REVIEW INNOVATIONS
MANILA – CEBU – DAVAO – BAGUIO
PHILIPPINES
FIRST PREBOARD FOR CIVIL ENGINEERING
CIVIL ENGINEERS Preboard Examination
Sunday, August 13, 2023
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.
A man wishes to provide a fund for his retirement such that from his 60th
to70th birthdays he will be able to withdraw equal sums of P18,000 for his
yearly expenses. He invests equal amount for his 41st to 59th birthdays is
a fund earning 10% compounded annually. How much should each of these
amounts be?
A. 2285
C. 8552
B. 5288
D. 5588
2.
What is the value of an asset after 8 years of use if it depreciates from
its original value of 120,000 to its salvage value of 3% in 12 years?
A. 44,200
C. 44200
B. 44,020
D. 42400
3.
Find the present value in pesos of a perpetuity of P15,000 payable semiannually if money is worth 8%, compounded quarterly.
A. 371287
C. 392422
B. 386227
D. 358477
4.
A loan of Php. 2,000 is made for a period of 13 months, from January 1 to
January 31 the following year, at a simple interest of 20%. What is the
future amount is due at the end of the loan period?
A. 2333.33
C. 2433.33
B. 2444.33
D. 2344.44
5.
Jones Corporation borrowed Php. 9000 from Brown Corporation on Jan. 1
1978 and P12,000 on Jan 1 1980. Jones Corporation made a partial payment
of P7000 on Jan. 1 1981. It was agreed that the balance of the loan would
be amortizes by two payments one of Jan. 1 1982 and the other on Jan. 1
1983, the second being 50% larger than the first. If the interest rate is
12%. What is the amount of each payment?
A. 3748.67 and 5623
C. 9137.18 and 13705.77
B. 2689.54 and 5669
D. 3667.5 and 5501.25
6.
An asphalt road requires no upkeep until the end of 2 years when P60,000
will be needed for repairs. After this P90,000 will be needed for repairs
at the end of each year. For the next 5 years, then 120,000 at the end of
each year for the next 5 years. If the money is worth 14% compounded
annually, what is the equivalent uniform annual cost for the 12-year
period?
A. 62459.82
C. 76789. 55
B. 79245.82
D. 69852.33
7.
A contract has been signed to lease a building at 20,000 per year with an
annual increase of 1500 for 8 years. Payments are to be made at the end
of each year, starting one year from now. The prevailing interest rate is
7%. What is the lump sum paid today would be equivalent to the 8-year
lease payment plan?
A. 164880
C. 147609
B. 155889
D. 169554
Page 1 of 5
Applied Mathematics, Surveying, Principles of Transportation and
Highway Engineering, Construction Management and Methods
SET A
8.
A man invests P10,000 now for the college education of his 2-year old
son. If the fund earns 14% effective, how much will the son get each year
starting from his 18th to 22nd birthday?
A. 20791.64
C. 17,153.62
B. 21556.32
D. 28,807.43
9.
Ten years ago a contractor was able to purchase a crane whose capacity is
2000 tons costing 125 per ton. The life was estimated to be 15 years with
a salvage value of 10% of the cost. At present abandoning the old crane
in favor a modern model is being considered. A market had been found for
the old crane at P80,000. If the depreciation has been figured on the
straight line basis, what is the difference between the depreciation book
value of old crane and its sale value?
A. 10,000
C. 30,000
B. 20,000
D. 40,000
10.
Using double declining balance method/ Matheson’s Method, determine the
book value at the end of 4 years of an equipment costing P7350 having a
life of 8 years and salvage value of P350?
A. 1604
C. 1066
B. 1406
D. 1644
11.
A coin making machine costing P200,000 has a salvage value of P20,000 at
the end of its economic life of 5 years. The schedule of production is as
follows:
YEAR
1
2
3
4
5
A. 64,000
B. 26,000
NO. OF COINS
100,000
80,000
60,000
40,000
20,000
C. 48,000
D. 19,000
12. A car dealer advertise the sale of a car model for a cash price of
P280,000.00. If purchased on installment, the required down payment is
15% and the balance is payable in 18 equal monthly installments at an
interest rate of 1.5% per month. How much will be required monthly
payments.
A. 15,185.78
C. 10,972.33
B. 11,588.72
D. 15,558.12
13. A businessman is faced with the prospect of fluctuating future budget for
the maintenance of the generator. During the first 5 years, 1000 per year
will be budgeted. During the second five years, the annual budget will be
1500 per year. In addition, P3500 will be budgeted for an overhaul of the
machine at the end of the fourth year and another 3500 for an overhaul at
the end of 8th year. Assuming compound interest at 6% per annum, what is
the equivalent annual cost of the maintenance?
A. 1888.87
C. 1777.38
B. 1738.34
D. 1999.34
14.
The original cost of a certain piece of equipment is 500,000. The value
after its useful life of 5 years is P100,000. Using the double declining
balance method or depreciation, find its value at the end of 3 years.
A. 392,000
C. 190,365.39
B. 108,000
D. 309,634.61
15. An equipment was bought for P1,800,000 with a salvage value of P350,000
after its life of 8 years. The cost of money is 12% per year. Using the
sinking fund method of depreciation, find its book value after 5 years.
A. 1,051,068.42
C. 1,236,569.23
B. 1,402,194.95
D. 843,307.51
16. 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
CIVIL ENGINEERS First Preboard Examination
Sunday, August 13, 2023
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
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
17. ABC is a triangle having an angle A equal to 800. Point D is a point
inside the triangle. If BD and CD are bisectors of angle B and C
respectively, find the angle BDC.
A. 500
C. 1300
0
B. 60
D. 1200
18. 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
19. A lighthouse is 10 units of length northwest of a dock. A ship leaves at
8:00 am and travels west at 12 units of length per hour. At what time
will the ship be 8 units of length from the lighthouse?
A. 9:01 am
C. 8:45 am
B. 8:54 am
D. 9:10 am
20. The flagship of the US Seventh Fleet guarding the Pacific Ocean is 3km
from the Destroyer, 4km from the Cruiser and 5km from the Battleship. The
flagship is within/inside the triangle formed by the three ships. The
triangle formed by the line connecting the Destroyer, Battleship and the
Cruiser is an equilateral triangle. Determine the area of the equilateral
triangle.
A. 7.42 sq.km
C. 16.40 sq.km
B. 12.96 sq.km
D. 19.83 sq.km
21. A speedboat has a velocity in still water of 25kph and heading of N 450
E. If its resultant direction is N 54.90 E, what is the rate of the current
which is moving due south?
A. 2.25 kph
C. 5.52 kph
A. 5.25 kph
D. 2.52 kph
22. The ratio of the sides of a triangle is 3:4:5. If the area of the triangle
is 42 cm2, find its perimeter.
A. 41.32 cm
C. 35.34 cm
B. 25.38 cm
D. 31.75 cm
23. Two towers A and B are placed at a certain distance apart horizontally.
The height of A is 40m and that of B is 30m. What is the vertical distance
from the ground up to the intersection of the lines forming the angles of
elevation of the two towers which are observed from the bases of towers
A and B respectively?
A. 17.143 m
C. 20.682 m
B. 18.431 m
D. 15.938 m
24. Which of the functions below correspond to the given graph?
A. y = sin(x/2 - 1/4)
B. y = sin(πx/2 - π/4)
C. y = cos(πx/2 - π/4)
D. y = sin(πx/2)
CIVIL ENGINEERS First Preboard Examination
Sunday, August 13, 2023
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
25. In triangle ABC, c = 30, a = 36 and b = 18. Find the radius of the circle
tangent to the side c and escribe outside the triangle.
A. 22.45
C. 18.17
B. 20.12
D. 23.65
26. Two sides of a triangle measure 3 cm
altitude to the third side measure 2.5
circle circumscribing this triangle.
A. 6π
C.
B. 8π
D.
and 5 cm, respectively, and the
cm. Find the circumference of the
6.5π
4π
27. A tree is situated on a hill and at a point P, 23m down the hill from the
tree, the angle subtended by the tree is 18.50. If the height of the tree
is 36.5m, at what angle is the hill inclined with the horizontal?
A. 300
C. 600
0
B. 45
D. 700
28. Find the area of the spherical triangle ABC if a = 23.27°, b = 45.317°,
c = 50.48° and r = 220m.
A. 3281 m2
C. 1831 m2
2
B. 2318 m
D. 8321 m2
29. Find the volume of the spherical pyramid if a = 39°, b = 49°, c = 62° and
r = 50m.
A. 31864 m3
C. 61438 m3
B. 13468 m3
D. 48631 m3
30. A ship sailed from Singapore (Latitude 13°30’N, Longitude 110°30’E). After
sailing for 6.6 hrs at a constant speed of 40 knots, it reaches Bangkok
(Latitude 14°50’N). What is the longitude of Bangkok?
A. 114°50’ E
C. 120°30’ E
B. 106°10’ E
D. 102° E
31. The amount by weight of gold, silver, and lead on alloys A, B, and C are
respectively in the ratios: 4:3:2; 3:5:1; and 2:2:5. It is desired to
make a 10-grams alloy containing equal amounts of gold, silver, and lead.
How many grams alloy B should be used?
A. 2 grams
C. 4 grams
B. 3 grams
D. 5 grams
32. 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
33. 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
34. A tank is supplied by two pipes A and B and emptied by a third pipe C.
If the tank is initially empty and all pipes are opened, the tank can be
filled in 20 hours. If the tank is initially full and A and C are opened,
the tank can be emptied in 4 hours. If the tank is initially full and B
and C are opened, the tank can be emptied in 2 hours. Pipe A supplies 50
liters per minute more than B. Find the capacity of the tank.
A. 10,000 liters
C. 11,000 liters
B. 21,000 liters
D. 12,000 liters
35. 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 = P275,000
C. Save = P376,000
CIVIL ENGINEERS First Preboard Examination
Sunday, August 13, 2023
08:00 a.m. — 11:00 a.m.
Page 4
Applied Mathematics, Surveying, Principles of Transportation and
Highway Engineering, Construction Management and Methods
B. Loss = P90,000
SET A
D. Loss = P86,000
36. 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
37. Indirect Mail Inc. had been mailing out coupons for a clearance sale at
a constant rate for 4 days, when they counted the coupons, they still had
mail out and discovered they had 120,000 left. After 7 total days of work
they had 75,000 left. At what rate are they mailing coupons out?
A. 11,000 coupons per day
C. 17,000 coupons per day
B. 13,000 coupons per day
D. 15,000 coupons per day
38. On a job, two power shovels can excavate 20,000 cu m of earth, the larger
shovel working 40 hours and the smaller shovel 35 hours. On another job,
they removed 40,000 cu m with the larger shovel working 70 hours and the
smaller shovel 90 hours. How much earth can the smaller shovel remove in
an hour?
A. 347.83 cu m
C. 173.91 cu m
B. 324.16 cu m
D. 189.33 cu m
39. While visiting Cape Kennedy, we came upon an engineer digging a hole.
“How deep is that hole?” we asked. “Guess,” said the engineer, being
evasive. “My height is exactly 5 feet 10 inches.”
“How much deeper are
you going?” we inquired. “I am one-third done,” was the answer, “and
when I am finished my head will be twice as far below the ground as it is
now above the ground.” How deep will that hole be when finished?
A. 10 feet 6 inches
C. 12 feet 4 inches
B. 11 feet 5 inches
D. 9 feet 7 inches
40. Find the term that is independent of x in the expansion of
𝟑
𝟐 𝟔
!𝟐 + 𝟐 & !𝒙 − &
𝒙
𝒙
A. 180
B. 160
C. -140
D. -160
41. If x + y = 5 and xy = 6, find the value of x3 + y3.
A. 35
C. 30
B. 40
D. 45
42. Solve for x in the following equation: x + 4x + 7x + 10x + ... + 64x =
1430
A. 3
C. 5
B. 4
D. 2
43. Forty-seven millionth is
A. 0.00000047
B. 0.000047
C. 0.0000047
D. 0.000000047
44. If the three positive numbers x, y, and z are in GP, then which of the
following is true?
A. log y = (log x + log z) / 2
C. log (x + y) = log 2z
B. log x = log y = log z
D. (log x)(log z) = 2 log y
45. If (x + 3)(x – 4) + 4 is divided by (x – k), the remainder is k. Find k.
A. 2
C. 4
B. 6
D. 8
~o0o~
~** NOTHING FOLLOWS **~
CIVIL ENGINEERS First Preboard Examination
Sunday, August 13, 2023
08:00 a.m. — 11:00 a.m.
Page 5