1.

Three numbers m+2, 4m – 6, 3m – 2 are in arithmetic

progression if m is equal to what value? 8. Which of the following is not an assumption implicit
in engineering economic analysis?
A. 0 C. 2
B. 1 D. 3 A. The beginning of the year convention is applicable.
B. There is no inflation now, nor will there be any
2. Using the wheel and the axle, a 400 N load can be inflation during the lifetime of the project.
raised by a force of 50N applied to the rim of the wheel. C. The effective interest rate in the problem will be
The radii of the wheel and the axle are 85 cm and 6 cm constant during the lifetime of the project.
respectively. Calculate the efficiency of the machine. D. Nonquantifiable factors can be disregarded.

A. 56% C. 12.5% 9. The number of triangles that can be formed with 6

B. 65 % D. 10 % points on a circle is

3. The sum of the reciprocals of three numbers in H.P. A. 6 C. 15

(harmonic progression) is 12 and the product of these B. 12 D. 20
numbers is 1/48. What is the largest number?
10. The term independent of x in the expansion of ( 2x +
A. 1/2 C. 1/6 1/3x) (raised to 6) is
B. 1/4 D. 1/3
A. 80/3 C. 160/27
4. A machine costing Php 720,000 is estimated to have a B. 80/9 D. 160/9
life of 10 years. If the annual rate of depreciation is 25%,
determine the total depreciation using the constant 11. An air-water vapor mixture is at a temperature of
percentage or declining balance method. 20oC. The partial pressure of water is 2.3 kPa, and the
partial pressure of the dry air is 99.1 kPa. The saturation
A. 523,845.34 C. 542,437.23 pressure for water vapor at 20 oC is 2.339 kPa. What is
B. 679,454.27 D. 753,243.33 most nearly the humidity ratio of the air-water vapor
mixture?
5. What is the geometric mean between – 4 and – 25?
A. 0.014 C. 0.35
A. 10 C. 16 B. 0.26 D. 0.38
B. – 10 D. - 16
12. If matrix A is equal to first row ( ab , b(squared) ) and
6. A train weighing 1000 KN is being pulled up a 2% second row ( - a (squared) , - ab), then A is a:
grade. The train’s resistance is 5 N/KN. Traveling the
distance of 300 m the speed of the train was increased A. Scalar matrix C. idempotent matrix
from 6 m/s to 12 m/s. What is the maximum power B. Nilpotent matrix D. involuntary matrix
developed by the locomotive.
13. In calculations using standard structural shapes of I-
A. 520.4 kW C. 503.5 kW beams, it is assumed that the shear stress is carried by
B. 432.8 kW D. 521.7 kW the
A. entire cross-sectional area. C. web only.
7. There are 15 men is a room shake hands with each B. top flange only when in compression. D. flanges
other, the total number of only.
handshakes is:
14. A torsional pendulum is composed of a 0.5 m long
A. 90 C. 110 shaft with a diameter of 0.5cm and a shear modulus of 8
B. 105 D 115 x 104 MPa, and a thin 3 kg disk with a radius of 30 cm.
The natural frequency of the pendulum is 8.5 rad/s. 21. A substance goes into solution at the rate of 25% of
What is most nearly the period of oscillation? the undissolved portion each minute. If the initial
amount was 64/27 lb, what amount is undissolved after
A. 0.61 s C. 0.87 s 6 minutes?
B. 0.74 s D. 0.96 s
A. 2/27 C. 27/64
15. Calculate the largest diameter circle that will fit B. 16/27 D. ¾
inside a regular pentagon with 2-cm sides?
22. On a certain day the sun is observed to subtend an
A. 1.54 cm C. 3.29 cm angle 0o32’10”. If the diameter of the sun is 866,500
B. 2.752 cm D. 1.54 cm miles, how far away from it?

16. Compute the sum of integers from 1 to 100 that are A. 9.26 x 10 (raised to 6) miles
divisible by 2 or 5. B. 4.63 x 10 (raised to 8) miles
C. 9.26 x 10 (raised to 5) miles
A. 5450 C. 3050 D. 4.68 x 10 (raised to 6) miles
B. 2520 D. 2050
23. All of the following processes can be found on a
17. If matrix A, first row (-3, 4 ) , second row ( 2 , - 1 ) , psychrometric chart except
then its characteristic roots are:
A. heating and humidifying. C. cooling and
A. ( 1, -5) C. (-1 , 5 ) dehumidification.
B. ( 1, 5) D. (-1, -5 ) B. black body radiation. D. evaporative cooling.

18. An engine is expected to have a maintenance cost of 24. The number of ways which 5 boys and 5 girls can be
P1000 the first year. It is believed that the maintenance seated so that no two girls sit next to each other.
cost will increase P 500 per year. The interest rate is 6%
compounded annually. Over a 10-year period, what will A. 5! (squared) C. 6!x5!
be the approximate effective annual maintenance cost? B. 10!/5! D. 10!/(5!)(squared)

A. P 3011.00 C. P 2450.00 25. The Carnot refrigeration cycle includes all of the
B. P 3452.00 D. P 1345.00 following processes except
A. isentropic expansion. C. isothermal heating.
B. isenthalpic expansion. D. isentropic compression.
19. There are 10 defectives per 1,000 items of a product
in the long run. What is the probability that there is one 26. Three posts are set in level ground in such a manner
and only one defective in random lot of 100? that their bases form an equilateral triangle with sides
20 ft long. If the heights of the posts are 12, 18, and 30
A. 0.01 C. 0.5 ft, find the area of the triangle formed by their tops?
B. 0.99(raised to 100) D. 0.3697
A. 342 sq ft C. 235 sq. ft
20. A company has N machines of equal capacity that B. 153 sq. ft D. 205 sq. ft.
produce a total of 180 pieces each work day. If 2
machines break down, the workload of the remaining is 27. Find the equation that must be satisfied by the
increased by 3 pieces each per day to maintain coordinates of every point(x, y) that is equidistant from
production. What is the value of N? the origin and the point (1,1)?

A. 8 C. 10 A. x + y = 1 C. 2x = y
B. 12 D. 15 B. x – y = 1 D. 3x – 2y = 1.
 A. k(square)/3 C. k(square)/2
28. Which of the following statements is false? B. 2k(square) D. 2.5 k(square)

A. The time rate of change of the angular momentum 35. When using net present worth calculations to
about a fixed point is equal to the total moment of the compare two projects, which of the following could
external forces acting on the system about the point. invalidate the calculation?
B. The coefficient of restitution can be less than zero.
C. Momentum is conserved during elastic collisions. A. differences in the magnitudes of the projects
D. The period of a simple pendulum is independent of B. evaluating over different time periods
the mass of the pendulum. C. mutually exclusive projects
D. nonconventional cash flows
29. A cubical box designed to hold 8 cu ft of water holds
only 7.997 cu.ft. What is the relative error in its edge? 36. The inclined plane is 15 m and rises 3 m. A force is
needed to slide a 20 kg box up the plane if friction is
A. – 0.00125 C. – 0.125 neglected. Find the AMA (Actual Mechanical Advantage)
B. – 0.00025 D. – 0.000125 if the force if a 70 N force is actually required.

30. A stone dropped into a calm lake causes series of A. 2.8 C. 3.1
circular ripple. The radius of the outer one increases at B. 3.6 D. 5.0
2 ft/sec. How rapidly is the disturbed area are changing
at the end of 3 seconds? 37. If a quantity increase by 0.1% of its current value
every 0.1 sec, the doubling time is approximately equal
A. 24pi sq.ft/s C. 12pi sq.ft/s to:
B. 48pi sq.ft/s D. 2pi sq.ft./s
A. 14 sec C. 690 sec
31. If the first term of an infinite geometric series is 1 B. 69 sec D. 69,000 sec
and its every term is the sum of the next successive
terms, the its fourth term will be: 38. One of the advantages of comparing interest rates
to the minimum attractive rate of return (MARR)is that
A. 1/8 C. 1/4
B. 1/16 D. 1/2 A. the MARR is easy to calculate.
B. an effective interest rate need never be known.
32. Find the area of the region bounded by y = C. it need not be used in numerical calculations.
x(squared)/ 4 and y = x/2 + 2. D. it is guaranteed by an agency of the federal
government.
A. 11 C. 12
B. 9 D. 10 39. The diameter of a sphere and the base of a cone are
equal. What percentage of that diameter must the
33. A solid is constructed with a circular base of radius 1 cone’s height be so that both volumes are equal?
and such that every plane section perpendicular to a
certain diameter of the base is an isosceles triangle A. 133% C. 166%
whose altitude is 2. Find the volume. B. 150% D. 200%

A. pi/2 C. pi 40. What do you think is the reason why does a spinning
B. 2pi D. 1.5 pi ice skater’s angular velocity increase as she brings her
arms in toward her body?
34. Find the area of the largest isosceles triangle that
can be drawn with equal sides k inch long. A. Her mass moment of inertia is reduced.
B. Her angular momentum is constant
C. Her radius of gyration is reduced. 47. A 1530 kg car is towing a 300 kg trailer. The
D. All of these coefficient of friction between all tires and the road is
0.80. The car and trailer are traveling at 100 km/h
41. A cubical container that measures 2 in. on a side is around a banked curve of radius 200 m. What is the
tightly packed with 8 marbles and is filled with water. necessary banking angle such that tire friction will not
All the 8 marbles are in contact with the walls of the be necessary to prevent skidding?
container and the adjacent marbles. All the marbles are
the same in size. What is the volume of water in the A. 8.0 C. 36
container? B. 21 D. 78

A. 0.38 cu in C. 2.5 cu in 48. A pickup truck is traveling forward at 25 m/s. The

B. 3.8 cu in D. 4.2 cu in bed is loaded with boxes whose coefficient of friction
with the bed is 0.40. What is most nearly the shortest
42. What is the product of the complex numbers 3 + 4j time that the truck can be brought to a stop such that
and 7 – 2j? the boxes do not shift?
A. 10 + 2j C. 13 + 34j
B. 13 + 22j D. 29 + 22j A. 2.3 s C. 5.9 s
43. What is the general solution to the following B. 4.7 s D. 6.4 s
differential equation?
2d(squared)y / dx(squared) – 4 dy/dx + 4y = 0 49. Solve for the value of x in the equation square root
of (x – 3 ) = - 6.
A. y = C1cosx + C2sinx
B. y = C1e(raised to x) + C2e(raised to –x) A. 0 C. 39
C. y = e(raised to –x) (C1cosx – C2sinx) B. - 3 D. no solution
D. y = e(raised to x) (C1cosx + C2sinx)
50. Two circles are such that the sum of their
44. A particle’s curvilinear motion is represented by the circumference is 24 pi and the sum of their areas is 84 pi
equation s (t) = 40t + 5t(squared) - 8t(cube).Calculate square ft. Find the smaller radius.
the initial acceleration of the particle?
A. 3.55 C. 6
A. 2 m/ s (squared) C. 8 m/ s (squared) B. 8.45 D. 48
B. 3 m/ s(squared) D. 10 m/ s (squared)
51. A debt of Php 10,000 with 10% interest
45. A particle position defined by S(t) = 2 sin t i + 4 cos t j compounded semi-annually is to be amortized by semi-
(t in radians) What the magnitude of the particle’s annual payments over the next 5 years. The first due is
velocity when t = 4 rad? 6 months. Determine the semi-annual payment.

A. 2.6 C. 3.3 A. Php 1,200.00 C. Php 1,295.05

B. 2.7 D. 4.1 B. Php 1,193.90 D. Php 1,400.40

46. A projectile has an initial velocity of 110 m / s and a 52. A gun is shot into a 0.50 KN block which is hanging
launch angle of 20o from the horizontal. The from a rope of 1.8 m long. The weight of the bullet is
surrounding terrain is level, and air friction is to be equal to 5 N with a muzzle velocity of 320 m/s. How
disregarded. Compute the flight time of the projectile? high will the bag swing after it was hit by the bullet?

A. 3.8 s C. 8.9 s A. 0.61 m C. 0.90 m

B. 7.7 s D. 12 s B. 0.51 m D. 0.34 m
53. All of the following units are acceptable for 59. If the nominal interest rate is 3%, how much is Php
quantifying work except 5000.00 worth in 10 years in a continuously
compounded account?
A. foot-pounds. C. joules.
B. watt-seconds. D. dynes. A. P 5,450.00 C. P 6,750.00
B. P 6,300.00 D. P 6,120.00
54. A conical vessel has a height of 24 cm and a base
diameter of 12 cm. It holds water to a depth of 18 cm 60. The population of a certain city doubles every 40 yr.
above its vertex. Find the volume of its content in cubic If the population is 1950 was 10,000, what was the
centimeter. population in 2010?

A. 387.4 cm3 C. 381.7 cm3 A. 2/27 C. 27/64

B. 383.5 cm3 D. 385.2 cm3 B. 16/27 D. 3/4

55. What is the minimum initial velocity a rocket must 61. A tank contains 100 L of brine made by dissolving 60
be fired if it is to be able to reach the target 1000 km kg of salt in pure water. Salt water with a concentration
away? of 1 kg/L enters the tank at a rate of 2 L/min. A well-
stirred mixture is drawn from the tank at a rate of 3
A. 3.1 km/s C. 4.4 km/s L/min. The mass of salt in the tank after one hour is
B. 3.4 km/s D. 2.4 km/s most nearly:

56. An object weighing 400 N is held by a rope that A. 13 kg C. 37 kg

passes over a horizontal drum. The coefficient of friction B. 43 kg D. 51 kg
between the rope and the drum is 0.25. If the angle of
contact is 150o, determine the force that will raise the 62. If the sum of first n terms of a series is be
object. 5n(squared) + 2n ,then the second term is

A. 350 N C. 540 N A. 7 C. 24
B. 770 N D. 780 N B. 17 D. 42

57. Two freight cars weighing 5 mtons each roll toward

each other and couple. The left car has a velocity of 1.5
m/s and the right car has a velocity of 1.2 m/s prior to 63. The first term of an infinite geometric progression if
the impact. What is the velocity of the two cars coupled 1 and each term is twice the sum of the succeeding
together after the impact? terms, then the sum of the series is:

A. 0.15 m/s right C. 0.15 m/s right A. 3/2 C. 5/3

B. 0.25 m/s left D. 0.17 m/s right B. 4/3 D. 5/2

58. A company issued 50 bonds of P 1,000.00 face value 64. The rule of 72 can be used to calculate the
each, redeemable at par at the end of 15 years to
accumulate the funds required for redemption. The firm A. number of monthly payments in six years.
established a sinking fund consisting of annual deposits, B. time to double an investment.
the interest rate of the fund being 4 %. What was the C. time to triple an investment.
principal in the fund at the end of the 12th year? D. time to decrease an investment to 1/72 of its original
value.
A. Php 32,938.00 C. Php 40,378.00
B. Php 38,453.00 D. Php 37,519.00 65. What is the area of an ellipse with an aspect ratio of
two and total perimeter of 18 inches?
 to continue indefinitely. The interest rate earned on the
A. 20.63 C. 14.53 initial investment is most nearly
B. 12.54 D. 22.54
A. 8.3% C. 10%
66. What percent increase in volume is achieved for a B. 9.0% D. 12%
sphere whose diameter increases from 3cm to 4cm?
72. An auditorium is designed to seat 200 people. The
A. 200% C. 105% ventilation rate is 2.50 x 10(raised to 4) cu m/h of
B. 137% D. 270% outside air, or 3.3 x 10(raised to 4) kg/h. The outside
temperature is -10oC dry-bulb, and the outside pressure
67. A current of 7 A passes through a 12 ohm resistor. is 101.3 kPa. Air leaves the auditorium at 23oC dry-bulb.
What is most nearly the power dissipated in the The air temperature entering the auditorium is 21.6oC.
resistor? Most nearly, how much heat should be supplied to the
ventilation air?
A. 0.10 Hp C. 0.60 Hp
B. 0.8 Hp D. 8 Hp
A. 120 kW C. 540 kW
68. A piece of equipment has an initial cost of Php5000 B. 290 kW D. 780 kW
in year 1. The maintenance cost is Php 300/yr for the
total lifetime of seven years. During years 1-3, the rate 73. Air enters a cooling tower at 50 oF dry-bulb and 49oF
of inflation is 5%, and the effective annual rate of wet-bulb temperature. It leaves the tower saturated at
interest is 9%. The uninflated present worth of then 70oF. Which condition is a likely outcome of this?
equipment during year 1 is most nearly
A. Adsorption C. Condensation
A. Php3200 C. Php3400 B. Fog D. Sublimation
B. Php3300 D. Php3500
74. The parameter that has the greatest limiting effect
69. Calculate the surface area (including both side and on the thermal performance of an open, evaporative
base) of a 4 m high right circular cone with a base 3 m in cooling tower is:
diameter?
A. Approach C. Range
A. 24 m2 C. 32 m2 B. Dry-bulb temperature D. Wet-bulb temperature
B. 27 m2 D. 36 m2
75. How many joules is equivalent to the energy of 1 kg
70. One item that differentiates the “Christmas club matter?
problem” from a standard cash flow problem is
A. 10 (raised to -10) J C. 1 MJ
A. varying interest rates through the life of the problem. B. 10(raised to -15) J D. 10 (raised to 17)
B. varying cash flows through the life of the problem.
C. the existence of a payment at the beginning of the 76. The Economic Order Quantity (EOQ) is defined as
time at t = 0 and the absence of a payment at the end of the order quantity which minimizes the inventory cost
the problem. per unit time. Which of the following is not an
D. the nonexistence of interest in the problem at all. assumption of basic EOQ model with no shortages?

71. Permanent mineral rights on parcel of land are A. The demand rate is uniform and constant.
purchased for an initial lump-sum payment of Php B. There is a positive cost on each unit inventoried.
5,000,000. Profits from mining activities are Php C. The entire reorder quantity is delivered
600,000 and each year, and these profits are expected instantaneously.
D. There is an upper bound on the quantity ordered.
 83. Comparing successive terms of an unknown series
77. Which of the following is NOT a correct derivative? to those of a series that is known to converge or diverge
is called :
A. d(cos x)/dx = –sin x
B. d( 1 – x) cubed / dx = – 3(1 – x )squared A. the comparison test. C. the ratio test.
C. d(1/x) / dx = – 1 /x(squared) B. L’Hôpital’s rule. D. the mean value theorem.
D. d(csc x )/dx = – cot x
84. A cable carrying a constant uniform load per unit
78. Which of the following is the engineering economic length along the length of the cable (e.g., a loose cable
analysis that is concerned with situations in which there loaded by its own weight) will have a shape of a
is not enough information to determine probability or
frequency for the variables involved? A. Straight line C. catenary
B. Parabola D. hyperbola
A. synthetical analysis
B. risk analysis 85. A room’s sensible space load is 72.5 kW. The latent
C. sensitivity analysis load from occupants and infiltration, but excluding
D. uncertainty analysis intentional ventilation, 3.2 kW. A total of 600 L/s of
outside air is required. What is most nearly the room
79. When exposed to the atmosphere, which of the sensible heat ratio?
following liquids is coldest?
A. 0.12 C. 0.96
A. oxygen C. nitrogen B. 0.39 D. 1.1
B. argon D. helium
86. A 12.5 mm diameter steel rod is pinned between
80. Find the locus of a point that moves so that it is two rigid walls. The rod is initially unstressed. The rod’s
always twice as far from (1, 2) as from (-3 , 4) temperature subsequently increases 50 oC. The rod is
adequately stiffened and supported such that buckling
A. 3x(squared) + 3y(squared) + 26x – 28y + 95 = 0 does not occur. The coefficient of linear thermal
B. 3x(squared) - 3y(squared) + 20x – 12y + 90 = 0 expansion for steel is 11.7 x 10-6
C. 5x(squared) - 5y(squared) + 25x – 10y + 45 = 0 1/oC. The modulus of elasticity for steel is 210 GPa.
D. 5x(squared) + 5y(squared) + 15x – 7y + 40 = 0 What is the approximate axial force in the rod?

81. Which of the following is the acceleration produced A. 2.8 kN C. 19 kN

when a particle moves away from its center of rotation? B. 15 kN D. 58 kN

A. tangential acceleration C. centripetal acceleration 87. Which of the following metals has the highest
B. coriolis acceleration D. centrifugal acceleration specific heat capacity at 1000C?

A. aluminum C. copper
B. bismuth D. iron

82. All of the following are recognized and accepted 88. Solve the spherical excess of the triangle formed by
methods of general systems modelling except: the North pole and two points on the earth’s equator
separated by 85o of longitude?
A. Monte Carlo simulation.
B. Replacement and renewal models. A. 85 deg C.275 deg
C. Decision trees. B. 60 deg D.95 deg
D. Rule of thumb methods.
89. Study the series of numbers to discover “system” in C. the IPC volume adjusted budget (fixed +
which they are arranged. For the series 1, 5, 14, 30, volume(variable IPC rate))
____, 91 the fifth term is: D. the IPC volume adjusted budget minus the total IPC
absorbed
A. 59 C.55
B. 53 D.50 96. The sinking fund method is seldom used in industry
because
90. If an all-positive term diverging series is equal term
for term to a converging series with alternating signs, A. the term “sinking fund” has a bad connotation for
the original series is said to be: business.
B. sometimes it gives misleading answers.
A. Monotonically increasing. C. Absolutely convergent. C. the initial depreciation is low.
B. Conditionally convergent. D. Finite. D. the initial depreciation is high.

91. The study of the practical laws of fluid flow and the 97. Second law limitation on the maximum horsepower
resistance of open pipes and channels is the purview of output from any power unit burning 1,000,000 BTU/hr
of fuel with high and low temperature extremes of
A. fluid mechanics. C. aerodynamics 1540oF and 40oF is:
B. hydraulics. D. thermodynamics.
A. 98. C. 1140.
B. 295. D. 3830.

92. A circular sector has a radius of 8 cm and an arc 98. Equilibrium conditions exist in all except which of
length of 13 cm. Calculate its area? the following:

A. 48 cm2 C. 52 cm2 A. in reversible processes.

B. 50 cm2 D. 60 cm2 B. along ideal frictionless, non dissipative paths where
forward and reverse processes occur at equal rates.
93. The relationship between the total volume of a C. in processes where driving forces are infinitesimals.
mixture of nonreacting gases and their partial volumes D. in a steady state flow process.
is given by
99. If one root of equation x(squared) + ax + 12 = 0 is 4
A. gravimetric fractions. C. Dalton’s law. while the equation x(squared) + ax + b = 0 has equal
B. Amagat’s law. D. mole fractions. roots, then the value of b is:

94. All of the following processes are irreversible except A. 4/7 C. 4/49
B. 7/4 D. 49/4
A. stirring of a viscous fluid.
B. a isentropic deceleration of a moving, perfect fluid. 100. The ratio of a load-bearing force to the applied
C. an unrestrained expansion of a gas. force for a lever is called its
D. phase changes.
A. Load factor C. mechanical advantage
95. What is the indirect product cost (IPC) spending B. Efficiency D. influence factor
variance

A. the difference between actual IPC and IPC absorbed

B. the difference between actual IPC and IPC volume
adjusted budget