.
d.
55 lbs
250 lbs
255 lbs
350 lbs
17. Consider the truss and loading shown below. Ignore self-weight. The magnitude of
the force in member AC due to the applied loads is most nearly:
a.
b.
c.
d.
8 kN
22 kN
25 kN
39 kN
35
18. Consider the rigid frame and applied loads below. Ignore self-weight. The magnitude
of the vertical reaction at D due to the applied loads is most nearly:
a.
b.
c.
d.
18 kips
22 kips
28 kips
36 kips
19. For the figure shown below, the location of the centroid, y, with respect to the X-axis
is most nearly:
a.
b.
c.
d.
5.0 mm
5.2 mm
5.5 mm
6.0 mm
36
20. The moment of inertia about the X-X axis of the shape below is most nearly:
a.
b.
c.
d.
270 cm^4
280 cm^4
290 cm^4
300 cm^4
21. The moment of inertia about the X-X axis of the shape below is most nearly:
a.
b.
c.
d.
90 cm^4
100 cm^4
110 cm^4
120 cm^4
37
22. Two blocks rest on a horizontal surface with one block on top of the other. The
surface between the blocks has been intentionally roughened so that the coefficient of
friction between blocks is 0.55. The coefficient of friction between the bottom block
and the horizontal surface is 0.40. The top block is restrained so that it cannot move
horizontally. The force P that is required to move the bottom block is most nearly:
a.
b.
c.
d.
6.7 kips
7.5 kips
7.9 kips
9.4 kips
23. A block with a mass of 200 kg rests on an inclined plate with an angle of 15 degrees.
The coefficient of static friction between the body and the plane is 0.35. A force P acts
horizontally through the center of mass of the body. The magnitude of force that will
cause motion to begin up the plane is most nearly:
a.
b.
c.
d.
1100 N
1200 N
1300 N
1400 N
38
Dynamics:
1. A boat accelerates at a constant rate of 12 ft/sec2. the boat travels 140 ft while its speed
changes to 60 ft/sec. the initial velocity (ft/sec) was most nearly:
a. 3.7
b. 5.0
c. 15.5
d. 31.0
2. A small rotating robotic arm weighs 8 N and has a mass radius of gyration of 4.0 cm. The
mass moment of inertia (kg*cm2) is most nearly:
a. 13.0
b. 32.0
c. 128
d. 256
3. A 5-kg block is sliding along a frictionless surface and is an acted on by a constant force
P of 20 N. the time (seconds) when the block is moving at 18 m/s is most nearly:
a.
b.
c.
d.
0.22
1.83
4.50
72.0
4. During impact of two objects, which of the following is true?
a. Energy is never conserved.
b. Energy is always conserved.
c. Momentum is never conserved.
d. Momentum is always conserved
39
5. A particle starting from rest experienced an acceleration of 3 m/s^2 for 2 s. The particle
then returned to rest in an additional distance of 8m. Assuming all accelerations were
uniform, what was the total time elapsed for the particle’s motion?
a.
b.
c.
d.
2.67 s
4.00 s
4.67 s
5.33 s
6. A 550 kg mass initially at rest is acted upon by a force F(t) = 50e^t, expressed in N. What
is the displacement of the mass at t = 4 s?
a.
b.
c.
d.
4.51 m
19.5 m
2466 m
3900 m
7. A 2 kg ball of clay moving at 40 m/s collides with a 5 kg ball of clay moving directly
toward the first ball with a velocity of 10 m/s. What is the final velocity if both balls stick
together after the collision?
a.
b.
c.
d.
4.29 m/s
23.0 m/s
30.0 m/s
42.9 m/s
8. A vehicle is moving uphill at a speed of 30 mph on a +2% grade. If a braking
deceleration of 10.0 ft/sec^2 is applied, the time it will take the vehicle to stop in seconds
is most nearly:
a.
b.
c.
d.
2.1
2.8
4.1
4.4
40
9. A disc is rotating in a clockwise direction with a constant counterclockwise acceleration
applied. At a time of 2 seconds, the angular velocity is 12 rad/sec and at 4 seconds, the
angular velocity is 9 rad/sec. The time in seconds (from time 0) that it takes the disc to
stop is most nearly:
a.
b.
c.
d.
8
10
12
16
10. In a carnival, a dirt bike launches off a ramp at an angle of 20 degrees at a speed 17.5
meters/sec. Another ramp of the same height is to be placed some horizontal distance
away from the first ramp for the bike to land. The distance the second ramp should be
placed away from the first ramp is most nearly:
a.
b.
c.
d.
18 m
19 m
20 m
21 m
11. Vehicle A is travelling at a speed of 90 km/hr along a highway. A side ramp with a radius
of 210 meters (to the centerline of travel) merges into the highway. A second vehicle,
Vehicle B, is traveling at 72 km/hr along the ramp at the location indicated below. Both
vehicles are 6 m long, and the speeds are maintained. When the center of Vehicle B
arrives at the PT, the front bumper of B will most nearly be:
a.
b.
c.
d.
18 m behind the back bumper of Vehicle A.
12 m behind the back bumper of Vehicle A.
6 m behind the back bumper of Vehicle A.
0 m behind the back bumper of Vehicle A.
41
12. A rod and cylinder are welded together to form a rigid assembly. They are supported by a
frictionless pin at one end and held horizontal. The rod diameter is 2-cm and the cylinder
diameter is 10-cm. The mass of the rod is 2.5 kg and the mass of the cylinder is 12 kg.
The mass moment of inertia about the point of rotation at the pin A is most nearly:
a.
b.
c.
d.
0.5 kg-m^2
5.5 kg-m^2
15.1 kg-m^2
15.4 kg-m^2
42
Mechanics of Materials:
1. The shear diagram for a particular beam is shown below. All lines in the diagram are
straight. The bending moment at each end of the beam is zero, and there are no
concentrated couples along the beam. The maximum magnitude of the bending
moment (kN*m) in the beam is most nearly:
a.
b.
c.
d.
8
16
18
26
2. The pressure gauge in a air cylinder reads 1,680 kPa. The cylinder is constructed of a
12-mm rolled-steel plate with an internal diameter of 700 mm. The tangential stress
(MPa) inside the tank is most nearly:
a. 25
b. 50
c. 77
d. 100
3. A 1-ft rod with a diameter of 0.5 in. is subjected to a tensile force of 1,300 lb and has
a elongation of 0.009 in. The modulus of elasticity (ksi) of the material is most
nearly:
a. 740
b. 884
c. 8,840
d. 10,000
43
4. The maximum inplane shear stress (ksi) in the element shown below is most nearly:
a.
b.
c.
d.
10
14.1
44.1
316
5. Based on the given stress-strain curves, which material has the largest plastic
deformation?
a.
b.
c.
d.
Material A
Material B
Material C
Material D
44
6. The piston of a steam engine is 50 cm in diameter, and the maximum steam gauge
pressure is 1.4 MPa. If the design stress for the piston rod is 68 Mpa, its crosssectional area (m^2) should be most nearly:
a.
b.
c.
d.
40.4 * 10-4
98.8 * 10-4
228.0 * 10-4
323.0 * 10-4
7. Which of the following is true when a circular shaft is subjected to torsion only?
a. Maximum shear stress occurs at the outermost fibers.
b. Maximum shear stress occurs at the center of the shaft.
c. Constant shear stress occurs throughout the shaft.
d. No shear stress is present throughout the shaft.
8. A 10 kg axial load is uniformly carried by an aluminum alloy pipe with an outside
diameter of 10 cm and an inside diameter of 9.6 cm/ The pipe is 1.2 m long. Young’s
modulus for the aluminum alloy is 75000 MPa. Neglecting the effects of buckling,
how much is the pipe compressed?
a.
b.
c.
d.
0.00026 mm
0.0026 mm
0.11 mm
25 mm
45
9. A steel pipe fixed at one end is subjected to a torque of 100,000 N-m. The pipe is
originally 3 m in length with an outside diameter of 35 cm and a wall thickness of 1
cm. Steel has a modulus of elasticity of 210 GPa and a Poisson’s ratio of 0.30. What
is the resulting angle of twist of the pipe?
a.
b.
c.
d.
0.0004 rad
0.0008 rad
0.012 rad
0.024 rad
10. A beam has a triangular cross-section as shown. What is the maximum compressive
stress in the beam?
a.
b.
c.
d.
7.8 MPa
15.6 MPa
23.4 MPa
31.3 MPa
11. A rectangular beam 4 cm wide and 6 cm high is subjected to a shear of 7,000 N at a
particular location. The beam is constructed of 2014-T3 aluminum. What is most
nearly the maximum shear stress at that location?
a.
b.
c.
d.
290 N/cm^2
440 N/cm^2
520 N/cm^2
660 N/cm^2
46
12. Given the following, what is most nearly the maximum shear stress?
a.
b.
c.
d.
100 MPa
160 MPa
200 MPa
210 MPa
13. A rectangular steel bar 37.5 mm wide and 50 mm thick is pinned at each end and
subjected to axial compression. The bar has a length of 1.75 m. The modulus of
elasticity is 200 GPa. What is the critical buckling load?
a.
b.
c.
d.
60 kN
93 kN
110 kN
140 kN
14. A beam with a width of 50 cm and depth of 100 cm is subjected to the loading below.
The magnitude of the moment that causes the maximum bending stress in the beam
due to the applied loads (ignore self-weight) is most nearly:
a.
b.
c.
d.
10 kN-m
15 kN-m
20 kN-m
25 kN-m
47
15. A beam with a width of 6 inches and depth of 12 inches is subjected to the loading
below. The magnitude of the moment that causes the maximum bending stress in the
beam due to the applied loads (ignore self-weight) is most nearly:
a.
b.
c.
d.
50 kip-ft
56 kip-ft
100 kip-ft
112 kip-ft
16. The shear force diagram of a beam is given below where the shear is in kips and
distances are measured in feet. No concentrated moments are applied to the beam and
all lines are straight. The section is rectangular. The magnitude of the moment that
causes maximum bending stress in the beam is most nearly:
a.
b.
c.
d.
32 kip-ft
65 kip-ft
80 kip-ft
92 kip-ft
48
17. The following beam is supported by two steel cables that each a modulus of elasticity
of 29,000 ksi and a cross-sectional area of 0.1 ft^2. In addition to supporting the
applied load, the weight of the beam is 200 lbs. The strain in cable A is most nearly:
a.
b.
c.
d.
0.2
0.002
2*10^-6
2*10^-9
18. A clevis is used to connect a steel bracket with a block of wood is shown below. If the
force P = 15 kN and the bolt has a diameter of 20 mm, the average shear stress in the
bolt along line A due to the load P is most nearly:
a.
b.
c.
d.
12 MPa
24 MPa
48 MPa
96 MPa
19. The maximum torsional shear stress developed in a 10-cm diameter solid steel shaft
subjected to an applied torque of 50 kN-m is most nearly:
a.
b.
c.
d.
0.25 MPa
3 MPa
30 MPa
255 MPa
49
20. The maximum angle of twist developed in a 4-m long aluminum shaft with a diameter
of 12-cm when subjected to a torque of 50 kN-m is most nearly;
a.
b.
c.
d.
0.40
1.40
5.40
220
21. A composite member is shown below with properties and dimensions given. The
magnitude of the axial force P that will cause the total length of the member to
increase by 5 mm is most nearly:
a.
b.
c.
d.
0.01 kN
0.1 kN
40 kN
40,000 kN
22. A copper pipe with a diameter of 19 mm and thickness of 1 mm is rigidly installed
between two fixtures that are 4 m apart at a temperature of 20 degrees Celsius. After
the initial installation, there is no axial stress in the pipe. If temperature of the liquid
used in the pipe is 5 degrees Celsius, the magnitude of the stress in the pipe is most
nearly:
a.
b.
c.
d.
5 MPa
29 MPa
48 MPa
53 MPa
50
23. The bracket shown in the figure below supports a force as shown. Assume buckling
will not control. The cross-section of the column is 10-cm * 10-cm square and the
force P = 15 kN. The maximum combined stress at the base of the column at point A
due to force P is most nearly:
a.
b.
c.
d.
1.5 MPa
43.5 MPa
45.0 MPa
46.5 MPa
24. An element experiences the axial and shear stresses indicated in the figure below. The
principal stresses are most nearly:
a.
b.
c.
d.
30 MPa, 90 MPa
0 MPa, 125 MPa
-3 MPa, 122 MPa
-62 MPa, 62 MPa
51
Materials:
1. Ready-mixed concrete being delivered to a jobsite is found to have a slump less than
specified. Without compromising strength, which of the following is the most
appropriate corrective action?
a. Decrease the amount of water in the mix before the truck leaves the ready-mix
plant.
b. Increase the water to the mix in the truck at the jobsite before the concrete is
poured.
c. Add a water-reducing admixture to the mix in the truck at the jobsite before
the concrete is poured.
d. Increase the rotation speed of mixing drum while the truck is in transit to the
jobsite.
2. The test that measures the energy required to fracture a specimen at a given
temperature is the:
a. Brinell Test
b. Rockwell Test
c. Endurance Test
d. Charpy Test
3. In general, a metal with high hardness will also have:
a. Good Formability
b. High Impact Strength
c. High Electrical Conductivity
d. High Yield Strength
52
4. The following preliminary concrete mix has been designed assuming that aggregates
are in oven-dry condition. However, the aggregates used are in SSD condition.
Water = 305 lb/ yd3
Cement = 693 lb/ yd3
Course Aggregate (SSD) = 1,674 lb/ yd3
Fine aggregate = 1,100 lb/ yd3
The properties of the aggregates are:
The amount of water (lb/yd3) that would be used in the final mix is most nearly:
a.
b.
c.
d.
206
222
305
388
5. The solid line represents results from a uniaxial tension test. The slope of the dashed
line is associated with which physical property of the material?
a.
b.
c.
d.
Yield Strength
Yield Strain
Secant Modulus
Modulus of Elasticity
53
6. The amount of water specified in a concrete mix is typically based on which of the
following conditions for the aggregate?
a.
b.
c.
d.
Oven dry
Air dry
Saturated Surface dry
Moist
7. Aggregate used in hot mix asphalt should be in which of the following conditions?
a.
b.
c.
d.
Oven dry
Air Dry
Saturated Surface dry
Moist
8. Variables evaluated for the design of hot-mix asphalt include all of the following
except:
a.
b.
c.
d.
Aggregate
Asphalt binder
Ratio of aggregate to asphalt binder
Water
54
9. A concrete mix design is provided for a job with the following requirements per cubic
yard:
The moisture content of the coarse and fine aggregates is measured at 2% at the batch
plant on a given day. For the aggregate moisture contents given, the amount of water
that needs to be added to the mix design per cubic yard is most nearly:
a.
b.
c.
d.
207 lbs
231 lbs
272 lbs
313 lbs
10. A concrete mix design requires 593 pounds of cement per cubic yard and has a
maximum water-cement ratio specified as 0.45. Portland cement is the only
cementitious material in the mix. If a 10-cubic yard truck arrives on-site with the
batch ticket indicating 310 gallons of water were already included in the batch
(excess aggregate moisture plus added water), the minimum number of gallons
required to make the water-cement ratio exceed the specification is most nearly:
a.
b.
c.
d.
0 (the w/c ratio already exceeds 0.45)
5 gallons
10 gallons
15 gallons
55
Use the graph below for questions 11-12:
11. The ultimate tensile strength in this material is most nearly:
a.
b.
c.
d.
47,500 psi
50,000 psi
52,000 psi
78,500 psi
12. The modulus of elasticity of this material is most nearly:
a.
b.
c.
d.
5,500,000 psi
1,750,000 psi
24,000,000 psi
30,000,000 psi
56
13. Select the materials that exhibit approximate linear elastic behavior to the points
indicated:
a.
b.
c.
d.
e.
f.
g.
Steel up to the yield strength, Fy
Steel up to the ultimate tensile strength, Fu
Steel up to the failure strength, Ff
Concrete up to 50% of its maximum compressive strength, fc’/2
Concrete up to its maximum compressive strength, fc’
Concrete up to its maximum compressive strain, εcu
Concrete up to its modulus of rupture, fr
14. Steel reinforcement is typically added to concrete flexural members for all the
following reasons except:
a.
b.
c.
d.
To allow for increased ductility and deformation in the beam prior to failure.
To resist tensile forces developed due to the bending moment.
Because steel and concrete have similar coefficients of thermal expansion.
To eliminate tension cracking when bending moments exceeds the rupture
capacity of the concrete.
15. The modulus of elasticity of normal-weight concrete with a compressive strength of
fc’ = 4,000 psi consistent with ACI 318 requirements is most nearly:
a.
b.
c.
d.
1.1 * 10^5 psi
3.6 * 10^6 psi
3.8 * 10^6 psi
4.0 * 10^6 psi
16. Which of the following material properties can typically be used to describe wood?
a.
b.
c.
d.
Incombustible
Impermeable
Isotropic
Orthotropic
57
17. From the following list, select the properties and characteristics that have an impact
on the design tensile strength of sawn lumber:
a.
b.
c.
d.
e.
f.
Moisture Content
Repetitive Use
Temperature
Size
Flat Use
Load Duration
58
Fluid Mechanics:
1. The pitot tube shown below is placed at a point where the velocity is 2.0 m/s. The
specific gravity of the fluid is 2.0, and the upper portion of the manometer contains air.
The reading, h (m), on the manometer is most nearly:
a.
b.
c.
d.
20.0
10.0
0.40
0.20
2. If the standard density of water is 1,000 kg/m^3, a fluid having a specific gravity of 1.263
and an absolute dynamic viscosity of 1.5 kg/(m*s) has a kinetic viscosity (m^2/s) of most
nearly:
a.
b.
c.
d.
1.19 * 10-3
1.50 * 10-3
1.89 * 10-3
528
3. Archimedes’ principle states that:
a.
b.
c.
d.
The sum of the pressure, velocity, and elevation head is constant
Flow passing two points in a stream is equal at each point
The buoyant on a body is equal to the volume displayed by the body
A floating body displays a weight of fluid equal to its own weight.
59
4. A 1-in-diameter jet of 50℉ water is deflected 90o by an angled shoot as shown. The water
enters with a velocity of 25 ft/sec and freely exists into the atmosphere with the same
velocity. The forces (lb) in the x and the y directions of the chute are most nearly:
a.
b.
c.
d.
Fx = 0 , Fy = 0
Fx = 9.33 lb, Fy = 0
Fx = 0, Fy = 9.33 lb
Fx = 9.33, Fy = 9.33
5. A water tank is shown. Assume no minor loses in the discharge and a common coefficient
of discharge C = 0.6. What is the discharge velocity.
a.
b.
c.
d.
13.6
11.8
14.3
15.2
60
Surveying:
1. The value of angle A in the figure below is most nearly:
a.
b.
c.
d.
300 18’ 47”
320 47’ 50”
390 05’ 38”
420 35’ 09”
2. The area inside the quadrilateral, PC, PI, PT, and O equals 83,164 ft^2. The shaded area
(ft^2) between the circular curve and the tangents is most nearly:
a.
b.
c.
d.
2,879
3,577
5,407
8,286
61
3. The cross-sectional areas to be excavated (cut) at certain sections of a road project are as
follows:
Using the prismoidal method, the volume of earth to be excavated (yd^3) between
stations 4+35 and 5+65 is most nearly:
a.
b.
c.
d.
1,460
1,840
1,860
1,900
4. The term projected as it relates to the state plane coordinate system means that the:
a.
b.
c.
d.
The survey is inaccurate and needs to be corrected.
The survey points from found monuments need to undergo a unit conversion.
Handwritten coordinates are entered into computer software.
Earth’s curvature needs to be taken into account for survey calculations.
5. A total station is set up 5 ft above a benchmark that has an elevation of 820.50 ft. A slope
angle and slope distance of -30 15’ and 645.90 ft, respectively, are measured to a reflector
that is set up 4.25 ft above a hub at point B. Neglecting curvature and refraction, the
elevation (ft) of the hub at Point B is most nearly:
a.
b.
c.
d.
785.76
784.63
783.88
779.63
62
6. A backsight of 7.76 ft is taken on a turning point with an elevation of 2,325.58 ft. If the
foresight taken on the top of an construction pin is 4.25 ft, the elevation (ft) of the top of
the pin is most nearly:
a.
b.
c.
d.
2,313.57
2,322.07
2,329.09
2,337.59
7. Determine the azimuth and bearing for the image below:
8. Using the trapezoidal rule, what is most nearly the area of the region below?
a.
b.
c.
d.
3600 sf.
3800 sf.
4000 sf.
4200 sf.
63
9. Using the method of area by coordinates, what is most nearly the area of the shaded
region shown?
a.
b.
c.
d.
14.00
16.75
18.25
21.50
64
Water resources and Environmental Engineering:
1. A 20-acre parcel of land has a rainfall intensity of 1.5 in/hr and a rational method runoff
coefficient C of 0.10. The flow rate (cfs) for this site is most nearly:
a.
b.
c.
d.
3.0
5.0
7.5
9.0
2. A flow of 15.5 cfs enters the pipe system at A as shown, and exits at B and C. Pipe data
are given in the following table.
Assume all of the pipes are all at the same elevation. The head loss (ft) in pipe CB is most
nearly:
a.
b.
c.
d.
0.05
0.13
0.18
0.23
65
3. A pump station delivers wastewater from a sump at an elevation of 78 ft to a maintenance
hole with a water surface elevation 112 ft. The static head (ft) for this pump is most
nearly:
a.
b.
c.
d.
17
34
44
78
4. A 24-in. water distribution pipeline carrying 15 cfs flow branches at Point A into two
pipelines, 1 and 2, both with Hazen-Williams C of 130. Pipeline 1 has an 18-in. diameter
and is 2,400 ft long. Pipeline 2 has a 12-in. diameter and is 1,200 ft long. The branched
pipes join at Point B to a 24-in. pipe to carry the flow downstream. The flow (cfs) in
Pipeline 1 is most nearly:
a.
b.
c.
d.
5.0
10.0
12.9
15.0
5. A suppressed rectangular weir rises from the bottom of the pond to an elevation of 37 ft.
The water is 50 ft deep, and the weir is 200 ft long. The flow (ft^3/s) of water over the
spillway is most nearly:
a.
b.
c.
d.
1,500
12,500
23,800
31,200
66
6. For a new development of 75 acres (0.117mi^2), the peak runoff for a 25-yr storm of 360
ft^3/s is to be limited to 180 ft^3/s through the use of a detention basin. Runoff (Q) is 3.4
in. Assume Type II rainfall. Using the TR-55 Method and figure below, the preliminary
estimate of the storage volume (ac-ft) is most nearly:
a.
b.
c.
d.
0.07
0.11
3.80
5.94
7. A 36-in diameter sewer is installed at a slope of 0.006 ft/ft. Assuming the roughness
coefficient (n) is constant with depth and equal to 0.015, the velocity (ft/s) of water in a
half-full pipe is most nearly:
a.
b.
c.
d.
4.3
5.8
6.3
10.1
67
8. Four monitoring wells, A,B,C and D, lie equidistant (200 ft) from a fifth well, E. The
depth to the water table is measured at each well and is shown below. The datum for the
top of the casing is equal for the five wells. Groundwater flow moves in which direction
from Point E?
a.
b.
c.
d.
South
East
North
West
9. A jar test is used to evaluate the efficiency of a coagulation process and allows the plant
operator to optimize which of the following parameters?
a.
b.
c.
d.
Alum Dosage
Temperature
Lime Dosage
Dissolved Oxygen
68
10. A residential development is composed of pavement, lawn and open area with CN values
given below. For a 100-year storm that produces approximately 7-inches of rainfall, the
discharge from the site (assuming no other inflow) is most nearly:
a.
b.
c.
d.
4.8 in.
5.1 in.
5.7 in.
7.0 in.
11. In stormwater management, the initial abstraction accounts for all the following except:
a.
b.
c.
d.
Infiltration
Evaporation
Retention
Runoff
12. A concrete-lined channel is used to convey water flow between point A at a surface
elevation of 510 m and point B at a surface elevation of 508 m above sea level over a
distance of 2 kilometers. The surface roughness coefficient of the is 0.012. The flow
conveyed by this channel in m^3/s is most nearly:
a.
b.
c.
d.
70
105
150
165
69
13. An 8-foot-wide rectangular channel carries 200 cubic feet per second of water at a depth
of 1.5 feet before entering a hydraulic jump. The water depth downstream of the jump is
most nearly:
a.
b.
c.
d.
2.4 ft.
2.7 ft.
3.4 ft.
4.4 ft.
14. A pump is used to lift water from a reservoir with a surface elevation of 210 feet to an
outlet elevation of 235 ft with a discharge pressure of 50 psi. The pump flow is 100
gal/min and uses a 2.5-inch diameter hose with a C value of 135. The distance from the
pump to the outlet is 200 feet. Head loss due to fittings is approximately 5 feet. To supply
100 gpm at 50 psi ate the outlet, the pump pressure in psi is most nearly:
a.
b.
c.
d.
20
40
50
70
15. A flow test is preformed at a fire hydrant top determine the flow rating at a pressure of 20
psi. The static pressure at the hydrant is 70psi. The test uses a hydrant with a 2.5 inch
orifice with a square outlet projecting into the barrel of the hydrant. A pitot tube of 45 psi
is observed during the test. The maximum flow rate that this system can provide at 20 psi
is most nearly:
a.
b.
c.
d.
875 gpm
1270 gpm
1560 gpm
3500 gpm
70
16. The purpose of an emergency spillway is most closely:
a. To lower reservoir levels in anticipation of a significant rainfall event that could cause
flooding.
b. To divert flows from a reservoir, if a dam safety inspection indicates a dam’s principal in
an unsafe condition.
c. To divert reservoir flows so that emergency responders can safely access a water body in
the event of a drowning or other serious injury.
d. To allow flow to pass that exceeds the capacity of the principal spillway and protect the
dam in the event of a flood.
17. A weir must be sized at a pond to pass flow into an emergency spillway for flood control.
Given a weir width of 10 ft, which is smaller than the width of the channel, the
approximant depth of flow required to pass 125 cfs is most nearly:
a.
b.
c.
d.
1’- 6”
2’- 0”
2’- 6”
3’- 0”
18. Characteristics that lead to eutrophication of a water body include all the following
except:
a.
b.
c.
d.
Nitrogen and Phosphorus rich runoff
Sediment deposition which reduces the volume of a water body
High levels of dissolved oxygen
An overabundance of plants and nutrients
71
19. Standard Stormwater Management Practices (SMPs) for water quality controls consider
all the following, except:
a. Capture and treat 100% of the water quality volume.
b. Achieve 80% reduction in TSS and 40% reduction in TP.
c. Maintain 100-year design storm peak site discharge flow to levels to a pre-construction
level.
d. Include a pretreatment mechanism and a maintenance plan.
20. To provide a minimum velocity, when half-full, of 2.0 ft/s in a 12-inch diameter sewer
pipe with an “n” value of 0.013, the drop per 100 ft must be most nearly:
a.
b.
c.
d.
0.02
0.15
0.20
0.44
21. The primary purpose of the federal National Discharge Pollutant Elimination System in
the United States is which of the following:
a.
b.
c.
d.
Limit and control pollutants from point source discharges to waters of the United States.
Develop new technologies to research and mitigate impacts of deleterious pollutants
Establish standards for maximum contaminant levels for safe drinking water.
Provide aid to comm unities to construct and maintain treatment plants for elimination of
pollutants.
22. An unseeded domestic wastewater BOD test is preformed. A 6-mL sample of wastewater
is diluted in a 300-mL test bottle. Initially, the dissolved oxygen content is measured as
8.0 mg/L. After 5 days, the dissolved oxygen is 4.0 mg/L. If the k-rate is 0.30 per day, the
ultimate BOD in mg/L is most nearly:
a.
b.
c.
d.
150
207
257
300
72
23. A chemical analysis of water sample indicates Ca++ is at a concentration of 10 mg/L and
Mg++ is at a concentration of 25 mg/L. The total hardness of the water expressed as
CaCO3 is most nearly:
a.
b.
c.
d.
35.0
58.5
102.5
127.5
73
Structural Engineering:
1. The 40-kip vertical load at Joint C in the steel truss shown below produces the forces
given in the accompanying table. The cross sectional area of each member is 4.0 in^2,
and the length of each member is given in the table. The elastic modulus of steel is
29,000 ksi. The downward vertical displacement (in.) of Joint C is most nearly:
a.
b.
c.
d.
1.046
0.294
0.132
0.102
2. The proportional limit and modulus of elasticity for a material are 40 ksi and 30,000 ksi,
respectively. A square column made from this material has a moment of inertia equal to
6.8 in.^4 and an area equal to 9in^2. Assume a pin-pin connected column so that the
effective length factor K is equal to 1.0. The maximum column length (in.) based on the
Euler formula is most nearly:
a.
b.
c.
d.
42.2
74.8
195.0
224.3
74
3. The frame in the figure below is:
a.
b.
c.
d.
Unstable
Stable and determinate
Indeterminate one degree
Indeterminate two degrees
75
4. Which combination of moment diagram and deflection shape most accurately
corresponds to the continuous beam with loading shown?
76
5. Which of the vertical-load influence lines shown below is correct for Member U2U3 of
the truss shown below?
a.
b.
c.
d.
Option A
Option B
Option C
Option D
77
6. The W21 * 57 steel beam shown in the figure has its compression flange laterally braced
at the one-third points over its full length. Assume Fy = 50 ksi and Cb = 1.0 for the
critical segment. The maximum factored load wu (kips/ft) that the beam can carry for this
length is most nearly:
a.
b.
c.
d.
2.658
3.360
4.302
4.778
7. According to the American Concrete Institute (ACI) 318-11, the value of ᶲ that should be
used in computing the design moment strength, ᶲMn for the beam section shown below is
most nearly:
a.
b.
c.
d.
0.80
0.81
0.84
0.90
78
8. In the truss shown, there is a pin connecting the members at each joint. The force (kips)
in Member CD is most nearly:
a.
b.
c.
d.
-81 (compression)
-113 (compression)
-122 (compression)
-169 (compression)
9. A reinforced concrete beam is subjected to a factored moment Mu = 648 ft-kips. For
concrete, fc’ = 4,000 psi. For steel fy = 60,000 psi. The beam is reinforced with eight #8
bars in two rows, positioned as shown in the figure. Assume that ᶲ = 0.90. The minimum
adequate overall width (b) for this beam is most nearly:
a.
b.
c.
d.
10
12
13
15
79
10. For the plane truss shown below, what is most nearly the axial force in member CG?
a.
b.
c.
d.
45.3 kip (Compression)
45.3 kip (Tension)
90.5 kip (Compression)
90.5 kip (Tension)
80
Geotechnical Engineering:
1. What is the area of the Atterberg chart provided is associated with elastic silt?
a.
b.
c.
d.
CH
CL
OL
MH
2. An undisturbed sample of soil has a specific gravity of solids of 2.70, a moisture content
of 10.5%, and a void ratio of 0.63. The degree of saturation is most nearly:
a.
b.
c.
d.
25%
45%
65%
85%
81
3. Direct shear test data of a sand are shown below:
The angle of internal friction is most nearly:
a.
b.
c.
d.
00
270
300
630
4. Subsurface exploration indicates that a level site has a 10-ft upper layer of sand. The
groundwater table is at the ground surface. The unit weight of the sand is 135 pcf. The
effective overburden stress (psf) at a depth of 10 ft is most nearly:
a.
b.
c.
d.
625
725
1,350
1,975
5. A 12-ft high retaining wall has backfill of granular soil with an angle of internal friction
of 300 and a unit weight of 125 pcf. The resultant Rankine active force (lb/ft) on the wall
is most nearly:
a.
b.
c.
d.
2,250
3,000
9,000
27,000
82
6. A consolidated, undrained triaxial shear test was preformed on an over consolidated clay
mix specimen with a diameter of 1.4 in. The test yielded a cohesion of 530 psf and an
angle of internal friction of 180. If the normal load at failure was 125 lb, the shear
strength (psi) of the soil is most nearly:
a.
b.
c.
d.
10
26
30
556
7. A strip footing having a width B = 2ft is to be constructed at ground surface (Df = 0).
Underlying the footing is sand having the following bearing capacity factors. Nc = 0 , Nᵧ
= 25, and Nq = 20. The unit weight of sand ᵧ = 120 pcf. The ultimate bearing capacity qult
(psf) of the footing is most nearly:
a.
b.
c.
d.
1,200
2,400
3,000
4,800
8. A three-story concrete building will be constructed on a vacant parcel in a city. The soil
boring log shows a 20-ft thick layer of loose soil over a 5-ft thick limestone layer. Which
of the following foundations will provide the least settlement for this building?
a.
b.
c.
d.
Spread Footing
Mats Foundation
Deep Foundation
Wall Foundation
83
9. A normally consolidated 10-ft clay layer is surcharged, which causes a decrease in
thickness. The coefficient of consolidation is 0.16 ft^2 per day and the time factor is 1.2
for U = 50%. The clay layer is confined between two layers of dense sand. The time
(days) required for 50% consolidation is most nearly:
a.
b.
c.
d.
5
38
188
750
10. A slope of clay-mix material experiences failure along a 100-ft long slip surface at an
angle of 270. The soil above the slip surface weighs 100 tons, has an angle of internal
friction of 200, and has a cohesion of 1.2 psi. The factor of safety at slope failure is most
nearly:
a.
b.
c.
d.
0.7
0.9
1.7
381.3
11. An undisturbed sample of clay has a wet weight of 220 lb, a dry weight of 205, and a
total volume of 1.73 ft^3. The solids have a specific gravity of 2.65. The void ratio is
most nearly:
a.
b.
c.
d.
0.24
0.40
0.61
1.00
84
12. A soil’s grain size distribution curve is as shown. Given that D60 = 0.49 mm and D10 =
0.19 mm, the coefficient of curvature is most nearly:
a.
b.
c.
d.
0.17
0.44
1.60
3.00
13. An inorganic soil has the following characteristics:
Using the Unified Soil Classification System, what is the soil’s classification?
a.
b.
c.
d.
GW
ML
MH
CH
85
14. For the soil profile shown, what is most nearly the effective stress at Point C?
a.
b.
c.
d.
92 kPa
128 kPa
186 kPa
222 kPa
15. A direct shear test is preformed on a dry silty sand. A normal stress of 150 kPa is applied
to a specimen with a diameter of 71 mm and a height of 25mm. The shear force at failure
is 276 N. What is most nearly the angle of internal friction?
a.
b.
c.
d.
15o
25o
35o
45o
86
16. A continuous footing is founded 3 feet below the ground surface in a clay for which γ =
125 pcf, c =1200 psf, and ө = 0o. If the factor of safety is to be at least 3.0, what is most
nearly the recommended allowable bearing capacity? For the purposes of this problem,
use Nc = 5.14, Nq = 1, and Nγ = 0.
a.
b.
c.
d.
2180 psf
3600 psf
6540 psf
9350 psf
17. A normally consolidated clay layer has a liquid limit of 45 and an initial effective stress
(at the midpoint of the layer) of 2000 psf. Placement of a sand fill over the layer causes a
vertical stress increase of 800 psf. Most nearly, how much will the void ratio at the
midpoint of the layer increase?
a.
b.
c.
d.
0.046
0.125
0.141
0.315
18. A 5-ft thick normally consolidated soil layer is located between two sand layers. Assume
an initial void ratio 0.900 and a compression index of 0.35. A surface load increases the
existing average stress in the layer from 1000 psf to 1500 psf. Most nearly, what is the
settlement of the clay layer?
a.
b.
c.
d.
0.033 in
0.160 in
0.263 in
1.960 in
87
19. A 10-ft. thick layer is drained by sand layers at the top and the bottom. It is to predicted
to settle a total of 2.0 inches under the stress increase due to a foundation load. The
coefficient of consolidation is 0.03 ft^2 / day. What is most nearly the settlement at the
end of year 1?
a.
b.
c.
d.
0.37 in
0.73 in
1.45 in
2.00 in
88
Transportation Engineering:
1. A highway profile is shown in the figure. If the design stopping sight distance is 600 ft,
the driver’s eye height above the roadway surface is 3.50 ft, and the height of an object in
the roadway to be avoided by stopping is 1.0 ft, the minimum design length (ft) of the
vertical curve is most nearly:
a.
b.
c.
d.
3,600
1,966
1,136
1,017
2. A flexible pavement system is to be designed using the AASHTO structural number
design method with the following criteria:
If the minimum thickness of the surfacing and aggregate base are used, the required
thickness (in.) of the aggregate subbase is most nearly:
a.
b.
c.
d.
4
5
6.5
8.5
89
3. A freeway lane has a volume of 1,400 vehicles/hr and an average vehicle speed of 45
mph. The time spacing (sec) between vehicles (center to center) is most nearly:
a.
b.
c.
d.
2.6
5.2
15
31
4. At an urban pedestrian crosswalk, the initial WALK signal is displayed for 6.0 sec, after
which a flashing DON’T WALK signal is displayed. The pedestrian walking speed is 3.5
ft/sec, and the street to be crossed is 31.5 ft wide. At the end of the green time, the
flashing DON’T WALK signal is terminated. The minimum length of time (sec) the green
must be displayed is most nearly:
a.
b.
c.
d.
6.0
9.0
12.5
15.0
5. An urban intersection is being reconstructed to address safety problems, at it is estimated
that the two mutually exclusive counter measures have a crash reduction factor of 0.25
and 0.15, respectively. If the expected number of crashs per year is 10 and noi significant
growth in traffic is anticipated, the expected numb er of avererage crashes per year after
reconstruction is most nearly:
a.
b.
c.
d.
3.6
4.0
6.0
6.4
90
6. A two-way stop-controlled intersections, the sight distance required for minor street
movements is determined by:
a.
b.
c.
d.
Approach sight triangles
Departure sight triangles
Stopping sight distance
Decision sight distance
7. For a given loading, soil conditions, and design life, which of the following pavement
types will most likely be the thinnest highway pavement design?
a.
b.
c.
d.
Hot-mix asphalt
Warm-mix asphalt
Portland Cement concrete
Composite hot-mix asphalt over Portland cement concrete
8. Which of the following statements about a basic freeway segment are true according to
the Highway Capacity Manual?
Select all that apply:
a. Freeway segments with 75-mpg free-flow speed experience a reduction in operating
speeds at a lower-volume threshold than a freeway segment with a 55mph free-flow
speed.
b. The free-flow speed of a freeway segment is impacted by the amount of lateral
clearance on the right side of the roadway.
c. The capacity of a freeway segment with a 75-mph free-flow speed is higher than a
similar facility with a 55-mph free-flow speed.
d. A freeway segment with 13-ft lanes has a higher free-flow speeds than a similar
facility with 12-ft lanes.
e. Increases in traffic volume lower the estimated operating speed of a freeway segment
for both low and high volume ranges.
91
9. To encourage more carpooling during the peak commute times, a metropolitan area is
considering adding HOV lanes to a busy interstate segment. An existing transit route has
a utility of -0.65, which is unaffected by the proposed change. If the existing non-HOV
lanes have a utility of +1.2 and the proposed change introducing a carpool mode has a
utility of -0.40, the percentage of trips expected to carpool is most nearly:
a.
b.
c.
d.
0%
15%
17%
74%
92
Construction Engineering:
1. Operation manuals, warranties, guarantees, and as-built drawings are generally provided
to the owner during which phase of the project?
a.
b.
c.
d.
Construction
Procurement
Close-out
Feasibility
2. A loader has a full-bucket of 3 yd^3, and the average time required to place one
bucketload of soil into a truck is 1 minute. The loader is supported by four trucks with a
volume of 15 yd^3 each and a cycle time of 12 min plus the time to load the truck. The
ideal productivity (yd^3/hr) of this system is most nearly:
a.
b.
c.
d.
180
212
277
300
3. A project has a CPI > 1 and an SPI> 1.This would indicate that the project is:
a.
b.
c.
d.
Behind schedule with a cost savings
Ahead of schedule with a cost savings
Behind schedule with a cost overturn
Ahead of schedule with a cost overturn.
93
4. An embankment having a volume of 320,000 yd^3 is to be constructed from local
borrow. The dry unit weight and moisture content of the borrow material were
determined to be 106 pcf and 18.2%, respectively. The embankment material has a total
unit weight of 122 pcf and a moisture content of 16.7%. The volume of borrow (yd^3)
needed to construct the embankment is most nearly:
a.
b.
c.
d.
274,100
315,500
324,500
373,600
5. Which set of orthographic views correctly represents the isometric view of the structure
shown below:
a.
b.
c.
d.
Option A
Option B
Option C
Option D
94
6. The average production of the excavator is the controlling factor in a highway ditchcleaning contract. Excavators with four different bucket sizes are available as rental units.
The hourly rental rate is already directly proportional to the bucket capacity of the
excavator. Assume that production (loose yd^3/hr) is equal to (excavator cycles per hour)
* (average bucket payload in LCY per cycle). The excavator characteristics are as
follows:
The optimally efficient excavator is:
a.
b.
c.
d.
Excavator 1
Excavator 2
Excavator 3
Excavator 4
7. A work task has a current cost of $3,400, with a budget cost at this same point of $3,200.
The total budget for this task is $4,000. The estimated cost at completion for this task is
most nearly:
a.
b.
c.
d.
$3,750
$4,000
$4,250
$4,850
95
8. A drawing of a roadway cross section is shown below. The arrow with a number
indicates:
a.
b.
c.
d.
Thickness of the surface coating is 0.025 in.
The slope of the roadway is 3 in. per 10 ft across the slope
The edge of the roadway will receive a chamfer of ¼ in.
Grooves ground into the surface of the roadway are ¼ in. deep.
9. For the following activity-on-node diagram, what is most nearly the length of the critical
path?
a.
b.
c.
d.
0 days
12 days
15 days
19 days
Answer Key:
Mathematics and Statistics:
1. C
2. A
3. A
4. C
5. A
6. B
7. D
8. B
9. C
10. C
11. B
12. A
13. B
14. A
15. D
16. B
17. D
18. D
19. A
20. C
21. C
22. A
23. C
24. D
25. B
26. C
27. D
28. B
29. D
30. D
31. A
32. B
33. A
34. B
35. C
36. B
Ethics and Professional Practice:
1. C
2. A,E
3. C
4. A
5. B
6. B
7. D
8. A
9. B
10. A
11. C
12. B
13. A,C,D,E
14. A
15. B,C,D
16. C
17. A
18. D
19. A
20. A
21. B
22. B,C
Engineering Economics:
1. B
2. B
3. B
4. C
5. C
6. C
7. $5,031
8. $658
9. $2,224 per month
10. C
11. B
12. A
13. C
14. D
15. D
16. C
17. B
18. C
19. C
20. C
21. C
22. C
23. C
24. A
25. D
Statics:
1. A
2. C
3. In Solution
4. A
5. ?
6. D
7. D
8. D
9. D
10. B
11. C
12. C
13. B
14. A
15. D
16. C
17. C
18. A
19. A
20. B
21. D
22. C
23. C
Dynamics:
1.
2.
3.
4.
5.
6.
7.
C
A
C
D
C
A
A
Mechanics Of Materials:
1. D
2. B
3. C
4. B
5. B
6. A
7. A
8. B
9. C
10. D
11. B
12. C
13. D
14. B
15. B
16. B
17. C
18. B
19. D
20. D
21. C
22. B
23. B
24. C
Materials:
1. C
2. D
3. D
4. B
5. D
6. C
7. A
8. D
9. B
10. C
11. D
12. D
13. A,D,G
14. D
15. B
16. D
17. A,C,D,F
Fluid Mechanics:
1.
2.
3.
4.
5.
D
A
D
C
A
Surveying:
1.
2.
3.
4.
5.
6.
7.
8.
9.
A
A
C
D
B
C
Azimuth: 145o , Bearing: S 35o E
C
B
Water Resources and Environmental Engineering:
1. A
2. B
3. B
4. B
5. D
6. D
7. C
8. A
9. A
10. A
11. D
12. B
13. D
14. D
15. B
16. D
17. C
18. C
19. C
20. C
21. A
22. C
23. D
Structural Engineering:
1. A
2. B
3. B
4. B
5. B
6. B
7. C
8. C
9. D
10. C
Geotechnical Engineering:
1. D
2. B
3. B
4. B
5. B
6. C
7. C
8. C
9. C
10. B
11. B
12. C
13. C
14. D
15. B
16. B
17. A
18. D
19. C
Transportation Engineering:
1.
2.
3.
4.
5.
6.
7.
8.
9.
B
C
A
D
D
B
C
B,C
B
Construction Engineering:
1.
2.
3.
4.
5.
6.
7.
8.
9.
C
A
A
B
B
C
C
B
D