A farmer is to plant rice in a rectangular field
30 meters by 40 meters. He started on the
edge and plant around the perimeter. How
wide a strip around he plant for each side in
order to do half the work?
A. 5 m
B. 2.5 m
C. 3 m
D. 5.5 m
Ans. A
If a mechanical engineer borrowed money
from his girl friend with simple interest of
12%, determine the present worth of
P75,000.00 which is due at the end of 7
months.
A. P72,200.20
B. P70,200.20
C. P73,900.50
D. P70,093.20
Ans. D
An Electrical Engineer obtained a loan of
P50,000 at the rate of 6% compounded
annually in order to repair his mistress’
house. How much must the Electrical
Engineer pay monthly to amortize the loan
within a period of ten years?
A. P605.20
B. P550.90
C. P505.90
D. P508.90
Ans. B
What is the value of 1 radian in degrees?
A. 89.55o
B. 57.3o
C. 60.3o
D. 45.58o
Ans. B
How many degrees are 4800 mills?
A. 180o
B. 315o
C. 90o
D. 270o
Ans. D
A force of 200 lb acts on a block at an angle
of 28o with respect to horizontal. The block is
pushed 2 ft horizontally. Find the work done
by this force.
A. 480 J
B. 408 J
C. 840 J
D. 804 J
Ans. A
A truck starts from rest and moves with a
constant acceleration of 6 m/s2. Find the
speed of the truck after 4 seconds.
A. 18 m/s
B. 28 m/s
C. 24 m/s
D. 35 m/s
Ans. C
A car starts from rest and has a constant
acceleration of 3 ft/s2. Determine the average
velocity during the first 10 seconds of motion.
A. 15 fps
B. 20 fps
C. 12 fps
D. 18 fps
Ans. A
Determine the value of each interior angle of
a regular pentagon.
A. 108o
B. 120o
C. 98o
D. 135o
Ans. A
Determine the first derivative with respect to
x of the functions g(x) = √10 - 35
A. ¾
B. 0
C. 4(9)3/4
D. 35
Ans. B
Determine the slope of a curve y = -x2 at the
point (2, 3).
A. 4
B. -4
C. 2
D. -2
Ans. B
What is the sum of the roots of the equation
2x2 + 5x + 5 = 0?
A. -2.5
B. 2.5
C. 2.25
D. -2.25
Ans. A
Determine the distance travelled by a particle
between a time interval of 0.2 seconds to 0.30
seconds if its velocity is v = 12t4 + 7/t, where v
is in cm/s and t is in seconds.
A. 3.75 cm
B. 2.84 cm
C. 2.75 cm
D. 3.84 cm
Ans. B
Compute the arithmetic mean of the
following set of numbers: 18, 24, 27, 30, 35,
42, 50.
A. 31.82
B. 32.29
C. 30
D. 29.96
Ans. B
Find the root mean square of 11, 23 and 35.
A. 25
B. 27
C. 26
D. 24
Ans. A
Five years ago the father is three times as old
as his son. Ten years from now, the father will
be twice as old as his son. How old is the son
twelve years from now.
A. 32 years old B. 20 years old C. 50
years old D. 38 years old
Ans. A
The sum of P15,000, deposited in an account
earning 4% per annum compounded
quarterly, will become P18,302.85.
Determine the effective rate of interest per
year.
A. 3.06%
B. 4.06%
C. 5.06%
D. 6.06%
Ans. B
If a machine is purchased on instalment and
the buyer makes an P80,000.00 down
payment and owes a balance of P150,000 in 2
years. Determine the machine cash value if
money is worth 14% compounded quarterly.
A. P199,312.00 B. P183,912.00 C.
P193,912.00
D. P139,912.00
Ans. C
A machine was purchased under these terms:
P30,000 down and P5,000 each month for 5
years. If money is worth 12% compounded
monthly, what is the cash price of the
machine?
A. P144,775.19 B. P245,775.19 C.
P542,775.91
D. P254,775.19
Ans. D
A.
B.
C.
D.
Find ∫(7x3 + 4x2) dx?
7x2 /3 + 4x2 /2 + C
7x4 /4 + 4x3 /3 + C
7x4 /4 + 4x2 /5 + C
7x4 /5 + 4x3 /5 + C
Ans. B
What is the least common denominator or
simply LCD of 1/12 and 1/18?
A. 24
B. 36
C. 72
D. 54
Ans. B
How many two digit numbers can be formed
from the number 1, 2, 3, and 4 if repetitions is
not allowed?
A. 8
B. 12
C. 16
D. 20
Ans. B
How many two digit numbers can be formed
from the number 1, 2, 3, and 4 if repetitions
is allowed?
A. 6
B. 12
C. 18
D. 64
Ans. D
The volume of the cube is increasingly at the
rate of 5 cu. M per minute. Determine the
rate at which the surface area is increasing in
m2/min, when its side is 10 m.
A. ½
B. 1.75
C. 1.5
D. 2
Ans. D
The segment from (-1, 4) to (2, -2) is extended
three times its own length. What is the
terminal point?
A. (11, -18)
B. (11, -24)
C. (11, -20)
D. (-11, -20)
Ans. C
Studyhi ni choy!
The midpoint of the line segment between
P1(x1, y1) and P2 (-2, 4) is Pm (2, -1). Find the
coordinate of P1.
A. (6, -5)
B. (11, -24)
C. (6, -6)
D. (-6, 6)
Ans. C
Find the coordinates of the point P(2, 4) with
respect to the translated axis with origin at (1,
3).
A. (1, -1)
B. (1, 1)
C. (-1, -1)
D. (-1, 1)
P(x-h, y-k)
Ans. B
What is the area bounded by y = 0, y = ex, x =
0, x = 2
A. 2.27
B. 6.389
C. 1.79
D. 1.27
Ans. B
The salary of an employee’s job has five levels,
each one 5% greater than the one below it.
Due to circumstances, the salary of the
employee must be reduced from the top
(fifth) level to the second level, which means a
reduction of 3000.00 per month. What is the
employees present salary per month?
A. P22,032.50
B. P23,022.50 C.
P22,320.50
D. 22,302.50
Present salary is s5
Ans. A
Twice the middle digit of a three-digit number
is the sum of the other two. If the number is
divided by the sum of its digit, the answer is
56 and the remainder is 12. If the digits are
reversed, the number becomes smaller by
594. Find the number.
A. 852
B. 285
C. 825
D. 582
Ans. A
Lucy sold 100-pirated DVD. Eighty of them
were sold at a profit of 30% while the rest
were sold at a loss of 40%. What is the
percentage gain or loss on the whole stock?
A. 15%
B. 20%
C. 16%
D. 12%
Ans. C
A pole cast a shadow 15 m long when the
angle of elevation of the sun is 61o. If the pole
has lean 15o from the vertical directly toward
the sun, what is the length of the pole?
A. 54.23 m
B. 48.64 m
C. 36.84 m
D. 64.84 m
Ans. A
A man finds the angle of elevation of the top
of the tower to be 30o. He walks 85 m nearer
the tower and finds angle of elevation to be
60o. What is the height of the tower?
A. 76.31 m
B. 73.31 m
C. 73.16 m
D. 73.61 m
73.61 m !!
Ans. A
How many 3 digit numbers may be formed
from the digits 0, 1, 2, 3, 4 and 5 if no digit
may be repeated in a given number?
A. 100
B. 180
C. 45
D. 52
120 !!
Ans. A
In how many ways can you line-up 4 marines
and 6 army soldiers must be side by side with
each other and the army soldiers are likewise?
A. 35,460
B. 34,560
C. 36,450
D. 30,546
Ans. B
A semiconductor company will hire 7 men and
4 women. In how many ways can the
company choose from 9 men and 6 women
who qualified for the positions?
A. 540
B. 480
C. 680
D. 840
Ans. A
A bag contains 3 white and 5 red balls. If two
balls are drawn at random, find the
probability that both are white.
A. 0.375
B. 0.10714
C. 0.46667
D. 0.28571
Ans. B
A certain job can be done by Jobelle and TJ in
10 hours, by Jobelle and Jessyl in 12 hours and
TJ and Jessyl in 20 hours. Find how long
would it take by Jobelle to do the job alone.
A. 30 hours
B. 60 hours
C. 15 hours
D. 25 hours
Ans. B
15 HOURS !!
In 1995, little cute Jobelle had a pocket
contains P11.65 of twenty five and ten
centavo coins. If the total number of coins is
70. Find how many twenty five coins did she
has?
A. 31
B. 39
C. 21
D. 29
Ans. A
A bullet weighing 4 grams was fired from a
gun with the barrel measuring 12 cm long. If
the bullet was fired with a speed of 380 m/s
solve the energy of the bullet in Joules .
A. 289
B. 345
C. 798
D. 1009
Ans. A
A pipe lining material of silicon carbide used
in the conveyance of pulvurized coal to fuel a
boiler, has a thickness of 2 cm and inside
diameter of 10 cm. Find the volume of the
material of a pipe length of 6 meters in liters.
A. 45.24
B. 47.45
C. 51.47
D. 68.97
Ans. A
A missile is fired with a speed of 100 fps in a
direction of 30o above the horizontal.
Determine the maximum height to which it
rises in feet.
A. 38.85
B. 19.43
C. 377.33
D. 1509.32
Ans. A
What time between 2 and 3 o’clock will the
hands of the clock be opposite one another.
A. 2:43 7/11
B. 2:44 7/11
C. 2:37 8/11
D. 2:46 7/11
Ans. A
From a deck of ordinary cards, what is the
probability of drawing a heart or face card?
A. 48.08%
B. 42.31%
C. 5.77%
D. 33.33%
43.75%
Ans. B
A perfect gas is expanded polytropically with
an initial volume and temperature of 0.06 m3
and 147oC respectively. If the final volume
and temperature are 0.21 m3 and 21oC
respectively, what is the index of the
expansion?
A. 1.285
B. 1.212
C. 1.333
D. 4.400
Ans. A
If the loan was for 15 months at 16.8%
interest a year and the repayment on a loan
was P12,100.00, how much was the principal?
A. P8,500.00
B. P9,500.00
C. P10,000.00
D. P10,500.00
Ans. C
The sum of P15,000, deposited in an account
earning 4% per annum compounded
quarterly, will become P18,302.85.
Determine the effective rate of interest per
year.
A. 3.06%
B. 4.06%
C. 5.06%
D. 6.06%
Ans. B
Find the number of years when P2,500.00 is
compounded to P5,800.00 at 12%
compounded quarterly.
A. 6.12 years
B. 7.12 years
C. 8.12 years
D. 5.12 years
Ans. B
What is the effective rate equivalent of 12%
compounded quarterly?
A. 12.55%
B. 11.55%
C. 12.98%
D. 13%
Ans. A
What rate compounded quarterly is
equivalent to 14% compounded semiannually?
A. 10.76%
B. 11.76%
C. 12.76%
D. 13.76%
Ans. D
Celestino owes P500, due in 3 years and P800
due in 7 years. He is allowed to settle these
obligations by a single payment on the 6th
year. Find how much he has to pay on the 6th
year if money is worth 14% compounded
semi-annually.
A. P1,449.12
B. P1,559.12
C. P1,339.12
D. P1,669.12
Ans. A
Determine the amount that must be
deposited every 3 months in a fund earning
12% compounded quarterly in order to have
P25,000 in 8 years.
A. P716.71
B. P476.17
C. P674.71
D. 1700.00
Ans. B
What is the value of 1 radian in degrees?
A. 89.55o
B. 57.3o
C. 60.3o
D. 45.58o
Ans. B
If the density of gas is 0.003 slug/ft3, what is
the specific weight of the gas?
A. 15.2 N/m3
B. 9.04 N/m3
C. 98.2 N/m3
D. 76.3 N/m3
Ans. A
If the specific weight of a liquid is 58.5 lb per
cubic foot, what is the specific volume of the
liquid?
A. 1.0675 cm3/g B. 0.5321 cm3/g C.
1.5502 cm3/g D. 0.9504 cm3/g
Ans. A
The atomic weight of hydrogen is 1 gram per
gram-atom. What is the mass of a hydrogen
atom?
A. 1.66 x 10-24 g/atom
B. 6.02 x 10-23 g/atom
C. 1 g/atom
D. The mass is too small to calculate
Ans. A
A ball is dropped from a height of 60 meters
above ground. How long it take to hit the
ground?
A. 4.5 seconds B. 3.5 seconds C. 2.5
seconds D. 1.5 seconds
Ans. B
A 5 meter extension ladder leans against the
wall; the bottom is 3 m from the wall. If the
bottom stays at the same place, how much
should the ladder be extended so that the top
would lean against the wall 1 meter higher?
A. 1.2 m
B. 1.5 m
C. 0.5 m
D. 0.83095 m
Ans. D
If a stone is dropped from a balloon while
ascending at the rate of 7.5 m/s reaches the
ground in 6 seconds, what was the height of
the balloon when the stone was dropped?
A. 110.12 m
B. 120.25 m
C. 131.81 m
D. 140.12 m
Ans. C
A cubical container that measures 50.8 mm
on a side is tightly packed with marbles and is
filled with water. All eight marbles are in
contact with the walls of the container and
the adjacent marbles. All of the marbles are
same size. What is the volume of water in the
container?
A. 434,096.51 mm3
B. 62,454.54 mm3
C. 431,960.51 mm3
D. 68,641.97 mm3
Ans. B
What is the determinant of the 2 x 2 matrix,
│7 6 │?
│5 9 │
A. -33
B. 33
C. -43
D. 43
Ans. B
What is the determinant of the 3 x 3 matrix,
│1 2 -1│?
│2 -1 1│
│1 1 1 │
A. 6
B. 7
C. -6
D. -7
Ans. D
Given the following vectors A = 3i + 2j, B = 2i
+ 3j + k, C = 5i + 2k. Simplify the expression
(A x B).C.
A. 20
B. 0
C. 60i + 24k
D. 5i + 2k
Ans. A
Determine the rationalized value of the
complex number (6 + 2.5i)/(3 + 4i).
A. 1.12 – 0.66i
B. 0.32 – 0.66i
C. -32 + 0.66i
D. -1.12 + 0.66i
Ans. A
Determine the type of flow of fluid flowing
inside 25.4 cm radius pipe at a velocity of 10
m/s and a viscosity of 1.131 Pa-s.
A. Laminar flow
B. Turbulent flow
C. Critical flow
4491.60
D. Transition flow
Ans. A
What is the probability of an examinee to pass
or fail the board exam?
A. 50%
B. 0%
C. 100%
D. 75%
Ans. C
How many even numbers of three different
digits each can be formed from the digits 1, 2,
3, 4, 5 and 7?
A. 20
B. 40
C. 36
D. 28
Ans. B
What is the measure of 1 ½ revolutions
counter-clockwise?
A. +540o
B. -540o
C. +90o
D. -90o
Ans. A
If the hypotenuse of a right triangle is 34 cm.
What is the length of the shortest leg if it is 14
cm shorter than the other leg. A. 17 cm
B. 15 cm
C. 16 cm
D. 18 cm
Ans. C
If AB = 15 cm, BC = 18 cm and CA = 24 cm,
find the point of intersection of the angular
bisector from the vertex C.
A. 11.3 cm
B. 13.4 cm
C. 12.1 cm
D. 14.3 cm
Ans. D
A car travels from point M northward for 30
minutes then eastward for one hour, then
shifted N30oW. If the constant speed is 40
kph, how far directly from M will be it after 2
hours?
A. 41.6 km
B. 47.9 km
C. 43.5 km
D. 45.2 km
Ans. B
If the sides of a triangle are 18 cm, 24 cm and
34 cm, respectively. What is the length of the
median to the 24-cm side?
A. 21.4 cm
B. 24.4 cm
C. 20.4 cm
D. 23.4 cm
Ans. B
From the third floor window of a building, the
angle of depression of an object on the
ground is 35o58’, while from a sixth floor
window, 9.75 m above the first point of
observation the angle of depression is 58o 35’.
How far is the object from the building?
A. 15.3 m
B. 9.3 m
C. 10.7 m
D. 11.9 m
Ans. C
In the following identities, which one is
different from the others?
A. 2cos2x – 1
B. Cos4x – sin4x
C. Cos3x – sin3x
D. 1 – 2sin2x
Ans. C
Estimate the median of the following set of
numbers: 18, 24, 27, 30, 35, 42, 50.
A. 31.82
B. 32.29
C. 30
D. 29.96
Ans. C
How many permutations can be made from
the letters a, b, and c taken two at a time?
A. 6
B. 8
C. 18
D. 64
Ans. A
Solve for the length of the hypotenuse of a
right triangle if length of the two legs are 7 m
and 16 m, respectively.
A. 10.363 m
B. 12.567 m
C. 15.648 m
D. 17.464 m
Ans. D
A car in overtaking a trailer, uniformly
accelerated its speed from 40 km/hr to 90
km/hr in 8 seconds. Calculate the distance
travelled during the period of acceleration in
meters.
A. 144.44 B. 156.09
C. 346.9
D. 500.78
Ans. A
An area of 25.6 cm2 on the map represents a
lot having an area of 640 m2. If the scale on
the map is 1:x, what is the remainder is 10.
Determine the value of x?
A. 50
B. 100
C. 500
D. 900
Ans. C
When the expression x4 + ax3 + 5x2 + bx + 6 is
divided by (x – 2), the remainder is 16. When
it is divided by (x + 1) the remainder is 10.
Determine the value of the constant a.
A. 6
B. 9
C. 5
D. 7
Ans. D
What is the simple interest rate if an
investment of P37,500.00 accumulates to
P45,937.5 in 18 months?
A. 0.15
B. 0.20
C. 0.21
D. 0.3
Ans. A
The JRF Corporation manufactures bookcases that
sells for P65.00 each. It costs JRF corporation
P35,000.00 per year to operate its plant. The sum
includes rentals, depreciation charges on equipment,
and salary payments. If the cost to produce one
book case is P50.00, how many bookcases must be
sold each year for the corporation to avoid taking a
loss?
A. 539 Bookcases
B. 750 Bookcases
C. 2333 Bookcases
D. 2334 Bookcases
Ans. D
A machine is purchased for P500,000.00. The
salvage value in 25 years is P100,000.00.
What is the depreciation in the first three
years using straight line method?
A. P24,000.00
B. P32,000.00
C. P48,000.00
D. P16,000.00
Ans. C
How much must be deposited at 6% each year
on January 1, year 1, in order to accumulate
P5,000.00 on the date of the last deposit,
January 1, year 6?
A. P676.24
B. P766.24
C. P667.2 D. P626.24
716.813
Ans. A
Jeffrey made a loan from a bank. The bank
charges him 12% simple interest on a P300.00
loan. How much will be repaid if the loan is
paid in one lump sum after three years?
A. P425.00
B. P408.00
C. P551.00
D. P450.00
Ans. B
My P5,000 shall accumulate for 10 years at 8%
compounded quarterly. What is the
compound interest of my money at the end of
10 years?
A. P6,005.30
B. P6,040.20
C. P6,000.00
D. P6,010.20
Ans. B
What is the effective rate corresponding to
18% compounded daily?
A. 17.72% B. 18.72%
C. 19.72% D. 20.72%
Ans. C
The management of a certain company
deposits P1,500.00 for each of its employees
in a retirement fund at the end of each year
for the next 12 years. How much is each
employee’s fund at the end of 12 years if it
accumulates 8% for the first 8 years and 6%
for the last 4 years?
A. P27,705
B. P26,705
C. P24,705
D. 23,705
Ans. B
What is the least number of years needed to
triple a certain amount of money at 5% per
annum compounded interest to the nearest
year?
A. 20.5 years
B. 18.5 years
C. 22.5 years
D. 16.5 years
Ans. C
The roots of the quadratic equation are 1/3
and -3/2. What is the equation?
A. 6x2 + 5x + 3 = 0
B. 6x2 – 7x – 3 = 0
C. 6x2 + 7x – 3 = 0
D. 6x2 + 7x + 3 = 0
Ans. C
What is the sum of the numerical coefficient
in the expansion of ( x – 2y)7?
A. -1
B. 1
C. -2187
D. 2187
Ans. A
Mr. PME covered a distance of 55 km in 4 hrs
by driving his car 40 kph, part of the way, and
by walking the remainder of the way at 5 kph.
What part of the total distance did Mr PME go
by car?
A. 7/11
B. 8/11
C. 9/11
D. 10/11
Ans. B
The water tank in Calamba Water District can
be filled by pipe A in half the time the pipe B
can empty the tank. When both pipes are
operating, the tank can be filled in 1 hour and
12 minutes. Determine the time, in hours, for
pipe A to fill the tank alone.
A. 0.6
B. 0.7
C. 0.75
D. 0.8
Ans. A
Of the 316 people attending the party, there
are 78 more children than women and 50
more women than men. Determine the
number of men in the party.
A. 46
B. 96
C. 112
D. 178
Ans. A
A house can be constructed in as many days
as there are men in the group of construction
personnel. If the number of men is reduced
by 4, the project is delayed by 5 days.
Determine the original number of number of
construction personnel.
A. 18
B. 16
C. 20
D. 24
Ans. C
Determine the distance between points A(2, 3, 5) and B(7, 2, -6).
A. 11.08 units
B. 12.08 units
C. 13.08 units
D. 14.08 units
Ans. C
What are the two positive numbers whose
sum is 8, if the product of one number by the
cube of the other number is to be maximum?
A. 1 & 7
B. 2 & 6
C. 3 & 5
D. 4 & 4
Ans. B
Forty liters of a 60% salt solution are
produced to a 45% solution. How much
solution must be drained off and replaced
with distilled water so that the resulting
solution contains only 45% solution. A. 6
liters
B. 8 liters
C. 10 liters
D. 12 liters
Ans. C
If ln y = 5 and ln x = 3, what is the value of
ln(x2/y1/2)?
A. 2.5
B. 3.5
C. 4.5
D. 1.5
Ans. B
A river is 580 ft wide. The bridge construction
cross the river is banked 1/7 of its length in
the east and 1/6 of the length in the west.
What is the length of the bridge?
A. 660 ft
B. 750 ft
C. 840 ft
D. 1670 ft
Ans. C
What is the area of the circle whose equation
is x2 + y2 – 6x + 8y = 0?
A. 25π
B. 5 π
C. 15 π
D. 20 π
Ans. A
An oblique triangle has sides a = 6 cm, b = 9
cm and angle C = 32o. Solve the angles of the
triangle.
A. 39o6’48”; 108o51’54”
C. 40o, 80o
B. 39o6’48”; 98o51’54”
D. 50o, 102o
Ans. A
Given a triangle with angle C = 28.7o, side a =
132 units and b = 224 units. Solve for the
angle B.
A. 140.94o B. 130.94o
C. 120.94o D. 80.94o
Ans. C
USE COSINE LAW
If the sides of a triangle are 18 cm, 24 cm and
34 cm, respectively. What is the length of the
median to the 24-cm side?
A. 21.9 cm
B. 24.4 cm
C. 20.4 cm
D. 23.4 cm
Lookscam!
Ans. B
What is the suppliment of an angle whose
compliment is 62o?
A. 152o
B. 118o
C. 28o
D. 60o
Ans. A
A certain angle has a supplimentary five times
its compliment. What is the angle?
A. 186o
B. 168.5º
C. 67.5o
D. 157.5o
Ans. C
Water is pouring into a swimming pool. After
t hours, there are t + √t gallons in the pool.
At what rate, in GPM is water pouring into the
pool when t = 9 hours?
A. 0.0194 B. 1.167
C. 1.235
D. 3.6
Ans. A
From the top of tower A, the angle of
elevation of the top of the tower B is 46o.
From the foot of tower B to the top of tower A
is 28o. Both towers are on a level ground. If
the height of tower B is 120 m, how high is
tower A?
A. 40.7 m B. 44.1 m
C. 42.3 m D. 38.6 m
Ans. A
In the problem of writing the equation of a
certain curve with respect to another axes in
which the new axes are parallel to the original
axes and similarly directed is known as
A. Translation of axes
C. Notation of axes
B. Reversal of axes
D. Relocation of axes
Ans. A
The index that gives the rate earned per share
based on current price per share is called as:
A. Price earning ratio
B. Operating expense ratio
C. Dividend yeild
D. Equity ratio
Ans. C
What is annuity?
A. The future worth of a present amount
B. A series of uniform amounts over a period
of time
C. The present worth of a future amount
D. An annual repayment of a loan
Ans. B
When using net present worth calculations to
compare two projects, which of the following
could invalidate the calculation?
A. Use the same discount rate for each
period
B. Differences in the magnitudes of the
projects
C. Evaluating over different time periods
D. Mutually exclusive projects
Ans. C
Which of the following situations has a conventional
cash flow so that an internal rate of return can be
safely calculated and used?
A. Your company undertakes a mining project in
which the land must be reclaimed at the end of
the project.
B. You invest in a safe dividend stock and
receive dividends each year.
C. You lease a car and pay by the month
D. Your company invest heavily in a new
product that will generates profit for two
years. To keep profits high for 10 years, the
company plans to reinvest heavily after two
years.
Ans. B
Which of the following elements and
compounds is unstable in its pure form?
A. Hydrochloric acid
B. Carbon dioxide
C. Sodium
D. Helium
Ans. C
A substance is oxidized when which of the
following occurs?
A. It losses electrons
B. It becomes more negative
C. It gives off heat
D. It absorbs energy
Ans. A
Which one of the following statements
regarding organic substances is false?
A. Organic matter is generally stable at
very high temperature
B. Organic substances generally dissolve
in high-concentration acids
C. All organic matter contains carbon
D. Organic substances generally do not
dissolve in water.
Ans. A
Which of the following affects most of the
electrical and thermal properties of materials?
A. The weight of the atoms
B. The weight of the protons
C. The electrons, particularly the
outermost one
D. The magnitude of electrical charge of
the protons
Ans. C
What are the valence electrons?
A. The electrons of complete quantum
shells
B. Electrode with positive charge
C. The outer-shell electrons
D. The K-quantum shell electrons
Ans. C
How do you call the strong bond between
hydrogen atoms?
A. Ionic and metallic bonds
B. The covalent bond
C. The ionic bond
D. The metallic bond
Ans. B
What are Van der Waals forces?
A. Forces present only in gases
B. Forces not present in liquids
C. Primary bonds between atoms
D. Weak secondary bonds between
atoms
Ans. D
Which of the following is false?
A. The acceleration of a body rotating with a
constant angular velocity is zero.
B. Angular momentum for rigid bodies may be
regarded as the product of angular velocity
and inertia
C. The radius of gyration for a mass of uniform
thickness is identical to that for a planar area
of the same shape.
D. Kinematics is the study of the effects of
motion, while kinetics is the study of the
causes of motion.
Ans. A
What do you call the replacement of the
original cost of an investment?
A. Pay off
B. Return on investment
C. Break-even
D. Capital recovery
Ans. A
Adding more solute to an already saturated
solution will cause the excess solute to settle
to the bottom of the container. What is this
process calle?
A. Precipitation
B. Hydration
C. Dehydration
D. Saturation
Ans. A
The length of time at which the original cost
of capital used to purchase a unit has already
been recovered.
A. Economic life
B. Write off period
C. Physical life
D. Salvage life
Ans. B
A family of circles having a common center is
said to be:
A. Annulus
B. Circularing
C. Eccentric circle
D. Concentric circles
Ans. D
A law, which states that the curvature of the
central fiber is proportional to the bending
moment in homogeneous bar.
A. Euclid
B. Thailus
C. Bernoulli-Euler
D. Torrecilli
Ans. C
Given two triangles lying in non-parallel planes such
that the lines joining their corresponding vertices
intersect at a common point. If the lines containing
the corresponding sides of the triangle intersect the
points of intersection are collinear. The preceeding
statements is known as
A. Desargue’s theorem
B. Euclid’s theorem
C. Heron’s theorem
D. Aristotole’s theorem
Ans. A
When two sellers control sufficient of the
supply of a commodity or service to control its
price is known as:
A. Duopoly
B. Monopoly
C. Oligopoly
D. Control
Ans. A
The ratio of total liabilities to total assets is
said to be:
A. Equity ratio
B. Debt ratio
C. Quick ratio
D. Price-earning ratio
Ans. B
A fraction is a quotient of two integers
because they are ratios of integers. The
integer on top is called the numerator and the
integer at the bottom is called as the:
A. Denominator B. Remainder
C. Dividend
D. Augend
Ans. A
In a thermodynamics process following, PVn =
C, what is the process if the value of n is
infinity?
A. Isentropic process
B. Polytropic process
C. Isometric process
D. Isobaric process
Ans. C
The products or services that are desired by
humans and will be purchased if money is
available after the required necessities have
been obtained.
A. Necessities
B. Luxuries
C. Elastic demand
D. Inelastic demand
Ans. B
A demand that occurs when a decrease in
selling price produces little or no effect in
sales.
A. Inelastic demand
B. Demand
C. Elastic demand
D. Necessity
Ans. A
An interest computed on the basis of 12
months of 30 days each or 360 days a year,
and one interest period is equal to 360 days.
A. Interest
B. Ordinary simple interest
C. Simple interest
D. Exact simple interest
Ans. B
What must two investments with the same
present worth and unequal lives have?
A. Identical equivalent uniform annual
cash flow
B. Different salvage values
C. Different equivalent uniform annual
cash flows
D. Identical salvage values
Ans. D
Which of the following statelemnts is not true?
A. A nominal rate of 12% per annum
compounded quarterly is the same as (3%)
÷ 4 = 3% per quarter
B. One Peso compounded quarterly at 3% for n
years has a worth of (1.03)4th Pesos.
C. 12.55% annual compounding is the effective
rate for a situation in which the principal is
actually compounded quarterly at an annual
rate of 12%
D. Effective rate of return in choices a through c
is the difference between 12.55% and 12%.
Ans. D
Firm A uses full absorption costing while firm B uses
variable product costing. How will the financial
statements of these companies differ?
A. Firm A has a higher cost of goods sold,
higher inventory value, and no change in
retained earnings.
B. Firm A has a higher cost of goods sold and,
therefore, a smaller profit.
C. Firm A has a smaller cost of goods sold and
a larger profit.
D. Firm A has a smaller cost of goods sold, no
change in inventory value, and no change in
retained earnings.
Ans. A
How is the material purchase price variance
defined?
A. Quantity purchaced – quantity used x
actual price
B. (Quantity purchased x actual price) –
(quantity purchased x standard price)
C. Actual price – standard price x quantity
used
D. Quantity issued – standard quantity x
standard price
Ans. B
Borobodor Corporation is applying for a short loan.
In reviewing Borobodor Corporation’s financial
records, the banker finds a current ratio of 2.0 an
acid-test ratio of 0.5, and an accounts receivable
period of 70 days. What should be the banker do?
A. Extend the loan, as Borobodor Corporation
will have no trouble repaying it.
B. Suggest that Borobodor Corporation lower its
inventories
C. Suggest that Borobodor Corporation be
more aggressive in collecting on its invoices.
D. Consider all the actions from a to c above.
Ans. D
Companies A and B are identical except for their inventory
accounting systems. Company A uses the last-in, first out
convention while company B uses the first in, fist out
convention. How will their financial statements differ in an
inflationary environment?
A. Company’s B profits will be higher and the book
value will be higher than for company A.
B. Company’s A profits will be higher and the book
value of their inventory will be higher than for
company
C. Company’s A profits will be higher and the book
value of their inventory will be lower than for
company B.
D. Company’s B profit will be higher than A’s but
inventory book value will be lower
Ans. A
Alternatives with different lives will generally
be compared by way of
A. Equivalent uniform annual cost
(EUAC)
B. Equivalent present cost
C. Equivalent future worth factor
D. Rate of return
Ans. A
A statement of equity between two ratios.
A. Variation
B. Inequity
C. Proportion
D. Fraction
Ans. C
How do you call the costs of things that are
neither labor nor materials?
A. Labor costs
B. Expenses
C. Material costs
D. Investment cost
Ans. B
A satellite orbiting the earth passes directly
overhead stations in Phoenix and Los Angeles,
340 miles apart. At an instant when the
satellite is between these two stations, its
angle of elevation is simultaneously observed
to be 60o at Phoenix and 75o at Los Angeles.
How far is the satellite from Los Angeles?
A. 170 mi
B. 416 mi
C. 653 mi D. 316 mi
Ans. B
Find the second derivative of the parametric
equations x = 4 – t2 and y = t2 + 4t.
A. -1/t3
B. 1/t3
C. -2/t3
D. 3/t2
Ans. A
What expression is equivalent to log x – log ( y
+ z)?
A. Log x + log y + log z
B. Log[x/(y + z)]
C. Log x – log y – log z
D. Logy + log (x + z)
Ans. B
If a = b, then b = a. This illustrates of which of
the following axioms in algebra?
A. Transitive axiom
B. Reflexive axiom
C. Replacement axiom
D. Symmetric axiom
Ans. D
What is the logarithm of a negative number?
A. Complex number
B. Real number
C. Irrational number
D. Imaginary number
Ans. A
A manufacturer of sports equipment produces
tennis rackets for which there is a demand of
200 per month. The production set up cost for
each lot of racket is P300.00. In addition, the
inventory carrying cost for each racket is P24
per year. Using the Economic Order
Quantity(EOQ) model, which is the best
production batch size for the rackets?
A. 245 units
C. 173 units
B. 71 units
D. 346 units
Ans. A
What is the Eigen value of the matrix .
│5 3 │
│0 2 │
A. 5, 2
B. 5, 3
C. 0, 2
D. 0, 3
Ans. A
What is the beta function β [3, 7/2].
16/693
integral from 0 to 1
(t)^(x-1)(1-t)^(y-1)
A car moving at 20 m/s with its horn blowing
at f = 1200 Hz …….
1.219
11011 is equal to
27
The reciprocal of 5 is:
A. 0.1
B. 0.4
C. 0.2
D. 0.5
Ans. C
The digits of measurement which a scientist
reads and estimates on a scale are called:
A. Accuracy
B. precision
C. significant figures
D. experimentation
Ans. C
Simplify: am/n
A. n√m
C. am+n
B. am/n
D. am x n
Ans. A
Factor the expression x2 + 7x + 12 as
completely as possible:
A. (x + 4)(x + 2) B. (x + 4)(x + 3) C. (x +
3)(x + 2) D. (x + 2)(x +5)
Ans. B
Factor the expression: 2x3 – 2x2 – 12x
A. 2x(x – 3)(x + 2)
B. 2x(x + 3)(x - 2)
C. 2x(x – 4)(x - 2)
D. 2x(x + 3)(x - 4)
Ans. A
If A can do the job in x days and B in y days,
how long will they finish the job working
together?
A. (x + y)/xy days
B. x + y days
C. (xy)(x + y) days
D. (x + y)/2 days
Ans. C
In a pile of logs, each layer contains one or
more log than the layer above and top
contains just one log. If there are 105 logs in
the pile, how many layers are there?
A. 10
B. 14
C. 12
D. 15
Ans. B
A and B working together can finish painting a
house in six days. A, working alone, can finish
it in five days less than B. How long will it take
B to finish the work alone?
A. 10 days B. 12 days
C. 11 days D. 15 days
Ans. D
Simplify (n√m )n
A. a
C. an/1
B. a1/n
D. a/n
Ans. A
Solve for x: 2x2 – y2 – 14 = 0 but y = x – 1
A. x = -5 and x = 3
B. x = -6 and x = 2
C. x = 5 and x = -3
D. x = 6 and x = -2
Ans. A
A manufacturing firm maintains one product
assembly line to produce signal generators.
Wekly demand for the generator is 35 units.
The line operates for 7 hours per day, 5 days
per week. What is the maximum production
time per unit in hours required of the line to
meet the demand?
A. 1 hour
B. 3 hours
C. 2 hours D. 4 hours
Ans. A
Which number has three significant digits?
A. 0.0011
B. 0.01111
C. 1.1111
D. 0.0111
Ans. D
An urn contains 6 black balls and 4 white
balls. What is the probability of getting 1
black and 1 white ball in two consecutive
draws from the urn?
A. 0.25
B. 0.53
C. 0.33
D. 0.76
Ans. B
If A to the ¾ power equals 18.8, A is equal to:
A. 35
B. 50
C. 45
D. 60
Ans. B
The value of (3 to 2.5 power) square is equal
to:
A. 730
B. 150
C. 243
D. 93
Ans. C
10 to the negative 12th power is the value of
the prefix:
A. micro
B. tera
C. nano
D. pico
Ans. D
The product of (a – b)2:
A. a2 + b2
B. a2 – 2ab + b2 C. a2 –
b2 D. a2 + 2ab + b2
Ans. B
The arithmetic mean of 2 and 5 is:
A. 3.5
B. 7
C. 3.16
D. 10
Ans. A
The geometric mean of 3 and 12 is:
A. 18
B. 7.5
C. 15
D. 6
Ans. D
Factor the expression: (1 – a to the 8 th
power) as completely as possible.
A. (1 + a to the 4 th power) x (1 +
a2)(1 + a)(1 – a)
B. (1 + a to the 4 th power) x (1 – a
to the 4 th power)
C. (1 + a to the 4 th power) x (1 + a2)
(1 – a2)
D. (1 + a2) (1 – a2) x (1 - a to the 4th
power)
Ans. A
In a quadratic equation, if the quantity under
the radical is equal to zero, the roots are:
A. imaginary numbers
C. real and unequal
B. complex and unequal
D. real and unequal
Ans. D
Solve for x and y: 3x – y – 6 = 9; 9x – y – 12 =
0
A. x = 3; y = 1
B. x = 1; y = -3 C.
x = 2; y = 2
D. x = 4; y = 2
Ans. B
Factor the expression (x4 – y4) as completely
as possible:
A. (x + y)(x2 + 2xy + y2)
B. (x2 + y2)(x2 – y2)
C. (x2 + y2)(x + y)(x – y)
D. (1 + x2)(1 + y)(1 – y2)
Ans. C
What is the sum of the following finite
sequence of terms? 18, 25, 32, 39, ………….,
67
A. 234
B. 181
C. 213
D. 340
Ans. D
Factor the expression: 16 – 10x + x2.
A. (8 + x)(2 – x) B. (x – 8)(x – 2) C. (8 –
x)(2 + x) D. (x + 8)(x + 2)
Ans. B
A father is 24 years older than his son. In 8
years he will be twice as old as his son. What
is the present age of the father?
A. 35
B. 45
C. 40
D. 50
Ans. C
A certain two digit number is four times the
sum of its digits, if 36 be added to the
number, the digits will be reversed. Find the
number.
A. 48
B. 74
C. 64
D. 84
Ans. A
A and B working together, can finish a piece of
work in 6 days. A working alone can finish it
in 10 days. How long will it take B to do the
work alone?
A. 15 days B. 10 days
C. 12 days D. 8 days
Ans. A
How much of a 40% solution of alcohol shouls
be mixed to an 80% solution to give 150 liters
of a 50% solution?
A. 127.5 liters
B. 112.5 liters
C. 122.5 liters
D. 37.5 liters
Ans. B
Two planes fly toward each other from points
2500 km apart, at the rates of 600 kph and
400 kph. When will they meet if they start at
the same instant?
A. 2 hrs
B. 3 hrs
C. 2 ½ hrs D. 1 hr
Ans. C
Twenty five potatoes are placed on the
ground 4 ft apart in a straight row. In line
with potatoes and 10 ft from the first one is a
basket. A runner starting from the basket
picks up the potatoes and carries them one at
a time to the basket. If he runs at an average
rate of 5 yards per second, how many
potatoes he put into the basket in 76
seconds?
A. 15 potatoes
B. 21 potatoes C.
19 potatoes
D. 25 potatoes
Ans. A
A man bought 23 chickens for P29.00. The
cocks cost P3.00 each, the hens P1.50 each,
and the chicks at 0.50 each. How many cocks,
hens and chicks did he buy?
A. 3, 4, 13 B. 4, 6, 12
C. 5, 5, 13 D. 5, 7, 12
Ans. C
At what time between 3 PM and 4 PM will the
hands of the clock be opposite to each other?
A. 3:15 PM
B. 3:45 PM
C. 3:35 PM
D. 3:49 PM
Ans. D
A and B together weigh 242 pounds. They
balance when A is seated 5 feet from the
fulcrum on one side of a lever and B is seated
6 feet from the fulcrum on the other side.
Find the weight of A.
A. 82 lbs
B. 110 lbs
C. 100 lbs D. 132 lbs
Ans. D
A group of students rented a convention hall
for P240.00. If there were 4 students less, the
share of each would have been P2.00 more.
How many students were in the group?
A. 40
B. 24
C. 30
D. 18
Ans. B
Resolve into partial fractions:
(8x – 8) / (x3 – 2x2 – 8x)
A.
B.
C.
D.
1/x + 1/(x – 4) – 2/(x + 2)
2/x + 1/(x – 4) + 1/(x + 2)
1/x - 1/(x – 4) + 2/(x + 2)
2/x - 1/(x – 4) – 1/(x + 2)
Ans. A
From a box containing 8 red balls, 10 white
balls and 12 blue balls, one ball is drawn at
random. Determine the probability that is
white:
A. ¼
B. ½
C. 1/3
D. 2/5
Ans. C
From a box containing 8 red balls, 10 white
balls and 12 blue balls, one ball is drawn at
random. Determine the probability that is
white or blue:
A. 0.9333 B. 0.733
C. 0.833
D. 0.333
Ans. B
From a box containing 8 red balls, 10 white
balls and 12 blue balls, one ball is drawn at
random. Determine the probability that one
is red and the other is blue:
A. 0.110
B. 0.330
C. 0.220
D. 0.440
Ans. C
From a box containing 8 red balls, 10 white
balls and 12 blue balls, one ball is drawn at
random. Determine the probability that is not
blue:
A. 0.60
B. 0.45
C. 0.50
D. 0.35
Ans. A
Determine the 7th term of the expansion (2y –
11)11.
A. 14,784 x5 y6 B. 11,784 x6 y7 C. 985
x6 y5
D. 765 x6 y7
Ans. A
Find the term involving y4 in the expansion of
(x + y)7.
A. 35 x4y3 B. 35 x3 y4
C. 25 x4y3 D. 25 x4 y4
Ans. B
Find the last term of the progression 10, -2, 14, ……. to 17 th term.
A. -182
B. -1462
C. -220
D. -1530
Ans. A
Find the sum of the integers between 2 and
100 which are divisible by 3.
A. 970
B. 1683
C. 1100
D. 1985
Ans. B
Find the last term of the progression: 2, 6, 18,
…….. 6 th terms.
A. 335
B. 555
C. 486
D. 728
Ans. C
Find the sum of the roots of: 2x2 + 5x + 5 = 0.
A. 5/2
B. -5/2
C. 2/5
D. -2/5
Ans. B
Find the value of x in the equation: (5x + 6)1/2
=x+2
A. 2 and 1 B. 2 and -1
C. -2 and -3
D. -2 and 3
Ans. B
The force F of attraction between two electric
charges varies inversely as the square of the
distance between them. If the force is 20
grams when they are 150 mm apart, find the
force when they are 75 mm apart.
A. 30 grams
B. 60 grams
C. 45 grams
D. 80 grams
Ans. D
Factor the given expression: 6 – 3m2 – 8m +
4m3
A. (3 + 4m)(2 + m2)
B. (3 + 4m)(2 – m2)
C. (3 – 4m)(2 – m2)
D. (3 – 4m)(2 + m2)
Ans. C
Which of the following is a prime number?
A. 100
B. 101
C. 99
D. 105
Ans. B
Funds supplied by others on which a fixed rate
of interest must be paid and the debt be
repaid at a specific place and time.
A. Borrowed capital
B. Investment
C. Salvage value
D. Interest
Ans. A
What is an annuity?
A. A series of equal payments at equal
time periods
B. The cost of manufacturing a product
C. An investment that yields an equal
amount of interest
D. The overhead cost per unit of
production
Ans. A
Estimated value at the end of the useful life:
A. salvage value
B. economic life
C. compounded annually
D. balance sheet
Ans. A
Consists of the actual counting or
determination of the actual quantity of the
materials on hands as of a given date:
A. physical inventory
B. technological assessment
C. material update
D. material count
Ans. A
A depreciation model where the value of an
asset decreases at a decreasing rate:
A. straight line
B. declining balance
C. sinking fund
D. sum of the years digit
Ans. B
What do you call an increase in the value of a
capital asset?
A. capital expenditure
B. capital stock
C. capital gain
D. profit
Ans. C
What is the value which a disinterested third
party, different from the buyer and seller, will
determine in order to establish price
acceptable to both parties?
A. francise value
B. goodwill value
C. fair value
D. market value
Ans. C
Liquid assets such as cash and other assets
that can be converted quickly into cash, such
as accounts receivables and merchandize are
called:
A. land and buildings
B. current assets
C. total assets
D. fixed assets
Ans. B
What is the recorded current value of an
asset?
A. salvage value
B. present worth
C. book value
D. scrap value
Ans. C
What is the method of depreciation where a
fixed sum of money is regularly deposited at
compound interest in a real or imaginary fund
in order to accumulate an amount equal to
the depreciation of an asset at the end of the
asset’s estimated life?
A. sinking fund method
B. SYD method
C. straight line method
D. declining balance
Ans. A
What do you call a radical expressing an
irrational number?
A. surd
B. radix
C. complex number
D. index
Ans. A
How long is each side of a regular pentagon
with perimeter of 90 inches?
A. 12 inches
B. 20 inches
C.
18 inches
D. 24 inches
Ans. C
What is the angle which the line of sight to
the object makes with the horizontal is below
the eye of the observer?
A. angle of depression
B. Bearing
C. angle of elevation
D. acute angle
Ans. A
What do you call a statement of truth which is
admitted without proof?
A. Postulate
B. Axiom
C. Corollary
D. theorem
Ans. B
What is an expression of two terms?
A. Binomial
B. Duomial
C. Monomial
D. polynomial
Ans. A
Use the slope-intercept equation of a line y =
mx + b with slope of 2/3 and y –intercept of 2.
A. y = 3/2 x + 2 B. y = 2/3 x + 2 C. y =
2x + 3/2 D. y = 3x/2 + 3/2
Ans. B
Solve for x: x – 1/x = 0.
A. x = 1, -1
B. x = -1
C. x = 1, ½
D. x = -1/2, -1
Ans. A
The general second degree equation has the
form: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. If B2 –
4AC = 0, the equation describes:
A. a circle B. a hyperbola
C. an ellipse
D. a parabola
Ans. D
Convert the expression (3a + 2b)2 into a
polynomial:
A. 9a2 + 6ab + 4b2
B. 9a2 + 12ab + 4b2
C. a2 + 3a(2b) + (ab)2
D. 3a2 + 6ab + 4b2
Ans. B
Find the 30 th term of an AP 4, 7, 10, ………
A. 91
B. 88
C. 90
D. 75
Ans. A
Find the area bounded by the curve y2 = 1 – x
and the line y = 1 + x.
A. 9/2
B. 5/2
C. 7/2
D. 3/2
Ans. A
An angle greater than the right angle but less
than a straight angle:
A. acute angle
B. obtuse angle
C. reflex angle
D. oblique angle
Ans. B
Integrate (t2 + 4)/(t3 + 12t + 2) dt
A. (1/2) ln(t3 + 12t + 2)2 + C
C. (1/2) (t3 + 12t + 2)2 + C
B. (1/3) ln(t3 + 12t + 2)2 + C
D. (1/3) (t3 + 12t + 2)2 + C
Ans. B
Integrate (x2/2 – 2/x2) dx
A. x2/6 – 6/x + C
B. x2/6 – 2/x + C
C. x2/4 + 2/x + C
D. x2/6 + 2/x + C
Ans. D
The radius of the sphere increases at the rate
of 3 cm per second from zero initially. How
fast is the volume increasing after 2 seconds?
A. 432π cm3/sec
B. 632 π cm3/sec
C. 532 π cm3/sec
D. 832 π cm3/sec
Ans. A
There are seven arithmetic means between 3
and 35. Find the sum of all the terms.
A. 169
B. 167
C. 171
D. 173
Ans. C
The logarithms of the quotient and the
product of two numbers are 0.352182518 and
1.556302501, respectively. Find the first
number.
A. 11
B. 9
C. 10
D. 12
Ans. B
Differentiate: 7x2 + 16x.
A. 14x – 16
B. 14x + 16
C. 7x + 16
D. none of these
Ans. B
What is the length of the latus rectum of the
curve: x2 = -12y?
A. 12
B. 3
C. -3
D. -12
Ans. A
Find the slope of the line whose parametric
equations are x = 4t + 6 and y = t – 1.
A. -4
B. 4
C. ¼
D. -1/4
Ans. C
In triangle ABC, AB = 8 m and BC = 20 m. One
possible dimension of CA is:
A. 13
B. 9
C. 11
D. 7
Ans. A
Determine the sum of the infinite geometric
series of 1 – 1/5 + 1/25.
A. 5/7
B. 4/7
C. 5/6
D. 4/5
Ans. C
Polygons are classified according to their:
A. diagonals
B. Angles
C. sides
D. vertices
Ans. C
An object moves along a straight line such
that, after t minutes, its distance from its
starting point is S = 20t + 5/(t + 1) meters. At
what speed, in m/min will it be moving at the
end of 4 minutes?
A. 39.8
B. 29.8
C. 49.8
D. 19.8
Ans. D
A cone was formed by rolling a thin sheet of
metal in the form of a sector of a circle 72 cm
in diameter with a central angle of 150
degrees. Find the volume of the cone in cc.
A. 7733
B. 7744
C. 7722
D. 7711
Ans. D
If n is the number of sides of a polygon, then
the number of diagonals of a polgon is
expressed as:
A. n!
B. (n/2)(n – 3)
C. (n – 1)! D. (n/3)(n – 2)
Ans. B
______
Find the second derivative of y = √x2 + x-2
-6x2
B. -2x-3
C. 6x-4
D. 6x3
Ans. C
A.
Where does the point of inflection occur in
the equation: x3 – 3x.
A. first quadrant
B. origin
C. third quadrant
D. y-axis
Ans. B
The value of e raise to the negative 5 power is
equal to:
A. 0.0067379
B. 0.0063779 C.
148.4130
D. 0.0076397
Ans. A
A quadrilateral with no side parallel:
A. Trapezoid
B. Rhombus
C. Rhomboid
D. trapezium
Ans. D
What is the slope of the curve: x2 + y2 – 6x +
10y + 5 = 0 at (1, 0)
A. 2/5
B. -2/5
C. 5/2
D. -5/2
Ans. A
What is the equivalent expression for sin 2x?
A. ½ sinx cosx
B. 2sinx/secx
C. -2sinx
D. -2sinx cosx
Ans. B
Given the function f(x) = x to the 3rd power 12x + 1, find the value of the first derivative at
x = 1.
A. 9
B. 12
C. -9
D. 3
Ans. C
Find the partial derivative with respect to x of
the function: 150 x2y – 10xy + 3y + 5
A. 300xy – 10y
B. 150x2 – 10x
C. 150y – 10y
D. 300xy – 10x + 3
Ans. A
As x increases uniformly at the rate of 0.001
ft/sec at what rate is the expression (1 + x)2
increasing when x = 4 ft?
A. 0.01
B. 0.001
C. 0.10
D. 1.01
Ans. A
What is the value of each interior angle of a
regular pentagon?
A. 3π/5
B. π/3
C. π/5
D. 2π/5
Ans. D
How many cubic meters is 150 gallons of
liquid?
A. 0.58761
B. 0.57871
C. 0.56781
D. 0.56871
Ans. C
Determine the center of the curve 2x2 + 2y2 –
8x + 4y – 40 = 0
A. (2, 1)
B. (2, -1)
C. (-2, -1) D. (-2, 1)
Ans. B
Factor the expression 2x2 + 12x + 16 as
completely as possible.
A. 2(x – 2)(x – 4)
B. 2(x + 2)(x – 4)
C. 2(x – 2)(x + 4)
D. 2(x + 4)(x + 2)
Ans. D
Body or space bounded by surface every point
of which is equidistant from a point within.
A. circle
B. Ellipsoid
C. spheroid
D. sphere
Ans. D
The slope of the line is ½. The slope of the
second line is -2/3. Both lines intercept at the
point
(3, 1). What is the acute angle between the
line?
A. 60.3o
B. 75.4o
C. 67.2o
D. 90.0o
Ans. A
The position of an object as a function of time
is described by x = 4t3 + 2t2 – t + 3. What is
the acceleration of the object at t = 2?
A. 52
B. 64
C. 56
D. 66
Ans. A
The velocity of a particle at time t is: v(t) =
12t4 + 7/t. What total distance is travelled
between t = 0.2 and t = 0.3?
A. 2.84
B. 3.85
C. 3.25
D. 2.48
Ans. A
The value of (4 to the 2nd power) square root
is equal to:
A. 2
B. 3
C. 16
D. 4
Ans. D
What is the simplified equivalent expression
of (cot2θ)(sin2θ) + 1/csc2 θ
A. 0
B. cos θ
C. sin2 θ
D. 1
Ans. D
An angle greater than a straight angle and less
than two straight angles are called:
A. right angle
B. reflex angle C.
obtuse angle
D. acute angle
Ans. B
A line segment joining two points on a circle is
called:
A. arc
B. sector
C. tangent D. chord
Ans. D
All circles having the same center but with
unequal radii are called:
A. encircle
B. Concyclic
C. tangent circles
D. concentric circles
Ans. D
The csc of 960 deg is equal to:
A. 1
B. - √3/2
C. ½
D. -2 √3/3
Ans. D
A quadrilateral with two and only two sides of
which are parallel is called:
A. parallelogram
B. quadrilateral
C. Trapezoid
D. rhombus
Ans. C
Compute for the torsional deflection in
degrees of a 100 mm diameter, 1.75 meter
long shaft subjected to a twist moment of 5.5
x 106 N-mm. The torsional modulus of
elasticity is 85000 N/mm2.
A. 0.22 deg
B. 0.33 deg
C. 0.55 deg
D. 0.66 deg
Ans. D
What diameter of bolt is required if the bolt is
subjected to a tensile load of 24,000 lb and a
torque (for tightening) of 7,000 in-lb and
maximum normal stress is not exceeded
30,000 psi?
A. ¾ inch
B. 1 inch
C. 1 ½ inch
D. 2 inches
Ans. B
A body weighing 1,019.36 kg was put on top
of a 3205 N/cm helical spring. What is the
deformation of the spring in cm due to the
body on top?
A. 2.1 cm
B. 3.1 cm
C. 4.1 cm
D. 5.1 cm
Ans. B
A steel rod 25 mm in diameter and 1000 mm
long has an allowable elongation not to
exceed 3 mm, find the allowable load in KN.
A. 604.5 KN
B. 504.5 KN
C. 404.5 KN
D. 304.5 KN
Ans. D
Find the section modulus in cubic inch of a
shaft with diameter 2.25 inches
A. 1.11
B. 2.22
C. 3.33
D. 4.44
Ans. A
What is the decrease in lateral dimensions
due to an axial tensile force of 40,000 lbs in a
bar 2.5 inches on each side and 5 feet long?
The material is steel (E = 3.0 x 107 psi, µ = 0.3)
A. 5.133 x 10-4 in/in
B. 4.133 x 10-4 in/in
C. 3.133 x 10-4 in/in
D. 2.133 x 10-4 in/in
Ans. D
A wire of length 1.90 m has a percentage
strain of 0.032% when loaded with tensile
force. Determine the extension of the wire in
mm.
A. 0.108
B. 0.408
C. 0.608
D. 1.208
Ans. C
Determine the polar section modulus, Zp (in3)
of a shaft delivering 15 HP at 300 rpm. The
diameter of the shaft is 2.0 in and allowable
shear stress of 4500 psi. Use a factor of safety
of 5.
A. 1.57 in3 B. 1.75 in3
C. 1.95 in3 D. 2.47 in3
Ans. A
Find the polar section modulus of a hollow
shaft with an outside diameter of 5 inches
and inside diameter of 3 inches.
A. 51.36 in3
B. 41.36 in3
C. 31.36 in3
D. 21.36 in3
Ans. D
A 16 ft horizontal beam is subjected toa load
of 500 lbs located at its center. The dimension
of the beam is 3 x 5 inches respectively and its
unit weight is 100 bl/ft. Find the flexural
stress in psi.
A. 2992 psi
B. 3255 psi
C. 4992 psi
D. 5982 psi
Ans. D
A horizontal platform with a diameter of 6 m
revolves about its center at 20 rpm. Find the
tangential speed, in m/s of a point at the edge
of the platform.
A. 6.34
B. 6.46
C. 6.28
D. 6.12
Ans. C
The radius of the earth is 3960 mi. The
gravitational acceleration of the earth’s
surface is 32.16 fps2. What is the velocity of
escape from the earth in mi/s?
A. 4.91
B. 7.83
C. 8.62
D. 9.36
Ans. A
A train running at 60 kph decelerated at
2m/min2 for 14 minutes. Find the distance
travelled, in km within this period.
A. 12.2
B. 13.8
C. 13.2
D. 12.8
Ans. B
An 18 in long rod floats vertically in water. It
has a 5 in2 cross section and a specific gravity
of 0.80. What length L is floating?
A. 14.4 in
B. 6.2 in
C. 14.9 in D. 3.6 in
Ans. D
A car travelling on a horizontal unbanked
circular track of radius rand the track is 0.30.
Determine the cars velocity while travelling at
a radius of 34 m, without skidding.
A. 15 m/s
B. 14 m/s
C. 12 m/s D. 10 m/s
Ans. D
A body weighing 180 lb starts from rest and
slides down a plane at an angle of 30o with
the horizontal for which the coefficient of
friction f = 0.3. How far will it move when t =
4 sec?
A. 68.11 ft B. 11.88 ft
C. 45.88 ft D. 61.88 ft
Ans. D
A force of 400 lbf acts on a block at an angle
of 30o with the horizontal. The block is
pushed 5 fthorizontally. What is the work
done by this force?
A. 2439 J
B. 2259 J
C. 2689 J D. 2349 J
Ans. D
Trailer travels at 85 mi/hr around a banked
highway curve with a radius of 1000 ft. What
banking angle is necessary such that friction f
= 0.3 to resist the centrifugal force?
A. 6o
B. 10o
C. 9o
D. 12o
Ans. C
Given the component velocities, whatis the
resultant accelerationwhen t = 4?
Vx = t4 – t, Vy = 6 – t3
A. 240
B. 270
C. 259
D. 310
Ans. C
An elevator weighing 5000 lb attainsan
upward velocity of 20 fps in 4 sec with
uniform acceleration. What is the tension in
the supporting cable when elevator resistance
is 20 lb per ton.
A. 5826.4 lb
B. 5676.8 lb
C. 5776.4 lb
D. 5576.2 lb
Ans. A
A 10 kg block was dropped 3 meters high.
What is the velocity of the block upon
reaching the ground?
A. 7.67 m/s
B. 7.76 m/s
C. 6.77 m/s
D. 6.67 m/s
Ans. A
150 g of water are mixed with 100 g of alcohol
(ρ = 790 kg/m3). What is the specific volume
of the mixture assuming the fluids mix
completely?
A. 1.1 cm3/g
B. 1.2 cm3/g
C. 0.95 cm3/g
D. 1.3 cm3/g
Ans. A
Absolute viscosity is essentially independent
of pressure and is primarily dependent on:
A. Temperature
B. Specific gravity
C. Density
D. Velocity
Ans. A
An instrument for measuring specific gravity
of fluids.
A. Hygrometer
B. Hydrometer
C. Flowmeter
D. Psychrometer
Ans. B
The sum of the pressure head, elevation head
and the velocity head remains constant, this is
known as
A. Boyle’s law
B. Bernoulli’s Theorem
C. Torrecelli’s law
D. Archimedes Principle
Ans. B
A liquid whose temperature is lower than the
saturation temperature corresponding to the
exesting pressure:
A. compressed liquid
B. subcooled liquid
C. saturated liquid
D. pure liquid
Ans. B
A company specializes in the shipment of
pressurized gaseous materials. An order is
received for 500 liters of a particular gas at
(32oF and 1 atm). What minimum volume of
tank is necessary to transport the gas at 90oF
and a maximum pressure of 10 atm?
A. 141 liters
B. 60 liters
C. 152 liters
D. 56 liters
Ans. D
Air is compressed in a diesel engine from an
initial pressure of 13 psia and a temperature
of 120oF to one-twelve of its initial volume.
Calculate the final temperature assuming the
compression to be adiabatic.
A. 1010oF
B. 980oF
C. 987oF
D. 1560oF
Ans. A
A closed vessel contains air at a pressure of
200 KN/m2 gauge and a temperature of 32oC.
The air is heated to 60oC with the atmospheric
pressure of 750 mm Hg. What is the final
gauge pressure?
A. 337.54 B. 127.54
C. 227.54 D. 427.54
Ans. C
A shot is fired at an angle of 45o with the
horizontal and velocity of 300 fps. Calculate
to the nearest, the range of the projectile.
A. 350 ft
B. 1200 m
C. 400 mi D. 932 yards
Ans. D
Steam with an enthalpy of 900 kcal/kg enters
a nozzle at a velocity of 50 m/s. Find the
velocity of the steam at the exit of the nozzle
if its enthalpy is reduced to 600 kcal/kg,
assuming the nozzle is horizontal and
disregarding heat losses.
A. 1685 m/s
B. 1568 m/s
C. 1658 m/s
D. 1586 m/s
Ans. D
A perfect venture with throat diameter of 2 in
is placed horizontally in a pipe with a 6 in pipe
diameter. What is the difference in static
pressure if water flows 100 lb per second.
A. 247.2 kpa
B. 242.7 kpa
C. 274.3 kpa
D. 224.7 kpa
Ans. A
What is the water pressure if manometer is
0.8 m Hg? Mercury is 13.6 times heavier than
water.
A. 106.73 kpa
B. 110.55 kpa C.
107.99 kpa
D. 120.22 kpa
Ans. A
Water is flowing in a pipe with radius of 25.4
cm and a velocity of 10 m/s. The viscosity of
water is 1.131 pa-s. What is the Reynold’s
Number?
A. 4492
B. 4429
C. 2449
D. 2944
Ans. A
What is the density of a stone in kg/m3 that
weighs 90 N in air and 50 N in water?
A. 2259
B. 2502
C. 2205
D. 2270
Ans. A
For a system to be in equilibrium, the sum of
the external forces acting on the system must
be:
A. equal to unity
B. Indeterminate
C. a maximum
D. zero
Ans. D
An air tight closed box of weight P is
suspended from a swing balance. A bird of
weight W is placed on the floor of the box,
and balance reads W + P. If the bird flies
around the box at a constant elevation
without accelerating, what is the balance
reading?
A. P
B. P + 2W
C. P + W
D. P – W
Ans. C
The vector which represents the sum of a
group of force vectors is called:
A. magnitude
B. sum
C. Resultant
D. component
Ans. C
Which of the following is not a vector
quantity?
A. velocity
B. Acceleration
C. speed
D. displacement
Ans. C
A hoist with a 100 hp engine is capable lifting
a 10,000 lb load to a height of 20 feet in 10
seconds. What is the efficiency of this
machine?
A. 34.6%
B. 36.4%
C. 46.3%
D. 43.6%
Ans. B
An object is placed 3 feet from the center of
horizontally rotating platform. The coefficient
of friction is 0.30. The object will begin to
slide off when the platform speed is nearest
to:
A. 12 rpm
B. 22 rpm
C. 17 rpm
D. 33 rpm
Ans. C
Two barges, one weighing 10 tons, the other
weighing 20 tons are connected by a cable in
quiet water. Initially the barges are at rest
100 feet apart. The cable is reeled in until the
barges are 50 ft apart. If the friction is
negligible, calculate the distance moved by
the 10 ton barge.
A. 33.33 ft
B. 20 ft
C. 50 ft
D. 16.66 f
Ans. A
A projectile wighing 100 lbs strikes the
concrete wall of a fort with an impact velocity
of 1200 ft/sec. The projectile comes to rest in
0.01 second, having penetrated the 8-foot
thick wall to a distance of 6 ft. What is the
average force exerted on the wall by the
projectile?
A. 3.73 x 105 lbs B. 3.33 x 105 lbs
C. 2.37 x 105 lbs D. 3.37 lbs
Ans. A
A projectile launched at 2000 ft/sec from A at
an angle of 30 deg with the horizontal,
impacts at the same elevation at B. Assume
no in-flight propulsion and no aerodynamic
drag. Horizontal distance in miles between A
and B is nearest to:
A. 7.9
B. 15.9
C. 10.2
D. 20.3
Ans. D
Kinematic viscosity may be expresse as:
A. ft2/sec
B. slugs/sec
C. sec2/ft
D. sec2/cm
Ans. A
An open chamber rests on the ocean floor in
160 ft of seawater (SG = 1.03). What air
pressure in psig must be maintained inside to
exclude water?
A. 45.6
B. 71.4
C. 60.9
D. 93.2
Ans. B
What head in feet of air, at ambient
conditions of 14.7 psia and 68oF, is equivalent
to 2 psia?
A. 146
B. 288
C. 395
D. 3830
Ans. D
An open topped cylindrical water tank has a
horizontal circular base 10 ft in diameter.
When filled to a height of 8 feet, the force in
lbs exerted on its base is nearest to:
A. 3,900
B. 10,000
C. 7,800
D. 39,200
Ans. D
A gas bubble rising from the ocean floor is 1
inch in diameter at a depth of 50 feet. Given
that sp gravity of sea water is 1.03, the
buoyant force in lbs being exerted on the
bubble at this instant is nearest to:
A. 0.014
B. 0.076
C. 0.020
D. 0.14
Ans. C
In fluid flow, if the fluid traveld parallel to the
adjacent layers and the paths of individual
particles do not cross, the flow is said to be:
A. laminar
B. critical
C. turbulent
D. dynamic
Ans. A
Normal boiling point of liquid oxygen is 90oK.
What is this temperature in deg R?
A. -330
B. 162
C. -183
D. 168
Ans. B
55,000 gallons of water passes through a heat
exchanger and absorbs 28,000,000 BTU. The
exit temperature is 110 deg F. The entrance
water temperature in deg F. The entrance
water temperature in deg F is nearest to:
A. 49
B. 68
C. 56
D. 73
Ans. A
The mass flow rate of Freon 12 through a heat
exchanger is 10 lbs/min. Enthalpy of Freon
entry is 102 Btu/lb and Freon exit is 26 Btu/lb.
Water coolant is allowed to rise 10oF. The
water flow rate in liters per minute is:
A. 76
B. 83
C. 34.5
D. 54.3
Ans. C
The maximum thermal efficieny that can be
obtained in an ideal reversible heat engine
operating between 1540 deg F and 340 deg F
is closet to:
A. 100%
B. 78%
C. 60%
D. 40%
Ans. C
Second law limitations on the maximum unit
burning 1,000,000 Btu/hr of fuel with high
and low temperature extremes of 1540 deg F
and 40 deg F is:
A. 98
B. 1140
C. 295
D. 3830
Ans. C
Work or energy can be a function of all of the
following except:
A. force and distance
B. power and time
C. torque and angular rotation
D. force and time
Ans. D
A high velocity flow of gas at 800 ft/sec
possesess kinetic energy nearest to which of
the following?
A. 1.03 Btu/lb
B. 9.95 Btu/lb
C. 4.10 Btu/lb
D. 12.8 Btu/lb
Ans. D
Power may be expressed in units of:
A. ft-lbs
B. HP-hrs
C. Btu/hr
D. kw-hr
Ans. C
A Carnot engine operating between 70oF and
2000 deg F is modified solely by raising the
higher temperature by 150 deg F and raising
the low temperature by 100 deg F. Which of
the statements is true?
A. thermodynamic efficiency decreased
B. thermodynamic efficiency increased
C. less heat rejected in the system
D. less heat added in the system
Ans. A
A company pays 3.5% interest quarterly.
What is the effective annual interest rate?
A. 10.75% B. 14.75%
C. 17.45% D. 24.75%
Ans. B
A savings certificate that costs P5000 now will
pay P8000 in five years. What is the interest
rate?
A. 9.85%
B. 11.85%
C. 18.55% D. 25.55%
Ans. A
If P20,000 is invested now, and P40,000 four
years from now (all at 5%), what will be the
total amount in ten years?
A. P110,505.37 B. P130,505.37 C.
P230,505.37
D. P330,505.37
Ans. B
What is the capitalized cost of a project that
will cost P20,000,000 now and will require
P3,000,000 in maintenance annually? The
effective annual interest rate is 15%.
A. P30,000,000 B. P40,000,000 C.
P50,000,000
D. P60,000,000
Ans. B
What is the present worth of 60,000 due in 5
years if money is worth 15% and is
compounded semi-annually?
A. P19,111.63
B. P29,111.63
C. P39,111.63
D. P49,111.63
Ans. B
A sum of money is deposited now in a savings
account. The effective annual interest rate is
12% and interest is compounded monthly.
How much money must be deposited to yield
P1,500.00 at the end of 10 months?
A. P1351.99
B. P1551.99
C. P2351.99
D. P3351.99
Ans. A
Find the compound amount if P7500 is
invested at 12% compounded quarterly for 7
years and 6 months.
A. P18,204.47
B. P28,204.47
C. P38,204.47
D. P48,204.47
Ans. A
How much money must be invested today in
order to withdraw P12,000 per year for 12
years if the interest rate is 12%?
A. P44,332.49
B. P54,332.49
C. P74,332.49
D. P94,332.49
Ans. C
How long will it take a sum of money to
double at 10% annual percentage rate?
A. 5.27 years
B. 7.27 years
C. 9.27 years
D. 12.27 years
Ans. B
In a small factory with a capacity of 500,000
units per year with a 75% efficiency, the
annual income is P500,000 and a fixed cost of
P180,000 and variable cost of P0.52 per unit.
What is the break-even point?
A. 222,223 units
B. 242,223 units
C. 252,223 units
D. 222,222 units
Ans. A