MANILA, CEBU and BAGUIO March 8,2025 (8:00 am - 1:00 pm)

APPLIED MATHEMATICS, SURVEYING, PRINCIPLE OF TRANSPORTATION AND HIGHWAY ENGINEERING,

CONSTRUCTION MANAGEMENT AND METHODS (SET A)

INSTRUCTION: Select the best answer to 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. Use pencil no. 2 only

1. A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole is leaned 15° from the vertical
directly towards the sun, determine the length of the pole.
A. 54.23 m B. 48.23 m C. 42.44 m D. 46.21 m

2. A circle is tangent to the line x + y = 4 at ( -3, 7) and its center lies on the y axis. Find the coordinate of the center of the
circle
A. ( 0, 12) B. ( 0, 10) C. ( 0, 5) D. ( 0, 6)

3. Write an equation of the sphere with radius 2 and center on the positive x-axis, and tangent to the yz-plane.
A. (𝑥 − 4)2 + 𝑦 2 + 𝑧 2 = 9 C. 𝑥 2 + 𝑦 2 + 𝑧 2 = 4
B. (𝑥 − 1)2 + 𝑦 2 + 𝑧 2 = 4 D. (𝑥 − 2)2 + 𝑦 2 + 𝑧 2 = 4

4. Two tangents, each 20 cm long, are drawn to a circle, the smaller arc between them is 1.5 radians. Find the radius of the
circle
A. 22.87cm B. 21.47cm C. 24.17cm D. 27.28cm

5. A company manufactures an article on which it makes a profit of P 40.00 on each if 600 or less are made and sold each
week. If over 600 are made, the profit decreases by 5 centavos per article. How many articles should be manufactured each
week to maximize its profit
A. 700 B. 200 C. 800 D. 300

6. Freeway control systems are intended to reduce congestion and queuing delays on freeways. Freeway control system
components currently deployed includes the following:
I. Ramp-metering
II. Variable-message signs
III. Incident detection
IV. Response systems
V. Radio communication systems

A. I, III, V only B. II, III, IV only C. II and V only D. All of the above

7. The chemical reaction between and water which produces hardened cement.
A. hydration B. curing C. shrinkage D. hardening

8. A motorboat goes 5 km upstream in the same time it requires to go 7 km downstream. If the river flows at 2 kph, find the speed
of the boat in still water.
A. 15 kph B. 4 kph C. 12 kph D. 8 kph

9. A homeowner plants 6 bulbs selected at random from a box containing 5 tulip bulbs and 4 daffodil bulbs. What is the
probability that he planted 2 daffodil bulbs and 4 tulip bulbs?
A. 5/14 B. 2/3 C. 3/16 D. 1/3

10. The following data were taken on five cars traversing a 1.5km highway.
CAR TIME (minutes)
A 1.3
B 1.1
C 1.4
D 1.0
E 1.2
Determine the space mean speed.
A. 81KPH B. 62KPH C. 72KPH D. 75KPH
11. Suppose the daily earnings x of a laborer are given by the following probability function. Determine the laborer’s mean
earnings.
Laboratory earnings (x) 0 6 12 16
Probability p(x) 0.30 0.20 0.30 0.20
A. 6 B. 5 C. 9 D. 8

12. student of mass 50 kg decides to test Newton’s laws of motion by standing on a bathroom scale placed on the floor of an
elevator. Assume that the scale reads in newtons. Determine the scale reading when the elevator is traveling upward with a
constant speed of 3 m/s.
A. 510 N B. 490 N C. 470 N D. 450 N

13. The world population at the beginning of 1970 was 3.6 billion. The weight of the earth is 6.586x10^21 tons. If the population
continuous to increase exponentially, with the growth constant k=0.02 and with the time measured in years, in what year will
the weight of all the people equal the weight of the earth, if we assume that the average person weighs 120 pounds? (Note:1
ton=2000 pounds)
A. 2015 B. 2870 C. 3523 D. 3647

14. At a batching plant, sand is falling off a conveyor and falling into a conical pile at rate of 19.4 ft 3/min. The diameter of the
base of the cone is approximately 4 times the altitude. When the pile is 8.6 ft high, at what rate is the radius of the pile
changing in ft/min.
A. 0.048 B. 0.058 C. 0.052 D. 0.042

15. A horizontal cylindrical tank, buried underground in a gasoline service station, has a diameter of 1.20 m and a length of 3m.
If it is filled with gasoline to a depth of 0.80 m, find the volume of gasoline in it in liters
A.1500 lit. B.1000 lit C.2400 lit D 3000 lit

16. Find the slope of the tangent line to the curve at the points where the curve crosses the y-axis.
A. -4 B. ½ C. 4 D. ¼

17. Find the scalar projection of the vector A = i – 2j + k on the vector B = 4i – 4j + 7k

A. 2.11 B. 7.76 C. 19 D. 0.86

18. A man is walking at the rate of 4 m/s across a bridge 30 m above a river. A boat traveling 12 m/s at right angle to the roadway
of the bridge pass directly beneath her. How fast is the distance between the boat and the woman increasing 5 sec later.
A. 11.43 m/s B. 14.22 m/s C. 12.11 m/s D. 13.45 m/s

19. The average daily amount of waste generated by each person in the United States is given below. This includes all wastes
such as industrial wastes, demolition wastes, and sewage.

What polynomial function could be used to model these data?

A. 𝑓 (𝑥) = −0.004𝑥2 + 0.911𝑥 + 9.353 C. 𝑓(𝑥) = 0.004𝑥2 − 0.911𝑥 + 9.353
B. 𝑓 (𝑥) = 0.004𝑥 2 − 0.119𝑥 + 3.593 D. 𝑓(𝑥) = −0.004𝑥 2 + 0.119𝑥 + 3.593

20. In triangle ABC, c=150 cm, angle c=70°, and angle A=45°. Determine the length of the median drawn from the vertex A to
the side “a”.
A. 136.12 cm B. 141.25 cm C. 132.54 cm D. 163.25 cm

21. A cable suspension bridge (in a shape of parabola) is suspended between two towers that are 125 meters apart and 25
meters above the road. The cable meets midway between the towers and is 5 meters above the roadway. Determine the
length of the parabolic cable.
A. 133.07 m B. 124.09 m C.142.6 m D. 117.3 m

22. A pump lifts 27 kg of water per minute though a height of 350 m. What minimum output rating (watts) must the motor have?
A. 94.50 watts B. 12.91 watts C. 15.44 watts D. 19.51 watts

23. The weight of food packed in certain containers is a normally distributed random variable with a mean weight of 500 pounds
and standard deviation of 5 pounds. Suppose a container is picked at random. Find the probability that it contains more than
510 pounds.
A. 0.0335 B. 0.0236 C. 0.977 D. 0.0228

24. A two-lane highway (3.6 m lanes) with a design speed of 100 kph has a 400 m radius horizontal curve connecting tangents
with bearings of N75˚E and S78˚E. Determine the superelevation rate if friction f = 0.12.
A. 0.057 B. 0.077 C. 0.047 D. 0.067

25. Calculate the area of a triangle with x-y coordinates of its corners given as (3, 1), (5, 1), and (5, 7).
A. 4 B. 6 C. 8 D. 10
26. A man estimates that it will take him 7 days to roof his house. A professional roofer estimates that it will take him 4 days to roof
the same house. How long will it take if they work together?
A. 1.5 days B. 3.2 days C. 2.22 days D. 2.55 days

27. A radio station advertises a contest with ten cash prizes totaling $5510. There is to be a $100 difference between each
successive prize. Find the amounts of the least and greatest prizes the radio station will award.
A. least = $100; greatest = $1001 C. least = $101; greatest = $999
B. least = $101; greatest = $1001 D. least = $100; greatest = $999

28. Three forces, 20 N, 30 N, and 40 N, are in equilibrium. Find the largest angle they make with each other.
A. 28.95° `` B. 46.57° C. 104.48° D. 156.23°

29. The measure of the largest angle of triangle is 80 more than the measure of the smallest angle, and the measure of the
remaining angle is 10 more than the measure of the smallest angle. Find the measure of each angle.
A. (40, 150, 60) B. (30, 110, 40) C. (10, 100, 50) D. (20, 120, 60)

30. A rectangle is to be inscribed in a semicircle with radius 4, with one side on the semicircle’s diameter. What is the largest area
this rectangle can have?
A. 16 B. 8 C. 32 D. 24

31. A conical tank with a diameter of 2 m across the top and 3 m high is filled with water. Find the work done in pumping the
contents of the tank to a point 1 m above the rim.
A. 23.114 KJ B. 53.933 KJ C. 94.031 KJ D. 46.612 KJ

32. For some computers, the time period between charges of the battery is normally distributed with a mean of 50 hours and a
standard deviation of 15 hours. Rohan has one of these computers and needs to know the probability that the time period
will be between 50 and 70 hours.
A. 0.41 B. 0.09 C. 0.91 D. 0.04

33. Which of the following are common methods of conducting topographic surveys?
I. Transit-tape and transit-stadia
II. Total Station
III. Global Positioning System (GPS)
IV. Metes and bounds
V. Photogrammetry
A. I, II, III and V B. I, III, and IV C. III, IV and V D. II, IV and V

34. An asset is purchased for P 9,000. Its estimated life is 10 years, after which it will be sold for P1,000. Find the book value during
the third year if sum-of-the-years digit (SOYD) depreciation is used.
A. 5072. 72 B. 4500.80 C. 3025.28 D. 2000.25

35. Refers to the complete removal of the old pavement structure and the construction of a new pavement
A. Reconstruction B. Recycling C. Restoration D. Resurfacing

36. The design target 28-day compressive strength of concrete for a bridge construction project is 6,000 psi. Concrete samples
will be tested as part of the QA/QC efforts that are part of the project. The sample standard deviation is 675 psi. The minimum
required average compressive strength (psi) to be used in concrete mix design is most nearly.
Hint: 𝑓𝑐𝑟′ = 𝑓𝑐′ + 1.34𝑠𝑠 and 𝑓𝑐𝑟′ = 0.9𝑓𝑐′ + 2.33𝑠𝑠
A. 6500 B. 6750 C. 7000 D. 7250

37. As part of the PERT analysis of a project, durations are estimated for activities A through G and summarized in the following
table. The critical path for the project is ACEF.

The probability (%) that the project will be completed in less than 25 weeks is most nearly
𝑎+4𝑏+𝑐 𝑐−𝑎
Hint: 𝜇 = and 𝜎 =
6 6
A. 12 B. 18 C. 20 D. 22

38. A material’s capacity to absorb impact without fracturing.

A. Toughness B. Damping C. Fatigue resistance D. Hardness
39. In the expression 3 + 4i, is a complex number. Compute its absolute value.
A. 6 B. 3 C. 8 D. 5

40. A horizontal beam l foot long is supported at one end and

unsupported at the other end (see the figure). If the beam is
subjected to a uniform load and if y denotes the deflection of the
beam at a position x foot from the supported end, then it can be
shown that
𝑦 = 𝑐𝑥 2 (𝑥 2 − 4𝑙𝑥 + 6𝑙 2 ),

Where c is a positive constant that depends on the weight of the load and the physical properties of the beam. If the beam
is 10 feet long and the deflection at the un supported end of the beam is 2 feet, find c.
A. 1/15000 B. 1/10000 C. 1/25000 D. 1/20000

41. A produce company has a 100-acre farm on which it grows lettuce and cabbage. Each acre of cabbage requires 600hours
of labor, and each acre of lettuce needs 400hours of labor. If 45,000hours are available and if all land and labor resources
are to be used, find the number of acres of each crop that should be planted?
A. 25 acres of cabbage and 75 acres of lettuce C. 75 acres of cabbage and 25 acres of lettuce
B. 45 acres of cabbage and 55 acres of lettuce D. 55 acres of cabbage and 45 acres of lettuce

42. Find the volume of a right truncated triangular prism with triangular base whose sides are measuring 100cm, 90cm and 120
cm respectively. The heights are 86cm, 71 cm and 55cm perpendicular to the triangular base respectively.
A. 123,567.88 cu.cm B. 211,567.67 cu. Cm C. 344,278.89 cu.cm D. 311,208.93 cu.cm

43. In a city, streets run north and south, and avenues run east and west. Streets and avenues are 850 feet apart. The city plans
to construct a straight freeway from the intersection of 25th street and 8th avenue to the intersection of 115th street and 64th
avenue. How long will the freeway be?
A. 13 miles B. 11 miles C. 15 miles D. 17 miles

44. Consider the sphere of radius 3 and center at the origin. Find the coordinates of the point P where the plane
tangent to this sphere at (1, 2,2) cuts the x-axis.
A. (9,0,0) B. (4,0,0) C. (8,0,0) D. (3,0,0)

1
45. The kinetic energy of an object with mass m is given by the formula 𝑘(𝑡) = 𝑚 ∙ 𝑣(𝑡)2 , where 𝑣(𝑡) is the velocity of the object
2
50
at time t. Suppose 𝑣(𝑡) = for all 𝑡 ≥ 0. What does the kinetic energy of the object approach as time approaches 100?
1+𝑡 2
A. 0.0000225 m B. 0.0000325 m C. 0.0000425 m D. 0.0000125 m

46. The probability that a person picked at random has cancer is 0. 02. If a person has cancer, the probability of his or her being
diagnosed as having it is 0.80. On the other hands, if a person does not have a cancer, the probability of his or her being
diagnosed as having it is 0.05. Given that a person is diagnosed as having cancer, what is the probability that the person
really does not have it?
A. 0.065 B. 0.754 C. 0.246 D. 0.05

47. The number of accidents for 6 years recorded in a certain section of a highway is 5892. If the average daily traffic is 476, what
is the accident rate per million entering vehicles?
A. 5653 B. 5211 C. 5356 D. 5563

48. The Asian Transmission Co. makes and sells certain automotive parts. Present sales volume is 500,000 units a year at a selling
price of P0.50 per unit. Fixed expenses total P80,000 per year. Determine the present total profit for a year
A. 180,000 B. 170,000 C. 150,000 D. 160,000

49. A method of protecting employees from cave-ins by excavating to form sides of an excavation that are inclined away from
the excavation so as to prevent cave-ins.
A. Sloping B. Shielding C. Shoring D. Benching
50. Two lane highway having a width of 3.6m on each lane with design speed of 100 kph. Has a 400m radius horizontal curve .
Determine the super elevation if friction factor f=0.12.
A. 0.08 B. 0.03 C. 0.88 D. 0.12
51. Radium decompose at the rate proportional to the amount present. If the half-life is 1600 years. Find the percentage
remaining at the end of 200 years.
A. 91.7 % B. 69 % C. 89.7 % D. 50%
52. The height s above ground of a ball dropped from the vista of Mines View Park is given by s= -4.9t2+ 192, where s is measured
in meters and t in seconds. Find the instantaneous velocity of the falling ball at t=3s.
A. -24.9 m/s B. 29.4 m/s C. 24.9 m/s D. -29.4 m/s

53. In order to distribute stress, mine tunnels are sometimes rounded. Suppose that the vertical cross sections of a tunnel can be
modeled by the parabola y = 6 – 0.06x2. If x and y are measured in feet, how much rock would have to be moved to make
such a tunnel that is 100 feet long?
A. 7000 ft3 B. 9000 ft3 C. 8000 ft3 D.10,000 ft3
54. The intensity of an earthquake wave is measured to be 2.0 x 106 J/m2-s at a distance of 48 km from the source. What was the
intensity when it passed a point only 1.0 km from the source?
Hint: 𝐼 = 𝑃/𝐴, where 𝐴 = 4𝜋𝑟 2
A. 4.6 x 109 J/m2-s B. 4.4 x 109 J/m2-s C. 6.4 x 109 J/m2-s D. 6.6 x 109 J/m2-s
55. How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve at of radius
85 m at a speed of 95 km/h?
A. 0.78 B. 0.84 C. 0.74 D. 0.88
56. A 600 N ball is thrown downward with an initial velocity of 3 m/s from a height of 1.5 m above a spring whose spring constant
is 15 N/mm. Determine the deformation of the spring at the instant the velocity of the ball is zero.
A. 395.85 mm B. 288.62 mm C. 437.87 mm D. 331.38 mm
57. The costs for two different kinds of heating systems for a three-
bedroom house are given below:
After how many years will total costs for both be the same?
A. 22 years B. 24 years C. 26 years D. 28 years
58. Mass-produced needles are packed in boxes of 1000. It is believed
that 1 needle in 2000 on average is substandard. What is the probability that a box contains 2 or more defectives?
A. 0.26 B. 0.62 C. 0.09 D. 0.18
59. A hexagram is formed by overlapping two equal equilateral triangles and is inscribed in a circle of radius 6.928 units. Find the
length of the side of the equilateral triangle.
A. 10 units B. 14 units C. 12 units D. 16 units
60. A company makes three types of hammers—good, better, and best. The cost of making each type of hammer is $4, $6, and
$7, respectively, and the hammers sell for $6, $9, and $12. Each day, the cost of making 100 hammers is $520, and the daily
revenue from their sale is $810. How many of each type are manufactured?
A. 20good hammers, 50better hammers, 30best hammers C. 20good hammers, 40better hammers, 30best hammers
B. 50good hammers, 30better hammers, 20best hammers D. 50good hammers, 20better hammers, 30best hammers
61. The current to a certain capacitor is given by 𝑖 = 2𝑡 3 + 𝑡 2 + 3. The initial charge on the capacitor is 6.83 C. Find the charge
when t = 5.00 s. Hint: 𝑞 = ∫ 𝑖 𝑑𝑡
A. 367 C B. 376 C C. 267 C D. 276 C
62. From his long experience, a car salesman has found out that the probability that a customer will buy a sports car is 0.10, that
he or she will buy a station wagon is 0.20 and that he or she will buy a truck is 0.15. What is the probability that a prospective
customer will buy one of the above types of vehicles?
A. 0.45 B. 0.55 C. 0.30 D. 0.35
63. A spiral easement curve has a length of 2200 m with a central curve having a radius of 320 m. Determine the degree of spiral
at the third quarter point.
A. 3.58 B. 2.69 C. 2.85 D. 3.21
64. A piece of machinery can be bought for 10000 cash or for 2000 down and payments of 750 per year for 15 years. What is the
annual rate of interest?
A. 4.60% B. 5.41% C. 3.56% D. 5.77%
65. These are circumstances or deviation from standard condition which could permit an occurrence of accident or incident.
A. Unsafe condition B. Risk. C. Hazard D. Unsafe act
66. During peak hours, 3800 vehicles pass through a certain highway from 9:00am to 11:00 am, with space mean speed of 20kph.
What is the average space headway per vehicle?
A. 105 B. 9.5 C. 95 D. 10.5
67. A certain light source produces an illumination of 655 lux on a surface at a distance of 2.75 m. Find the rate of change of
illumination with respect to distance, and evaluate it at 2.75 m. Hint : I=kd2
A. -529.6 lux/m B. -476.4 lux/m C. -352.9 lux/m D. -414.8 lux/m
68. A dam will have a first cost of 5,000,000, an annual maintenance cost of 25,000 and minor reconstruction costs of 100,000
every five years. At an interest rate of 8% per year, the capitalized cost of the dam is nearest to:
A. 5,525,570 B. 525,625 C. 213,125 D. 5,312,500
69. n empirical formula for the bankroll B (in dollars) that is needed to survive a scatter gambling session with confidence C (a
percent expressed as a decimal) is given by the formula
𝐺𝑊
𝐵=
29.3 + 53.1𝐸 − 22.7𝐶
where G is the number of games played in the session, W is the wager per game, and E is the player’s edge on the game
(expressed as a decimal). Approximate the bankroll needed for a player who plays 500 games per hour for 3 hours at $5 per
game with a 5% edge, provided the player wants a 95% chance of surviving the 3-hour session.
A. $492 B. $1 C. $1476 D. $9
70. Is the bringing of a concrete surface to true grade with enough mortar to produce the desired finish.
A. Leveling B. Screeding C. Edging D. Grading
71. The process of giving natural soils enough abrasive resistance and shear strength to accommodate traffic and loads
A. Ground modification B. Soil compaction C. Earthmoving D. Tamping
72. It takes a force of 130N to stretch a spring 50cm. Find the work done in stretching the spring 20cm beyond its natural length?
A. 3.2 B. 4.2 C. 5.2 D. 6.
73. Find the time of oscillation of a pendulum having a length of 12m long? (HINT: 𝑡 = 2𝜋√𝐿/𝑔)
A. 0.1158 s B. 6.95 s C. 7.66 s D. 4.5 s
74. The probability is 0.02 that an item produced by a factory is defective. A shipment of 10,000 items is sent to its warehouse.
Find the standard deviation σ.
A. 14 B. 18 C. 19 D. 20
75. The eccentricity of an ellipse is 0.8 and the distance between its foci is 5 units. Find the distance between its directrices.
A. 7.82 B. 2.25 C. 6.25 D. 10.42