REVIEW INNOVATIONS
MANILA – CEBU – DAVAO – BAGUIO
PHILIPPINES
FIRST PREBOARD FOR CIVIL ENGINEERING
CIVIL ENGINEERS Preboard Examination
Sunday, August 4, 2024
08:00 a.m. — 11:00 a.m.
---------------------------------------------------------------------Applied Mathematics, Surveying, Principles of Transportation
SET A
and Highway Engineering, Construction Management and Methods
INSTRUCTION: Select the correct answer for each of the following questions.
Mark only one answer for each item by shading the box corresponding to the
letter of your choice on the answer sheet provided. STRICTLY NO ERASURES
ALLOWED.GOOD LUCK.
NOTE:
A times B is represented by A × B or A*B. A raised to the power n is
expressed as A^n. All problems are 1 point each.
1.
In a class of 40 students, 27 like Calculus and 25 like Chemistry. How
many like Calculus only?
A. 12
C. 13
B. 14
D. 15
2.
A tennis tournament has 8 players. The number a player draws from a hat
decides his first-round rung in the tournament ladder. See diagram below.
If the best player always defeats the rest of the players and the second
best player always defeats all the rest except the best, what is the
probability that the second best wins the runner-up trophy?
1
2
3
4
5
6
7
8
A. 1/2
B. 4/7
First
Second
Finals
Winner
C. 2/3
D. 3/7
3.
A man owns a triangular lot on the corner of two intersecting streets
which intersects at an angle of 620. The frontage of one street is 200m
and on the other side is 150m. If the land is worth P1000 per m2 and the
man has P1.2million with which to increase the size of the lot, by how
much can he lengthen the 150m frontage?
A. 13.53 m
C. 13.59 m
B. 19.35 m
D. 15.39 m
4.
If the areas of a regular pentagon and regular decagon are equal, what is
the ratio of their perimeters?
A. 0.94
C. 1.06
B. 0.67
D. 1.25
5.
Simplify the expression (2i510 - i1027 + 1)2 in the form a + bi.
A. -2
C. -2i
B. 2i
D. 2
6.
A surveyor forgot to indicate the area of a rectangular lot. However, he
remembers that the area remains the same if the length is decreased by
12.5 m and the width is increased by 10 m or the length is decreased by
50 m and the width is increased by 50 m. What was the original area of
the rectangular lot?
A. 30,000 sq.m.
C. 32,000 sq.m.
B. 40,000 sq.m.
D. 42,000 sq.m.
Page 1 of 6
Applied Mathematics, Surveying, Principles of Transportation and
Highway Engineering, Construction Management and Methods
SET A
7.
An airplane could travel a distance of 1000 miles with the wind in the
same time it could travel a distance of 800 miles against the wind. If
the wind velocity is 40 mph, what is the speed of the plane?
A. 300 mph
C. 320 mph
C. 340 mph
D. 360 mph
8.
A train 250 m long and moving at 25 kph is to cross a railway bridge 1 km
long. How long will it take it to pass the bridge completely?
A. 3 min
B. 2 min
B. 1.5 min
D. 2.5 min
9.
Find two consecutive positive even integers such that the square of the
second, decreased by twice the first is 124. Find the smaller number.
A. 8
C. 12
B. 10
D. 14
10. Find the equivalent of 6% compounded semi-annually in a rate of compounded
quarterly?
A. 5.56%
C. 6.21%
B. 5.96%
D. 6.05%
11. Allan and Bernard start at the same time from two places 136 km apart and
travel toward each other. Allan travels 10 kph and Bernard 8 kph. If
Bernard rests 1 hour on the way, in how many hours will they meet?
A. 5
C. 7
B. 6
D. 8
12. 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. 733 m
C. 625 m
B. 928 m
D. 854 m
13. Robert is 15 years older than his brother Stan. However, y years ago,
Robert was twice as old as Stan. If Stan is b years old now and b > y,
find the value of b – y.
A. 15
C. 30
B. 20
D. 10
14. Two planes leave Manila for Tokyo, a distance of 900 miles. The fourmotored plane A travels at a ground speed of 90 mph faster than the twomotored plane B. Plane A arrives in Tokyo 2 hr 15 min ahead of plane B.
What is the ground speed of plane B?
A. 190 mph
C. 170 mph
B. 250 mph
D. 150 mph
15. After 8:00 pm, a ride in a cab cost P25.00 plus P3.00 for every fifth of
a kilometer traveled. If a passenger traveled x kilometers, what is the
cost of the trip in pesos, as a function of x?
A. 28x
C. 25 + 15x
B. 25 + 3x
D. 25 + 0.6x
16. In a certain barangay, 80% of the population have cellphone. Two people
from the barangay were selected at random. Find the probability that one
has cellphone and the other has none.
A. 0.64
C. 0.08
B. 0.08
D. 0.32
17. Find the area of a pentagram (regular five-pointed star) inscribed in a
circle of radius 180 cm.
A. 34,256
C. 36,372
B. 42,128
D. 38,754
18. A piece of wire of length 72 cm is cut into two unequal parts. Each part
is bent to form a square. It is found that the total area of the two
squares is 194 cm2. Find the difference between the sides of the squares.
A. 6
C. 4
B. 12
D. 8 cm
CIVIL ENGINEERS First Preboard Examination
Sunday, August 4, 2024
08:00 a.m. — 11:00 a.m.
Page 2
Applied Mathematics, Surveying, Principles of Transportation and
Highway Engineering, Construction Management and Methods
SET A
19. In triangle ABC, if a = 7 cm, b = 5 cm, and B = 40°, then the value of C
is _______.
A. 35.43°
C. 42.51°
B. 32.74°
D. 24.15°
20. A steel tower for Globe cell site was erected in a square lot having a
side of 800 meters long. The steel tower was erected inside but not
necessarily at the midpoint of the lot. The angle of elevation of the tip
of the tower as observed from one corner of the lot at A, is 300, while
its angle of elevation as observed at the midpoint along the edge of the
lot, at B, is 450, and when it was observed at the opposite corner of the
lot but at the same edge at C, the angle of elevation of the tip of the
tower is 600. Find the height of the tower.
A. 520 m
C. 478 m
B. 500 m
D. 490 m
21. I was walking along the road at 6kph when a car dashed past me and only
missed me by a few inches. From the moment it passed me to its
disappearance round a corner I took thirty one steps and walking on
reached that corner with four hundred and thirty four steps more. Assuming
that I walked and the car ran at uniform speeds, what was the speed of
the car?
A. 60kph
C. 70kph
B. 84kph
D. 90kph
22. An equipment cost P480,000 and has a salvage value of 10% of its cost at
the end of its life of 36000 operating hours in a period of 5 years. In
the first year of service, it was used for 12,000 hours. If at the end of
the 2nd year, it was used for 15,000 hours, Find the depreciation at the
end of 2nd year.
A. 324,000
C. 144,000
B. 160,000
D. 180,000
23. Larry Development owns the last vacant parcel thriving industrial park.
There are three proposals for developing the property (see table). In
each case, Larry builds and maintains the structure and receives income
from it. Larry Development uses an interest rate of 12% and horizon of 25
years for its analyses. Which proposal is preferred using PW criteria?
A. Miracle Lab
B. Arteezy Instrument Maintenance
C. Dendi Snowboard Manufacturing
D. Titikman
24. A rectangle ABCD which measures 18 cm by 24 cm is folded once,
perpendicular to diagonal AC, so that the opposite vertices A and C
coincide. Find the length of the fold.
A. 20.5 cm
C. 22.5 cm
B. 21.5 cm
D. 23.5 cm
25. Bossing works in the electrical and mechanical engineering department of
CentralEast Tech. He is evaluating the benefits of installing a more
efficient motor on one of the assembly lines. The line is producing (and
operating) 8% more each year. The more efficient motor has no salvage
value after life of 5 years, costs Php3000 more installed, and will save
Php 800 the first year. What is PW if i=10%?
A. 506.5
C. 565.50
B. 560.5
D. 556.50
CIVIL ENGINEERS First Preboard Examination
Sunday, August 4, 2024
08:00 a.m. — 11:00 a.m.
Page 3
Applied Mathematics, Surveying, Principles of Transportation and
Highway Engineering, Construction Management and Methods
SET A
26. Find the value of m in the equation:
1 + cos x + cos 2x
= m
sin x + sin 2x
A. cos x
B. sec x
C. tan x
D. cot x
27. Find the common area of two circles of radial 25 cm and 26 cm respectively,
if the distance between their centers is 17 cm.
A. 1,911.36 cm2
C. 1,191.36 cm2
B. 1,119.39 cm2
D. 1,191.63 cm2
28. A farmer bought a farm and he paid P10,000 cash and agreed to pay P2000
at the end of each 6 months for 5 years. He failed to pay the first
payments. At the end of 3 years, he is required to pay by the seller the
entire debt consisting of his accumulated and future liabilities,
otherwise the farm would be foreclosed by the seller. What must he pay if
money is worth 12% compounded semi-annually?
A. 17860.35
C. 19,711.04
B. 20,880.85
D. 18648.22
29. In a CE review class, there were 120 students. 60 of them are from Luzon,
20 from Visayas, and 30 are from Mindanao. If three students are randomly
selected to get out of the room one after the other, what is the
probability that all three are from Mindanao?
A. 0.75
C. 0.0156
B. 0.0145
D. 0.0126
30. 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
circle to the point of tangency of the two circles B and C which are
identical.
A. 2.55
C. 4.15
B. 4.67
D. 3.33
31. Two old women started at sunrise and each walked at a constant speed. One
went from A to B and the other from B to A on the same road. They met at
noon and, continuing with no stop, arrived respectively at B at 4 p.m.
and at A at 9 p.m. At what time was the sunrise that day?
A. 6:00 am
C. 5:20 am
B. 5:40 am
D. 5:00 am
32. If a hen and a half lays an egg and a half in a day and a half, how many
eggs will five hens lay in six days?
A. 20
C. 16
B. 24
D. 28
33. The angle of elevation of the top of the tower A from the foot of tower
B is twice the angle of elevation of the top of the tower B from the foot
of tower A. At a point midway between the two towers, the angles of
elevation of the top of the towers are complementary. If the two towers
are 120m apart, determine the height of tower A.
A. 40 m
C. 80 m
B. 50 m
D. 90 m
34. The parallel sides of a trapezoidal lot measure 160 m and 240 m and are
40 m apart. Find the length of the dividing line parallel to the two sides
that will segregate one-fourth of the total area along the 160 m side.
A. 183.30 m
C. 190.44 m
B. 186.54 m
D. 203.96 m
35. Determine the approximate size of an annual payment needed to retire Php
70,000 in issued by a city to build a dam. This must be repaid over a 50
year period, and they earn interest at an annual rate of 6 % compounded
annually. Hint: 50 years make ba taken as an infinite time horizon.
A. 4,240,000
C. 4,200,000
B. 2,240,000
D. 2,400.000
CIVIL ENGINEERS First Preboard Examination
Sunday, August 4, 2024
08:00 a.m. — 11:00 a.m.
Page 4
Applied Mathematics, Surveying, Principles of Transportation and
Highway Engineering, Construction Management and Methods
SET A
36. The roof and ceiling of a commercial building will be insulated by blownin insulation, which can be specified in 1-inch depth increments. The
minimum amount of insulation that will meet code is 6 inches, and the
maximum amount that will fit is 12 inches. What is the optimal depth of
the insulation (The most economical)?
The firm uses an interest rate of 8% and 30-years building life. The
installed cost of the insulation for 10,000 square foot ceiling is
$1.75 per cubic foot. Thicker insulation will reduce the capacity of
HVAC equipment and the annual heating and cooling costs. With 6 inches
of insulation, the annual bill for heat gains and losses through the
roof will be $1200.
Insulation
thickness
HVAC first cost
6”
7”
8”
9”
10”
11”
12”
$10,000
9643
9375
9167
9000
8864
8750
A. 6 inches (EAC=2866)
B. 7 inches (EAC=2792)
C. 8 inches (EAC=2769)
D. 9 inches (EAC=2750)
37. An equipment costing P250,000 has a salvage value of P35,000.00 after 18
years. The rate of annual interest is 7%. Which of the following has the
highest depreciation on the 15th year?
A. Declining Balance Method
B. Sum of the year’s Digit Method
C. Double Declining Balance Method
D. Sinking Fund Method
38. Find the sum of all the of roots of x4 + x3 – x2 + x – 2 = 0, given that
i is a root.
A. i
C. -i
B. -1
D. 1
39. Which of the following has the greatest effective annual rate of interest?
A. 6.30% compounded annually
B. 6.25% compounded semi-annually
C. 6.20% compounded quarterly
D. 6.15% compounded monthly
40. A machine costing P140,000 has a salvage value of P10,000 after its useful
life of 8 years. Determine the fourth-year depreciation using the Double
Declining Balance Method.
A. 16,250.00
C. 18,055.56
B. 15,130.44
D. 14,765.62
41. The areas of two similar polygons are 80 and 5.
If the side of the
smaller polygon has a length 2, find the length of the corresponding side
a larger polygon.
A. 10
C. 8
B. 12
D. 14
42. Suppose a man receives an initial annual salary of P60,000, increasing at
the rate of P5000 a year. If money is worth 10%, determine his equivalent
uniform salary for a period of 8 years.
A. 70,994.07
C. 79,831.52
B. 75,022.39
D. 85,007.88
43. A father wants to set aside money for his 5 years old son’s future college
education. Money can be deposited in a bank account that pays 8% per year,
compounded annually. What equal deposits should be made by the father on
his son’s 6th birthday through 17th birthdays in order to provide Php 5000
on the son’s 18th 19th 20th and 21st birthday?
A. 822.67
C. 877.67
B. 827.67
D. 872.67
CIVIL ENGINEERS First Preboard Examination
Sunday, August 4, 2024
08:00 a.m. — 11:00 a.m.
Page 5
Applied Mathematics, Surveying, Principles of Transportation and
Highway Engineering, Construction Management and Methods
SET A
44. Determine the area of the quadrilateral ABCD shown if OB = 80 cm, OA =
120 cm, OD = 150 cm, and 𝛉 = 25°.
A. 2722 cm2
B. 2272 cm2
C. 2227 cm2
D. 2772 cm2
45. A company is considering a new project that will yield cash flows starting
at $10,000 in the first year. The cash flows are expected to increase by
5% annually in addition to a 3% increase due to inflation, making the
total increase 8% per year. The project has a lifespan of 6 years. The
company's required rate of return is 12%. Calculate the present worth?
A. 51,840
C. 48,510
B. 52,480
D. 84,520
~o0o~
*** NOTHING FOLLOWS ***
CIVIL ENGINEERS First Preboard Examination
Sunday, August 4, 2024
08:00 a.m. — 11:00 a.m.
Page 6