CE Refresher Course for May 2020 – Math 1
Review Innovations
1. A contractor has 50 men of the same capacity at work on
a job. They can complete the job in 30 days, but the
contract expired in 20 days. He decides to put 20
additional men. If all the men get P600/day for a full or
part day and if the liquidated damages are P50,000 for
every full or part of the day he requires over his contract
time. How much money he saves or loss by putting 20
additional men?
A. save = P376,000
C. loss = P650,000
B. loss = P376,000
D. even
2. Stations A and B are 120 miles apart on a single-track
railroad. At the same time that a train leaves A for B at
25 mph, a train leaves B for A at 15 mph. Just as the train
leaves A, a botfly flies from the front of the engine
straight toward the other train at 100 mph. On meeting
the second train it immediately turns back and flies
straight for the first train. It continuous to fly back and
forth with undiminished speed until it is crushed in the
eventual collision. How far had the fly flown?
A. 350 miles
C. 400 miles
B. 550 miles
D. 300 miles
3. One hose can fill a goldfish pond in 45 minutes, and two
hoses can fill the same pond in 20 minutes. Find how
long it takes the second hose alone to fill the pond.
A. 16 minutes
C. 46 minutes
B. 56 minutes
D. 36 minutes
4. The amount of pollutants P produced varies directly
with the population N of people. Kansas City has a
population of 442,000 and produces 260,000 tons of
pollutants. Find how many tons of pollution we should
expect St. Louis to produce, if we know that its
population is 348,000. Round to the nearest whole ton.
A. 104,606 tons
C. 204, 806 tons
B. 204,706 tons
D. 104, 706 tons
5. An army of troops is marching along a road at 5 kph. A
messenger on horseback was sent from the front to the
rear of the column and returns immediately back. The
total time taken being 10 minutes. Assuming the
messenger rides at the rate of 10 kph, determine the
length of the column.
A. 526 m
C. 854 m
B. 1 km
D. 625 m
6. Labor laws in a certain country require factory owners to
give every worker a holiday whenever one of them has
birthday and to hire without discrimination on grounds
of birthdays. Except of these holidays, they work 365day year. The owner wants to maximize the expected
total number of man days worked per year in a factory.
How many workers do factories have in certain country?
A. 726
C. 363
B. 364
D. 728
A. 1437 ft
B. 1734 ft
C. 1347 ft
D. 1374 ft
9. A block weighing 100 N rests on a floor whose coefficient
of friction with the block is 0.3. Find the least force P to
produce an impending motion.
A. 20.64 N
C. 30.64 N
B. 28.73 N
D. 24.32 N
10. Find the values of b for which the line y = 3x + b and the
parabola y2 = 5x will have no common point.
A. b > 12/5
C. b < 12
B. b > 5/12
D. b < 14
11. Smith and Jones, both 50% marksmen, decide to fight a
duel in which they exchange alternate shots until one is
hit. What are the odds in favor of the man who shoots
first?
A. 1/3
C. 2/3
B. 1/2
D. 1/4
12. Find the volume of the parallelepiped whose edges are
represented by the following vectors:
A=2i−3j+4k
B=i+2j–k
C=3i−j+2k
A. 5
C. 7
B. 6
D. 8
Situation 1. Four army recruits went to the supply room to
get their military boots. Their shoe sizes were 7, 8, 9 & 10.
The supply officer, after being informed of their sizes,
prepared the four pairs of boots they need. If the boots
are handed to each of the four recruits at random, what
is the probability that...
13. exactly 3 of them will receive the correct shoe size?
A. 1/16
C. 1/12
B. 1/24
D. 0
14. all of them will receive the correct shoe size?
A. 1/16
C. 1/12
B. 1/24
D. 0
15. none of them will receive the correct shoe size
A. 3/8
C. 1/16
B. 23/24
D. 5/12
Situation 2. From where he stands, one step toward the cliff
would send the drunken man over the edge. He takes
random steps, either toward or away from the cliff. At
any step his probability of taking a step away is 2/3, of a
step toward the cliff 1/3.
16. What is his chance of escaping the cliff in exactly 3 steps?
A. 16/27
C. 2/27
B. 8/243
D. 1/2
17. What is his chance of falling in exactly 5 steps?
A. 16/27
C. 2/27
B. 8/243
D. 1/2
18. What is his chance of escaping the cliff?
A. 16/27
C. 2/27
B. 8/243
D. 1/2
7. A box contains 5 defective and 195 non-defective cell
phones. A quality control engineer selects 2 cell phones
at random with replacement. What is the probability
that exactly one is defective?
8. A new kind of atom smasher is to be composed of two
tangents and a circular arc which is concave toward the
point of intersection of the two tangents. Each tangent
and the arc of the circle is 1 mile long, what is the radius
of the circle? Use 1 mile = 5280 ft.
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CE Refresher Course for May 2020 – SEC 12
Review Innovations
Situation 1: As shown in Figure MEC-101, a weight W hangs
from two wires each with cross-sectional area of 113 mm2. If
θ = 30° and α = 45°,
1.
Find the largest weight, W (kN), that can be carried by
the wires if the maximum stress in the wires is not to
exceed 124 MPa.
A. 19.14
C. 16.91
B. 15.62
D. 22.04
2.
If the weight W = 25 kN, what is the resulting stress in
wire AC (MPa)?
A. 161.96
C. 198.35
B. 114.52
D. 158.28
3.
If the weight W = 25 kN, determine the required crosssectional area (sq. mm) of the wires so that the max stress
does not exceed 124 MPa.
A. 148
C. 105
B. 181
D. 127
Situation 2: The two 200-N blocks, shown in Figure MEC102, are pushed apart by the 15° wedge of negligible weight.
The angle of static friction is 12° at all contact surfaces.
4.
Determine the reaction (in N) between the wedge and
the block if the block starts moving.
A. 47.6
C. 229.3
B. 53.5
D. 48.6
5.
Determine the reaction (in N) between the block and the
floor if the block starts moving.
A. 47.6
C. 229.3
B. 53.5
D. 48.6
6.
Determine the force P (in N) required to start the blocks
moving.
A. 47.6
C. 229.3
B. 53.5
D. 48.6
10. If q = 1200 N/m, which of the following most nearly
gives the reaction (in N) at A?
A. 518
C. 1,906
B. 698
D. 2,942
11. If q = 1200 N/m, which of the following most nearly
gives the reaction (in N) at B?
A. 12,753
C. 23,350
B. 11,254
D. 22,564
12. Which of the following most nearly gives the smallest
load q (in N/m) that would cause the structure to tip
over?
A. 1,268
C. 1,200
B. 1,585
D. 890
Situation 5: A right-angled rigid pipe is fixed to a wall at A
and is additionally supported through the cable CD as
shown Figure MEC-105. The tension in the cable is 3 kN.
13. Neglecting the weight of the pipe, which of the following
most nearly gives the largest shear force (in kN) on the
pipe’s cross section?
A. 3.00
C. 2.71
B. 1.28
D. 2.97
14. Neglecting the weight of the pipe, which of the following
most nearly gives the maximum bending moment (in
kN-m) at A?
A. 2.71
C. 4.88
B. 3.47
D. 2.31
15. Neglecting the weight of the pipe, which of the following
most nearly gives the maximum twisting moment (in
kN-m) about x-axis?
A. 1.90
C. 0.53
B. 0.84
D. 0.79
Situation 3: Using Figure MEC-103,
Given: P1 = 1.8 kN
θ = 30°
P2 = 0.9 kN
β = 45°
P3 = 0.45 kN
7.
Determine the resultant of the three forces (in kN) P1, P2,
and P3.
A. 1.24
C. 2.12
B. 2.46
D. 2.75
8.
Determine the reaction (in kN) at A.
A. 1.06
C. 1.24
B. 1.31
D. 1.63
9.
Determine the reaction (in kN) at B.
A. 1.06
C. 1.24
B. 1.31
D. 1.63
Situation 4: The supporting structure of the billboard is
attached to the ground by a pin at B, and its rear leg rests on
the ground at A. Friction may be neglected. Point G is the
center of gravity of the billboard and structure, which
together has a mass of 1400 kg. To prevent tipping over in
high winds, a 1200-kg mass is placed on the structure near
A, as shown in Figure MEC-104.
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Review Innovations
A
B
C
θ
α
W
Figure MEC-102
Figure MEC-101
P2
P1
P3
A
θ
β
a
B
a
Figure MEC-103
Figure MEC-104
Figure MEC-105
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CE Refresher Course for May 2020 – Math 2
Review Innovations
1. An equilateral triangle is inscribed within a circle whose
diameter is 12 cm. In this triangle a circle is inscribed;
and in this circle, another equilateral triangle is
inscribed; and so on indefinitely. Find the sum of the
areas of all the triangles.
A. 84.67 cm2
C. 56.23 cm2
B. 62.35 cm2
D. 76.84 cm2
2. Point P has cylindrical coordinates of (8, 30, 5). Find the
value of x in the Cartesian coordinates.
A. 5.21
B. 6.93
C. 6.12
D. 5.94
3. A battalion, 20 miles long, advances 20 miles. During
this time, a messenger on a horse travels from the rear of
the battalion to the front and immediately turns around,
ending up precisely at the rear of the battalion upon the
completion of the 20-mile journey. How far has the
messenger traveled?
A. 40 miles
C. 50 miles
B. 48.28 miles
D. 52.42 miles
4. If a pair of dice is tossed 6 times, what is the probability
of obtaining a total of 7 or 11 twice, a matching pair once,
and any other combination 3 times?
A. 0.0019
C. 0.1127
B. 0.0129
D. 0.2156
5. The king’s minter boxes his coins 100 to a box. In each
box he puts 1 false coin. The king suspects the minter and
from each of 100 boxes draws a random coin and has it
tested. What is the chance the minter’s peculations go
undetected?
A. 0.99
C. 0.01
B. 0.267
D. 0.366
6. At an ordinary rate a man can row the distance from
Pasig to Manila, about 15km, in 5 hours less time than it
takes him to return. Could he double his rate, his time to
Manila would only be one hour less than his time to
Pasig. What is the rate of Pasig River?
A. 1 kph
C. 1.5 kph
B. 2 kph
D. 2.5 kph
7. What is the probability of getting at least 1 one in 2
throws of a die?
A. 5/6
B. 5/18
C. 11/36
D. 25/36
8. A and B working together can do a job in 4 days, B and
C together can do the job in 3 days, and A and C together
can do it in 2.4 days. In how many days can A do the job
working alone?
A. 6
B. 12
C. 4
D. 8
9. A freely falling body, starting from rest, falls 16 ft during
the 1st second, 48 ft during the 2nd second, 80 ft during
the 3rd second, etc. Calculate the distance it falls during
the 15th second.
A. 464 ft
C. 644 ft
B. 3600 ft
D. 6300 ft
10. An engineer selects a sample of 5 iPods from a shipment
of 100 that contains 5 defectives. Find the probability that
the sample contains at least one defective.
A. 0.23
B. 0.43
C. 0.83
D. 0.63
11. Shureka Washburn has scores 72, 67, 82 and 79 on her
algebra tests. Use an inequality to find the scores she
must take on the final exam to pass the course with an
average of 77 or higher, given that the final exam counts
as two test.
A. greater than or equal to 81
B. greater than or equal to 51
C. greater than or equal to 61
D. greater than or equal to 71
12. What time between 2 and 3 o’clock will the angle
between the hands of the clock be bisected by the line
connecting the center of the clock and the 3 o’clock mark?
A. 2:18:27.6
C. 2:17:56.3
B. 2:16:00.0
D. 2:19:03.1
13. The local weather forecaster says “no rain” and his
record is 2/3 accuracy of prediction. But the Federal
Meteorological Service predicts rain and their record is
3/4. With no other data available, what is the chance of
rain?
A. 3/5
C. 1/6
B. 1/4
D. 5/12
14. Mike saves 20% of his income. If his expenditure is
increased by 35%, how many percent must his income be
increased so that he may save 10% of it?
A. 15%
B. 22.5%
C. 20%
D. 25%
15. A certain ball rebounds 1/3 the distance it falls. If the
ball is dropped from a height of 9 ft, how far does it travel
before coming to rest?
A. 21 ft
C. 27 ft
B. 18 ft
D. 15 ft
16. A water park is considering two location for
development - one in Laguna and one in Cavite. Based
on the following weightings for the factors below, which
area represents the best location?
Factor description
Proximity to Market
Infrastructure
Weather
Labour Availability
A. Cavite
B. Laguna
Weight
0.30
0.20
0.25
0.25
Laguna
80
50
30
60
Cavite
50
40
70
80
C. All of the above
D. None of the above
17. A farmer owned a square field measuring exactly 2261
yards on each side. 1898 yards from one corner and 1009
yards from an adjacent corner stood a beech tree. A
neighbor offered to purchase a triangular portion of the
field, stipulating that a fence should be erected in a
straight line from one side of the field to an adjacent side
so that the beech tree was part of the fence. The farmer
accepted the offer but made sure that the triangular
portion was a minimum area. Calculate the minimum
area.
A. 972,325 m2
C. 939,120 m2
B. 972,325 m2
D. 946,350 m2
Situation 1. A uniform chain that weighs 0.50 kg per meter
has a 15-liter bucket hanged at its end. The bucket is
full of liquid and 30 meters of chain is out. Liquid weighs
1 kg per liter and weight of bucket is negligible.
18. How much work is done in winding-up the upper half
of the chain?
A. 675.0 kg-m
C. 562.5 kg-m
B. 458.2 kg-m
D. 393.8 kg-m
19. How much work is done in winding-up the full length
of the chain?
A. 675.0 kg-m
C. 562.5 kg-m
B. 458.2 kg-m
D. 393.8 kg-m
20. If the bucket is leaking at a uniform rate so that it is halffull when no chain is out, how much work is done in
winding-up the 30-m length?
A. 675.0 kg-m
C. 562.5 kg-m
B. 458.2 kg-m
D. 689.3 kg-m
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CE Refresher for May 2020 – SEC 13
Review Innovations
Situation 1: A horizontal beam is supported by springs at its
ends, as shown in Figure MEC-101. The springs are
originally constructed so that the beam is in the horizontal
position when it is unloaded. At point C of the beam, an 800N force is applied.
1.
2.
3.
If each spring has a stiffness of 5 kN/m, determine the
deformation of the spring (in m) at A.
A. 0.160
C. 0.107
B. 0.080
D. 0.053
If each spring has a stiffness of 5 kN/m, determine the
angle of tilt of the beam?
A. 1.02°
C. 1.53°
B. 2.04°
D. 3.05°
If the stiffness of the spring at A is kA = 5 kN/m,
determine the required stiffness (in kN/m) of the spring
at B so that the beam remains in the horizontal position.
A. 2.5
C. 5.0
B. 3.0
D. 3.5
Situation 2: As shown in Figure MEC-102, the mast hinged
at B was used to lift the load W. Neglect the weight of the
mast.
Given:
x1 = 8 m
H=9m
The ladder will not slide.
The ladder will slide at point A.
The ladder will slide at point B.
The ladder will slide at A and B.
Situation 4: The homogenous 860-kg bar AB in Figure MEC104 is supported by a ball and socket joint at A and two cables
attached to B.
10. Which of the following most nearly gives the tension (in
kN) in cable BC?
A. 7.64
C. 8.60
B. 7.01
D. 8.11
11. Which of the following most nearly gives the tension (in
kN) in cable BD?
A. 7.64
C. 8.60
B. 7.01
D. 8.11
12. Which of the following most nearly gives the vertical
reaction (in kN) at A?
A. 12.87
C. 20.27
B. 15.66
D. 16.27
Situation 5: Consider the truss in Figure MEC-105.
Given: P1 = 1200 N
L1 = 6 m
x2 = 4 m
4.
What is the resultant force ( in kN) at B if W = 24 kN?
A. 36.0
C. 39.4
B. 20.0
D. 16.0
5.
What is the tensile force (in kN) in the cable AC if W = 48
kN?
A. 20.0
C. 22.3
B. 87.3
D. 40.0
6.
A.
B.
C.
D.
What is the biggest load W (in kN) that can be lifted if
the maximum tensile force in the cable AC is 50 kN and
the mast weighs 8 kN?
A. 64.0
C. 60.0
B. 50.0
D. 56.0
P2 = 1600 N
L2 = 9 m
L3 = 12 m
13. Which of the following most nearly gives the force (in N)
in member DC?
A. 1,900 (T)
C. 900 (T)
B. 1,900 (C)
D. 900 (C)
14. Which of the following most nearly gives the force (in N)
in member HI?
A. 1,900 (T)
C. 900 (T)
B. 1,900 (C)
D. 900 (C)
15. Which of the following most nearly gives the force (in N)
in member JI?
A. 1,900 (T)
C. 900 (T)
B. 1,200 (T)
D. 0
Situation 3: As shown in Figure MEC-103, a stepladder
consisting of two legs pinned together at C is resting on a
rough floor. A worker weighing 800 N is required to climb to
a height of 1.3 m to be able to change a light bulb. The
uniform legs AC and BC weigh 110 N and 70 N, respectively.
7.
Which of the following most nearly gives the minimum
coefficient of static friction required to prevent sliding at
point A?
A. 0.502
C. 0.346
B. 0.267
D. 0.189
8.
Which of the following most nearly gives the minimum
coefficient of static friction required to prevent sliding at
point B?
A. 0.502
C. 0.346
B. 0.267
D. 0.189
9.
If the coefficient of friction at all contact points is 0.48,
which of the following statements is true?
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C
W
A
H
B
x1
Figure MEC-101
x2
Figure MEC-102
Figure MEC-104
Figure MEC-103
L1
L2
G
L1
L2
E
F
L1
P1
H
J
D
P2
L1
K
I
C
A
B
L3
Figure MEC-105
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CE Refresher Course for May 2020 – Math 3
Review Innovations
1. A bus travels a distance of 350 km in exactly the same
time that a car travels a distance of 600 km. If the car is
50 kph faster than the bus, how fast was the bus?
A. 70 kph
C. 90 kph
B. 80 kph
D. 60 kph
2. A parabola has an equation of y2 = 8x. Find the equation
of the diameter of the parabola, which bisect chords
parallel to the line x – y = 4.
A. y = 2
B. y = 3
C. y = 4
D. y = 1
3. If it were two hours later, it would be half as long until
midnight as it would be if it were an hour later. What
time is it now?
A. 20:00
C. 20:30
B. 21:00
D. 21:30
4. Three people toss a coin and the odd man pays for the
coffee. If the coins all turn up the same, they are tossed
again. Find the probability that fewer than 4 tosses are
needed.
A. 61/64
C. 53/64
B. 59/64
D. 63/64
5. A contractor can buy trucks for P800,000 each, or rent
them for P1,200 per truck per day. The truck has a
salvage value of P100,000 at the end of its useful life of 5
years. The annual maintenance cost is P20,000 per truck.
Using the annual-cost method and 14% interest rate,
determine the number of days per year that each truck
must be used to warrant its purchase. Use sinking fund
method of depreciation.
A. 187
B. 177
C. 155
D. 199
6. A Toyota Land Cruiser drives east from point A at 30
kph. Another car, Ford Expedition, starting from B at the
same time, drives S30W toward A at 60 kph. B is 30 km
from A. How fast in kph is the distance between two cars
changing after 30 minutes? Hint: Use the Cosine Law.
A. 70 kph
C. 55 kph
B. 80 kph
D. 60 kph
7. The Wollomombi Falls in Australia have a height of 1100
ft. A pebble is thrown upward from the top of the falls
with an initial velocity of 20 ft/sec. The height of the
pebble h after t sec is given by the equation h = -16t2 + 20t
+ 1100. How long after the pebble is thrown will hit the
ground?
A. 1.25 sec
C. 8.94 sec
B. 7.69 sec
D. 3.42 sec
8. Find the equation of the curve passing through the point
(3, 2) and having s slope 5x2 – x + 1 at every point (x, y).
A. y = 5x3/3 – 0.5x2 + x + 34/3
B. y = 5x3/3 – 0.5x2 + x – 41.5
C. y = 5x3/3 – 0.5x2 + x – 31/3
D. y = 5x3/3 – 0.5x2 + x + 45.1
9. Find the polar equation that has the same graph as the
circle x2 + y2 = 4y.
A. r = 4 cos 
C. r = 4 sin 
B. r2 = 4 cos 
D. r2 = 4 sin 
10. Two trains going in opposite directions leave at the same
time. One train travel 15 mph faster than the other. In 6
hours, the trains are 630 miles apart. Find the speed of
each.
A. 65 mph, 50 mph
C. 55 mph, 40 mph
B. 70 mph, 55 mph
D. 60 mph, 45 mph
12. Suppose you receive x dollars in January. Each month
thereafter you receive $100 more than you received the
month before.
Write a factored polynomial that
describes the total dollar amount you receive from
January through April.
A. 2(x + 150)
C. 4(x + 300)
B. 2(2x + 150)
D. 4(x + 150)
13. A polyhedron having 12 faces and has for its face 12
regular pentagon is called dodecahedron. Determine the
number of edges.
A. 20
B. 30
C. 40
D. 50
14. How many different ways are there to arrange six people
in a round table?
A. 720
B. 24
C. 120
D. 840
15. From the given data shown:
Score
Frequency
1
14
2
15
3
14
4
17
Determine the standard deviation.
A. 1.35
B. 1.53
C. 1.27
5
10
D. 1.72
16. During the Winter Olympics game in Torino, Italy, the
total number of gold medals won by Germany, Canada,
and United States were three consecutive odd integers.
Of these three countries, Germany won the most of gold
medals and Canada won the fewest. If the sum of the
first integer, twice the second integer, and four times the
third integer is 69, find the number of gold medals won
by United States.
A. 13
B. 7
C. 9
D. 11
17. To stimulate his son in the pursuit of partial differential
equations, a math professor offered to pay him $8 for
every equation correctly solved and to fine him $5 for
every incorrect solution. At the end of 26 problems,
neither owed any money to the other. How many did the
boy solved correctly?
A. 10
B. 12
B. 13
D. 11
18. Newton’s Law of Cooling states that the rate of which
the object cool is directly proportional to the difference
in temperature between the object and its surrounding
medium. Newton’s law can be used to show that under
certain conditions the temperature T (in C) of an object
at t (in hours) is given T = 75e-2t. express t as a function
of T.
A. t = ln (75/T)1/2
C. t = ln (T/75)2
B. t = ln (75/T)2 D.
t = ln (T/75)1/2
19. The passenger on an excursion bus consisted of 14
married couples, 8 of whom brought no children, and 6
of whom brought 3 children a piece. Counting the
driver, the bus had 31 occupants. How is this possible?
A. 2 single passengers are onboard
B. 18 children are onboard
C. 8 couples are onboard with their parents
D. all of the above
20. Inside a box are 5 balls; three whites and two blacks. If
balls are randomly drawn and tallied according to color,
what is the chance that at least once after the first tally
the colors have the same number of tallies?
A. 1/5
B. 2/5
C. 4/5
D. 3/5
11. AB is a diameter of a circle. BC is a chord 10 cm long.
CD is another chord. Angle BDC = 18. What is the area
of the circle in square cm.?
A. 633.4
B. 822.5
C. 744.3
D. 955.2
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Situation 1: A load of 6 kN is supported as shown in Figure
MEC-101. The weight of the pulley is 2 kN. Neglect the
weight of the bars.
1.
Which of the following most nearly gives the reaction (in
kN) at D?
A. 8.49
C. 6.00
B. 10.0
D. 8.00
2.
Which of the following most nearly gives the reaction (in
kN) at C?
A. 29.65
C. 24.16
B. 37.61
D. 33.40
3.
Which of the following most nearly gives the reaction (in
kN) at B?
A. 25.13
C. 20.91
B. 16.85
D. 21.38
Situation 2: The cable shown in Figure MEC-102 supports
three 400-N loads. If the maximum allowable tension in the
cable is 900 N,
4.
Find the smallest possible sag hc (in m) at C.
A. 5.43
C. 10.46
B. 6.53
D. 13.03
5.
Determine the tensile force (in N) at cable BC.
A. 744.31
C. 652.69
B. 601.67
D. 786.13
6.
Determine the tensile force (in N) at cable CD.
A. 744.31
C. 652.69
B. 601.67
D. 786.13
12. If P = 4,000 N, what is the amount of frictional force, in
N?
A. 1,012
C. 708
B. 880
D. 902
Situation 5: The hook is subjected to three forces as shown in
Figure MEC-105.
13. Determine the value of θ such that the resultant of the
three forces is 800 N acting vertically upward.
A. 33.75°
C. 56.25°
B. 26.39°
D. 63.61°
14. Determine the value of P (in N) such that the resultant of
the three forces is 800 N acting vertically upward.
A. 442.61
C. 800.01
B. 348.33
D. 506.23
15. Determine the magnitude of force P (in N) such that the
three forces are in equilibrium.
A. 448.53
C. 1,148.53
B. 406.23
D. 1,248.53
Situation 3: As shown in Figure MEC-103, the 800-kg wall
section is supported by the three vertical cables A, B and C.
7.
Which of the following most nearly gives the tension (in
N) at A?
A. 2,596.33
C. 2,616.00
B. 3,717.47
D. 1,534.20
8.
Which of the following most nearly gives the tension (in
N) at B?
A. 2,596.33
C. 2,616.00
B. 3,717.47
D. 1,534.20
9.
Which of the following most nearly gives the tension (in
N) at C?
A. 2,596.33
C. 2,616.00
B. 3,717.47
D. 1,534.20
Situation 4: The 2,225-N block shown in Figure MEC-104 is
in contact with 45° incline. The coefficient of static friction is
0.25 and the coefficient of kinetic friction is 0.20.
10. Compute the value of the horizontal force P (in N)
necessary to just start the block up the incline.
A. 4,523.11
C. 2,387.65
B. 3,708.33
D. 5,634.98
11. If P = 3,500 N, what is the amount of frictional force, in
N?
A. 1,012
C. 708
B. 880
D. 902
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B
C
D
3m
750 N/m
0.75 m
6 kN
A
2m
0.5 m
2m
2.5 m
Figure MEC-102
Figure MEC-101
Figure MEC-103
P
45º
Figure MEC-105
Figure MEC-104
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Mathematics (MSTE 5)
Review Innovations
1. Two lovers, Benben and Kaykay, are at different points 7. In the sequence
along the incline of Mt. Ulap, which is inclined 45°
. . . . . . , a, b, c, d, 0, 1, 1, 2, 3, 5, 8, . . . . . . . .
from the horizontal. Benben determines that the angle
each term is the sum of the two terms to its left. Find a.
of elevation of a hot air balloon to be 60°. At the same
A. -5
C. -1
instant, Kaykay measures the angle of elevation of the
B. -3
D. 0
same hot air balloon to be 75°. If Benben is 225 m down
the hill from Kaykay, find the distance between 8. A large rectangle is partitioned into four rectangles by
Kaykay and the hot air balloon.
two segments parallel to its sides. The areas of three of
A. 62.47 m
C. 467.25 m
the resulting rectangles are shown. What is the area of
B. 97.60 m
D. 225.00 m
the fourth rectangle?
2. A square flag has a red cross of uniform width with a
blue square in the center on a white background as
shown. (The cross is symmetric with respect to each of
the diagonals of the square.) If the entire cross (both the
red arms and the blue center) takes up 36% of the area
of the flag, what percent of the area of the flag is blue?
A. 20
B. 15
C. 25
D. 21
9. Three circles A, B and C are tangent externally to each
other and each tangent internally to a larger circle
having a radius of 10 cm. Radius of circle A is 5 cm.
Compute the distance from the center of the larger
A. 2%
C. 4%
circle to the point of tangency of the two circles B and
B. 3%
D. 5%
C which are identical.
A. 2.55
C. 4.15
3. Five equilateral triangles, each with side 2√3, are
B. 4.67
D. 3.33
arranged so they are all on the same side of a line
containing one side of each. Along this line, the 10. Find the equation of the line passing through the
midpoint of the base of one triangle is a vertex of the
points of intersection of the circles:
next. Find the area of the region of the plane that is
x2 + y2 – 4x – 6y + 4 = 0
covered by the union of the five triangular regions.
x2 + y2 + 2x + 4y + 1 = 0
A. 10
C. 10√3
A. 6x + 10y – 3 = 0
C. 6x + 10y + 3 = 0
B. 12
D. 12√3
B. 6x - 10y - 3 = 0
D. none of these
4. A square of perimeter 20 is inscribed in a square of 11. Two tangents were drawn from T to a circle and has its
perimeter 28. What is the greatest distance between a
point of tangency on the circle at A and B. The angle
vertex of the inner square and a vertex of the outer
between the tangents is 540. Point C is along the
square?
periphery of the circle and is nearer to T than A and B.
A. √58
C. √65
If the lines AC and BC are constructed, determine the
B. 8
D. 5√3
angle between the lines AC and BC at point C.
A. 1170
C. 1000
0
5. A student on vacation for “d” days observed that (1) it
B. 82
D. 600
rained 7 times morning or afternoon, (2) when it rained
in the afternoon, it was clear in the morning, (3) there 12. An earthquake is usually measured by the magnitude
were five clear afternoons, (4) there were six clear
M on the Richter Scale. The intensity I of an earthquake
mornings. Find the number of days “d”.
and the magnitude M are related by the formula:
A. 7
C. 10
M = log ( I / Io )
B. 9
D. 12
where Io is the intensity of an arbitrary chosen
earthquake. The earthquake that hit Kobe, Japan,
6. Kaykay and Benben start their new jobs on the same
measured 5.7 on the Richter Scale. The earthquake that
day. Kaykay’s schedule is 3 work-days followed by 1
hit Baguio, Philippines measured 7.8. How many times
rest-day. Benben’s schedule is 7 work-days followed
stronger is the earthquake that hit Baguio?
by 3 rest-days. On how many of their first 1000 days do
A. 148 times
C. 137 times
both have rest-days on the same day to have their “you
B. 126 times
D. 37 times
and me” time? :D
A. 50
C. 48
B. 100
D. 72
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13. A spherical triangle has a radius of 6m. Compute the
area of a bi-rectangular spherical triangle having an
angle of 800.
A. 46.18 m2
C. 50.27 m2
B. 48.36 m2
D. 52.72 m2
14. A spherical triangle ABC has an angle C = 900 and sides
a = 500 and c = 800. Find the value of side b.
A. 73.340
C. 74.330
0
D. 73.430
B. 74.44
15. Two chords AB and AC are equal and OB is also equal
to OC where point O is the center of the circle
circumscribing triangle ABC. If the angle BOC is 2280,
find the value of angle ABO.
A. 150
C. 280
B. 200
D. 330
16. A circle having a radius of 4cm is inscribed in a square
section. A smaller circle is also tangent to the two sides
of the square and to the bigger circle which is inscribe
in the square. Compute the radius of the smaller circle.
A. 0.50 cm
C. 0.61 cm
B. 0.58 cm
D. 0.69 cm
17. A cylindrical tank, 4m in diameter and 6m high is full
of water. It is then tilted to a position enough for the
water surface to cut the diameter of the base. How
much water is retained?
A. 12m3
C. 16m3
3
B. 14m
D. 18m3
18. The hypotenuse of a right triangle is 20cm long. Find
the circumference of its circum-circle.
A. 62.83 cm
C. 31.42 cm
B. 24.12 cm
D. can’t be determined 
19. Find y if log (xy) = 1.20412 and log (x/y) = 0.60206.
A. 4
C. 3
B. 2
D. 1
20. A spherical sector has a central angle of 600 and the
radius of the sphere is 15cm. Find the volume of the
spherical sector.
A. 944.27 cc
C. 946.61 cc
B. 945.88 cc
D. 947.19 cc
let’s do this. laban lang ha?ha?
- sir mike
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The cubic tank shown is half full of water.
1.
2.
3.
Find the pressure on the bottom of the tank in kPa.
A. 37.4
C. 17.8
B. 14.7
D. 22.7
Calculate the force exerted by the fluids on the tank
wall in kN.
A. 69
C. 83
B. 105
D. 124
Determine the location of the center of pressure on the
wall from the water surface in meters.
A. 0.315
C. 1.815
B. 1.185
D. 0.500
An 8 – m high triangular dam with a base width of 4.2 m
has water on its vertical face. The coefficient of friction at
the base may be assumed 0.6.
10. What depth of water will make the safety factor
against overturning 2.0?
A. 5.7
B. 6.3
C. 7.0
D. 7.7
11. What depth of water on its vertical upstream face will
make the safety factor against sliding 1.5 assuming a
coefficient of 0.6?
A. 5.7
C. 7.0
B. 6.3
D. 7.7
12. What depth of water on its vertical upstream face will
avoid tension at the base?
A. 5.7
B. 6.3
C. 7.0
D. 7.7
Three pipes steadily deliver water to a large exit pipe
shown in the figure. The velocity V2 = 5 m/s, and the exit
flow rate Q4 = 120 m3 /h. Find the following if it is known
that increasing Q3 by 20 percent would increase Q4 by 10
percent.
Water flows in an earth canal, trapezoidal, bottom width 3
m, sides sloped 3 horizontal on 1 vertical, at a depth of 62
cm. The canal is on a slope of 0.0008 and Manning’s n =
0.022.
4.
Calculate the amount of flow in m3/s.
A. 1.67
C. 2.22
B. 3.04
D. 3.82
5.
Calculate the shearing stress in Pa.
A. 2.27
C. 2.94
B. 3.42
D. 3.08
13. V1.
12. If the seepage rate is estimated at 46 cm /day, what
is the discharge after a length of flow of 1 kilometer?
A. 1.08
C. 2.26
B. 3.29
D. 2.18
14. V3.
6.
A jet of water issues out from a fire hydrant nozzle fitted
at a height of 3 m from the ground at an angle of 45° with
the horizontal. If the jet under a particular flow condition
strikes the ground at a horizontal distance of 15 m from the
nozzle,
7.
Find the jet velocity, in m/s.
A. 9.85
B. 11.07
A. 5.11
B. 5.45
C. 5.24
D. 5.89
A. 5.11
B. 5.45
C. 5.24
D. 5.89
A. 5.11
B. 5.45
C. 5.24
D. 5.89
15. V4.
C. 10.29
D. 13.33
8.
Determine the maximum height the jet can reach
above the nozzle, in meters.
A. 2.47
C. 2.85
B. 4.05
D. 3.12
9.
How far horizontally is the location of the maximum
height from the nozzle, in meters?
A. 7.21
C. 6.25
B. 8.15
D. 15
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Mathematics (MSTE 6)
Review Innovations
1. The distance between the foci of an ellipse is equal to 8 and the 8. The polar equation of the curve is expressed as:
second eccentricity is equal to 1.333. Compute the shortest focal
r = 2(sin θ + cos θ)
radius from point (x, 2). Consider the major axis along x-axis and
Compute the total length of the curve.
center at the origin.
A. 12.57
C. 8.89
A. 1.10
C. 3.03
B. 4.44
D. 6.29
B. 2.02
D. 4.04
9. Find the length of the conjugate axis of the equilateral hyperbola
xy = 16.
2. Ten people form a circle. Each picks a number and tells it to the
A. 5.66
C. 11.31
two neighbors adjacent to him in the circle. Then each person
B. 4
D. 8
computes and announces the average of the numbers of his two
neighbors. The figure shows the average announced by each 10. Points A, B, and C are on a circular track with AB as a diameter
person (not the original number the person picked). What is the
of the track. The angle of elevation of the top of a vertical pole
number picked by the person who announced the average 6?
standing at A as observed from B is 25°. If the horizontal angle
subtended by BC at A is 30°, what is the angle of elevation of the
top of the pole as observed from C?
A. 21.5°
C. 22.7°
B. 28.3°
D. 26.6°
A. 1
B. 5
11. A road is tangent to a circular lake. Along this road and 3 km
from the point of tangency, another road opens towards the
lake. The distance from this point of intersection of the two
roads to the periphery of the lake measured along this new road
is 2 km. If this new road is prolonged to cross the lake, what
would be the length of bridge required?
A. 2 km
C. 2.5 km
B. 3 km
D. 4.5 km
C. 6
D. 10
3. A circle centered at A with radius of 1 and a circle centered at B
with a radius of 4 are externally tangent. A third circle is tangent
to the first two and to one of their common external tangents as
shown. What is the radius of the third circle?
12. A lot has a frontage of 120m long along a road. The other sides
which are both perpendicular to the road are 90m and 60m
respectively. It is desired to subdivide the lot into two parts by
another perpendicular line to the road such that the area of the
lot that adjoins the 90m side is equal to 1/3 of the whole area.
Determine the length of the dividing line.
A. 71.41 m
C. 81.24 m
B. 74.11 m
D. 82.14 m
13.
Determine the area of the quadrilateral ABCD shown if OB
= 80cm, OA = 120cm, OD = 150cm and θ = 250.
A. 2/3
B. 4/9
C. 1/3
D. 5/9
4. Let a1, a2, . . . ., an be a finite arithmetic sequence with
a4 + a7 + a10 = 17 and
a4 + a5 + a6 + . . . + a12 + a13 + a14 = 77.
If an = 13, then find the value of n.
A. 16
B. 18
C. 20
D. 22
A. 2535.32 cm2
B. 2721.66 cm2
C. 2135.69 cm2
D. 2855.72 cm2
Situation 1:
The equation of the ellipse is given as:
5. A plane travels in a direction of N300W at an air speed of 600kph.
If the wind has a speed of 80kph on a direction of N400E, what is
the ground speed of the plane?
A. 631.85 kph
C. 605.31 kph
B. 613.85 kph
D. 650.31 kph
16x2 + 36y2 = 576
14.
Find the equation of polar of the point (4, -6) with respect
to the ellipse.
A. 4x – 3y = 36
C. 27x - 8y = 72
B. 3x – 4y = 36
D. 8x - 27y = 72
6. A hexagram formed by overlapping two equal equilateral
triangles, is inscribed in a circle of radius 6.928. Find the sides of
the equilateral triangle.
A. 10
C. 12
B. 11
D. 14
15.
Determine the equation of the diameter of ellipse which
bisects all chords having a slope of 3.
A. 4x + 27y = 0
C. 3x - 8y = 0
B. 27x – 4y = 0
D. 8x - 3y = 0
7. Find the volume of the solid whose equation is:
16.
25
A. 167.55
B. 146.82
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16
4
1
Compute the second eccentricity of the ellipse.
A. 1.12
C. 0.75
B. 1.21
D. 0.57
C. 154.12
D. 125.66
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1.
2.
3.
4.
The pressure of air inside a tank of oil is -12.5 kPa.
What is the absolute pressure, in kPa, if a barometer in
the locality registers 690 mm Hg?
A. 80
C. 98
B. 89
D. 114
Evaluate the amount of flow in a 4 – m Ø semicircular
channel if it is flowing full at critical stage. n = 0.011.
A. 20
C. 30
B. 25
D. 35
A 150-mm-diameter jet of water is discharged from a
nozzle into the air. The velocity of the jet is 36.0 m/s.
Find the power in the jet, in kW.
A. 346
C. 458
B. 412
D. 391
A block of steel (sg = 7.85) will float at a water mercury interface as shown. What will be the ratio of
distances “a” and “b” for this condition?
A. 0.63
C. 0.77
B. 0.70
D. 0.84
8.
9.
Calculate the pressure of gas.
A. – 7.52
B. – 3.12
C. 8.12
D. 10.2
Calculate the vertical force F applied at the apex of the
cone needed to hold it in position, in Newtons?
A. 1640
C. 3460
B. 2638
D. 4380
A 6 – m Ø cylindrical tank, 5.7 m high, discharges water
thru a 90 – mm Ø orifice, C = 0.61, in the conical bottom 30
– cm high.
10. Determine the time needed to empty the cylinder.
A. 1 hr 24 min
B. 1 hr 44 min
C. 1 hr 34 min
D. 1 hr 54 min
11. Compute the time needed to empty the conical part of
the tank.
A. 6 min
B. 10 min
C. 8 min
D. 12 min
12. Compute the total time needed to empty the tank.
A. 1 hr 50 min
B. 1 hr 54 min
C. 1 hr 52 min
D. 1 hr 56 min
The flow of water from reservoir A is 600 L/s.
5.
An 80-mm high glass, 75 mm in diameter, sits on the
edge of a merry-go-round 2.4 m in diameter, rotating
at 12 r/min. How full can the glass be before it spills,
in mm?
A. 68.9
C. 72.7
B. 66.1
D. 75.2
Two parallel pipes, 250 mm and 300 mm in diameter, bring
water from reservoir A to B. The difference in elevations
between the two reservoirs is 46 m. The 250 mm pipe is
3011 m long while the 300 mm one runs 3029 m. f = 0.02.
6.
7.
Evaluate the total discharge, in m3/s.
A. 0.200
C. 0.244
B. 0.222
D. 0.266
13. The water surface elevation of reservoir B is nearest to:
What size (m) of a single pipe 3008 m long, f = 0.016, is
needed to replace the 2 pipes?
A. 0.35
C. 0.45
B. 0.41
D. 0.50
A. 174.8
B. 162.5
C. 196.5
D. 181.3
14. The flow in line 2 in liters per second is nearest to:
A. 280
B. 270
C. 250
D. 260
The pressure gage shown reads 9.75 kPa.
15. The flow in line 3 in liters per second is nearest to:
A. 330
B. 350
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D. 320
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1.
2.
Given the perimeter of a triangle is 180 in. If the
angles of the triangle are in the ratio of 5:6:7. Find
the area of the triangle.
A. 1500
C. 1740
B. 1470
D. 1527
Given that (x,y) satisfies:
𝑥
𝑦
9, what is the largest possible value of
𝑥
3𝑦
4𝑥?
A. 29
B. 24
C. 36
D. 30
11.
Calculate the effective rate 18% compounded
semi-quarterly.
A. 19.25%
C. 18.81%
B. 19.1%
D. 19.48%
12. DK is being pursued by Jerwin. DK is ahead by 30
of his pace. How many paces must Jerwin take if he
takes 4 paces for the same time span that DK takes 5
paces, but 3 of the Jerwin’s paces is as long as 4 of
DK’s paces.
A. 480
C. 420
B. b.450
D. 360
If it were eight hours later, it would be half as long
until midnight as it would be if it were two hours
later. What time is it now?
A. 10AM
C. 8AM
B. 8PM
D. 10PM
13. Determine the value of k so that when
(kx + 1)(x-1)(x+3) + 2 is divided by
x + 2, the remainder is 11.
4.
Find the perimeter of an equilateral triangle
inscribed in a circle whose circumference is 12pi?
A. 31.18
C. 50.39
B. 20.78
D. 62.35
5.
Consider the arithmetic sequence 1,4,7,10,13… Find
the 200th element in the sequence.
A. 601
C. 598
B. 604
D. 595
14. A side of a square is 40 inches. The midpoints of its
sides are joined to form an inscribed square.
Another square is drawn in such a way that its
vertices would lie also at the midpoints of the sides
of the second square. This process is continued
infinitely. Find the sum of the areas of these infinite
squares in square inches.
A. 3200
C. 6400/3
B. b.800
D. 5463
6.
Find the units digit of 13
– 12
A. 3
B. 7
C. 5
D. 1
7.
Trigonometry: Suppose that tan 𝜃 5/12 ; cos 𝜃
0. Find sin 𝜃
A. 5/13
C. -5/13
B. 12/13
D. -12/13
8.
Two cars started at the same time, travelling
towards each other, from places 200km apart.
Determine the speed of the faster car if they meet
each other at the end of 3 hours and if the speed of
one is 10 km/hr greater than that of the other.
A. 25 kph
C. 35 kph
B. 40 kph
D. 30 kph
3.
9.
The sum of the first three elements in an arithmetic
sequence is 219. The sum of the first nine elements
in the same arithmetic sequence is 603. Find the
143rd element in this sequence.
A. 143
C. -209
B. 359
D. 169
10. Two sisters go up the 60-step escalator. The older
rides up the escalator, but can only take 20 steps up
during the ride since it is quite crowded. Her
younger sister runs up the down escalator, arriving
at the top at the same time as her sister. How many
steps does the younger take, assuming that both
escalators have the same rate?
A. 100
C. 80
B. 240
D. 120
A. 2/5
B. b.-5/3
C. 2
D. -9/5
15. The mean marks of 25 students is 95. It was later
discovered that two marks were incorrectly taken
as 65 and 75 instead of 56 and 57. What would be
the correct mean?
A. 96.08
C. 94.64
B. b.93.92
D. 92.26
16. What payment 10 years from now, is equivalent to
a payment of Php 1000 six years from now, if
interest is 15% compounded monthly?
A. 1749.01
C. 1815.35
B. b.1783.48
D. 1479.01
17. What is the future amount of Php 35,000 after 8
years if money is worth 7% compounded
continuously?
A. 62713.45
C. 62731.45
B. 61273.54
D. 67231.54
18. A businessman borrowed Php 10,000.000 with
interest at the rate of 5% payable annually. The debt
will be paid, principal and interest by equal
installments at the end of each year for 3 years.
Compute the annual payment.
A. 3276
C. 3267
B. b.3672
D. 3627
19. What is the angle of inclination of a line with slope
3/2?
A. 42°
C.56°
B. 34°
D.40°
20. Find the quadratic mean of the following numbers:
3,4,5,4,8,10,7.
A. 6.3133
C. 11.7143
B. 5.8571
D. 34.3061
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21. A point selected at random inside a circle. Find the
probability that the point is closer to the center of
the circle that to its circumference.
A. 1/4
C. 1/8
B. 1/2
D. 16/33
22. A student discovers that his grade on a recent test
was the 72nd percentile. If 90 students took the test,
how many students sure received a higher grade
than he did?
A. 25
C. 65
B. b.23
D. 27
23. Rosemarie was driving in a 500 mile race. After 250
miles, Rosemarie’s average speed was 150 miles per
hour. Approximately how fast should she drive the
second half of the race if she wants to attain an
overall average of 180 miles per hour?
A. 215
C. 230
B. b.220
D. 225
Find the ordered pair (a,b).
A. 1,-6
B. (-7/3, 22/3)
C. (7/3,-22/3)
D. (-1,6)
31. What is the fifth term of 2𝑥 𝑦 .
A. 8064𝑥 𝑦
C. 3360𝑥 𝑦
D. 4032𝑥 𝑦
B. 13440𝑥 𝑦
32. Find the exact value of the continues fraction
below.
2
1
A. ½
B. 1.5
2
1
1
2
⋯
C. 3/4
D. 1
33. The line segment joining any two non – adjacent
vertices.
A. Diameter
C. Secant line
B. Chord
D. diagonal
24. Suppose a and b are positive different from 1
satisfying:
𝑎𝑏 𝑎 ;
𝑎
Determine the value of 8a + 3b
a. 27
b. 28
30. Suppose that x – 1 and x + 2 are factors of
f(x)= 2𝑥
𝑎𝑥
7𝑥
𝑏.
C. 29
D. 30
25. Let x denote the smallest positive integer satisfying
12𝑥 25𝑦 for some positive integer y. What is the
value of x + y?
A. 75
C. 83
B. 81
D. 88
26. What is the area of the triangular region in the first
quadrant bounded on the left by the y-axis,
bounded by the line 7x + 4y = 168 and bounded by
the line 5x + 3y = 121
A. 106/3
C. 53/3
B. 50/3
D. 100/3
34. The distance between two parallel sides of a
quadrilateral
A. Skewed
C. base
B. Perpendiculars
D. altitude
35. It is the amount, which a willing buyer will pay to a
willing seller for the property where each has equal
advantage and is under no compulsion to buy or
sell.
A. Fair value
B. Utility value
C. Junk Value
D. Market Value
27. Analytic Geometry: Calculate the length of the
major axis of an ellipse if its eccentricity is 2/3 and
the distance between its directrices is 9√2.
A. 6√2
C. 12√2
D. 24√2
B. 3√2
28. Matthew borrowed money from a bank. He
received from the bank P1340 and promised to pay
P1500 at the end of 9 months. Determine the
corresponding discount rate.
A. 13.73%
C. 10.67%
B. 15.92%
D. 11.94%
29. Find the sum of all values of x that satisfy the
equation:
𝑥
5𝑥
5
A. 5
B. 17
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C. 20
D. 15
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SITUATION 1 - Refer to SA – 1. Wood planks are used to retain 3
m height of backfill. The active earth pressure increases
from zero at the free end to 24.5 kPa at the fixed end.
Given: Plank dimensions
Thickness
= 100 mm
Width
= 300 mm
Modulus of elasticity = 8.5 x 10ˆ3 MPa
1. Which of the following gives the maximum bending stress
(MPa) in the cantilevered wood planks?
A. 22.1
C. 15.6
B. 73.5
D. 13.0
2. Which of the following gives the lateral reaction (kN/m)
at the propped end if the planks are propped at the free
end but has a lateral displacement of 12.7mm?
A. 7.35
C. 6.35
B. 29.40
D. 17.40
3. If the wood planks are supported by a strut at mid-height,
what pulling force (kN/m) should be applied at the strut
prevent the free end from deflecting?
A. 11.1
C. 9.3
B. 13.9
D. 23.5
SITUATION 2 – Refer to Fig. SCM 10.07 and Fig. SA-1. A car hit
a tubular steel post at B. The post is fixed to the ground
at A.
Given:
Force from the car, P = 175 kN
Section of the Post
= 300mm x 300mm
Thickness of the post = 12mm
Modulus of elasticity, E = 200 GPA
H2 = 1.0m
H1 = 1.5m
4. What is the deflection (mm) at point B?
A. 1.53
C. 5.15
B. 14.58
D. 4.68
SITUATION 4 - A 3.5 m cantilever beam is reinforced with 3-28
mmØ tension bars. Concrete covering to centroid of
reinforcement is 65 mm at top and bottom of the section.
The beam has a total depth of 450 mm and width of 300
mm. fc’=21 MPa, fy=415 MPa and pb = 0.02161.
Use U = 1.2D + 1.6L.
10. Determine the nominal flexural strength of the section.
A. 200 kN-m
C. 240 kN-m
B. 220 kN-m
D. 260 kN-m
11. Determine the ultimate moment capacity of the section.
A. 180 KN-m
C. 216 KN-m
B. 161 KN-m
D. 193 KN-m
12. Determine the allowable concentrated service liveload
located at the free end the beam could support if it already
carries a total factored uniform load 15kN/m.
A. 22 KN
C. 35 KN
B. 18 KN
D. 28 KN
SITUATION 5 – Refer to Fig. SAM 10.04.
Given : b = 400 mm
h = 600 mm
t = 100 mm
S = 2.5 m
L1 = L2 = 7.5 m
Superimposed Dead Load, DL = 4.452 kPa
Live Load, LL
= 3.825 kPa
Unit Weight of Concrete
= 24 kN/m^3
Beam DEF is simply supported at D, E, and F.
For 2 spans both loaded, the negative moment at the interior
support is wL2/8.
For 1 span loaded, the negative moment at the interior
support is wL2/16.
For maximum stresses, apply the following:
1. Pattern loadings for Live Load
2. Ultimate Load Combination, U = 1.2D + 1.6L
5. What is the resulting displacement (mm) at point C?
A. 23.8
C. 28.6
B. 12.9
D. 10.3
6. What is the resulting maximum bending stress (MPa)?
A. 645
C. 344
B. 206
D. 387
SITUATION 3 - SA-2 and SAM-10.03
Given:
L1 = L2 = L3 = 8.0 m
S1 = 3.0 m
S2 = 2.5 m
Total dead load = 4.6 kPa
Live load = 1.9 kPa
The interior beam IJKL is to be analyzed for the
maximum forces at ultimate condition. U = 1.2D + 1.6L
13. What is the maximum moment (kN-m) at the interior
support E of beam DEF?
A. 293
C. 93
B. 146
D. 186
14. What is the maximum reaction (kN) at the interior support
E?
A. 390
C. 124
B. 312
D. 195
15. If the loads at ultimate condition are as follows:
Total DL wu = 24.0 kN/m
LL wu = 12.2 kN/m
find the maximum positive moment (kN-m) at span DE.
A. 212
C. 254
B. 195
D. 160
7. Which of the following gives the maximum reaction (kN) at
K?
A. 164
C. 247
B. 214
D. 207
8. Which of the following most nearly gives the maximum
positive moment on beam KL?
A. 120.5 kN-m
C. 131.5
B. 152.2
D. 117.1
9. Given:
Factored uniform dead load = 15kN/m
Factored uniform live load = 20kN/m
Which of the following most nearly gives the maximum
shear (kN)on beam KL?
A. 159 kN
C. 171
B. 168
D. 180
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Fig. SA-1
Fig. SAM 10.04
Fig. SCM 10.07
Figure SAM-10.03
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SA-2
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REFRESHER SET SEC-6
Situation: A double-angle tension member, 100
mm x 100 mm x 8 mm is subjected to a tensile load,
P = 210 kN. The diagonal member is on a slope
2V:1H and is connected to the supporting beam by
a wide tee.
S1 = 38 mm
t1 = 20 mm
S2 = 75 mm
t2 = 18 mm
S3 = 100 mm
t3 = 16 mm
Allowable strength and stresses:
Yield strength, Fy = 248 MPa
Ultimate strength, Fu = 400 MPa
Bolt shear strength, Fv = 150 MPa
Bolt tensile stress, Ft = 195 MPa
Bolt bearing stress, Fp = 1.2Fu
Assume that the bolts are equally loaded.
CE Refresher for May 2020
Situation: The deck of a bridge consist of ribbed
metal deck with 100 mm concrete slab on top. The
superstructure supporting the deck is made of
wide flange steel beams strengthened by cover
plate 16 mm x 260 mm, one at the top and one at
the bottom, and are spaced 1.2 m on centers. The
beams are simply supported over a span of 25 m.
The loads on each beam are as follows:
Dead load = 12 kN/m (including weight of beam
and deck)
Wheel live loads:
Front wheel = 18 kN
Rear wheel = 72 kN
Wheel base = 4.3 m
15
 30%
Impact factor = L  37
,
where L = length in m.
Properties of W 850 x 185:
A = 23.750 mm2
tw = 15 mm
d = 850mm
Ix = 2662 x 106 mm4
bf = 290 mm
Iy = 81.52 x 106 mm4
tf = 20 mm
4. Calculate the maximum bending stress in the
beam due to dead load.
A. 123 MPa
C. 92 MPa
B. 107 MPa
D. 98 MPa
5. Calculate the maximum bending stress in the
beam due to live load plus impact
A. 79 MPa
C. 68 MPa
B. 62 MPa
D. 56 MPa
6. Calculate the maximum average
web shear stress in the beam due to live load plus
impact
A. 7.6 MPa
C. 9.1 MPa
B. 8.5 MPa
D.12.4 MPa
1. Determine the required diameter “d1” (mm) of
the 3 bolts in shear connecting the double-angle
member to the wide tee.
A. 16
C. 12
B. 20
D. 25
2. Determine the required diameter “d2” (mm) of
the four bolts in tension connecting the wide
tee to the flange of the supporting beam.
A. 16
C. 12
B. 20
D. 25
3. Determine the required diameter “d2” (mm) of
the four bolts connecting the wide tee to the
flange supporting beam.
A. 16
C. 12
B. 20
D. 25
Situation: An 8 m propped cantilever beam
supports a uniformly distributed service dead
load (including its own weight) of 15 kN/m.
Properties of beam (Wide flange):
A = 19226 mm2
d = 540 mm bf = 312 mm
tf = 20 mm
tw = 12 mm
Sx = 3.72 x 106 mm3 Sy = 0.66 x 106 mm3
Zx = 4.14 x 106 mm3 Zy = 1.01 x 106 mm3
Ix = 1.00 x 109 mm3 Fy = 248 Mpa
E = 200 GPa
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7. Calculate the maximum uniformly distributed
service live load that the beam can support
considering flexure in the beam only. Assume
that the beam is compact and lateral-torsional
buckling is not critical. Use 1.2D+1.6L and
resistance factor (flexure): b = 0.9
A. 30 kN/m
C. 60 kN/m
B. 90 kN/m
D. 120 kN/m
8. Calculate the maximum uniformly distributed
service live load that the beam can support
considering shear in the beam only. Use
1.2D+1.6L
and resistance factor (shear): v = 1.0
A. 67 kN/m
C. 93 kN/m
B. 109 kN/m
D. 81 kN/m
9. Calculate the maximum uniformly distributed
service live load that the beam can support
considering deflection of the beam only if
maximum allowable deflection is L/360.
A. 130 kN/m
C. 145 kN/m
B. 165 kN/m
D. 185 kN/m
Refer to Figure. The butt connection shows 8 – 22
mm diameter A325 bolts spaced as follows:
S1 = 40 mm; S2 = 80 mm
S3 = 50 mm; S4 = 100 mm
Thickness of plates:
t1 = 16 mm; t2 = 12 mm
Steel strength and stresses are:
Yield strength, Fy = 248 MPa
Ultimate strength, Fu = 400 MPa
Allowable tensile stress on the gross area = 148
MPa
Allowable tensile stress on the net area = 200 MPa
Allowable shear stress on the net area = 120 MPa
Allowable bolt shear stress, Fv = 120 MPa
12. Based on block shear strength.
A. 230
C. 480
B. 307
D. 608
Situation: An 8-m long steel column is pinned at
the top and fixed at the bottom. The column is
provided with lateral support at mid height in the
 2 EI
weak direction. The Euler critical load is Pc 
(kL)2
The properties of the column section:
k
=
effective length factor
Ix = 178.1 x 106 mm4
Iy = 18.8 x 106 mm4
A = 8129 mm2
k = 1.0 when both ends are pinned
k = 0.5 when both ends are fixed
k = 0.7 when one end is fixed and other end is
pinned
13. What is the critical effective slenderness ratio of
the column?
A. 38
C. 54
B. 83
D. 58
14. Calculate the critical load Pc in kN?
A. 11210
C. 4733
B. 5493
D. 2319
15. Determine the minimum length of the column
for which the Euler’s formula is valid if the
proportional limit of the steel used is 320 MPa.
A. 11.7m
C. 3.8m
B. 7.6m
D. 10.8m
Calculate the allowable tensile load, T (kN), under
the following conditions:
10. Based on the gross area of the plate.
A. 571
C. 762
B. 381
D. 286
11. Based on the net area of the plate.
A. 528
C. 264
B. 352
D. 432
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REFRESHER SET MATH-11
1. [May 2019] A person driving her car at 45
km/hr approaches an intersection just as
traffic light turns yellow. She knew that the
yellow light lasts only 2 seconds before
turning red, and she is 28 m away from the
near side of the intersection. Should she try
to stop, or should she try to speed up to
cross the intersection before the light turns
red? The intersection is 15 m wide. Her car’s
maximum deceleration is 5.8 m/s^2, where
it can accelerate from 45 km/h to 65 km/h
in 6 seconds. Ignore the length of her car
and her reaction time.
A. She should stop
B. She should speed up
C. The accident is inevitable
D. She should turn off the car at the
start
2. Of 550 adults, 260 belong to A, 280 belong
to B, 340 belong to C and 280 belong to D.
130 belong to A and B, 90 Belong to A and
C, 140 to A and D, 160 belong to B and C, 70
belong to B and D, and 190 belong to C and
D. 40 belong to A,B, and C, and 50 belong to
A,B,D 60 belong to A,C,D, and 30 belong to
B,C,D. Determine the total number of adults
belong to A,B,C, and D, if all adults belong
to any of the said organization?
A. 8
B. 9 C. 10 D. 11
3. [May 2019] Solve for X from the following
equations:
XY = 12 ; YZ = 20 ; ZX = 15
A. 3
B.5
C.4
A. 1488.09 km
B. 2080 km
log 2 3 × log 3 4 × log 4 5 × … log 2012 2013
C. 2.321
D. 9.321
5. Suppose that an arithmetic sequence
begins with 1. Find the next element of the
sequence if the sum of the first five
elements is a quarter of the sum of the next
five elements.
A. 4
b. -2 c. ¼ d. 7/4
c. 480 km
d. 1040 km
7. A container is filled with 70 liters which is
40% alcohol by volume. How much mixture
must be taken and then replaced with equal
amounts of water so that the resulting
solution is 30% alcohol by volume.
A. 17.5 L
C. 20 L
B. 15 L
D. 22.5 L
8. In how many minutes after 10 o’clock will
the hands of the clock be perpendicular for
the second time?
A. 39.18 min
C. 37.18 min
B. 38.18 min
D. 36.18 min
9. The arithmetic mean and geometric mean of
two numbers are 17 and 8, respectively.
Find their harmonic mean.
A. 3.45
C. 3.54
B. 3.76
D. 3.67
10. Solve for E
𝑥 4 − 𝑥 3 + 14𝑥 2 − 2𝑥 + 22
(𝑥 + 1)(𝑥 2 + 4)(𝑥 2 − 2𝑥 + 5)
𝐴
𝐵𝑥 + 𝐶
=
+ 2
𝑥+1 𝑥 +4
𝐷𝑥 + 𝐸
+ 2
𝑥 − 2𝑥 + 5
A. 1
B. 2
D.60
4. Which of the following gives the simplified
value of:
A. 10.9751
B. 3.3038
6. Two aircrafts leave an airfield at the same
time. One travels due north at an average
speed of 300 kph and the other due west an
average speed of 220 kph. Calculate their
distance apart after 4 hours.
C. 3
D. 4
11. [May 2014] A box contains 100 washers.
Thirty-six are copper washers, 24 are brass
washers, and the rest are steel washers. A
washer is drawn from the box, retained,
then a second washer is drawn. Determine
the probability that both washers are steel.
A. 0.1600
C. 0.8000
B. 0.1480
D. 0.1576
12. [May 2014] A box contains 100 washers.
Thirty-six are copper washers, 24 are brass
washers, and the rest are steel washers. A
washer is drawn from the box, retained,
then a second washer is drawn. Determine
the probability that one washer is brass and
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A. 0.1910
B. 0.1920
CE Refresher for May 2020
C. 0.1939
D. 0.1857
13. [May 2014] A box contains 100 washers.
Thirty-six are copper washers, 24 are brass
washers, and the rest are steel washers. A
washer is drawn from the box, retained,
then a second washer is drawn. Determine
the probability that the first washer is brass
and the second is copper.
A. 0.0873
C. 0.1745
B. 0.1296
D. 0.0864
14. [May 2014] A tourist bus has 71 passengers
of which 10 of them are Chinese, 24 are
Japanese, and 37 are Filipinos. Three
passengers are randomly asked to get out of
the bus, one after the other. What is the
probability that the three passengers are
Chinese?
A. 0.0029
C. 0.0019
B. 0.0021
D. 0.0028
15. [May 2014] A tourist bus has 71 passengers
of which 10 of them are Chinese, 24 are
Japanese, and 37 are Filipinos. Three
passengers are randomly asked to get out of
the bus, one after the other. What is the
probability that the three passengers are
Japanese?
A. 0.0406
C. 0.0319
B. 0.0354
D. 0.0386
C.
16. [May 2014] A tourist bus has 71 passengers
of which 10 of them are Chinese, 24 are
Japanese, and 37 are Filipinos. Three
passengers are randomly asked to get out of
the bus, one after the other. What is the
probability that the three passengers are
Filipinos?
A. 0.1415
B. 0.1224
C. 0.1486
D. 0.1359
17. [May 2011] In a certain barangay, 80% of the
population has cellphones. If two persons
are selected at random from the population,
find the probability that one of the two
persons selected has one and the other has
none.
A. 0.48
C. 0.16
B. 0.64
D. 0.32
18. [May 2014] A box contains 100 washers.
Thirty-six are copper washers, 24 are brass
washers, and the rest are steel washers. A
washer is drawn from the box at random
and returned, then a second washer is
drawn. Determine the probability that both
washers are steel.
A. 0.1600
C. 0.8000
B. 0.1480
D. 0.1576
19. [Nov 2015] According to statistics 30% of
smokers want to quit smoking in a random
of 12 smokers. What is the probability that
the number of who want to quit smoking is
exactly 6?
A. 0.0093
B. 0.0544
C. 0.0679
D. 0.0792
20. The probability of heads on a toss of a bias
coin is 0.6. The coin is tossed six times. What
is the probability of getting exactly 4 heads?
A. 0.4147
C. 0.3110
B. 0.0664
D. 0.1382
21. 12 percent of cellphone parts produced by a
manufacturer are defective. Find the
probability that a sample of 20 parts
contains more than 4 defective ones.
A. 0.0886
C. 0.1299
B. 0.2127
D. 0.0827
22. [May 2014] A smartphone battery
manufacturer knows that for large
quantities, the lifetime of the battery is
normally distributed with an average
lifetime of 500 days, and a standard
deviation of 61 days. What percent of a
huge stock of batteries will have a lifetime
greater than 561 days?
A. 15.87%
C. 22.13%
B. 84.13%
D. 18.67%
23. [May 2015] A population has a mean of 84
and a standard deviation of 4. Find the
probability that a certain sample is within
80 and 88.
A. 0.7286
B. 0.7826
C. 0.6287
D. 0.6827
“Don’t stop when you’re tired, stop
when you’re done”
-
Johnny Sins
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Surveying & Transportation Engineering (MSTE 15)
1. A highway fill at stations 5+040 has a uniform ground slope.
above mean sea level and the mean ground elevation was 120
It has a side slope of 2:1 and width of roadway is 12 m. Find
m.
the area of Sta. 5+040.
12. What is the scale of the photograph?
STA. 5+040
A. 1:100
C. 1:10000
?
−4
−5
−6
?
B. 1:1000
D. 1:100000
13. Using this scale, what is the actual ground distance on a
?
6
0
6
?
map distance of 6.5 cm?
A. 216 m2
C. 166 m2
A. 6500 m
C. 650 m
B. 226 m2
D. 126 m2
B. 65 m
D. 65000 m
14. Using the same scale, what is the actual area (in square
A vertical curve must begin at the center of manhole 1 (Sta.
meter) on a map area of 10 square inches?
56+000, Elev. 60 m) and end at manhole 2 (Sta. 56+266, Elev.
A. 653,750
C. 620,740
58.78 m). The entering grade (at manhole 1) of -4% and the
B. 638,450
D. 645,160
exiting grade (at manhole 2) of +3% cannot be changed. It is
required to design an asymmetrical (unsymmetrical) vertical
A 20-mile section of a highway had the following reported
curve from manhole 1 to manhole 2.
accidents:
2. At what distance from manhole 1 will the two grades
YEAR
PROPERTY
INJURY FATAL
ADT
intersect?
1980
110
40
3
12000
A. 135.2
C. 131.4
1
12500
1981
215
52
B. 128.6
D. 125.4
5
16000
1982
170
60
3. What is the grade of the line connecting the PI of the first
x
13500
vertical curve with the PI of the second vertical curve
1983
250
74
through the asymmetrical curve?
y
14000
1984
160
96
A. +0.87%
C. -0.46%
15. What is the rate of total accidents if the severity ratio for a
B. +0.52%
D. -0.39%
period of 5 years is 0.2766?
4. What is the elevation of the CVC (compound vertical curve
A. 252
C. 283
point)?
B. 310
D. 301
A. 56.78
C. 54.74
B. 58.63
D. 57.07
16. It is defined as the number of vehicles per unit distance
occupying a section of roadway at a given instant time.
From the field notes of a closed traverse shown below:
A. Density
C. Flow
LINES
BEARING
DISTANCES
B. Capacity
D. Volume
AB
Due north
400
17. The number of vehicles moving in a specified direction on
BC
N 450 E
800
a given lane or roadway that pass a given point during
CD
S 600 E
700
specified unit time.
DE
S 200 W
600
A. Traffic Volume
C. Traffic Density
EA
S 870 W
966
B. Traffic Capacity
D. Basic Capacity
5.
What is the linear error of closure?
A. 0.70
C. 1.312
B. 2.015
D. 2.404
6. What is the relative error?
A. 1/1720
C. 1/1442
B. 1/4930
D. 1/2642
7. Using compass rule, what is the adjusted distance of line
EA?
A. 965.425
C. 966.123
B. 966.580
D. 964.891
8. Using compass rule, what is the adjusted bearing of
line EA?
A. S86058’49’’W
C. S86010’20’’W
0
B. S88 56’20’’W
D. S8700’50’’W
A reverse curve has perpendicular distance between two
parallel tangents equal to 6 m, the central angle being equal to
70 and the radius of curvature of the first curve is 163.8 m.
9. Find the offset distance from back tangent to PRC.
A. 1.98 m
C. 0.75 m
B. 1.39 m
D. 1.22 m
10. Determine the offset distance from the forward tangent to
PRC.
A. 4.78 m
C. 4.02 m
B. 4.61 m
D. 5.25 m
11. Compute the radius of the second curve.
A. 641.28 m
C. 614.16 m
B. 578.32 m
D. 498.25 m
An aerial photograph was taken using a camera with a focal
length 12 cm. The plane was flying at an altitude of 1320 m
18. The ability of a roadway to accomodate traffic volume. It is
expressed as the maximum number of vehicle in a lane or a
road that can pass a given point in unit time.
A. Traffic Volume
C. Traffic Density
B. Traffic Capacity
D. Basic Capacity
19. The maximum number of passenger cars that can pass a
given point on a lane or roadway during one hour under
the most nearly ideal roadway and traffic conditions which
can possibly be attained.
A. Possible Capacity
C. Traffic Capacity
B. Practical Capacity
D. Basic Capacity
20. The maximum number of passenger cars that can pass a
given point on a lane or roadway during one hour under
prevailing roadway and traffic conditions.
A. Possible Capacity
C. Traffic Capacity
B. Practical Capacity
D. Basic Capacity
21. The maximum number of passenger cars that can pass a
given point on a lane or roadway during one hour without
traffic density being so great as to cause unreasonable delay,
hazard, or restrictions to the driver’s freedom to maneuver
under traffic conditions.
A. Posible Capacity
C. Traffic Capacity
B. Practical Capacity
D. Basic Capacity
22. The instantaneous speed of a vehicle at a specified section
or location.
A. Average speed
C. Travel speed
B. Running speed
D. Spot speed
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23. The average speed of vehicles in a certain road length at any
35. Signs used to guide drivers through a change in horizontal
time.
alignment of the road.
A. Instantaneous speed
C. Space mean speed
A. Chevron signs
C. Guide signs
B. Average speed
D. Spot speed
B. Supplementary signs
D. Delineators
24. The average of the spot speeds of all vehicles passing a
given point in the highway.
A. Average speed
C. Travel speed
B. Instantaneous speed
D. Spot speed
25. The speed distribution of vehicles at a point on the roadway
and it is the average of instantaneous speeds of observed
vehicles at the spot.
A. Instantaneous speed
C. Time mean speed
B. Average speed
D. Space mean speed
26. Device mounted on a fixed support (permanent signs) or
portable support (temporary signs) whereby a specific
message is conveyed by means of words or symbols placed
or erected for the purpose of regulating, warning or guiding
traffic.
A. Roadwork signs
C. Overhead signs
B. Traffic signs
D. Special instruction signs
27. Signs that inform road users of the traffic laws and
regulations which is disregarded will constitute an offense.
A. Warning Signs
C. Overhead Signs
B. Regulatory Signs
D. Guide Signs
28. Signs that instruct road users to meet certain traffic rule
requirements on road condition.
A. Special Instruction Signs C. Warning Signs
B. Regulatory Signs
D. Guide Signs
29. Signs which warn road users of condition on or adjacent to
the road maybe unexpected or hazardous.
A. Overhead Signs
C. Warning Signs
B. Roadwork Signs
D. Guide Signs
30. Signs which warns or advise temporary hazardous
conditions that could endanger road users or the men and
equipment engaged on roadworks.
A. Overhead Signs
C. Warning Signs
B. Roadwork Signs
D. Guide Signs
31. Signs which provide means of displaying essential traffic
information on wide multi-lane roads, where some degree
of lane use control is required or where side of road
clearance is insufficient to accomodate a road side sign.
A. Overhead Signs
C. Warning Signs
B. Roadwork Signs
D. Guide Signs
32. Signs which inform and advise road users of directions,
distances, routes and the location of services for road users
and point of interest.
A. Overhead Signs
C. Warning Signs
B. Roadwork Signs
D. Guide Signs
33. Type of sign used in advance of an intersection where the
two roads cross at a common point.
A. T-junction sign
C. Supplementary sign
B. Crossroad sign
D. Priority Cross
34. Sign used only in conjunction with another warning sign to
indicate the desirable speed in good weather, traffic and
road conditions.
A. Advisory speed sign
C. Supplementary speed sign
B. Crossroad speed sign
D. Side road speed sign
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Situation 1: The force P is acting along the centroidal
axis of the welds at a distance “a” from the weld (L2).
Do not include end turns.
Properties of vertical member:
2 angles 75 mm x 75 mm x 8 mm thick
Area of 2 angles = 2290 mm2
Fy = 248 MPa Fu = 400 MPa
Allowable tensile stress based on gross area = 0.6Fy
Allowable tensile stress based on net area = 0.5Fu
Properties of the fillet weld:
Allowable weld shear stress = 0.3Fu
Fu = 414 MPa
Weld thickness = 8 mm
4. Which of the following gives the maximum
bending stress (MPa) in beam BF?
A. 217
C. 248
B. 145
D. 98
5. Lateral supports are to be provided. Find the
biggest distance (m) between lateral supports so
that the maximum allowable flexural stress can be
utilized.
A. 1
C. 3
B. 2
D. 4
6. What is the permissible flexural stress (MPa) if the
compression flange of the beam is laterally
supported only at midspan? Cb = 1.0
A. 117
C. 130
B. 126
D. 142
1. Which of the following gives the maximum tensile
force P based on tension in the of the angles? Use U
= 0.85
A. 341 kN
C. 713 kN
B. 682 kN
D. 357 kN
2. If L1 = 50 mm and L2 = 130 mm, which of the
following gives the allowable load P based on shear
in the weld?
A. 159 kN
C. 184 kN
B. 167 kN
D. 253 kN
3. If P = 540 kN, which of the following gives the
required length of weld at the right (L2), so that each
fillet weld is equally stressed in shear?
A. 280 mm
C. 320 mm
B. 340 mm
D. 300 mm
Situation 2: Refer to figure:
Given: S = 3 m L = 10 m
Superimposed dead load = 6.0 kPa Live load = 4.8 kPa
Properties of beam BF:
Section = W 468 mm x 97 kg/m Areas, A = 12,324 mm2
d = 465 mm, bf = 193 mm, tf = 19 mm, tw = 11 mm
Ix = 445x106 mm4 Iy = 23x106 mm4 Yield strength = 344
MPa rt = 50 mm
Considering bending about x-axis.
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Situation 3: A hollow circular steel column is
supported on a steel base plate and a concrete pedestal.
Column ends are hinged and sidesway is prevented.
Given:
Column axial load = 780 kN Column inside diameter
= 250 mm
Allowable column compressive stress = 55 MPa
Allowable concrete bearing stress = 10 MPa
7. Calculate the critical slenderness ratio of the
column if its thickness is 10 mm and a height of 3
m.
A. 32.6
C. 84.9
B. 23.6
D. 48.9
Assume pinned ends for both axes. Sidesway is
prevented.
13. Compute the effective slenderness ratio with
respect to the x-axis.
A. 127.45
C. 94.16
B. 117.66
D. 34.00
14. Compute the effective slenderness ratio with
respect to y-axis.
A. 94.16
C. 34.00
B. 117.66
D. 127.45
15. Compute the bucking stress of the column.
A. 431 MPa
C. 138 MPa
B. 381 MPa
D. 223 MPa
8. Find the minimum required thickness (mm) of the
column.
A. 16
C. 14
B. 18
D. 20
9. What is the safe diameter (mm) of the base plate?
A. 280
C. 340
B. 320
D. 300
Situation 4: A simply supported steel beam spans 9 m.
It carries a uniformly distributed load of 10 kN/m,
beam weight already included.
Beam (wide flange) properties:
Area = 8530 mm2
Depth = 306 mm
Flange Width = 204 mm
Flange Thickness = 8.5 mm
Moment of Inertia, Ix = 145 x 106 mm4
Modulus of elasticity, E = 200 GPa
10. What is the maximum flexural stress in the beam?
A. 106.8 MPa
C. 111.2 MPa
B. 101.3 MPa
D. 118.5 MPa
11. To prevent excessive deflection, the beam is
propped at mid span using a pipe column. Find the
resulting axial stress in the column. Outside
diameter = 200 mm, thickness = 10 mm, height = 4
m.
A. 9.4 MPa
C. 5.2 MPa
B. 7.8 MPa
D. 6.6 MPa
12. How much is the maximum bending stress in the
propped beam?
A. 22.0 MPa
C. 26.7 MPa
B. 19.8 MPa
D. 33.8 MPa
Situation 5: A column is built-up from 4 – 300mm x
16mm plates, welded to form a box section having a
width of 300mm along the x-axis and a depth of 332mm
along y-axis. Unbraced column length with respect to
lateral bucking about the x-axis is 12m. With respect to
lateral bucking about the y-axis, the column is braced
at third points so that the unbraced length is 4m.
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From the measured values of distance
following trials were recorded.
TRIALS
DISTANCE
1
120.76
2
120.68
3
120.84
4
120.64
1. Find
A.
B.
2. Find
A.
B.
3. Find
A.
B.
AB,
the
14. A line was measured by a 100m tape and found
out to be 400m long. It was found out that the
first pin was displaced 20cm to the left of the
line, the second pin was displaced 40cm to the
right, and the third pin was stuck 30cm to the
left of the line. Determine the error in the
measurement in cm.
A. 0.31
C. 0.23
B. 0.54
D. 0.49
the probable error.
±0.030
C. ±0.044
±0.089
D. ±0.091
the standard deviation.
±0.030
C. ±0.044
±0.089
D. ±0.091
the standard error.
±0.030
C. ±0.044
±0.089
D. ±0.091
15. The maximum allowable rate of crashes at
intersections is 9 per million entering vehicles.
At an intersection of 2 roadways, average daily
traffic (ADT) values are 10,000 and 8,265.
Determine the maximum number of crashes per year
before corrective action is needed.
A. 30 crashes
C. 60 crashes
B. 40 crashes
D. 80 crashes
Given the following sections:
4.05
+0.84
Station 3+080
3.00
0
3.00
+3.50
2.85 +2.12
7.05
+3.24
7.80
+3.84
Station 3+100
2.00
0
4.00
+2.42 +3.25 +2.50
5.65
+2.12
The base of road is 6 m and the sideslope 1.25:1
4. Find the area of the first station.
A. 32.15 m2
C. 31.14 m2
B. 28.52 m2
D. 23.11 m2
5. Find the area of the second station.
A. 24.36 m2
C. 35.22 m2
B. 22.97 m2
D. 27.11 m2
6. Compute the volume between the two stations
using end area method.
A. 460.80 m3
C. 502.20 m3
B. 474.70 m3
D. 583.30 m3
The deflection angles of two intermediate points A
and B along the simple curve are 3° 30’ and 8° 30’
respectively from PC. If the chord distance between
A and B was 40 m, determine the following:
7. Radius of the curve.
A. 286.48
C. 229.47
B. 190.99
D. 254.32
8. Arc distance from PC to B.
A. 63.01
C. 70.70
B. 65.31
D. 68.09
9. Offset distance from back tangent to point B.
A. 13.06
C. 12.04
B. 8.02
D. 10.03
A grade of -5% is followed by a grade of +1%, the
grades intersecting at the vertex (Sta.10+060).
The change of grade is restricted to 0.40% in 20m.
10. Compute the length of the vertical parabolic
sag curve in meters.
A. 200 m
C. 300 m
B. 250 m
D. 350 m
11. Find the value of K (length of curve for every
1% of change in slope/grade).
A. 25 m
C. 75 m
B. 50 m
D. 100 m
12. A 50 m tape weighing 1.075 kg has a standard
pull of 8 kg. The tape’s cross-sectional area
and modulus of elasticity are 0.05 cm2 and 200
GPa respectively. What pull is required in order
that the effect of sag will be eliminated when
the tape is supported at the end points only?
A. 385.06 N
C. 20.12 N
B. 84.91 N
D. 197.40 N
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13. A line was measured with a 20 m tape. There
were 3 tallies and 6 pins, and the distance from
the last pin and the end of the line was 3.75 m.
Find the length of the line in meters.
A. 732.75 m
C. 725.32 m
B. 723.75 m
D. 727.57 m
16. The driver of a vehicle traveling at 80 kph
up a grade requires 9 m less to stop after he
applies the brakes than the driver traveling at
the same initial speed down the same grade. If
the coefficient of friction between the tires and
pavement is 0.50, what is the percent grade?
A. 3.84%
C. 5.34%
B. 6.12%
D. 4.43%
17. Two cars are approaching each other from the
opposite directions at a speed of 120 kph and 90
kph respectively. Assuming a reaction time of 2.0
seconds and a coefficient of friction of 0.60
with a brake efficiency of 50%. Compute the
minimum sight distance required to avoid a head
on collision of the two cars.
A. 394.44 m
C. 411.62 m
B. 255.44 m
D. 156.18 m
18. Determine the elevation of the design low
tide (DLT), which is the water level that
guarantees about 98% of tide, which is safe to
the ships using the sheet pile type.
Elev. of HWL = +1.31 m
Elev. of RWL = +0.75 m.
A. -0.31 m
B. -0.33 m
19. Compute
gravity type
level.
Elev. of
Elev. of
Elev. of
C. -0.35 m
D. -0.37 m
the distance
quaywall to
A. 2.57 m
B. 2.68 m
from the top of a
the residual water
HWL = +1.52 m
LWL = -0.28 m
the top of the quaywall = +3.00 m
C. 1.80 m
D. 2.10 m
20. A rectangular barge is 20 m long, 12 m wide
and 8 m deep. It enters the harbor of Cebu City
having a low tide (DLT) equal to -0.30 m. The
harbor facility is protected by riprap to prevent
scouring. The weight of the barge when empty is
equal to 1000 tons. Assuming sp. gr. of seawater
to be 1.03 m and that max. depth of water in the
harbor is 6.4 m deep, determine the maximum weight
of tons that the barge can carry safely based on
the specification of the (PPA) Phil. Ports
Authority regarding standard water depth.
A. 508
C. 847
B. 1020
D. 765
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21.
A wave at a point where the depth is equal
to ½ of the wavelength or greater to be
expressed in terms of the parameters of
significant wave.
A. Deep Water Wave
C. Significant Wave
B. Highest Wave
D.Equivalent Depth Wave
22.
A hypothetical wave having a wave height and
period equal to average values of the wave
height and period of the largest 1/3 of all waves
in the train as counted in the order of greater
wave height.
A. Deep Water Wave
C. Significant Wave
B. Gravity Wave
D.Equivalent Depth Wave
23. A maximum wave height
maximum wave height in
A. Transitional Wave
B. Highest Wave
and wave period of the
the wave train.
C. Significant Wave
D.Equivalent Depth Wave
24. Waves formed by the frictional drag of wind
across the water surface.
A. Shallow Wave
C. Significant Wave
B. Transitional Wave
D. Gravity Wave
25. The pressure against a vertical wall due to
waves.
A. Wave Decay
C. Rankines Active Pressure
B. Dynamic Pressure D. Clapotis
26. The distance that the wind blows over the sea
in generating the waves is known as:
A. clapotis
C. seiche
B. wakes
D. Fetch
27. The regular periodic rise and fall of the
surface of the seas, observable along their
shores.
A. wave
C. period of wave
B. tide
D. Current
34. Tides which occurs only one high tide a day
is called:
A. Semi-diurnal tide
C. Neap tide
B. Diurnal tide
D. Spring tide
35. Waves formed by moving ship or boats are
called:
A. Wakes
C. Breaking waves
B. Swell
D. Seiching
36. The distance between the front of a vehicle
and the front of the followingg vehicle
A. Spacing of vehicles C. Lag
B. Space Headway
D. Gap
37. The difference between the
of a vehicle arrives at a point
and the time the front of the next
at the same point.
A. Time Headway
C. Gap
B. Regression time
D. Time
time the front
on the highway
vehicle arrives
lag
38. The time interval between the arrival of a
vehicle wishing to cross an uninterrupted stream
of vehicles on an intersecting path and the
arrival of the next vehicle in that stream is
known as:
A. Lag
C. Headway
B. Gap
D. Time delay
39. The separation between the corresponding
points on two successive vehicles minus the
separation occupied by a vehicle is known as:
A. Lag
C. Headway
B. Gap
D. Time delay
40. Which
of
the
following
standard
abbreviation of signs is not correct?
A. EX for Expressway
C. RD for Road
B. HWY for Highway
D. AVE for Avenue
28. The falling tide is known as:
A. Ebb tide
C. Neap tide
B. Flood tide
D. Spring tide
29. Waves generated by storms, which occur outside
area of observation.
A. Swells
C. Skewd
B. Shoal
D. Ebb
30. A very long standing wave on a large but limited
body of water generally occurring when a storm
dies down after producing a wind tide.
A. Seiche
C. Ebb
B. Shoal
D. Skewd
31. An instrument use to measure the intensity of
wind.
A. Buchanan’s scale
C. Beuforts scale
B. Fiboracci scale
D. Antwerp scale
32. In many parts of the world, the high waters
reach their greatest height and the low waters
at the least height, soon after the time of full
moon and new moon. These tides are called:
A. Spring tide
C. Neap tide
B. Flood tide
D. Ebb tide
33. When the lines connecting the earth with the
sun and the moon form a right angle, that is the
moon is in its quarters, then the actions of the
moon and sun are subtractive, and the lowest
tides of the month occur, this is called:
A. Neap tide
C. Diurnal tide
B. Lunar tide
D. Ebb tide
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1.
2.
3.
A ship having a displacement of 20,000 metric tons
enters a harbor of fresh water. The ship captain
recorded a draft of 8.4 m while the ship was still in
seawater (specific gravity = 1.03). Obtain the draft, in
meters, of the ship in fresh water if the horizontal
section of the ship below the waterline is 3000 m2 in
both instances.
A. 8.79
C. 9.54
B. 7.78
D. 8.59
If aluminum weighs 25.9 kN/m3, how much will a 305mm-diameter sphere weigh (N) when immersed in
water.
A. 146
C. 1912
B. 385
D. 239
Gate AB in the given figure is a quarter circle 3 m wide
into the paper. Find the force F (kN) to prevent rotation
about hinge B. Neglect the weight of the gate.
A. 42.4
C. 14.1
B. 36.4
D. 28.1
F
A
water
r=2.4
B
4.
Water is flowing in an 8 – m wide rectangular channel
at a rate of 17.6 m3/s. What smallest amount of energy
can maintain this discharge, in meters?
A. 1.2
C. 2.0
B. 1.6
D. 2.4
5.
A 1.2 m Ø steel pipe, 10 mm thick, carries water at a
velocity of 1.56 m/s. For the pipe, E=200,000 MPa and
for water, Eb = 2158 MPa. The pipe is 910 m long and a
valve at the discharge end is shut in 3s. What is the
water hammer pressure, in kPa?
A. 1513
C. 1207
B. 946
D. 1065
6.
A hydrometer weighs 0.0216 N and has a stem at the
upper end that is cylindrical and 2.8 mm in diameter.
How much deeper (mm) will it float in oil of sp gr 0.780
than in alcohol of sp gr 0.821?
A. 25
C. 21
B. 27
D. 23
9.
At what speed, in rpm, would the tank be rotated if the
pressure at the center of the bottom of the tank is zero?
A. 218.9
C. 206.1
B. 223.8
D. 231.7
A rectangular canal is 5.2 meters wide and 1.2 meters
depth. The canal is laid on a uniform slope of 0.001 and
roughness coefficient is 0.012.
10. Calculate the discharge in the canal, in m3/s.
A. 14.4
B. 15.8
11. What savings in lining (m2), per meter length of canal
could have been attained if the most efficient section
rectangular section were used for the same discharge
and slope?
A. 0.66
C. 0.49
B. 0.57
D. 0.75
12. What savings in earth excavation (m3) per meter length
of canal could have been attained if the most efficient
rectangular section were used for the same discharge
and slope?
A. 0.33
C. 0.41
B. 0.17
D. 0.22
In the figure, reservoir A is the source of water supply and
is at Elev. 150 m, B is the junction at Elev. 91.46 m, C is a
town at Elev. 30.49 m with 25,000 inhabitants, D is another
town at Elev. 15.24 m with a population of 30,000. Length
AB is 15,240 m, BC is 9150 m, BD is 6100 m. Determine the
size of the pipes if the consumption is 150 liters per capita
per day. For the pipes, frictional factor f = 0.02. Determine
the required diameter, in meters, of.
13. Pipe AB.
An open cylindrical tank 0.40 m in diameter and 1.20 m
high is partially filled with water.
14. Pipe BC.
If it is rotated about its vertical axis at 200 rpm,
determine the depth of water if there is no water
spilled out.
A. 0.894
C. 0.753
B. 0.447
D. 0.306
15. Pipe BD.
7.
8.
C. 12.7
D. 14.9
A. 0.450
B. 0.330
C. 0.390
D. 0.420
A. 0.366
B. 0.500
C. 0.216
D. 0.196
A. 0.450
B. 0.205
C. 0.300
D. 0.150
At what speed, in rpm, would the tank be rotated if 3.5
liters of water is spilled out?
A. 231.7
C. 223.8
B. 206.1
D. 218.9
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CE Refresher for May 2020 - Hydraulics 1
Review Innovations
1.
A vertical clean glass piezometer tube has an inside diameter
of 1 mm. When a pressure is applied, water (σ = 0.0728 N/m)
rises into the tube to a height of 25 cm. After correcting for
surface tension, estimate the applied pressure in Pa.
A. 2452
C. 2747
B. 2158
D. 2205
2.
What is the best width for a rectangular brick channel
designed to carry 5 m3/s of water in uniform flow with So =
0.001? use n = 0.015
A. 1.12
C. 2.24
B. 1.27
D. 2.54
3.
A 100 – mm diameter solid cylinder of height 95 mm
weighing 3.78 N is immersed in liquid (γ=8168 N/m3)
contained in a tall, upright metal cylinder having a diameter
of 120 mm. Before immersion the liquid was 75 mm deep.
What is the increase in the depth of water in the container, in
mm?
A. 59
C. 68
B. 41
D. 35
4.
Water in the pressurized tank flows out and creates a vertical
jet as shown. Assuming steady frictionless flow, determine
the height (m) H to which the jet rises.
A. 8.5
C. 6.5
B. 7.5
D. 9.5
10. A water- filled bulb within a chamber is connected to the
outside by two U- tube manometers as shown in the figure.
Determine the gauge pressure (kPa) in the bulb.
A. 102.8
C. 78.1
B. 85.7
D. 93.2
11. In a bakery, water enters a mixing chamber at the rate of
150 liters per sec through Pipe A, while cooking oil with
specific gravity of 0.80 is forced at 30 liters per sec through
pipe B. Assuming the liquids are incompressible and
from a homogeneous mixture of oil globules in water,
evaluate the density of the mixture
in kg/m3 leaving
through a pipe of diameter 300 mm.
A. 712
C. 967
B. 876
D. 1000
12. A block of wood floats in water with 50 mm projecting above
the water surface. When placed in glycerin of sp gr 1.35, the
block projects 76 mm above the surface of that liquid.
Determine the specific gravity of the wood.
A. 0.67
C. 0.57
B. 0.84
D. 0.91
5.
The fuel gage for a gasoline tank in a car reads proportional
to the bottom gage pressure. If the tank is 30 cm deep and
accidentally contains 2 cm of water plus gasoline, how many
centimeters of air remain at the top when the gage
erroneously reads “full”? For gasoline, sg = 0.68.
A. 0.94
C. 1.12
B. 0.86
D. 1.25
6.
An open cylindrical vessel having a height equal to its
diameter is half filled with water and rotated about its own
vertical axis at a constant speed of 120 rpm. Evaluate its
minimum diameter so that there can be no liquid spilled?
A. 0
C. 0.497
B. 0.368
D. 0.551
7.
A symmetrical trapezoidal channel having sides sloping
1V:1.5H is laid on a slope of 0.00065 m. Calculate the
hydraulic mean depth for a base width of 4.1 m, depth of
flow is 1.6 m and n = 0.014.
A. 0.93
C. 1.17
B. 1.05
D. 1.29
8.
A cubic tank is filled with 1.5 m of oil, sp gr 0.752. Find the
force acting on the side of the tank, in kN, when the
acceleration is 4.9 m/s2 vertically upward.
A. 12.4
C. 18.7
B. 9.30
D. 6.22
9.
A turbine is rated at 450 kW when the flow of water through
it is 0.609 m3/s. Assuming an efficiency of 87%, what head is
acting on the turbine, in meters?
A. 75.3
C. 65.5
B. 90.8
D. 86.6
13. A block of wood (SG = 0.6) floats in fluid X in the figure such
that 75 percent of its volume is submerged in fluid X.
Estimate the vacuum pressure (Pa) of the air in the tank.
A. - 3234
C. -2874
B. - 3139
D. -2946
14. A cubical float, 1.22 m on a side, weighs 1.78 kN and is
anchored by means of a concrete block that weighs 6.67 kN
in air. If 229 mm of the float is submerged when the chain
connected to the concrete is taut, what rise in water level, in
mm, will lift the concrete off the bottom? Concrete weighs
23.56 kN/m3.
A. 225
C. 390
B. 195
D. 160
15. Evaluate the discharge (m3/m·s) if hydraulic jump occurs in
a rectangular channel from 0.22 m to 0.84 m.
A. 0.98
C. 1.48
B. 1.28
D. 1.65
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CE Refresher for May 2020 – Geotechnical Engineering 1
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A prestressed concrete pile, 300 mm x 300 mm in crosssection, is to be driven in a clayey soil (γ = 18.5 kN/m3). The
design pile has a design capacity of 450 kN. Use factor of
safety of 2. The unconfined compression shear strength, qu of
the soil is 110 kPa. Use Nc = 9.
1. What is the end bearing capacity of pile in kN.
A. 44.6
C. 62.7
B. 58.6
D. 75.4
2. Compute the skin friction in kN expected to develop
along the shaft of the pile.
A. 855.5
C. 754.2
B. 963.2
D. 689.1
3. Compute the length of pile if frictional constant α =
0.6.
A. 14.5 m
C. 21.6 m
B. 28.4 m
D. 18.5 m
Two footings rest in a layer of sand 2.7 m thick. The bottom
of the footings are 0.90 m below the ground surface. Beneath
the sand layer is a 1.8 – m thick clay layer. Underneath the
clay layer is solid rock. Water table is at a depth of 1.8 m
below the ground surface. See Figure 1.
4. Compute the stress increase in kPa below the footing
A (1.5 m x 1.5 m) at the center of the clay layer.
Assume that the pressure beneath the footing A is
spread at an angle of 2 vertical to 1 horizontal.
A. 20.15
C. 22.50
B. 30.75
D. 25.51
5. Determine the size of footing B so that the settlement
in the clay layer is the same beneath footings A and
B.
A. 2.85 m x 2.85 m C. 1.80 m x 1.80 m
B. 3.24 m x 3.24 m D. 3.68 m x 3.68 m
6. Determine the settlement in mm beneath footing A.
A. 34.70
C. 58.10
B. 30.85
D. 46.65
7.
8.
9.
A rectangular footing is to support two square
columns each 12” x 12” and spaced 12 feet of centers.
One column carries a load of 40 kips and the others
carries a load of 50 kips. The footing is 2 ft thick and
its length shoe extend 2.5 ft beyond the center of the
column carrying the 40 kip load. The base of the
footing is 5 ft below the ground surface. Assume
specific gravity of concrete and soil above the footing
to be 2.4 and 1.78 respectively. Determine the length
of the footing if the allowable soil bearing capacity is
2000 psf.
A. 18.34 ft
C. 20.74 ft
B. 15.21 ft
D. 17.23 ft
A soil sample has a moisture content of 30% and
degree of saturation of 45%. The solids has a specific
gravity of 2.61. Determine the dry unit weight of the
soil in kN/m3.
A. 8.52
C. 9.34
B. 12.14
D.10.25
A cohesionless soil sample is subjected to an axial
stress with liquid pressure of 18 kPa in the chamber.
It was observed that shear failure occurs when the
axial compressive stress is 34 kPa. Calculate the
angle of shear resistance
A. 20.68°
C. 16.32°
B. 29.06°
D. 19.47°
10. The permeameter in a falling head permeability test
set up involves a cylindrical soil sample 50 mm in
diameter and a height of 200 mm. The hydraulic
head in the 10 mm standpipe dropped from 900 mm
to 500 mm in one-minute of observation. In that
duration, the water collected in the graduate was
recorded at 1.5 liters. Evaluate the coefficient of
permeability of the soil sample in cm/s.
A. 0.00857
C. 0.00784
B. 0.00724
D. 0.00932
11. In a falling head permeability test, the head causing
flow was initially 50 cm and it drops 2 cm in 5
minutes. How much time is required for the head to
fall to 25 cm?
A. 45.7 min
C. 73.5 min
B. 84.9 min
D. 62.3 min
A retaining wall 7 m high supports a cohesionless soil having
a dry density of 1600 kg/m3, the angle of shearing resistance
is 33° and void ratio of 0.68. The surface of the soil is
horizontal and level with the top of the wall. Neglect wall
friction and use Rankine’s formula for active pressure of a
cohesionless soil.
12. Determine the nearest value of the total earth thrust
on the wall in kN per lineal meter if the soil is dry.
A. 113.4
C. 125.7
B. 154.2
D. 138.4
13. Determine the nearest value to the thrust on the wall
in kN per lineal meter if owing to inadequate
drainage, it is water logged to a level 3 m below the
surface.
A. 214
C. 312
B. 178
D. 236
14. Determine the nearest value to the height above the
base of the wall where the thrust acts during the
waterlogged condition.
A. 1.58 m
C. 1.97 m
B. 1.75 m
D. 2.54 m
15. Evaluate the resisting capacity against axial load, in
kN, due to skin friction of a round wooded pile
embedded into a layer of plastic clay, in kN, given
the following conditions:
Size of Pile = 0.35 m average diameter
Depth of penetration into the clay layer = 20 m
Unconfined compression strength qu of the clay =
110 kPa
A. 726
C. 1540
B. 924
D. 1210
16. A practice of procedure used to asses the particle
size distribution (also called gradation) of a
granular material. The size distribution is often of
critical importance to the way the material performs
in use.
A. Consolidation test
B. Standard penetration test
C. Liquid limit test
D. Sieve Analysis
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CE Refresher for May 2020 – Geotechnical Engineering 1
FIGURE 1
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