FE Exam Review Practice MO S&T
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CIVIL, ARCHITECTURAL AND ENVIRONMENTAL ENGINEERING
FUNDAMENTALS OF ENGINEERING REVIEW
Whenever you feel like jumping to a different portion of the review, just open the bookmarks from the left and click on the section you want.
Welcome to the Missouri S & T Fundamentals of Engineering (FE) Review This review is designed to help you prepare for taking the NCEES Fundamentals of Engineering Exam, more commonly known as the FE. The exam is administered by Pearson VUE, and takes
You will find an answer key between the question and solution sections of the review.
There are 18 knowledge areas covered in the NCEES Civil FE exam, this review will help you determine what areas you need to concentrate on.
place in certified testing centers throughout the country. We have our own Pearson VUE testing center located on the Missouri S & T campus, in Norwood Hall.
PREPARING FOR THE EXAM When you are beginning to prepare for the exam, you should start by registering with NCEES, which you can do by clicking the link here link here and following the instructions on creating an account. Once you have created an account, you may then
Be sure to allow enough time for studying before you
manual will be very important to your success on the
exam.
exam.
download a copy of the NCEES Handbook. This reference
Allow Time to Study Most students will give themselves a minimum of 4-6 weeks to study before taking the exam. This is important to avoid “cramming”, giving yourself time to study properly can be the difference between passing and not.
There are multiple ways to review the questions at the end of sections, use this to separate question types for evaluation.
Finding a group to study with, and scheduling regular times has been shown to be one of the most effective ways to study for the exam. When you begin to study for the exam, review the NCEES calculator policy that can be found found here. here. Purchase or obtain a calculator that complies and use it. Using the calculator will allow you to familiarize yourself with the functions and button placement. Being familiar with you calculator can save you a lot of time on the exam. When studying for the FE, note placement of commonly used equations and their placement in the Reference. DO NOT rely on page numbers of the PDF file, the
The two sections of the exam share the same time, if you take too long on part one, you will be rushed on the second half. Budget time accordingly.
If you don’t know something, move on; just remember remember to come back to that question at the section review.
reference used in the exam will not have the examination standards, and page numbers of the PDF could be different. Knowing sections and placement can be time saving when you are searching for specific equations. The NCEES Examinee Guide gives you step-by-step instructions on how to register and can be found found here here , where you can download the PDF.
Don’t leave a question blank, a quick look at the topic in the reference could narrow down the possible answers. answers.
MATHEMATICS 1. What is the equation of an ellipse with a center at (0,0) that passes through points: (-2,0), (0,3), and (2,0) ? A)
B)
C)
D)
9 9 +
= 1
+
= 1
9
= 1
= 1
9
2. What is the equation of a sphere with a center at (0,1,-2) and a radius of 9?
A)
( + 1) + ( + 1) + ( + 2) = 9
B)
( + 1) + ( + 1) + ( + 2) = 81
C) D)
+ ( + 1) + ( +(
2) = 81
1) + ( + 2) = 81
3. What are the center coordinates and radius of the circle represented by the equation,
+
A) (1, -6) ; 12
+ 12
2 + 12 = 0
√
B) (-1, 6) ; 12 C) (1, -6) ; 25 D) (1, -6) ; 5
4. A (40cm) outside diameter pipe has walls (4cm) thick. What is the area of flow if it is filled to a depth 1/3 of its diameter?
A) 65 B) 150 C) 235 D) 258
5. Evaluate the following integral.
11 3 31 3 3 3 3 sin
A) B)
C) D)
+
+
+
+
6. What is dy/dx if y = (2 ) ?
A) (2 ) (2 + l n 2 )
B) 2 (1 + l n 2 ) C) (2 ) (ln 2
)
D) (2 ) (1 + l n 2 )
7. What is the matrix product “AB” of matrices A and B ?
A = [1
2
3]
B=
2 A) 6 12 B) [8] C) [20] D) [2
6
12]
8. What is the determinant of matrix A?
3 4
A=
A) 0 B) 10 C) 18 D) 30 E)
2 3 4
2 6
9. What is the cross product, A x B, of vectors A and B ?
= + + = + +
A) B)
+ + C) 2 + 7 5 D) 2 + 7 + 5
10. What is the angle between the two given vectors A and B ?
= =
A) -84.3° B) 84.3° C) 101.2° D) 122.4°
+
+ +
∙
11. Given vectors A, B, and C, what is the value of ( + ) ( + )?
= = =
A) 42 B) 84 C) 122 D) 288
+ + +
+ + +
PROBABILITY AND STATISTICS
12. What is the mean and sample standard deviation of the following numbers?
71.3 74.0 74.25 78.54 80.6 A) 74.3 ; 2.7
B) 74.3 C) 75.0 ;; 3.7 2.7 D) 75.7 ; 3.8
Questions 13 & 14 Refer to the Following Situation Samples of Aluminum were tested for stiffness. The following frequency distribution was observed. The distribution is assumed to be normal. Stiffness 2480 2440 2400 2360 2320
Frequency
23 35 40 33 21
3
What is the mean of the observed stiffness measurements? A) 2367 B) 2398 C) 2402
D) 2419
14. What is the standard deviation of the population from which the samples were taken? A) 19 B) 23 C) 37 D) 51
5
If you toss a standard coin 10 times, what is the probability of getting exactly 4 heads? A) 0.1 B) 0.2 C) 0.4 D) 0.5
COMPUTATIONAL TOOLS 16.
In a spreadsheet, the number in Cell A4 is set to 6. Then A5 is set to A4+$A$4. This formula is copied into Cells A6 and A7 with automatic referencing. The number shown in Cell A7 is _______.
A) 6 B) 12 C) 18 D) 24
17. 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 referencing. The formula in Cell B5 will be: A) $A1^3+A$5^2_3 B) A5^3+B$1^2-3 C) $A5^3+A$1^2-3 D) A5^3+A5^2-3
18. The following segment of code describes a segment of a program: Set A = 17 Set K = 2
4
While K
≤
A = A/K
K=K+1 End While Print A The value of A that is printed is most nearly: A)
0.71
B)
2.83
C)
4.25
D)
408
19. The flowchart for a computer program contains the following segment: VAR = 0 IF VAR 0.005 > (3.46 /0.85) = 0.90
= 0.90(286.9) = 258
Answer is “A”
79. What is the flexural design strength of the reinforced concrete beam shown? Assume = 4,0 ,00 00 , and = 60,0 60,000 00 .
A) 354 B) 319 C) 297 D) 267
∙∙
SOLUTION
Reference Manual Search Term:
“BEAM”
Reinforced Beam (pg. 155)
80 ∙ = 18
.
= 3(1.27
) = 3.81
Calculate “a “a”:
=
Find
:
Convert to
=
:
=
0.85
(3.81)(60) = 4.80 .80 0.85(4)(14) (3.81)(60) 18 18
.
.
= 3,56 3,564 4
∙
3,564
1 12
∙ ∙ = 297
Calculate the resistance factor “φ”:
∙ =
= 0.003
18 18
(4.8 /0.85) = 0.0066 > 0.005 (4.8 /0.85) = 0.90
= 0.90(297) = 267
Answer is “D”
GEOTECHNICAL ENGINEERING
80. The direct shear test results of a sand are shown below, what is the
ℎ
angle of friction?
A) 0° B) 27° C) 30° D) 63°
= 16 = 512 = 16
SOLUTION
Reference Manual Search Term:
“SHEAR STRESS”
Shear stress (pg. 149)
Solve for the total normal stress:
=
=
(512
= 32
= 16
−1 ≅ (16
Solve for “φ”:
) )
= tan
16 32
Answer is “B”
27°
81. An undisturbed sample of soil contains solids with a specific gravity of 2.70, a moisture content of 10.5%, and a void ration of 0.63. What is the degree of saturation of this sample? A) 22% B) 36% C) 45% D) 65%
SOLUTION
Reference Manual Search Term:
“SATURATION”
Degree of saturation (pg. 146)
Looking at the relationships between the formulas:
( ) = ( )( )
(2.70)(0.105) = ( )(0.63) = 45%
Answer is “C”
82. A soil test indicates a level site has a 10-ft upper layer of sand. The groundwater table is located at the surface. The unit weight of the sand is 135.0 pcf. What is the effective overburden stress at a depth of 10 ft?
A) 1,985 B) 1,450 C) 725 D) 615
SOLUTION
Reference Manual Search Term:
“EFFECTIVE STRESS”
Effective stress (pg. 149)
Calculate the effective stress:
=
= (135)( 135)(10 10)) (62.4)( 62.4)(10 10)) = 726 Answer is “C”
83. A retaining wall is 12-ft tall, and is backfilled with a granular soil type. The soil has an internal angle of friction of 30°, 30°, and and a unit weight of 125 pcf. pcf. What What is the Rankine passive earth pressure on the wall?
A) 2,250 / B) 3,000 / C) 9,000 / D) 27,000 /
SOLUTION
Reference Manual Search Term:
“RANKINE”
Rankine active (pg. 149)
Calculate the passive pressure:
(45°) +
=
1
2
=
(45°) +
1
30 2
=
(60) = 3.0
= 2 ( )(
)
= 2 (125)( 125)(12 12 )(3.0 )(3.0)) = 27,0 27,000 00
Answer is “D”
/
84. A normally-consolidated clay layer has a thickness of 10-ft. The layer is surcharged. The coefficient of consolidation is 0.16 and
the time factor is 1.2 for = 50% . The clay layer is located between two layers of dense sand. What is the time required for 50% consolidation? A) 750 days days B) 188 days days C) 38 days days D) 5 days days SOLUTION
Reference Manual Search Term:
“CONSOLIDATION”
Consolidation (pg. 147-148)
Calculate the time required for 50% consolidation:
= ( )
= (1.2)
Answer is “B”
(5 )
0.16
= 187. 187.5 5
85. The flow net shown is the cross-section of a dam with a length of 600-ft (perpendicular to the cross-section). Assuming uniformity, what is the total seepage ( A) 453,600 B) 51,840 C) 37,800 D)
3
/day) under the dam?
63
SOLUTION
Reference Manual Search Term:
Flow nets (pg. 146)
Using the equation for flow nets:
“FLOW NET”
=
= (0.0004)
.
11 385
(50 )
3
= 0.000 0.00072 729 9
/sec per ft.
3 ℎ ℎ 3 3 0.000729
s
per ft. (3600
= ( )( ) = (63
)(24
/
/
) = 63
/ day per ft of wall
/ day per ft of wall )(600 ) = 37,800
/ day
Answer is “C”
TRANSPORTATION ENGINEERING 86. At a two-way controlled intersection, determining the sight distance required for minor street movements is controlled by: A) Decision sight distance B) Stopping sight distance
C) Departure sight distance D) Approach sight distance
SOLUTION
Departure sight is based on a vehicle stopped, looking at major street vehicles for acceptable gaps.
Answer is “C”
87. A highway lane has a volume of 1,400 vehicles/hr, and an average vehicle speed of 45 mph. What is the time spacing between vehicles (center to center) in seconds? A) 2.6 B) 5.2 C) 15 D) 31
SOLUTION ,
=
Vehicle Spacing:
,
/
= 2.57 .57
/
/
1 003 600 ℎ Answer is “A”
88. At a crosswalk, the initial “WALK” signal is displayed for 6.0 sec, after which a “DON’T WALK” is displayed. The pedestrian walking speed is 4 ft/sec, and the intersection is 50-ft wide. After the green light, the yellow interval is 3.5 sec. The all-red interval is 0.5 sec, during which, no pedestrians are in the crosswalk. What is the length of time the green must be displayed?
A) 8.5 B) 10.5 C) 15.0 D) 22.0
SOLUTION
The green light signal length equals the length of the WALK signal, plus the time to cross the crosswalk, minus the yellow signal length:
ℎ
= (6.0
)+
50 4 / /
Answer is “C”
3.5 sec = 15.0
89. A person is driving on a gravel road. A moose suddenly leaps into the road. The car was travelling 50 mph, and is on a 10% downgrade when the moose appears. Assume a reaction time of 1.5 sec, and a friction coefficient of the gravel of 0.65.What is the total distance required to stop? A) 153 ft B) 220 ft C) 239 ft D) 262 ft
SOLUTION
Reference Manual Search Term:
“STOPPING”
Stopping Sight Distance (pg.169)
Distance to stop:
1.47(50 × 1.5)
= 1.47
+
30
50
30 (0.65)
32.2
0.10
±
= 261. 261.8 8
Answer is “D”
90. An equal tangent vertical curve has the following characteristics:
ℎ
= 800 = 3 0 + 0 0 = 200. 200.0 0 = +4% = 6%
The elevation of the curve at Station 31+00 is: A) 244.6 ft B) 211.6 ft C) 209.6 ft D) 190.4 ft
SOLUTION
Reference Manual Search Term:
“CURVE”
Vertical Curve (pg. 176)
Calculate the PVC station:
=
2
= (3 0 + 0 0)
Find the elevation of PVC:
1
800 = 26 + 00 2
( 6) 8 = 224. 224.0 0 2
1 1
=
2
= 200
Find elevation of station 31+00:
=
+
+
= (224.0) + ( 6)(5) +
(
)
2
(10) (5) = 209. 209.6 6 2(8)
Answer is “C”
91. Using a given loading condition, which of the following pavement design types will result in the thinnest pavement? A) Composite hot-mix asphalt over Portland cement concrete B) Portland cement concrete C) Warm-mix asphalt
D) Hot-mix asphalt
SOLUTION
Under ideal conditions, any design containing asphalt mixture will result in a thicker product.
Answer is “B” 92. Two crash reduction measures are being considered to address safety for an urban intersection reconstruction project. The crash reduction factors are 0.25 and 0.15, and are mutually exclusive. If the expected number of crashes per year is 10, and no growth in traffic is anticipated, what is the number of expected crashes per year? A) 3.6 B) 4.2 C) 6.4 D) 7.2
SOLUTION
Reference Manual Search Term:
“CRASH” Crash Reduction (pg. 172)
The reduction measures are mutually exclusive:
1 1 ℎ ℎℎ ℎ + (1
=
= 0.25 + (1
)
.025)0.15 = 0.36
Crashes prevented:
(0.36) = 3.6
= 10
3.6 = 6.4
Answer is “C”
93. A horizontal curve has the following characteristics:
What is the station of “PT”? A) 22+30.21 B) 22+22.37 C) 22+04.27 D) 22+01.52
= 40°50 = 600. 600.00 00 = 20 + 00
SOLUTION
Reference Manual Search Term:
“CURVE”
Horizontal Curve (pg. 175)
Using the formula for tangent distance:
= tan 2
=
180
=
=
= (600)
40.833° = 223. 223.34 34 2
= (600)(40.833°)
180
= 427. 427.61 61
= (20 + 00.00)
223.34 = 17 + 76.66
= (17 + 76.66)
427.61 = 22 + 04.27
Answer is “C”
ENVIRONMENTAL ENGINEERING
94. A municipal softening plant produces a supply of 5 MGD. The plant operates two clarifiers, each has a diameter of 65 ft, and a side depth of 12 ft. What is the clarifier residence time assuming parallel operation? A) 3.42 hr B) 2.86 hr C) 1.82 hr D) 0.85 hr SOLUTION
Residence time equals flow rate divided by volume: Volume of clarifiers:
3 6 3 24ℎ 3 ℎ 3 3 ℎ ℎ (12 )
2
(65) 4
=
10 10
/ /
79 79,6 ,640 40
Flow volume per hour:
=
5 7.48
/ /
/
= 27,8 27,853 53
Residence Time:
79,640 27,853 /
= 2.8 2.86
/
Answer is “B”
. 95. A water treatment plant uses filters with a surface area of 100 The backwash cycle flow rate is 15 gpm/ , with a duration of 12 min.
What is the quantity of water required for the backwash cycle? A) 3,800 gal B) 12,600 gal C) 18,000 gal D) 144,000 gal
SOLUTION
Solve for the volume required:
= (100
)(15
/
)(12
Answer is “C”
) = 18,0 18,000 00
96. A municipal wastewater treatment facility processes a flow with a 5day BOD of 200 mg/L at 20°C. If the BOD rate constant at 20°C is
−1
0.23 A) 413 B) 293 C) 187
, what is the ultimate BOD (mg/L) of the raw wastewater?
D) 135
SOLUTION
Reference Manual Search Term:
“BOD”
BOD Exertion (pg. 185)
Solving for BOD ultimate:
− −0 3 5 66
200
=
]
[1
=
(
1
.
)( )
= 292. 292.7 7
/
Answer is “B”
97. Your firm has been tasked with designing as aerobic system to biodegrade benzene (
). The biodegradation process follows the
reaction below. The benzene concentration is 500 mg/L. What is the amount of oxygen is required to completely biodegrade the benzene?
66 → +
A) 400 mg/L B) 520 mg/L C) 870 mg/L D) 1,540 mg/L
+
SOLUTION
First, balance the equation:
+ (7.5)
(1) 500
(6)
+ (3)
→ 66 (
)
1 78
7.5 7.5
32
= 1,54 1,540 0
Answer is “D” 98. Which of the following is associated with the corrosion of sanitary sewer piping? A) BOD
3
B) Fats, oils, grease C) D)
SOLUTION
is the primary product produced under conditions that can cause
corrosion in piping systems.
Answer is “C”
/
99. A mixture of gas at 25°C and at 1 atm contains 100mg/L of partial pressure exerted by the A) 0.14 B) 0.072 C) 0.0056 D) 0.0029
is:
SOLUTION
Calculate the molar weight of
:
= 34 g/mol
=
1 1,000
100
34
= 0.00 0.0029 29
Using ideal gas law:
=
=
(0.0029
))((0.08206)(298 ) 1
Calculate the partial pressure:
0.072 1
= 0.072
Answer is “B”
= 0.07 0.072 2
. The
CONSTRUCTION
100. As-built drawings, warranties, and manuals are provided to the owner/client during which phase of construction? A) Feasibility B) Bidding C) Procurement D) Close-out
SOLUTION
All of these items are generally provided to the owner/ client during the close-out phase of construction.
Answer is “D”
101. A loader has a bucket capacity of 3
3
, and the time required to
place one bucket of soil into a waiting truck is 1 min. The loader is
3
supported by 4 trucks, each truck has a haul capacity of 15 , and a drive time of 12 min. What is the ideal productivity of this system? A) 142 B) 180 C) 212 D) 287
33 ℎℎ 33 ℎℎ / / / /
SOLUTION
Calculate the time to load 1 truck: 15
3 3 /3
/ min = 5 min
There are 4 trucks, 5 minute loading plus drive = 17 min. 17 min
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