Multiple Choice Questions in Engineering Mathematics by Perfecto b. Padilla Jr

MULTIPLE CHOICE QUESTIONS IN

MATHEMATICS

PERFECTO B. PADILLA JR

AND

DIEGO INOCENCIO TAPANG GILLESANIA

1. What is the allowable error in

measuring the edge of a cube that is

intended to hold 8 cu.m, if the error

of the compound volume is not to

exceed 0.03m3?

a. 0.002

b. 0.001

c. 0.0025

d. 0.0001

2. Find the area bounded by the

parabola and its latus

rectum.

a.10.67 sq. units

b. 32 sq. units

c. 48 sq. units

d. 16.67 sq. units

3. The effective rate of 14%

compounded semi-annually is:

a. 14.49%

b. 12.36%

c. 12.94%

d. 14.88%

4. is the equation of

_______?

a. Parallel sides

b. Parabola

c. Circle

d. Ellipse

5. A section in a coliseum has 32 seats

in the 1st row, 34 in the 2

nd row, 36 in

the 3rd

row, . . and 48 in the 9th row.

From the 10th up to the 20

th row, all

have 50 seats. Find the seating

capacity of this section of the

coliseum.

a. 908

b. 900

c. 920

d. 910

6. Smallest term that can be factored

from a number

a. Greater

b. None of these

c. equal

d. lesser

7. How many horsepower are there in

800 kW?

a. 2072.4 hp

b. 746 hp

c. 1072.4 hp

d. 3072.4 hp

8. A man roes downstream at the rate

of 5 mph and upstream at the rate of

2 mph. how far downstream should

he go if he is to return 7/4 hour after

leaving?

a. 2.5 mi

b. 3.3 mi

c. 3.1 mi

d. 2.7 mi

9. Find the angular velocity of a

flywheel whose radius is 20 ft. if it is

revolving at 20 000 ft/min

a. 500 rad/min

b. 750 rad/min

c. 1000 rad/min

d. 800 rad/min

10. Find the area of parabolic segment

whose base is 10 and height of 9

meters.

a. 60 m2

b. 70 m2

c. 75 m2

d. 65 m2

11. A line which a curve approach

infinity but will never intersect.

a. Parallel line

b. Assymptote

c. Inclined line

d. Skew line

12. An organization that aims to block

the entry of a new comer.

a. Monopoly

b. Cartel

c. Competitor

d. Proprietor

13. The tens digit of a two-digit number

is 1 less than twice the unit’s digit.

They differ by 4. Find the number.

a. 65

b. 95

c. 84

d. 73

14. At the surface of the earth g=9.806

m/s2. Assuming the earth to be a

sphere of radius 6.371x106m.

Compute the mass of the earth.

a. 5.97x1024

kg

b. 5.62 x1024

kg

c. 5.12 x1024

kg

d. 5.97 x1023

kg

15. A material has a modulus of

elasticity of 200 GPa. Find the

minimum cross sectional area of the

said material so as not to elongate by

more than 5mm for every 2m length

when subjected to 10 kN tensile

force.

a. 20 mm2

b. 10 mm2

c. 30 mm2

d. 40 mm2

16. At what temperature is the ˚C and ˚F

numerically the same?

a. 40˚

b. 32˚

c. -40˚

d. -32˚

17. On ordinary day, 400 m3 of air has a

temperature of 30˚C. During El Nino

drought, temperature increased to

40˚C. Find the volume of air of

k=3670x10-6

.

a. 416.86 m3

b. 418.86 m3

c. 414.68 m3

d. 416.48 m3

18. A sphere has a volume of 36π cubic

meters. The rate of change in volume

is 9π cubic meters per minute. Find

the rate of change in area of the

sphere.

a. 6 π m2/min

b. 2 π m2/min

c. 3 π m2/min

d. 4 π m2/min

19. Sin A=2.5x, cos A= 5.5x. Find A.

a. 34.44˚

b. 24.44˚

c. 44.44˚

d. 64.44˚

20. A ladder 5 meter long leans on a wall

and makes an angle of 30˚ with the

horizontal. Find the vertical height

from the top to the ground.

a. 2.5 meter

b. 1.5 meter

c. 2.0 meter

d. 2.75 meter

21. A rectangular lot is bounded on its

two adjacent sides by existing

concrete walls. If it is to be fenced

along two remaining sides and the

available fencing material is 30

meters long, find the largest possible

area of the lot.

a. 200 sq. m

b. 225 sq. m

c. 175 sq. m

d. 250 sq. m

22. A tangent line intersects a secant line

to a circle. If the distance from the

point of tangency to the point of

intersection is 6, and the external

distance of the secant line is 4, find

the length of the secant line.

a. 5

b. 7

c. 8

d. 9

23. In an oblique triangle, a=25, b=16,

angle C=94˚06’. Find the measure of

angle A.

a. 54.5˚

b. 45.5˚

c. 24.5˚

d. 54.5˚

24. Q=25 when t=0. Q=75 when t=2.

What is Q when t=6?

a. 185

b. 145

c. 150

d. 175

25. Pipes A and B can fill an empty tank

in 6 and 3 hours respectively. Drain

C can empty a full tank in 24 hours.

How long will an empty tank be

filled if pipes A and B with drain C

open?

a. 1.218 hours

b. 2.182 hours

c. 5.324 hours

d. 3.821 hours

26. Find the tangential velocity of a

flywheel whose radius is 14 ft. if it is

revolving at 200 rpm.

a. 17 593 ft/min

b. 18 593 ft/min

c. 19 593 ft/min

d. 12 593 ft/min

27. A ball is thrown vertically upward at

a velocity of 10 m/s. What is its

velocity at the maximum height?

a. 10 m/s

b. 0

c. 5 m/s

d. 15 m/s

28. The volume of a sphere is tripled.

What is the increase in surface area

if the radius of the original sphere is

50 cm.?

a. 34 931.83 sq. units

b. 33 931.83 sq. units

c. 35 931.83 sq. units

d. 36 931.83 sq. units

29. Given a right triangle ABC. Angle C

is the right triangle. BC=4 and the

altitude to the hypotenuse is 1 unit.

Find the area of the triangle.

a. 2.0654 sq. units

b. 1.0654 sq. units

c. 3.0654 sq. units

d. 4.0645 sq. units

30. Find the equation of a parabola

passing through (3, 1), (0, 0), and (8,

4) and whose axis is parallel to the x-

axis.

a.

b.

c.

d.

31. Pedro runs with a speed of 20 kph.

Five minutes later, Mario starts

running to catch Pedro in 20

minutes. Find the velocity of Mario.

a. 22.5 kph

b. 25 kph

c. 27.5 kph

d. 30 kph

32. How much do ten P2000 quarterly

payments amount at present if the

interest rate is 10% compounded

quarterly.

a. P17 771.40

b. P17 504.13

c. P18 504.13

d. P71 504.13

33. A man bought a machine costing

P135 000 with a salvage value of

P20 000 after 3 years. If the man will

sell it after 2 years, how much is the

loss or gain (i.e. the cost of

equipment) if i=10%.

a. P134 350

b. P143 350

c. P153 350

d. P163 350

34. P1000 becomes P1500 in three years.

Find the simple interest rate.

a. 16.67%

b. 15.67%

c. 17.67%

d. 18.67%

35. Form of paper money issued by the

central bank.

a. T-bills

b. Check

c. Cash

d. Stocks

36. _________ is the concept of finding

the derivative of an exponential

expression.

a. Logarithmic derivative

b. Chain rule

c. Trigonometric derivative

d. Implicit derivative

37. The line y=5 is the directrix of a

parabola whose focus is at point (4, -

3). Find the length of the latus

rectum.

a. 8

b. 4

c. 16

d. 24

38. 2.25 revolutions are how many

degrees?

a. 810˚

b. 730˚

c. 190˚

d. 490˚

39. The sum of two numbers is 21 and

their product is 108. Find the sum of

their reciprocals.

a.

b.

c.

d.

40. What is the accumulated amount of

five years annuity paying P 6000 at

the end of each year, with interest at

15% compounded annually?

a. P40 454.29

b. P41 114.29

c. P41 454.29

d. P40 544.29

41. Ana is 5 years older than Beth. In 5

years, the product of their ages is 1.5

times the product of their present

ages. How old is Beth now?

a. 25

b. 20

c. 15

d. 30

42. In , x=

distance in meters, and t= time in

seconds. What is the initial velocity?

a. 2000 m/s

b. 3000 m/s

c. 4000 m/s

d. 5000 m/s

43. The highest point that a girl on a

swing reaches is 7 ft above the

ground, while the lowest point is 3 ft

above the ground. Find its tangential

velocity at the lowest point.

a. 16.05 ft/sec

b. 12.05 ft/sec

c. 20.05 ft/sec

d. 12.05 ft/sec

44. If m=tan25˚, find the value of ˚ ˚

˚ ˚ in terms of m.

a. -1/m

b.

c.

d. –m

45. A VOM has a current selling price of

P400. If it’s selling price is expected

to decline at the rate of 10% per

annum due to obsolence, what will

be its selling price after 5 years?

a. P236.20

b. P200.00

c. P213.10

d. P245.50

46. Evaluate ∫

dx

a. 1.051

b. 1.501

c. 3.21

d. 2.321

47. Fin the eccentricity of an ellipse

when the length of the latus rectum

is 2/3 the length of the major axis.

a. 0.577

b. 0.477

c. 0.333

d. 0.643

48. What is the book value of an

electronic test equipment after 8

years of use if it depreciates from its

original value of P120 000 to its

salvage value of 13% in 12 years.

Use straight line method.

a. P20 794.76

b. P50 400

c. P40 794.76

d. P50 794.76

49. What is the book value of an

electronic test equipment after 8

years of use if it depreciates from its

original value of P120 000 to its

salvage value of 13% in 12 years.

Use declining balance method.

a. P20 794.76

b. P30 794.76

c. P40 794.76

d. P50 794.76

50. A balloon is released from the

ground 100 meters from an observer.

The balloon rises directly upward at

the rate of 4 meters per second. How

fast is the balloon receding from the

observer 10 seconds later?

a. 1.4856 m/s

b. 2.4856 m/s

c. 3.4856 m/s

d. 5 m/s

51. Divide 120 into two parts so that

product of one and the square of

another is maximum. Find the small

number.

a. 60

b. 50

c. 40

d. 30

52.

. What is the period?

. π

.2 π

.4 π

.3 π

53. A horizontal force of 80 000 N is

applied unto a 120 ton load in 10

seconds. Find its acceleration.

a. 0.67 m/s2

b. 0.75 m/s2

c. 1.05 m/s2

d. 1.35 m/s2

54. A plane is headed due to east with

airspeed 240 mph. if a wind at 40

mph from the north is blowing; find

the groundspeed of the plane.

a. 342 mph

b. 532 mph

c. 243 mph

d. 4123 mph

55. The ratio of radii of cone and

cylinder is 1:2 while the ratio of

radius of cone to its altitude is 1:3. If

lateral surface area of cylinder equals

volume of cone, find the radius of

the cone if the altitude of cylinder is

4.

a. 5

b. 4

c. 3

d. 6

56. If a derivative of a function is

constant, the function is:

a. First degree

b. Exponential

c. Logarithmic

d. Sinusoidal

57. 2700 mils is how many degrees?

a. 151.875˚

b. 270˚

c. 180˚

d. 131.875˚

58. An air has an initial pressure of

100kPa absolute and volume 1 m3. If

pressure will be increased to 120

kPa, find the new volume.

a. 1.2 m3

b. 0.83 m3

c. 0.63 m3

d. 1.5 m3

59. The pistons (A&B) of a hydraulic

jack are at the same level. Pistol A is

100 cm2 while piston B is 500 cm

2.

Piston A carries a 500 kg load. Find

the required force F at piston B to

carry the load.

a. 3.5 tons

b. 2.5 tons

c. 4.5 tons

d. 1.5 tons

60. A rectangular dodecagon is inscribed

in a circle whose radius is 1 unit.

Find the perimeter.

a. 5.21

b. 6.21

c. 7.21

d. 8.21

61. In a box, there are 52 coins,

consisting of quarters, nickels, and

dimes with a total amount of $2.75.

If the nickel were dimes, the dimes

were quarters and the quarters were

nickels; the total amount would be

$3.75. How many quarters are there?

a. 16

b. 10

c. 5

d.12

62. A stone is thrown vertically upward

at 12 m/s. Find the time to reach the

ground.

a. 2.45 secs.

b. 1.35 secs.

c. 2.15 secs.

d. 1.95 secs.

63. A regular polygon has 27 diagonals.

Then it is a :

a. Pentagon

b. Heptagon

c. Nonagon

d. Hexagon

64. A 50 meter cable is divided into two

parts and formed into squares. If the

sum of the areas is 100 sq. meter,

find the difference in length?

a. 21.5

b. 20.5

c. 24.5

d. 0

65. What theorem is used to solve for

centroid?

a. Pappus

b. Varignon’s

c. Castiglliano’s

d. Pascal’s

66. ∫

a. tan x – x + c

b. x - tan x + c

c. sec x

d. sec x tan x

67. A hyperbola has its center at point

(1, 2), vertex at (2, 2) and conjugate

vertex at (1, 0). Find the equation.

a. 4x2-y

2-8x+4y-4=0

b. x2-4y

2-8x+4y-4=0

c. 4x2-y

2-8x-4y-4=0

d. x2-4y

2+8x-4y-4=0

68. A pipe can fill a tank in 2 hours. A

drain can empty a full tank in 6

hours. If the pipe runs with the drain

open, how long will take to fill-up an

empty tank?

a. 2.5 hrs

b. 4 hrs

c. 3 hrs

d. 3.5 hrs

69. Fin the 7th

term in the series:

,

,

,

. .

a.

b.

c.

d.

70. Find the length of the larger base of

the largest isosceles trapezoid if the

legs and smaller base measure 8

units.

a. 8

b. 16

c. 10

d. 20

71. y=arctan ln x. Find y’.

a.

b.

c.

d.

72. The general equation of a conic

section whose axis is inclined is

given by

Ax2+Bxy+Cy

2+Dx+Ey+F=0. When

B2-4 Ac=0, the curve is a/an _____.

a. Hyperbola

b. Parabola

c. Ellipse

d. Circle

73. The time required for two examinees

to solve the same problem differs by

two minutes. Together they can solve

32 problems in one hour. How long

will it take for the slower problem

solver to solve the problem?

a. 2 min

b. 3 min

c. 4 min

d. 5 min

74. cos4

θ – sin4 θ= ?

a. sin 2θ

b. cos 2θ

c. cos 4θ

d. cos 3θ

75. A function wherein one variable is

not yet readily expressed as function

of another variable is said to be:

a. symmetric

b. implicit

c. explicit

d. exponential

76. Given an ellipse

+

=1.

Determine the distance between

directrix:

a. 3

b. 4

c. 2

d. 8

77. Three forces 20N, 30N, and 40N are

in equilibrium. Find the angle

between 30N and 40N forces.

a. 28.96˚

b. 25.97˚

c. 40˚

d. 30˚15’25”

78. At the inflection point where x=a

a. f”(a) > 0

b. f”(a) < 0

c. f”(a) = 0

d. f”(a) is no equal to zero

79. A merchant has three items on sale

namely: a radio for $50.00, a clock

for $30.00 and a flashlight for $1.00.

At the end of the day, she has sold a

total of 100 of the three sale items

and has taken in exactly $1, 000.00

on the total sales, how many radios

did she sell?

a. 4

b. 80

c. 16

d. 20

80. Which of the following is true?

a. sin(-θ)= sin θ

b. tan(-θ)= tan θ

c. cos(-θ)= cos θ

d. csc(-θ)= csc θ

81. _______ is the loss of value of the

equipment with use over a period of

time. It could mean a difference in

value between a new asset and the

used asset currently in service.

a. Loss

b. Depreciation

c. Gain

d. Extracted

82. Find the area bounded by the curve

defined by the equation x2=8y and its

latus rectum.

a. 11/3

b. 32/3

c. 16/3

d. 22/3

83. The height of a right circular

cylinder is 50 inches and decreases at

the rate of 4 inches per second.

While the radius of the base is 20

inches and increases at the rate of

one inch per second. At what rate is

the volume changing?

a. 11 130 cu. in/sec

b. 11 310 cu. in/sec

c. 1 275 cu. in/sec

d. 1 257 cu. in/sec

84. This occurs in a situation where a

commodity or service is supplied by

a number of vendors and there is

nothing to prevent additional vendors

entering the market.

a. Elastic demand

b. Perfect competition

c. Monopoly

d. Oligopoly

85. The graphical representation of the

cumulative frequency distribution in

a set statistical data is called?

a. Frequency polygon

b. Mass diagram

c. Ogive

d. Histogram

86. If the product of the slopes of two

straight lines is negative 1, one of

these lines are said to be:

a. Skew

b. Non-intersecting

c. Parallel

d. Perpendicular

87. Pedro can paint a fence 50% faster

than Juan and 20% faster that Pilar

and together they can paint a given

fence in 4 hours. How long will it

take Pedro to paint the same fence if

he had to work alone?

a. 10 hrs

b. 13 hrs

c. 11 hrs

d. 15 hrs

88. If you borrowed money from your

friend with simple interest of 12%,

find the present worth of P50 000,

which is due at the end of 7 months.

a. P46 200

b. 44 893

c. P46 729

d. 45 789

89. The amount of P12 800 in 4 years at

5% compounded quarterly is?

a. P14 785.34

b. P15 614.59

c. P16 311.26

d. P15 847.33

90. What is the effective rate

corresponding to 18% compounded

daily? Take 1 year =365 days.

a. 17.35%

b. 19.72%

c. 17.84%

d. 16.78%

91. In how many ways can 2 integers be

selected from the integers 1 to 100 so

that their difference is exactly 7?

a. 74

b. 81

c. 69

d. 93

92. A 2 lbs liquid has an specific heat of

1.2 Btu/ lb-˚F. How much heat is

required to increase its temperature

by 10˚C?

a. 100BTU

b. 110BTU

c. 120 BTU

d. 130 BTU

93. A machine costing P100 000

depreciates at 10% annually. What is

its book value after 5 years?

a. P59 049

b. P69 049

c. P49 049

d. P79 049

94. Find the length of the latus rectum of

the parabola y2=-8x?

a. 8

b. 9

c. 7

d. 6

95. The property by virtue of which a

body tends to return to its original

size and shape after a deformation

and when the deforming forces have

been removed.

a. Elasticity

b. Malleability

c. Ductility

d. Plasticity

96. A man wants to make 14% nominal

interest compounded semi-annually

on a bond investment. How should

the man be willing to pay now for

12% -P10 000 bond that will mature

in 10 years and pays interest semi-

annually?

a. P2 584.19

b. P3 118.05

c. P8 940.60

d. P867.82

97. Evaluate ∫

a. -3/2 cos 2 + C

b. -3 cos 2

c. 3/2 cos 2 + C

d. 3 cos 2 + C

98. Find the maximum height which a

cannonball fired at an initial velocity

of 100 m/s at 30˚ above the

horizontal.

a. 127.42 m

b. 172.42 m

c. 137.42 m

d. 177.42 m

99. A man expects to receive P20 000 in

10 years. How much is that money

worth now considering interest at 6%

compounded quarterly.

a. P 12 698.65

b. P11 025.25

c. P17 567.95

d. P15 678.45

100. The area of a rhombus is 24. One

diagonal measures 6 units, find the

length of the other diagonal.

a. 9

b. 7

c. 6

d. 8

101. The area of a rhombus is 24. One

diagonal measures 6 units, find the

length of a side.

a. 5

b. 6

c. 7

d. 8

102. The sum of the coefficients in the

expansion of (x+y-z)8 is:

a. From 2 to 5

b. From 5 to 10

c. Above 10

d. Less than 2

103. A banca traveled at an average speed

of 15 kph downstream and then back

at an average speed of 12 kph

upstream. If the total time of travel is

3 hours, find the total distance traveled

by the banca.

a. 40 km

b. 30 km

c. 60 km

d. 50 km

104. A father is now 41 and his son 9.

After how many years will his age be

just triple his son’s age?

a. 6

b. 5

c. 4

d. 7

105. Find the area of the largest rectangle

which you can inscribe in a semi-

circle whose radius is 10.

a. 1000 sq. units

b. √ sq. units

c. 100 sq. units

d. 2√ sq. units

106. Given y = 4 cos 2x. Determine its

amplitude.

a. 2

b. 4

c. 8

d. √

107. A central angle of 45˚ subtends an

arc of 12cm. What is the radius of the

circle?

a. 12.58 cm

b. 15.28 cm

c. 15.82 cm

d. 12.85 cm

108. The volume of two spheres is in the

ratio of 27:343 and the sum of their

radii is 10. Find the radius of the

smaller sphere.

a. 6

b. 3

c. 5

d. 4

109. The integral of any quotient whose

numerator is the differential of the

denominator is the:

a. Product

b. Derivative

c. Cologarithm

d. Logarithm

110. Find the sum of the roots 5x2 -10x +

2 = 0

a. -2

b. 2

c. 1/2

d. -1/2

111. Determine the vertical pressure due

to a column of water 85 cm high.

a. 8.33 x 103 N/m

2

b. 8.33 x 104 N/m

2

c. 8.33 x 105 N/m

2

d. 8.33 x 106 N/m

2

112. A rectangular hexagonal pyramid has

a slant height of 4 cm and the length

of each side of the base is 6 cm. find

the lateral area.

a. 52 cm2

b. 62 cm2

c. 72 cm2

d. 82 cm2

113. If a =b, the b = a. This illustrates

which axiom in algebra?

a. Replacement axiom

b. Symmetric axiom

c. Transitive axiom

d. Reflexive axiom

114. If arc tan x + arc tan 1/3 = π/4, find

the value of x.

a. 1/2

b. 1/3

c. 1/4

d. 1/5

115. It is the measure of relationship

between two variables.

a. Correlation

b. Function

c. Equation

d. Relation

116. It is a polyhedron of which two faces

are equal, polygons in parallel planes

and the other faces are parallelograms.

a. Cube

b. Pyramid

c. Prism

d. Parallelepiped

117. What is the distance in cm. between

two vertices of a cube which are

farthest from each other, if an edge

measures 8 cm?

a. 12.32

b. 13.86

c. 8.66

d. 6.93

118. A loan of P5000 is made for a period

of 15 months at a simple interest rate

of 15%. What future amount is due at

the end of the loan period?

a. P 5 842.54

b. P5 900.00

c. P5 637.50

d. P5 937.50

119. To compute for the value of the

factorial, in symbolic form (n!) where

n is a large number, we use a formula

called:

a. Matheson formula

b. Diophantine formula

c. Stirlings Approximation

formula

d. Richardson-Duchman

formula

120. Find the distance of the directrix

from the center of an ellipse if its

major axis is 10 and its minor axis is

8.

a. 8.1

b. 8.3

c. 8.5

d. 8.7

121. A 200 gram apple is thrown from the

edge of a tall building with an initial

speed of 20 m/s. What is the change is

kinetic energy of the apple if it strikes

the ground at 50 m/s?

a. 100 joules

b. 180 joules

c. 81 joules

d. 210 joules

122. When two planes intersect with each

other, the amount of divergence

between the two planes is expressed

by the measure of:

a. Polyhedral angle

b. Dihedral angle

c. Reflex angle

d. Plane angle

123. The median of a triangle is the line

connecting a vertex and the midpoint

of the opposite side. For a given

triangle, the medians intersects at a

pint which is called the:

a. Circumcenter

b. Incenter

c. Orthocenter

d. Centroid

124. A five-pointed star is also known as:

a. Quintagon

b. Pentagon

c. Pentatron

d. Pentagram

125. The altitudes of the sides of a

triangle intersect at the point, which is

known as:

a. Centroid

b. Incenter

c. Orthocenter

d. Circumcenter

126. The arc length equal to the radius of

the circle is called:

a. 1 grad

b. 1 radian

c. π radian

d. 1 quarter circle

127. One gram of ice at 0˚C is placed on a

container containing 2,000,000 cu. m

of water at 0˚C. Assuming no heat

loss, what will happen?

a. The volume of ice will not

change

b. Ice will become water

c. Some part of ice will not

change

d. All of the above

128. The angular bisector of the sides of a

triangle at a point which is known as:

a. Centroid

b. Incenter

c. Orthocenter

d. Centroid

129. A pole cast a shadow of 15 meters

long when the angle of elevation of

the sun is 61˚. If the pole has leaned

15˚ from the vertical directly toward

the sun, what is the length of the pole?

a. 53.24 m

b. 54.25 m

c. 52.43 m

d. 53.25 m

130. Each side of a cube is increased by

1%. By what percent is the volume of

the cube increased?

a. 3%

b. 23.4%

c. 33.1%

d. 34.56%

131. MCMXCIV is a Roman numeral

equivalent to:

a. 2174

b. 3974

c. 2974

d. 1994

132. The sum of the digits of a two digit

number is 11. If the digits are

reversed, the resulting number is

seven more than twice the original

number. What is the original number?

a. 44

b. 83

c. 38

d. 53

133. A regular octagon is inscribed in a

circle of radius 10. Find the area of the

octagon.

a. 288.2

b. 282.8

c. 228.2

d. 238.2

134. Find the probability of getting

exactly 12 out of 30 questions on the

true or false question.

a. 0.04

b. 0.15

c. 0.12

d. 0.08

135. Find the length of the vector (12, 4,

4).

a. 8.75

b. 5.18

c. 7

d. 6

136. According to this law, “The force

between two charges varies directly as

the magnitude of each charge and

inversely as the square of the distance

between them”.

a. Newton’s law

b. Inverse Square law

c. Coulomb’s law

d. Law of Universal Gravitation

137. Mr. J. Reyes borrowed money from

the bank. He received from the back

P1842 and promised to pay P2000 at

the end of 10 months. Determine the

simple interest.

a. 15.7%

b. 16.1%

c. 10.29%

d. 19.45%

138. Evaluate the expression (1 + i2 )

10

where I is an imaginary number.

a. -1

b. 10

c. 0

d. 1

139. The amount of heat needed to change

solid to liquid.

a. Latent heat of fusion

b. Solid fusion

c. Condensation

d. Cold fusion

140. Solve for x in the equation: 2 log4 x

– log4 9 = 2

a. 12

b. 10

c. 11

d. 13

141. Two post, one 8m and the other 12 m

high are 15 m apart. If the posts are

supported by a cable running from the

top of the first post to a stake on the

ground and then back to the top of the

second post, find the distance from the

lower post to the stake to use the

minimum amount of wire.

a. 4 m

b. 6 m

c. 8 m

d. 9m

142. A 40 gm rifle bullet is fired with a

speed of 300 m/s into a ballistic

pendulum of mass 5 kg suspended

from a chord 1 m long. Compute the

vertical height through which the

pendulum arises.

a. 29.88 cm

b. 28.89 cm

c. 28.45 cm

d. 29.42 cm

143. If the roots of an equation are zero,

then they are classified as:

a. Trivial solution

b. Hypergolic solution

c. Zeros of function

d. Extraneous roots

144. Of what quadrant is A, if secA is

positive and cscA is negative?

a. IV

b. II

c. III

d. I

145. The reciprocal of bulk modulus of

any fluid is called ______.

a. Volume stress

b. Compressibility

c. Shape elasticity

d. Volume strain

146. Assuming that the earth is a sphere

whose radius is 6,400 km. Find the

distance along 3 deg arc at the equator

of the earth’s surface.

a. 335.10 km

b. 533.10 km

c. 353.10 km

d. 353.01 km

147. Equations relating x and y that

cannot readily solved explicitly for y

as a function of x or for x as a function

of y. Such equation may nonetheless

determine y as a function of x or vice

versa, such as function is called

_____.

a. Logarithmic function

b. Implicit function

c. Continuous function

d. Explicit function

148. What is the integral of (3t-1)3 dt?

a. 1/12 (3t-1)4 + c

b. 1/12 (3t-1)3 + c

c. ¼ (3t-1)3 + c

d. ¼ (3t-1)4 + c

149. If 16 is 4 more than 4x, find x-1

a. 14

b. 3

c. 12

d. 5

150. A frequency curve which is

composed of a series of rectangles

constructed with the steps as the base

and the frequency as the height.

a. Histogram

b. Ogive

c. Frequency distribution

d. Bar graph

151. It is a sequence of numbers such that

successive terms differ by a constant

a. Arithmetic progression

b. Infinite progression

c. Geometric progression

d. Harmonic progression

152. If the second derivative of the

equation of a curve is equal to the

negative of the equation of that same

curve, the curve is:

a. A paraboloid

b. A sinusoid

c. A cissoids

d. An exponential

153. Determine x, so that: a, 2x + 4, 10x –

4 will be a geometric progression.

a. 4

b. 6

c. 2

d. 5

154. The angular distance of a point on

the terrestrial sphere from the north

pole is called its:

a. Co-latitude

b. Altitude

c. Latitude

d. Co-declination

155. If one third of the air in a tank is

removed by each stroke of an air

pump, what fractional part of the air

removed in 6 strokes?

a. 0.7122

b. 0.9122

c. 0.6122

d. 0.8122

156. The linear distance between -4 and

17 on the number line is

a. 13

b. 21

c. -17

d. -13

157. Determine the angle of the super

elevation for a 200 m highway curve

so that there will be no side thrust at a

speed of 90 kph.

a. 19.17˚

b. 17.67˚

c. 18.32˚

d. 20.11˚

158. A ball is dropped from a building

100 m high. If the mass of the ball is

10 grams, after what time will the ball

strike the earth?

a. 4.52s

b. 4.42s

c. 5.61s

d. 2.45s

159. Centrifugal force is _____

a. Directly proportional to the

radius of the curvature

b. Directly proportional to the

square of the tangential

velocity

c. Inversely proportional to the

tangential velocity

d. Directly proportional to the

square of the weight of the

object

160. Each of the faces of a regular

hexahedron is a _____

a. Triangle

b. Square

c. Rectangle

d. Hexagon

161. Find the mean proportion of 4 and 36

a. 72

b. 24

c. 12

d. 20

162. Simplify the expression i1999

+ i1999

where I is an imaginary number.

a. 0

b. -1

c. 1+1

d. 1-i

163. In a club of 40 executives, 33 likes to

smoke Marlboro and 20 like to smoke

Philip Moris. How many like both?

a. 13

b. 10

c. 11

d. 12

164. The graph of r=a+bcos θ is a :

a. Lemniscates

b. Limacon

c. Cardioids

d. Lituus

165. Solve for A in the equation: cos2A =

1- cos2A

a. 15˚, 125˚, 225˚, 335˚

b. 45˚, 125˚, 225˚, 315˚

c. 45˚, 135˚, 225˚, 315˚

d. 45˚, 150˚, 220˚, 315˚

166. Momentum is the product of velocity

and

a. Acceleration

b. Mass

c. Force

d. Time

167. If 15 people can win prices in a

estate lottery (assuming that there are

no ties). How many ways can these 15

people win first, second,, third, fourth

and fifth prizes?

a. 4,845

b. 116,280

c. 360,360

d. 3,003

168. Find the 30th term of the A.P 4, 7,

10,…

a. 75

b. 90

c. 88

d. 91

169. Mary is 24. She is twice as old as

Ann was when Mary was as old as

Ann now. How old is Ann now?

a. 16

b. 17

c. 12

d. 15

170. Find the ratio of an infinite

geometric series if the sum is 2 and

the first term is ½

a. 1/3

b. 1/2

c. 3/4

d. 1/4

171. Given a cone of diameter x and

altitude of h. What percent is the

volume of the largest cylinder which

can be inscribed in the cone to the

volume of the cone?

a. 44%

b. 46%

c. 56%

d. 65%

172. Find the equation of the curve at

every point of which, the tangent line

has a slope of 2x.

a. x

b. y=x2+c

c. y=x1/2

+c

d. x=y2+c

173. csc 520˚ is equal to

a. cos 20˚

b. csc 20˚

c. tan 45˚

d. sin 20˚

174. A rotating wheel has a radius of 2 ft.

and 6 in. A point on the circumference

of the wheel moves 30 ft in 2 seconds.

Find the angular velocity of the wheel.

a. 2 rad/sec

b. 4 rad/sec

c. 6 rad/sec

d. 5 rad/sec

175. It is a series equal payments accruing

at equal intervals of the time where the

first payment is made several periods

after.

a. Deferred annuity

b. Delayed annuity

c. Progressive annuity

d. Simple annuity

176. Exact angle of the dodecagon equal

to ________ deg.

a. 135

b. 150

c. 125

d. 105

177. A load of 100 lb. is hung from the

middle of a rope, which is stretched

between wo rigid walls of 30 ft apart.

Due to the load, the rope sags 4 ft in

the middle. Determine the tension in

the rope.

a. 165 lbs

b. 173 lbs

c. 194 lbs

d. 149 lbs

178. How far does an automobile move

while its speed increases uniformly

from 15 kph to 45 kph in 20 seconds?

a. 185 mi

b. 167 mi

c. 200 mi

d. 172 mi

179. A block weighing 500 kN rest on a

ramp inclined at 25˚ with horizontal.

The force tending to move the block

down the ramp is:

a. 100 kN

b. 211 kN

c. 255 kN

d. 450 kN

180. What is the value of log25+log35?

a. 7.39

b. 3.79

c. 3.97

d. 9.37

181. The distance between the center of

the three circles which are mutually

tangent to each other externally are 10,

12 and 14 units. The area of the largest

circle is

a. 72 π

b. 23 π

c. 64 π

d. 16 π

182. To maximize the horizontal range of

the projectile, which of the following

applies?

a. Maximize velocity

b. Maximize the angle of

elevation and velocity

c. Maximize the angle of

elevation

d. The tangent function of the

angle of trajectory must be

equal to one

183. What is the lowest common factor of

10 and 32?

a. 320

b. 2

c. 180

d. 90

184. The distance that the top surface is

displaced in the direction of the force

divided by the thickness of the body is

known as __________

a. Longitudinal strain

b. Linear strain

c. Shear strain

d. Volume strain

185. It can be defined as the set of all

points on a plane whose sum of

distances of any of which from two

fixed points is constant.

a. Circle

b. Hyperbola

c. Parabola

d. Ellipse

186. A statue 3m high is standing on a

base of 4m high. If an observer’s eye

is 1.5m above the ground, how far

should he stand from the base in order

that the angle suspended bu the statue

is maximum.

a. 3.41 m

b. 3.51 m

c. 3.71 m

d. 4.41 m

187. A baseball is thrown from a

horizontal plane following a parabolic

path with an initial velocity of 100 m/s

at an angle of 30˚ above the

horizontal. How far from the throwing

point well the ball attains its original

level.

a. 882.2 m

b. 8.828 m

c. 288.8 m

d. 82.88 m

188. A balloon is rising vertically over a

point A on the ground a rate of 15

ft/sec. A point B on the ground is level

with and 30 ft from A. When the

balloon is 40 ft from A, at what rate is

its distance from B changing?

a. 13 ft/sec

b. 15 ft/sec

c. 12 ft/sec

d. 10 ft/sec

189. The diameter of a circle described by

9x2 + 9y

2 = 16 is ______

a. 4/3

b. 16/9

c. 8/3

d. 4

190. A man finds the angle of elevation of

the top of a tower to be 30 degrees. He

walks 85 m nearer the tower and find

its angle of elevation to be 60 degrees.

What is the height of the tower?

a. 76.31 m

b. 73.31 m

c. 73.16 m

d. 73. 61 m

191. Two electrons have speeds of 0.7c

and x respectively at an angle of 60.82

degrees between each other. If their

relative velocity is 0.65c, find x.

a. 0.02c

b. 0.12c

c. 0.09c

d. 0.25c

192. Arc tan{2 cos(arcsin

) )} is equal

to:

a. π/3

b. π/4

c. π/6

d. π/2

193. Determine B such that 3x + 2y – 7 =

0 is perpendicular to 2x – By + 2 = 0

a. 5

b. 4

c. 3

d. 2

194. Find the point in the parabola y2 = 4

at which the rate of change of the

ordinate and abscissa are equal.

a. (1, 2)

b. (-1, 4)

c. (2, 1)

d. (4, 4)

195. Find the equation of the axis of

symmetry of the function y= 2x2-7x+5

a. 7x+4=0

b. 4x+7=0

c. 4x-7=0

d. 7x-4=0

196. The major axis of the elliptical path

in which the earth moves around the

sum is approximately 186, 000, 000

miles and the eccentricity of the

ellipse is 1/60. Determine the apogee

of the earth

a. 93 000 000 miles

b. 91 450 000 miles

c. 94 335 100 miles

d. 94 550 000 miles

197. The angle of inclination of ascends

of a road having 8.25% grade is _____

degrees.

a. 4.72˚

b. 4.27˚

c. 5.12˚

d. 1.86˚

198. Find the sum of the first term of the

geometric progression 2,4,8,16,…

a. 1 023

b. 2 046

c. 225

d. 1 596

199. Find the sum of the infinite

geometric progression 6, -2, 2/3

a. 9/2

b. 5/2

c. 11/2

d. 7/2

200. Evaluate (

)

a. Undefined

b. 0

c. Infinity

d. 1/7

201. What is the speed of asynchronous

earth’ satellite situated 4.5x107 m

from the earth

a. 11 070.0 kph

b. 12 000.0 kph

c. 11 777.4 kph

d. 12 070.2 kph

202. 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 position

a. 680

b. 540

c. 480

d. 840

203. The wheel of a car revolves n times

while the car travels x km. The radius

of the wheel in meter is:

a. 10 000x/π n

b. 500 00x/ π n

c. 500x/ π n

d. 5 000x/ π n

204. The volume of a gas under standard

atmospheric pressure, 76 cm. Hg is

200 in3. What is the volume when the

pressure is 80 cm. Hg, if the

temperature is unchanged?

a. 190 in3

b. 110 in

3

c. 90 in

3

d. 30.4 in

3

205. Find the 100th

term of the sequence,

1.01, 1.00, 0.99, ….

a. 0.05

b. 0.03

c. 0.04

d. 0.02

206. 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)

207. The roots of a quadratic equation are

1/3 and ¼. What is the equation?

a. 12x2+7x+1=0

b. 122-7x+1=0

c. 12x2+7x-1=0

d. 12x2-7x-1=0

208. Covert θ=π/3 to Cartesian equation

a. x=31/2

x

b. 3y=31/2

x

c. y=x

d. y=31/2

x

209. A piece of wire is shaped to enclose

a square whose area is 169 sq cm. It is

then reshaped to enclose a rectangle

whose length is 15 cm. The area of the

rectangle is:

a. 165 m2

b. 170 m2

c. 175 m2

d. 156 m2

210. If (x+3) : 10=(3x-2): 8, find (2x-1).

a. 1

b. 4

c. 2

d. 3

211. In complex algebra, we use a

diagram to represent a complex plane

commonly called:

a. De Moivre’s diagram

b. Argand diagram

c. Funicular diagram

d. Venn diagram

212. The quartile deviation is a measure

of:

a. Division

b. Certainty

c. Central tendency

d. Dispersion

213. The velocity of an automobile

starting from rest is given by

ft/sec. determine its acceleration

after an interval of 10 sec. (in ft/sec2)

a. 2.10

b. 1.71

c. 2.25

d. 2.75

214. An automobile accelerates at a

constant rate of 15 mi/hr to 45 mi/hr in

15 seconds, while traveling in a

straight line. What is the average

acceleration?

a. 2 ft/sec

b. 2.12 ft/sec

c. 2.39 ft/sec

d. 2.93 ft/sec

215. A comfortable room temperature is

72˚F. What is the temperature,

expressed in degrees Kelvin?

a. 290

b. 263

c. 275

d. 295

216. 15% when compounded semi-

annually will have effective rate of:

a. 15.93%

b. 16.02%

c. 18.78%

d. 15%

217. A non-square rectangle is inscribed

in a square so that each vertex of the

rectangle is at the trisection point of

the different sides of the square. Find

the ratio of the area of the rectangle to

the area of the square.

a. 4:9

b. 2:7

c. 5:9

d. 7:72

218. If the radius of the circle is decreased

by 20%, by how much is its area

decreased?

a. 46%

b. 36%

c. 56%

d. 26%

219. A flowerpot falls off the edge of a

fifth-floor window, just as it passes the

third-floor window someone

accidentally drops a glass of water

from the window. Which of the

following is true?

a. The flowerpot and the glass

hit the ground at the same

instant

b. The flowerpot hits the ground

at the same time as the glass

c. The glass hits the ground

before the flowerpot

d. The flowerpot hits the

ground first with a higher

speed than the glass

220. Is sinA=2.571x, cosA=3.06x, and

sin2A=3.939, find the value of x.

a. 0.100

b. 0.150

c. 0.250

d. 0.350

221. How many terms of the sequence -9,

-6, -3 … must be taken so that the sum

is 66?

a. 12

b. 4

c. 11

d. 13

222. A man in a hot air balloon drops an

apple at a height of 50 meters. If the

balloon is rising at 15 m/s, find the

highest point reached by the apple.

a. 141.45 m

b. 171.55 m

c. 151.57 m

d. 161.47 m

223. If sin A=4/5 and A is in the second

quadrant, sin B= 7/25 and B is in the

first quadrant, find sin (A+B)

a. 3/5

b. 3/4

c. 2/5

d. 4/5

224. If cosθ=-15/17 and θ is in the third

quadrant, find cos θ/2.

a. -1/√

b. -8/√

c. 2/√

d. 3/√

225. What is the maximum moment of a

10 meter simply supported beam

subjected to a concentrated load of

500kN at the mid-span?

a. 1250 kN-m

b. 1520 kN-m

c. 1050 kN-m

d. 1510 kN-m

226. It represents the distance of a point

from the y-axis

a. Ordinate

b. Abscissa

c. Coordinate

d. Polar distance

227. The logarithm of a number to the

base e (2.7182818….0 is called

a. Characteristic

b. Mantissa

c. Briggsian logarithm

d. Napierian logarithm

228. Terms that a differ only in numeric

coefficients are known as:

a. Unequal terms

b. Like terms

c. Unlike terms

d. Equal terms

229. In Plain Geometry, two circular arcs

that together make up a full circle are

called:

a. Conjugate arcs

b. Co-terminal arcs

c. Half arcs

d. Congruent arcs

230. For a particular experiment you need

5 liters of a 10% solution. You find

7% and 12% solution on the shelves.

How much of the 7% solution should

you mix with the appropriate amount

of the 12% solution to get 4 liters of a

10% solution.

a. 1.43

b. 1.53

c. 1.63

d. 1.73

231. A mango falls from a branch 5

meters above the ground. With what

speed in meters per second does it

strike the ground? Assume g=10m/s2.

a. 10 m/sec

b. 14 m/sec

c. 12 m/sec

d. 8 m/sec

232. When two waves of the same

frequency speed and amplitude

traveling in opposite directions are

superimposed.

a. The phase difference is

always zero

b. Distractive waves are

produced

c. Standing waves are

produces

d. Constructive interference

always results

233. The work done by all the forces

except the gravitational force is

always equal to the _____of the

system

a. Total mechanical energy

b. Total potential energy

c. Total kinetic energy

d. Total momentum

234. Ten less than four times a certain

number is 14. Determine the number

a. 7

b. 5

c. 4

d. 6

235. Equal volumes of two different

liquids evaporate at different, but

constant rates. If the first is totally

evaporated in 6 weeks, and the second

in 7 weeks, when will be the second

be ½ the volume of the first.

a. 3.5 weeks

b. 4 weeks

c. 5/42 weeks

d. 42/5 weeks

236. Find the fourth term of the

progression ½ , 0.2, 0.125 …

a. 0.099

b. 1/11

c. 1/10

d. 0.102

237. The time required by an elevator to

lift a weight varies directly through

which it is to be lifted and inversely as

the power of the motor. If it takes 30

seconds for a 10 hp motor to lift 100

lbs through 50 feet. What size of

motor is required to lift 800 lbs in 40

seconds through a distance of 40 feet.

a. 58 hp

b. 48 hp

c. 50 hp

d. 56 hp

238. Find the dimensions of the right

circular cylinder of greatest volume that

can be inscribed in a right circular cone

of radius r and altitude h.

a. Radius=2/3r; altitude=2/3h

b. Radius=1/3r; altitude=1/3h

c. Radius=2/3r; altitude=1/3h

d. Radius=1/3r; altitude=2/3h

239. An angular unit equivalent to 1/400

of the circumference of a circle is

called:

a. Grad

b. Mil

c. Degree

d. Radian

240. A condition where only few

individuals produce a certain product

and that any action of one will lead to

almost the same action of the others.

a. Monopoly

b. Perfect competition

c. Semi-monopoly

d. Oligopoly

241. Ivory soaps floats in water because:

a. The specific gravity of ivory

soap is less than that of

water

b. The specific gravity of ivory

soap is greater than that of

water

c. The density of ivory soap is

unity

d. All matters has mass

242. On a certain test, the average passing

score is 72 while the average for entire

test is 62, what part of the group of

students passed the test?

a. 5/9

b. 6/11

c. 7/13

d. 4/7

243. Ghost images are formed in a TV set

when the signal from the TV

transmitter is received directly at the

TV set and also indirectly after

reflection from a building or other

large metallic mass. In a certain 25

inch TV set, the ghost is about 1 cm,

to the right of the principal image of

the reflected signal arrives 1

microsecond after the principal signal.

What is the difference in the path

length of the reflected and principal

signals in this case?

a. 100 meters

b. 300 meters

c. 200 meters

d. 400 meters

244. A stone is dropped into a well, and

the sound of the splash was heard

three seconds later. What was the

depth of the well?

a. 37 meters

b. 41 meters

c. 53 meters

d. 30 meters

245. Two thermometers, one calibrated in

Celsius and the other in Fahrenheit,

are used o measure the same

temperature, the numerical reading

obtained on the Fahrenheit

thermometer.

a. Is greater than that obtained

on the Celsius thermometer

b. Is less than that obtained on

the Celsius thermometer

c. May be greater or less than

that obtained on the Celsius

thermometer

d. Is proportional to that

obtained on the Celsius

thermometer

246. 1 atm of pressure is equal to

_______.

a. 101300 Pa

b. 14.7 bars

c. 1.013 psi

d. 2117 psi

247. Find the least number of

years required to double a certain

amount of money at 5% per annum

compound interest to the nearest year

a. 14 years

b. 12 years

c. 18 years

d. 20 years

248. The replacement of the original cost

of an investment

a. Capital recovery

b. Breakeven

c. Payoff

d. Return on investment

249. When comparing leasing against

outright purchase of equipment, which

of the following is not correct?

a. Leasing frees needed

working capital

b. Leasing reduces maintenance

and administrative expenses

c. Leasing offers less flexibility

with respect to technical

obsolescence

d. Leasing offers certain tax

advantages

250. Find the volume of the solid above

the elliptic paraboloid 3x2+y

2=z and

below the cylinder x2+z=4

a. 2π cubic units

b. π/4 cubic units

c. π cubic units

d. 4 π cubic units

251. An oil well that yields 300 barrels of

cure oil a month will run dry in 3

years. If is estimated that t months

from now, the price of crude oil will

be P(t)=18 + 0.3√ dollars per barrel.

If the oil is sold as soon as it is

extracted from the ground, what will

be the total future revenue from the oil

well?

a. $253,550

b. $207,612

c. $150,650

d. $190,324

252. A point on the graph of a

differentianble function where the

concavity changes is called a point of

______

a. Inflection

b. Mean value

c. Local minimum value

d. Deflection

253. Find the maximum and minimum

values of 3sinθ

for 0˚ a. 3, 1/3

b. 1, 0

c. 2, -2

d. 1, -1

254. The spherical excess of a spherical

triangle is the amount by which the

sum of its angles exceed

a. 180˚

b. 90˚

c. 360˚

d. 270˚

255. the area of three adjacent surfaces of

a rectangular block are 8 sq cm, 10 sq

cm and 20 sq cm. the volume of the

rectangular block is

a. 200 cu m

b. 40 cu m

c. 10 cu m

d. 20 cu m

256. In the story about the crow who

wanted to drink water from a

cylindrical can but could not reach the

water, it is said that the crow dropped

a pebble which was a perfect sphere 3

cm in radius into the can. If the can

was 6 cm radius, what was the rise in

water level inside the can after that

pebble was dropped?

a. 2 cm

b. 1 cm

c. 3 cm

d. 2.5 cm

257. When a line y=mx+b slopes

downwards from left to right, the

slope m is

a. Less than 0

b. Greater than 0

c. Equal to 0

d. Equal to 1

258. A line perpendicular to a plane

a. Is perpendicular to only two

intersecting lines in the plane

b. Makes a right angle in the

plane which passes through

its foot

c. Is perpendicular to every line

is the plane

d. Makes a right angle with

every line is the plane

259. If the area of an equilateral triangle

is 9√ sq cm then its perimeter is

a. 9√ cm

b. 18 cm

c. 18√ cm

d. 12 cm

260. A transport company has been

contracted to transport a minimum of

600 factory workers from a gathering

point in Makati to their working place

in Canlubang daily. The transport

company has nine 5-passenger cars,

six 10-passenger mini buses and 12

drivers. The cars can make 14 trips a

day while the mini busses can make

10 trips a day. How should the

transport company use their cans and

mini buses in order to carry the

maximum number of passengers each

day?

a. 9 cars and 3 mini buses

b. 3 cars and 9 mini buses

c. 6 cars and 6 mini buses

d. 7 cars and 5 mini buses

261. When a certain polynomial p(x) is

divided by (x-1), remainder is 12.

When the same polynomial is divided

by (x-4), the remainder is 3. Find the

remainder when the polynomial is

divided by (x-1)(x-4)

a. x+5

b. -2x-8

c. -3x+15

d. 4x-1

262. The scalar product of A and B is

equal to the product of the magnitudes

of A and B and the ______ of the

angle between them

a. Sine

b. Value in radians

c. Tangent

d. Cosine

263. If the surd (√ √ ) , then

x is equal to:

a. √

b. √

c. √ √

d.

√ √

264. A certain electronics company has

16 tons of raw materials, of which 10

tons are stored in warehouse in

Quezon city, and 6 tons are stored in

warehouse in Makati. The raw

materials have to be transported to

three production points in Dasmarinas

Cavite, Canlubang Laguna and

Batangas city in the amounts of 5, 7

and 4 tons respectively, the cost per

ton for transporting the raw materials

from the two warehouses to the three

production points areas as follows

To/Fro

m

Damarin

as

Canluba

ng

Batang

as

Q.C P 700 P500 P800

Makati P 200 P300 P400

Find the minimum possible

transportation cost. HINT let a=no of

tons to be shopped from Q.C to

Dasmarinas, b=no of tons to be

shipped ftom Q.C to Canlubang, c=no

of tons to be shipped from Q.C to

Batangas, d= no of tons to be shopped

from Makati to Dasmarinas, e= no of

tons to be shopped from Makati to

Canlubanga and f= no of tons to be

shopped from Makati to Batangas.

a. 7 300.00

b. 8 300.00

c. 9 300.00

d. 10 300.00

265. Which of the following is a correct

relationship for any triangle whose

sides are a, b, c and the respective

sides are a, b, c and the respective

opposite angles are A, B and C.

a. a2=b

2+c

2-bc cos A

b. a2=b

2+c

2-2bc cos A

c. a2=b

2+c

2-2bc sin A

d. a2=b

2+c

2-2bc cos B cos C

266. find the product MN of the following

matrices

M=|

| N=|

|

a. |

|

b. |

|

c. |

|

d. |

|

267. Arrange the following surds in

descending order: a=√ √ ,

b=3+√ , c=√ √ , d=√ √

a. c, d, a, b

b. b, a, d, c

c. c, d, b, a

d. d, c, a, b

268. If

, which of

the following relationship is correct?

a. x+z=y

b. x=y+z

c. x+y=z

d. x-y=z

269. evaluate u= ( )

a. 2

b. 9

c. 6

d. 8

270. Evaluate: I= ∫ ∫

a. 88/3

b. 89

c. 3

d. 79/3

271. The probability for the ECE board

examinees from a certain school to

pass the subject in mathematics is 3/7

and for the subject of Communication

is 5/7. If none of those examinees fail

both subjects and there are four

examinees who passed both subjects,

find the number of examinees from

that school who took the examinations

a. 21

b. 14

c. 28

d. 35

272. A number when divided by 6 leaves

a remainder of 5, when divided by 5

leaves a remainder of 4, by 4 leaves a

remainder of 3, by 3 leaves a

remainder of 2, and by 2 leaves a

remainder of 1. Find the smallest

possible value of the number.

a. 29

b. 39

c. 49

d. 59

273. _________ are irrational numbers

involving radical signs

a. Radicals

b. Surd

c. Irrational number

d. Transcendental number

274. When rounded off to two significant

figures, the number 4.371x10-10

becomes ______

a. 4.4x 10-10

b. 4x10-10

c. 4.3x10-10

d. 4.2x10-10

275. The __________ of a and b is the

smallest positive integer that is a

multiple of both a and b.

a. Least common multiple

b. Least common denominator

c. Least common factor

d. Greatest common factor

276. If soldering lead contains 63% silver,

______ grams of soldering lead can be

made from 520 grams of silver.

a. 852.4

b. 825.4

c. 845.2

d. 842.5

277. In the equation ÿ=mx+b”, m

represents the _______

a. Distance from a point

b. Coordinate of the line

c. Coefficients

d. Slope of the line

278. In the equation “n x m=q”, the

multiplicand is _______

a. n

b. m

c. q

d. none of the choices

279. The hypotenuse of an isosceles right

triangle whose perimeter is 24 inches

is ____ inches.

a. 9.94 inches

b. 7.94 inches

c. 7.03 inches

d. 6.94 inches

280. An arc equal to one-fourth of a circle

is called a ____

a. Quarter circular arc

b. Quarter circle

c. Conjugate circle

d. Complimentary circle

281. If angle θ=2, then angle (180˚-θ)=

__________

a. 1.1416 radian

b. 1.1614 radian

c. 1.6141 radian

d. 1.4161 radian

282. The logarithm of a number to a

given base is called the ______

a. Exponent

b. Index

c. Base

d. Matrix

283. One is to fifty-two and one half as

three and one-third is to ______

a. 185

b. 175

c. 165

d. 155

284. Adjacent angles whose sum is 90

degrees are said to be _____

a. Complimentary

b. Supplementary

c. Explementary

d. Reflex angles

285. If x >y and y>z, then x _____z.

a. Less than

b. Greater than

c. Equal to

d. Less than or equal to

286. If any given triangle with sides a, b,

and c _______is equal to b(

)

a. sin A

b. sin B

c. b

d. a

287. if a>b and c>d, then (a+c) is

_______ of (b+d)

a. less than

b. greater than

c. equal to

d. less than or equal to

288. the following Fourier series equation

represents a periodic ____wave

i(x)= i + i cos x + i2 cos 2x+ i

3 cos 3x

+…+i sin x + i2 sin 2x+ i

3 sin 3x+…

a. cosine

b. tangent

c. cotangent

d. sine

289. a percentage is a fraction whose

denominator is ____

a. 1000

b. 100

c. 10

d. 10000

290. A swimming pool is constructed in

the shape of two partially overlapping

identical circle. Each of the circles has

a radius of 9 meters, and each circle

passes through the center of the other.

Find the area of the swimming pool.

a. 409.44 sq m

b. 309.44 sq m

c. 509.44 sq m

d. 209.44 sq m

291. The dartboard has nine numbered

blocks. Each block measuring 20cm x

20 cm. The number on each block is

the score earned when a dart hits that

block. A dart, which hits the

unnumbered portion of the dartboard,

gets a score of zero. Assuming all the

darts hit the dartboard and with two

darts, what is the probability of getting

a total score of 11?

a. 0.0128

b. 0.0328

c. 0.228

d. 0.0168








darts hit the dartboard, what is the

probability of getting a score of zero

with one dart?

a. 0.64

b. 0.04

c. 0.44

d. 0.54








darts hit the dartboard, what is the

probability of getting a score of seven

with one dart?

a. 0.04

b. 0.10

c. 0.07

d. 0.70

294. A rectangular metal sheet measures

22 ft long and 2R ft wide. From this

rectangular metal sheet, three identical

circles were cut, each circle measuring

R/3 ft. radius. If the area of the

remaining metal sheet is 66 sq ft, find

R.

a. 1.56 ft

b. 40.47 ft

c. 2.56 ft

d. 13.56 ft

295. If a and y are complimentary, find

the value of P if: P= cos (540˚+x)

sin(540˚+y) +cos(90˚+x)sin (90+y)

a. sin 2x

b. cos 2x

c. –cos 2x

d. –cos 2y

296. Given: ,

,

. Find a, n, and m.

a. 2, 16, 4

b. 16, 2, 4

c. 4, 16, 2

d. 2, 4, 16

297. Given: P= A sin t + B cos t, Q= A

cos t – B sin t. From the given

equations, derive another equation

showing the relationship between P,

Q, A, and B not involving any of the

trigonometric functions of angle t.

a. P2-Q

2=A

2+B

2

b. P2+Q

2=A

2-B

2

c. P2-Q

2=A

2-B

2

d. P2+Q

2=A

2+B

2

298. In a certain electronic factory, the

ratio of the number of male to female

workers is 2:3. If 100 new female

workers are hired, the number of

female workers will increase to 65%

of the total number of workers. Find

the original number of workers in the

factory.

a. 420

b. 450

c. 480

d. 490

299. During installation, a section of an

antenna was lifted to a height of 5

meters with a force of 400 kg moving

by the use of a pulley mounted on a

frame. If the efficiency of the input

multiplied by 100%, what is the

efficiency of the pulley? The tower

section weighs 1000 kg

a. 62.5%

b. 52.5%

c. 72.5%

d. 82.5%

300. An elevator can lift a load of 5000

Newtons from ground level to a height

of 20.0 meters in 10 seconds. What

horsepower, hp can the elevator

develop?

a. 12.4 hp

b. 13.4 hp

c. 14.4 hp

d. 15.4 hp

301. What is the force in Newtons,

required to move a car with 1000 kg

mass with an acceleration of 12.0

meters/sec2?

a. 12 000N

b. 10 000N

c. 8 000N

d. 6 000N

302. If the same car in problem 301, with

1000 kg mass is driven around a curve

with radius of 10.0 meters at a speed

of 20 meters per second, find the

centrifugal force in Newtons.

a. 40000N

b. 30000N

c. 20000N

d. 10000N

303. Crew 1 can finish the installation of

an antenna tower in 200 hours while

crew 2 can finish the same job in 300

hours. How long will it take both

crews to finish the same job working

together?

a. 180 hours

b. 160 hours

c. 140 hours

d. 120 hours

304. Evaluate the limit of x2+3x-4 as x

approaches the value of 4

a. 24

b. 42

c. 35

d. 12

305. log Mn is equal to

a. log nM

b. log Mn

c. n log M

d. M log n

306. The volume of a cube is reduces to

______ if all the sides are halved

a. 1/2

b. 1/4

c. 1/8

d. 1/16

307. Evaluate the value of the determinant

|

|

a. -101

b. 011

c. -001

d. 111

308. Give the factors of a2-x

2

a. 2a-2x

b. (a+x)(a-x)

c. 2x-2a

d. (a+x)(x-a)

309. Give the area of a triangle in square

meters when the base is equal to

24.6cm and the height is equal to 50.8

cm. One of the sides is equal to 56.53

cm

a. 0.062484

b. 0.1252

c. 2877.44

d. 1252.1

310. The cost of running an electronic

shop is made up of the following:

Office rental=40% Labor=35%

Materials=20% Miscellaneous=5%. If

the office rental is increased by 24%,

labor increased by 15%, cost of

materials increased by 20%, and the

miscellaneous costs are unchanged,

find the percentage increase in the cost

of running the shop.

a. 18.85%

b. 28.85%

c. 16.85%

d. 10.85%

311. The selling price of a TV set is

double that of its net cost. If the TV

set is sold to a customer at a profit of

255 of the net cost, how much

discount was given to the customer?

a. 27.5%

b. 47.5%

c. 37.5%

d. 30.5%

312. Find the sum of the interior angles of

a pentagram

a. 180 degrees

b. 360 degrees

c. 540 degrees

d. 720 degrees

313. Find the value of P if it I equal to

sin2 1˚ + sin

22˚ + sin

23˚ + .. + sin

2 90˚

a. Infinity

b. 0

c. 44.5

d. Indeterminate

314. Find the value of P if it is equal to

a. 0

b. 1

c. 2

d. 4

315.

√

= ?

a. 0.3

b. 0.4

c. 0.5

d. 0.6

316. Find the value of

a. 4

b. 2

c. 0

d. 1

317. Find the value of √ √ √

a. 3/2

b. 2

c. 3

d. 1/2


(

)

a. 25/48

b. 125/48

c. 125/16

d. 125/8


a. 2

b. 4

c. 8

d. 16

320. Simplify (

)

a. 2

b. 4

c. 8

d. 16

321.

= ?

a. tan B

b. sec B

c. cot B

d. csc B

322. Simplify the following:

a. 0

b. 1

c. 2

d. cot (A+B)

323. Solve for the following:

a. -7a

b. +7a

c. -7-a

d. +7-a

324. Simplify {

*

+

}

a.

b.

c.

d.

325. Simplify ( )

( )

a.

b.

c.

d.

326. If A was originally a range of

numbers with four significant figures

which, when rounded off to three

significant figures yielded a value of

3.10, what was the original range of

values of A?

a. 3.10 to 3.105

b. 3.101 to 3.105

c. 3.101 to 3.109

d. 3.101 to 3.104

327. Round off: 6785768.342 to the

nearest one tenth

a. 6785768.34

b. 6785768.3

c. 7000000.0

d. 6785770.00

328. Round off: 2.371x10-8

to two

significant figures

a. 2.3x10-8

b. 2.4x10-8

c. 2.0x10-8

d. 2.5x10-8

329. Round off: 0.003086 to two

significant figures

a. 0.00308

b. 0.00310

c. 0.00300

d. 0.00311

330. Round off: 0.00386 to three

significant figures

a. 0.00308

b. 0.00309

c. 0.003

d. 0.00310

331. Round off: 34.2814 to four

significant figures

a. 34.2814

b. 34.2800

c. 35.0000

d. 34.2000

332. Round off: 30 562 to three

significant figures

a. 30 500

b. 30 600

c. 30 400

d. 30 300

333. Round off: 149.691 to one decimal

place

a. 149.6

b. 149.7

c. 148.5

d. 148.4

334. Round off: 149.691 to the nearest

integer

a. 149

b. 148

c. 147

d. 150

335. Round off: 149.691 to two decimal

places

a. 149.69

b. 149.70

c. 148.69

d. 148.70

336. Which of the following is equivalent

to the expression:

a. sin

b. cos

c. sec

d. csc

337. A stone is thrown outward, at an

angle of 30 with the horizontal, into

the river from a cliff, which is 120

meters above the water level at a

velocity of 36 km/hr. At what height

above the water level will the stone

start to fall?

a. 121.274 m

b. 131.274 m

c. 141.274 m

d. 161.274 m

338. A stone is thrown outward, at an

angle of 30 with the horizontal, into

the river from a cliff, which is 120

meters above the water level at a

velocity of 36 km/hr. how far from the

cliff will the stone strike the water?

a. 57.46 meters

b. 47.46 meters

c. 67.46 meters

d. 77.46 meters

339. The speed of light is closest to:

a. 30x108 m/sec

b. 300x108 m/sec

c. 3000x108 m/sec

d. 3x108 m/sec

340. When a ray of light is incident from

a medium, such as air, to a denser

medium, like water, the refracted ray

lie _____ to the perpendicular than

does the incident ray.

a. Closer

b. Farther

c. Parallel

d. Perpendicular

341. In nuclear energy, the splitting apart

of the heavy nuclei of uranium is

called

a. Fusion

b. Fission

c. Neutron

d. Diffusion

342. A parabola which opens upward and

whose vertex is at the origin is defined

by what equation?

a.

b.

c.

d.

343. The curve traced by a point moving

in a plane is shown as the _____ of

that point.

a. Parameter

b. Pattern

c. Locus

d. Formula

344. (a-b)3 is equivalent to which of the

following?

a.

b.

c.

d.

345. Payment for the use of borrowed

money is called

a. Loan

b. Maturity value

c. Interest

d. Rate

346. Area of a triangle is given by the

formula

a. 1/2bh

b. bh

c. 1/4bh

d. 3/4bh

347. Evaluate ∫

dx

a. 37.6

b. 47.6

c. 27.6

d. 57.6

348. In the Cartesian coordinate, the

coordinates if the vertices of a square

are (1, 1), (0, 8), (4, 5), and (-3, 4).

What is the area of the square?

a. 25 sq units

b. 16 sq units

c. 32 sq units

d. 50 sq units

349. Given log2=0.30 and log3=0,477.

Find the value of log 48

a. 1.681

b. 1.683

c. 1.685

d. 1.687

350. sinAcosB + sinBcosA= ?

a. sin(A+B)

b. sin(A-B)

c. cos(A+B)

d. cos(A-B)

351. sinh2x+tanh

2 x= ?

a. cosh2x-sech

2x

b. cosh2x+sech

2x

c. sech2x-cosh

2x

d. sech2x+cosh

2x

352. If the freezing point of water is zero

deg Celsius or 32 Fahrenheit, and its

boiling point is 100 deg Celsius or 212

Fahrenheit, which relationship is

correct?

a. F=9/5C+32

b. F=5/9C+32

c. C=9/5F+32

d. C=5/9F+32

353. What is the probability of obtaining

either four or five heads if a fair coin

is tossed 10 times?

a. 231/512

b. 233/512

c. 221/512

d. 235/512

354. Find the volume generated by

revolving the ellipse whose equation is

about the x-axis

a. 4/3πab2

b. 2/3 πab2

c. 4/3 πba2

d. 2/3 πa2b

355. A telephone pole 3ft high is to be

guyed from its middle section with a

guy wire making an angle of 45

degrees with the ground. Find the total

length of the guy wire if an additional

three feet is to be provided for

splicing. Solve by using trigonometric

functions.

a. 24.21 ft

b. 34.21 ft

c. 44.21 ft

d. 25.21 ft

356. A rubber ball is made to fall from a

height of 50 feet and is observed to

rebound 2/3 of the distance it falls.

How far will the ball travel before

coming to rest if the ball continues to

fall in this manner?

a. 200 m

b. 225 m

c. 250 m

d. 300 m

357. The slope of a family of curves at

any point (x, y) is equal to 3x4-x

2.

Find the equation of the curve that is

passing through point (1, 1).

a. (

)

(

)

b. (

)

(

)

c. (

)

(

)

d. (

)

(

)

358. The slope of a family of curves at

any point (x, y) is equal to (x+1)(x+2).

Find the equation of the curve that is

passing through the point (-3, -3/2)

a.

b.

c.

d.

359. Reduce the following complex

fraction into simple functions

a.

b.

c.

d.

360. Reduce the following complex

fraction into simple fractions

a. –

b. +

c. –

d. +

361. A missile with a mass of 2200

kilograms was fired the rocket burns

for a short period of time causing a

constant force of 100 000 N to be

exerted on the missile for 10 seconds.

After the 10 second period, what is the

final velocity, v in m/sec of the

missile? a. 365.45 m/sec b. 352.45 m/sec c. 356.45 m/sec d. 256.45 m/sec

362. A missile with a mass of 2200

kilograms was fired the rocket burns

for a short period of time causing a

constant force of 100 000 N to be

exerted on the missile for 10 seconds.

After the 10 second period, what is the

acceleration of the missile in m/s2?

a. 35.64 b. 33.64 c. 30.64 d. 39.64

363. A consortium of international

telecommunication companies

contracted for the purchase and

installation of a fiber optic cable

linking two major Asian cities at a

total cost of US$ 960M. This amount

includes freight and installation

charges that are estimated at 10% of

the above total price, if the cable shall

be depreciated over a period of 15

years with zero salvage value, what is

the depreciation charge during the 8th

year using the sum of the year’s digit

method? a. $64 M b. $74 M c. $84 M d. $54 M

364. A consortium of international

telecommunication companies

contracted for the purchase and

installation of a fiber optic cable

linking two major Asian cities at a

total cost of US$ 960M. This amount

includes freight and installation

charges that are estimated at 10% of

the above total price, if the cable shall

be depreciated over a period of 15

years with zero salvage value. Given

the sinking fund deposit factor of

0.0430 at 6% interest where n=15,

what is the annual depreciation

charge? a. $43.28M b. $42.28M c. $44.28M d. $41.28M

365. Find the derivative of y with respect

to x in the following equations

a.

( )

b.

c.

d.

366. Find the value of y

’ at x=1 of the

equation

a. 21

b. -21

c. 12

d. -12

367. An equipment can be purchased by

paying P100 000 down payment and

24 equal monthly installments of P10

000 with 6% interest compounded

monthly? Find the cash value of the

equipment given the following:

present value of an annuity where

n=24 at 0.5% interest, PV

factor=22.563

a. P235630

b. P352630

c. P325630

d. P253630

368. Simplify the following expression:

a.

b.

c.

d.

369. Solve for the values of a in the

equation a8-17a

4+16=0

a.

b. c.

d. All of the choices

370. Log(MN) is equal to

a. logM-N

b. log M+N

c. nlogM

d. logM+logN

e. NMlog10

371. Snell’s law on light incidence and

refraction gives us the following

equation: n1sinθ1=n2sinθ2 where n1

and n2 denote the indexes on

refraction θ1 and θ2 are the angle of

incidence and refraction, respectively

through the first and second medium.

If light beamed at an angle of 30

degrees with the vertical is made pass

from air to a transparent glass with an

index of refraction equal to 1.25, what

is the angle of refraction in the glass?

a. θ=33.6˚

b. θ=43.6˚

c. θ=53.6˚

d. θ=23.6˚

372. If

, y’=?

a.

b.

c. -

d.

373. Sin215˚+sin

275˚

a. 1

b. 2

c. 3

d. 4

374. In the ECE board examinations, the

probability that an examinee pass in

each subject is 0.8. What is the

probability that he will pass in at least

2 subjects?

a. 0.896

b. 0.986

c. 0.689

d. 0.869

375. A Morse code transmitter at station

A sending out either a dot or dash

signal. The signal is received at station

B, from where it is retransmitted to

station C. The probability that the

signal being sent from A is receives

correctly at B is 0.98, while the

probability that the signal being

received correctly at C is 0.965. What

is the probability that when a dot

signal is transmitted from A, a dot

signal is also received at C?(Express

your answer up o four decimal places)

a. 0.9557

b. 0.9457

c. 0.4957

d. 0.5947

376. In the figure shown, ABCD is a

square and BEC is an equilateral

triangle. Find angle AED.

a. 75˚

b. 150˚

c. 120˚

d. 140˚

D

eeeee

B B C

377. Solve for the radius of the circle

shown. Large circle r=4m, small circle

r=radius=?

E

A D

4-r

4+r

45˚

a. 0.686 m

b. 0.688 m

c. 0.866 m

d. 0.868 m

378. Differentiate the equation

a.

b.

c. d. 1

379. Give the slope of the curve at

point (1, 1)

a. 1/4

b. -1/4

c. 4

d. -1/3

380. Evaluate b in the following

equation logb 1024=5/2

a. 2560

b. 2

c. 4

d. 16

381. Obtain the differential equation of the family of straight lines with slope and -intercept equal.

a. b. c. d.

382. Obtain the differential equation

of all straight lines with algebraic sum of the intercepts fixed as .

a. b. c. d.

383. Obtain the differential equation of all straight lines at a fixed distance from the origin.

a. [ ]

b. [ ] c. . [ ] d. [ ]

384. Determine the differential

equation of the family of lines passing through the origin.

a. b. c. d.


of all circles with center on line and passing through the origin.

a.

b.

c.

d. ( )

( )


of all parabolas with axis parallel to the -axis.

a. b. c. d.

387. What is the differential

equation of the family of parabolas having their vertices at the origin and their foci on the -axis.

a. b. c. d.

388. Obtain the particular solution of

/ when , .

a.

b.

c.

d.

389. Obtain the general solution of

the differential equation

a. b. c. d.

390. Obtain the general solution of

.

a. ( )

b. c. d.

391. Solve the equation

.

a.

b. c. d.

392. Obtain the particular solution of ; when , .

a. b. c. d.


. a. b. c. d.


.

a. b. c. d.


.

a. b. c. d.

396. Solve

.

a.

b.

c.

d.


. a. b. c. d.


. a. | | b. | | c. | | d. | |


.

a. b. c. d.

400. Solve the equation .

a. b. c. d.


<MATHEMATICS>

<DIEGO INOCENCIO TAPANG

GILLESANIA>

ENCODED BY: BORBON, MARK

ADRIAN C.

401. Evaluate

.

A. 0

B. 1

C. 2

D. 3

402. Simplify the expression:

.

A. 1

B. 8

C. 0

D. 16

403. Evaluate the following limit,

.

A. 2/5

B. infinity

C. 0

D. 5/2

404. Evaluate the limit / (

.

A. 0

B. undefined

C. 1/7

D. infinity

405. Evaluate the limit / as x

approaches positive infinity.

A. 1

B. 0

C. e

D. infinity

406. Evaluate the limit:

.

A. 1

B. indefinite

C. 0

D. 2

407. Evaluate:

.

A. 0

B. ½

C. 2

D. -1/2

408. Evaluate the following:

.

A. infinity

B.

C. 0

D.

409. Find / if .

A.

B.

C.

D.

410. Find / if √ .

A. √ / √

B. √ /√

C. / √

D. √ √

411. Find / if and

.

A.

B.

C.

D.

412. Evaluate the first derivative of the

implicit function: .

A.

B. -

C.

D. -

413. Find the derivative of /

with respect to x.

A.

/

B.

/

C.

/

D.

/

414. If is a simple constant, what is the

derivative of ?

A.

B.

C.

D.

415. Find the derivative of the function

with respect to x.

A.

B.

C.

D.

416. What is the first derivative / of

the expression ?

A. - /

B. 0

C. - /

D. /

417. Find the derivative of / .

A.

B.

C.

D.

418. Given the equation: ,

find .

A.

B. /

C.

D.

419. Find the derivatives with respect to x

of the function √ .

A. - /√

B. - /√

C. - /√

D. - /√

420. Differentiate to the ½

power.

A. -

B.

C.

D.

421. Find / if √ .

A. √ /

B. x/

C. 1/2x

D. 2/x

422. Evaluate the differential of .

A.

B.

C.

D.

423. If , what is / ?

A.

B. -

C.

D. -

424. Find / : .

A.

B. /x

C.

D. /

425. The derivative of is:

A.

B. -

C. -

D.

426. A function is given below, what x

value maximizes ?

A. 2.23

B. -1

C. 5

D. 1

427. The number of newspaper copies

distributed is given by

, where is in years.

Find the minimum number of copies

distributed from 1995 to 2002.

A. 9850

B. 9800

C. 10200

D. 7500

428. Given the following profit-versus-

production function for a certain

commodity:

(

)

Where P is the profit and x is the unit

of production. Determine the

maximum profit.

A. 190000

B. 200000

C. 250000

D. 550000

429. The cost C of a product is a function

of the quantity of the product given

by the relation:

. Find the quantity for

which the cost is a minimum.

A. 3000

B. 2000

C. 1000

D. 1500

430. If to the 3rd

power - . Find

the maximum value of .

A. 0

B. -1

C. 1

D. 2

431. Divide 120 into two parts so that the

product of one and the square of the

other is maximum. Find the

numbers.

A. 60 & 60

B. 100 & 120

C. 70 & 50

D. 80 & 40

432. If the sum of two numbers is , find

the minimum value of the sum of

their squares.

A. ⁄

B. ⁄

C. ⁄

D. ⁄

433. A certain travel agency offered a tour

that will cost each person P 1500.00

if not more than 150 persons will

join, however the cost per person

will be reduced by P 5.00 per person

in excess of 150. How many persons

will make the profit a maximum?

A. 75

B. 150

C. 225

D. 250

434. Two cities and are 8 km and 12

km, respectively, north of a river

which runs due east. City being 15

km east of . A pumping station is to

be constructed (along the river) to

supply water for the two cities.

Where should the station be located

so that the amount of pipe is a

minimum?

A. 3 km east of

B. 4 km east of

C. 9 km east of

D. 6 km east of

435. A boatman is at , which is 4.5 km

from the nearest point on a straight

shore . He wishes to reach, in

minimum time, a point situated on

the shore 9 km from . How far

from should he land if he can row

at the rate of 6 kph and walk at the

rate of 7.5 kph?

A. 1 km

B. 3 km

C. 5 km

D. 8 km

436. The shortest distance from the point

(5,10) to the curve is:

A. 4.331

B. 3.474

C. 5.127

D. 6.445

437. A statue 3 m high is standing on a

base 4 m high. If an observer’s eye is

1.5 m above the ground, how far

should he stand from the base in

order that the angle subtended by the

statue is a maximum?

A. 3.41 m

B. 3.51 m

C. 3.71 m

D. 4.41 m

438. An iron bar 20 m long is bent to

form a closed plane area. What is the

largest area possible?

A. 21.56 square meter

B. 25.68 square meter

C. 28.56 square meter

D. 31.83 square meter

439. A Norman window is in the shape of

a rectangle surmounted by a semi-

circle. What is the ratio of the width

of the rectangle to the total height so

that it will yield a window admitting

the most light for a given perimeter?

A. 1

B. 2/3

C. 1/3

D. ½

440. A rectangular field is to be fenced

into four equal parts. What is the size

of the largest field that can be fenced

this way with a fencing length of

1500 feet if the division is to be

parallel to one side?

A. 65,200

B. 62,500

C. 64,500

D. 63,500

441. Three sides of a trapezoid are each 8

cm long. How long is the 4th side,

when the area of the trapezoid has

the greatest value?

A. 16 cm

B. 15 cm

C. 12 cm

D. 10 cm

442. An open top rectangular tank with

square bases is to have a volume of

10 cubic meters. The material for its

bottom cost P150.00 per square

meter, and that for the sides is

P60.00 per square meter. The most

economical height is:

A. 2 meters

B. 2.5 meters

C. 3 meters

D. 3.5 meters

443. A rectangular box having a square

base and open top is to have a

capacity of 16823cc. Find the height

of the box to use the least amount of

material.

A. 16.14 cm

B. 32.28 cm

C. 18.41 cm

D. 28.74 cm

444. The altitude of a cylinder of

maximum volume that can be

inscribed in a right circular cone of

radius and height is:

A. ⁄

B. ⁄

C. ⁄

D. ⁄

445. What is the least amount of tin in

sheet, in sq. inches, that can be made

into a closed cylindrical can having a

volume of 108 cu. inches?

A. 125 square meter

B. 137 square meter

C. 150 square meter

D. 120 square meter

446. The volume of the closed cylindrical

tank is 11.3 cubic meter. If the total

surface area is a minimum, what is

its base radius, in m?

A. 1.44

B. 1.88

C. 1.22

D. 1.66

447. A cylindrical steam boiler is to be

constructed having a capacity of

1000 cu. m. The material for the

sides cost P 2000.00 per square

meter and for the ends P 3000.00 per

square meter. Find the radius so that

the cost is least.

A. 3.52 m

B. 4.12 m

C. 4.73 m

D. 5.25 m

448. A box is to be constructed from a

piece of zinc 20 inches square by

cutting equal squares from each

corner and turning up the zinc to

form the side. What is the volume of

the largest box that can be so

constructed?

A. 599.95 cubic inches

B. 579.50 cubic inches

C. 592.59 cubic inches

D. 622.49 cubic inches

449. A load of 40kN is to be raised by

means of a lever weighing 250N/m,

which is supported at one end. If the

load is placed 1 m from the support,

how long should the lever be so that

the force required be a minimum?

A. 13.43 m

B. 20.19 m

C. 18.56 m

D. 17.89 m

450. As increases uniformly at the rate

of 0.002 feet per second, at what rate

is the expression (1+ ) to the 3rd

power increasing when becomes 8

feet?

A. 430 cfs

B. 0.300 cfs

C. 0.486 cfs

D. 0.346 cfs

451. Integrate:

A.

B.

C.

D.

452. Evaluate ∫

A.

B.

C.

D.

453. Evaluate the integral of .

A.

B.

C.

D.

454. What is the integral of

?

A. -

B.

C.

D. -

455. The integral of with respect to

; ∫ is:

A.

B.

C.

D. -

456. Integrate .

A. ⁄

B.

C. ⁄

D. ⁄

457. Evaluate ∫

.

A.

B.

C. ½

D.

458. Evaluate ∫ .

A.

B.

C.

D. √

459. Evaluate ∫ .

A.

B.

C. ½

D. ½

460. Evaluate ∫

.

A. ½

B.

C. ½

D. arctan

461. Evaluate ∫

√ .

A. arcsec

B.

[ ]

C. √

D. arcsin

462. Evaluate ∫

.

A.

B.

C.

D.

463. Evaluate ∫

.

A. ½

B.

C.

D.

464. Evaluate ∫

.

A.

B.

C.

D.

465. Evaluate the integral of .

A. -

B. -

C.

D. -

466. Evaluate ∫ .

A.

B. -

C. -

D.

467. Evaluate ∫ .

A. √

B.

C. √

D.

468. Integrate the square root of

.

A. √

B. - √

C. -

D. - √

469. Evaluate the integral of

with limits from 0 to .

A. 0.143

B. 0.258

C. 0.114

D. 0.186


with limits from 5 to 6.

A. 81/182

B. 82/182

C. 83/182

D. 84/182


if it

has an upper limit of 1 and a lower limit of

0.

A. 0.022

B. 0.056

C. 0.043

D. 0.031

472. Find the integral of

if lower limit = 0 and

upper limit = .

A. 0.2

B. 0.8

C. 0.6

D. 0.4

473. Using lower limit = 0 and upper limit

= , what is the integral of ?

A. 6.783

B. 6.857

C. 6.648

D. 6.539


using lower limit of 0 and

upper limit = .

A. 2.0

B. 1.7

C. 1.4

D. 2.3


using lower limit = 0 and

upper limit = .

A. 0.5046

B. 0.3068

C. 0.6107

D. 0.4105

476. Find the area under the curve

and the x-axis between

and .

A. 28 sq. units

B. 46 sq. units

C. 36 sq. units

D. 54 sq. units

477. Find the area bounded by

, the lines and ,

and the X-axis.

A. 19.456 sq. units

B. 20.567 sq. units

C. 22.567 sq. units

D. 21.478 sq. units

478. Find the area of the region bounded

by the curves

, the -axis, ,

and .

A.

B.

C.

D.

479. Find the area bounded by the -axis

and .

A. 25.6

B. 28.1

C. 12.8

D. 56.2

480. Find the area of the region bounded

by one loop of the curve .

A. sq. units

B. sq. units

C. sq. units

D. sq. units

481. Find the area bounded by the curve

A.

B.

C.

D.

482. What is the area within the curve

?

A. 26

B. 28

C. 30

D. 32

483. Find the area enclosed by

A.

B.

C.

D.

484. Find the curved surface (area) of the

solid generated by revolving the part

of the curve from to

√ about the -axis.

A. 62 sq. units

B. 62 /3 sq. units

C. 62 /5 sq. units

D. 5/62 sq. units

485. Find the volume generated by

rotating the region bounded by

, , and , about

the -axis.

A.

B.

C.

D.

486. The area bounded by the curve

and the line is

revolved about the line . What

is the volume generated?

A. 186

B. 179

C. 181

D. 184

487. Given is the area in the first quadrant

bounded by , the line

and the -axis. What is the volume

generated by revolving this area

about the y-axis?

A. 50.26

B. 52.26

C. 53.26

D. 51.26

488. Given is the area in the first quadrant

bounded by , the line

and the -axis. What is

the volume generated when this area

is resolved about the line ?

A. 28.41

B. 26.81

C. 27.32

D. 25.83

489. Find the length of the arc of

from - to - , in the

second quadrant.

A. 2.24

B. 2.61

C. 2.75

D. 2.07

490. How far from the -axis is the

centroid of the area bounded by the

curve , the line , and the

-axis.

A. 1.2

B. 1.4

C. 1.6

D. 1.8

491. The area in the first quardrant,

bounded by the curve , the

-axis and the line is

revolved about the line . Find

the centroid of the solid formed.

A. (2.2,6)

B. (1.6,6)

C. (1.8,6)

D. (2.0,6)

492. A solid is formed by revolving about

the -axis, the area bounded by the

curve , the -axis, and the

line . Find its centroid.

A. (0,9.6)

B. (0,12.4)

C. (0,8.3)

D. (0,12.8)

493. A solid is formed by revolving about

the -axis, the area bounded by the

curve , the -axis, and the

line . Find its centroid.

A. (0,4.75)

B. (0,4.5)

C. (0,5.25)

D. (0,5)

494. Find the moment of inertia of the

area bounded by the parabola

, -axis and the line ,

with respect to the -axis.

A. 1.067

B. 1.244

C. 0.968

D. 0.878

495. Find the work done in stretching a

spring of natural length 8 cm from

10 cm to 13 cm. Assume a force of 6

N is needed to hold it at a length of

11 cm.

A. 21 N-m

B. 2.1 N-m

C. 0.21 N-m

D. 0.021 N-m

496. A conical tank that is 5 meters high

has a radius of 2 meters, and is filled

with a liquid that weighs 800 kg per

cubic meter. How much work is

done in discharging all the liquid at a

point 3 meters above the top of the

tank?

A. 21,256 kg-m

B. 21,896 kg-m

C. 23,457 kg-m

D. 22,667 kg-m

497. How much work is required to pump

all the water from a right circular

cylindrical tank, that is 8 feet in

diameter and 9 feet tall, if it is

emptied at a point 1 foot above the

top of the tank?

A. 49,421 ft-lb

B. 52,316 ft-lb

C. 54,448 ft-lb

D. 56,305 ft-lb

498. A 60-m cable that weighs 4 kg/m has

a 500-kg weight attached at the end.

How much work is done in winding

up the last 20m of the cable?

A. 9,866 kg-m

B. 10,800 kg-m

C. 12,500 kg-m

D. 15,456 kg-m

499. A uniform chain that weighs 0.50 kg

per meter has a leaky 15-liter bucket

attached to it. If the bucket is full of

liquid when 30 meters of chain is out

and half-full when no chain is out,

how much work is done in winding

the chain? Assume that the liquid

leaks out at a uniform rate and

weighs 1 kg per liter.

A. 356.2 kg-m

B. 458.2 kg-m

C. 562.5 kg-m

D. 689.3 kg-m

500. The velocity of a body is given by

, where the velocity

is given in meters per second and is

given in seconds. The distance

covered in meters between

and second is close to:

A. 2

B. -5

C. 5

D. -2

501. If equals are added to equals, the

sum is equal.

A. theorem

B. postulate

C. axiom

D. corollary

502. Any number multiplied by ________

equally unity.

A. infinity

B. itself

C. its reciprocal

D. zero

503. If every element of a column (or

row) of a square matrix is multiplied

by m, the determinant of the matrix

will be:

A. unchanged

B. multiplied by m

C. it depends

D. none of these

504. In probability theory, the set of

possible outcomes of an experiment

is termed as:

A. a sample space

B. a set of random events

C. a set of random variables

D. a fuzzy set

505. Which of the following is not a

property of probability:

A. If events and are mutually

exclusive, then the probability that

both events can happen is zero.

B. The probability that an event can

happen is always positive and is less

than one or equal to one.

C. If is an event which cannot

occur in the sample space, the

probability of is zero.

D. If events & are mutually

exclusive, then

506. An angle greater that a straight angle

and less than two straight angles is

called:

A. right angle

B. obtuse angle

C. reflex angle

D. acute angle

507. A line segment joining two point in a

circle is called:

A. arc

B. tangent

C. sector

D. chord

508. All circles having the same center

but with unequal radii are called:

A. encircle

B. tangent circles

C. concyclic

D. concentric circles

509. A triangle having three sides equal is

called:

A. equilateral triangle

B. scalene triangle

C. isosceles triangle

510. In a regular polygon, the

perpendicular line drawn from the

center of the inscribed circle to any

of the sides is called:

A. radius

B. altitude

C. median

D. apothem

511. A quadrilateral with two and only

two sides of which are parallel, is

called:

A. parallelogram

B. trapezoid

C. quadrilateral

D. rhombus

512. A polygon with fifteen sides is

called:

A. dodecagon

B. decagon

C. pentedecagon

D. nonagon

513. A rectangle with equal sides is

called:

A. rhombus

B. trapezoid

C. square

D. parallelogram

514. The sum of the sides of a polygon is

termed as:

A. circumference

B. altitude

C. apothem

D. perimeter

515. A line that meets a plane but not

perpendicular to it, in relation to the

plane, is:

A. parallel

B. collinear

C. coplanar

D. oblique

516. A quadrilateral whose opposite sides

are equal is generally termed as:

A. a square

B. a rectangle

C. a rhombus

D. a parallelogram

517. A part of a line included between

two points on the line is called:

A. a tangent

B. a secant

C. a sector

D. a segment

518. The section of the sphere cut by a

plane through its center is termed as:

A. small circle

B. incircle

C. big circle

D. great circle

519. Line that pass through a common

point are called:

A. collinear

B. coplanar

C. concurrent

D. congruent

520. Point which lie on the same plane,

are called:

A. collinear

B. coplanar

C. concurrent

D. congruent

521. In two intersecting lines, the angles

opposite to each other are termed as:

A. opposite angles

B. vertical angles

C. horizontal angle

D. inscribed angle

522. A normal to a given plane is:

A. perpendicular to the plane

B. lying on the plane

C. parallel to the plane

D. oblique to the plane

523. The chord passing through the focus

of the parabola and perpendicular to

its axis is termed as:

A. directrix

B. translated axis

C. latus rectum

D. axis

524. The locus of the point which move

so the sum of its distances between

two fixed points is known as:

A. a parabola

B. a circle

C. an ellipse

D. a hyperbola

525. A tangent to a conic is a line

A. which is parallel to the normal

B. which touches the conic at only

one point

C. which passes inside the conic

D. all of the above

526. The locus of a point that move so

that its distance from a fixed point

and a fixed line is always equal, is

known as:

A. a parabola

B. a circle

C. an ellipse

D. a hyperbola

527. The locus of a point, which moves so

that it is always equidistant from a

fixed point, is known as:

A. a parabola

B. a circle

C. an ellipse

D. a hyperbola

528. In polar coordinate system, the polar

angle is positive when:

A. measured clockwise

B. measured counterclockwise

C. measured at the terminal side of

D. none of these

529. The plane rectangular coordinate

system is divided into four parts

which are known as:

A. coordinates

B. octants

C. quadrants

D. axis

530. The rectangular coordinate system in

space is divided into eight

compartments, which are known as:

A. quadrants

B. octants

C. axis

D. coordinates

531. A conic section whose eccentricity is

less than one (1) is known as;

A. a parabola

B. a circle

C. an ellipse

D. a hyperbola

532. A conic section whose eccentricity is

equal to one (1) is known as:

A. a parabola

B. a circle

C. an ellipse

D. a hyperbola

533. In polar coordinate system, the

distance from a point to the pole is

known as:

A. polar angle

B. -coordinate

C. radius vector

D. -coorcinate

534. The curve represented by the

equation is:

A. a parabola

B. a line

C. an ellipse

D. a circle

535. When two lines are perpendicular,

the slope of one is:

A. equal to the other

B. equal to the negative of the other

C. equal to the reciprocal of the other

D. equal to the negative reciprocal

of the other

536. The axis of the hyperbola, which is

parallel to its directrices, is known

as:

A. conjugate axis

B. transverse axis

C. major axis

D. minor axis

537. The axis of the hyperbola through

the foci is known as:

A. conjugate axis

B. transverse axis

C. major axis

D. minor axis

538. A polygon is _____ if no side, when

extended, will pass through the

interior of the polygon.

A. convex

B. equilateral

C. isopometric

D. congruent

539. Which of the following statements is

correct?

A. all equilateral triangles are

similar

B. all right-angled triangles are

similar

C. all isosceles triangle are similar

D. all rectangles are similar

540. The volume of any solid of

revolution is equal to the generating

area times the circumference of the

circle described by the centroid of

the area. This is commonly known

as:

A. First proposition of Pappus

B. Second proposition of Pappus

C. Cavalier’s Principle

D. Simpson’s Rule

541. If the product of the slopes of any

two straight lines is negative 1, one

of these lines are said to be:

A. parallel

B. skew

C. perpendicular

D. non-intersecting

542. When two planes intersect with each

other, the amount of divergence

between the two planes is expressed

to be measuring the:

A. dihedral angle

B. plane angle

C. polyhedral angle

D. reflex angle

543. The angle which the line of sight to

the object, makes with the

horizontal, which is above the eye of

the observer is called:

A. angle of depression

B. angle of elevation

C. acute angle

D. bearing

544. The median of a triangle is the line

connecting a vertex and the midpoint

of the opposite side. For a given

triangle, these medians intersect at a

point which is called the:

A. orthocenter

B. incenter

C. circumcenter

D. centroid

545. The altitudes of the side of a triangle

intersect at the point known as:

A. orthocenter

B. circumcenter

C. centroid

D. incenter

546. The angular bisector of the sides of a

triangle intersects at the point which

is known as:

A. orthocenter

B. circumcenter

C. centroid

D. incenter

547. The arc length equal to the radius of

the circle is called:

A. 1 radian

B. 1 quarter circle

C. radian

D. 1 grad

548. A five pointed star is also known as:

A. pentagon

B. pentatron

C. pentagram

D. quintagon

549. The area bounded by two concentric

circles is called:

A. ring

B. disk

C. annulus

D. sector

550. The line passing through the focus

and perpendicular to the directrix of

a parabola is called:

A. latus rectum

B. axis of parabola

C. tangent line

D. secant line

551. The altitudes of the sides of a

triangle intersect at the point known

as:

A. orthocenter

B. circumcenter

C. centroid

D. incenter

552. The length of time during which the

property may be operated at a profit

is called:

A. life

B. length of time

C. physical life

D. economic life

553. What is the graph of the equation

?

A. circle

B. ellipse

C. parabola

D. hyperbola

554. Prisms are classified according to

their _____.

A. diagonals

B. sides

C. vertices

D. bases

555. It is a polyhedron of which two faces

are equal polygons in parallel planes

and the other faces are

parallelograms

A. tetrahedron

B. prism

C. frustum

D. prismatoid

556. In Plain Geometry, two circular arcs

that together make up a full circle are

called:

A. coterminal arcs

B. conjugate arcs

C. half arcs

D. congruent arcs

557. It represents the distance of a point

from the -axis.

A. ordinate

B. coordinate

C. abscissa

D. polar distance

558. Polygons are classified according to

the number of:

A. vertices

B. sides

C. diagonals

D. angles

559. In a conic section, if the eccentricity

> 1, the locus is;

A. an ellipse

B. a hyperbola

C. a parabola

D. a circle

560. The family of curves which intersect

a given family of curves at an angle

less than 90° are called:

A. orthogonal trajectories

B. intersecting curves

C. isogonal trajectories

D. acute angle

561. A line perpendicular to the -axis

has a slope of:

A. zero

B. unity

C. infinity

D. none of these

562. The locus of points generated when a

circle is made to roll externally along

the circumference of another circle.

A. Cissoid of circles

B. Folium of Descartes

C. Epicycloid

D. Cardioid

563. It is the surface generated by moving

a straight line (called the generator)

which is always parallel to a fixed

line and which always intersect a

fixed plane curve (called the

directrix) is:

A. cylindrical surface

B. locus of a point

C. spherical surface

D. paraboloid

564. How many faces have an

icosahedron?

A. 16

B. 18

C. 20

D. 22

565. Each of the faces of a regular

hexahedron is a:

A. square

B. triangle

C. hexagon

D. circle

566. An arc length, which is equal to the

radius of the circle, is called:

A. 1 degree

B. 2 radians

C. 1 radian

D. 1 radians

567. Polygons with all interior angles less

than 180° are called:

A. concave polygon

B. convex polygon

C. acute polygon

D. supplemental polygon

568. To cut a right circular cone in order

to reveal a parabola, it must be cut

A. perpendicular to the axis of

symmetry

B. at any acute angle to the axis of

symmetry

C. parallel to an element of a cone

and intersecting the axis of

symmetry

D. parallel to the axis of symmetry

569. To find the angles of a triangle,

given only the lengths of the sides,

one would use

A. the law of cosines

B. the law of tangents

C. the law of sines

D. the inverse square law

570. In finding the distance between two

points and , the

most direct procedure is to use:


B. the slope of the line

C. the translation of axes

D. the Pythagorean Theorem

571. In finding the distance between two

points and , the

most direct procedure is to use:


B. the slope of the line

C. the translation of axes

D. the Pythagorean Theorem

572. The area of a region bounded by two

concentric circles is called:

A. washer

B. ring

C. annulus

D. circular disk

573. It can be defined as the set of all

points in the plane the sum of whose

distance from two fixed points is a

constant.

A. circle

B. ellipse

C. hyperbola

D. parabola

574. If the equation is unchanged by the

substitution of – for , its curve is

symmetric with respect to the:

A. -axis

B. -axis

C. origin

D. line 45° with the axis

575. A line which is perpendicular to the

-axis has a slope equal to:

A. zero

B. either

C. one

D. infinity

576. In an ellipse, a chord which contains

a focus and is in a line perpendicular

to the major axis is a:

A. latus rectum

B. minor

C. focal width

D. conjugate axis

577. In general triangles the expression

/ / / is called:

A. Euler’s formula

B. law of cosines

C. law of sines

D. Pythagorean theorem

578. What type of curve is generated by a

point which moves in uniform

circular motion about an axis, while

travelling at a constant speed, ,

parallel to the axis?

A. helix

B. spiral of Archimedes

C. hypocycloid

D. cycloid

579. An angle more than radian but less

than radians is:

A. straight angle

B. obtuse angle

C. related angle

D. reflex angle

580. The sum of the sides of a polygon:

A. perimeter

B. square

C. hexagon

D. circumference

581. A plane closed curve, all points of

which are the same distance from a

point within, called the center:

A. arc

B. circle

C. radius

D. chord

582. One-fourth of a great circle:

A. cone

B. quadrant

C. circle

D. sphere

583. Points that lie in the same plane:

A. coplanar

B. oblique

C. collinear

D. parallel

584. The study of the property of figures

of three dimensions;

A. physics

B. plane geometry

C. solid geometry

D. trigonometry

585. The volume of a circular cylinder is

equal to the product of its base and

altitude.

A. postulate

B. theorem

C. corollary

D. axiom

586. A point on the curve where the second

derivative of a function is equal to zero is called:

A. maxima

B. minima

C. point of inflection

D. point of intersection

587. The point on the curve where the first

derivative of a function is zero and the

second derivative is positive is called:

A. maxima

B. minima

C. point of inflection

D. point of intersection

588. At the minimum point, the slope of the

tangent line is:

A. negative

B. infinity

C. positive

D. zero

589. At the point of inflection where ,

A. is not equal to zero

B.

C.

D.

590. Point of the derivatives, which do not

exist ( and so equals zero) is called:

A. stationary point

B. maximum points

C. maximum and minimum point

D. minimum point

591. If the second derivative of the equation

of a curve is equal to the negative of the

equation of that same curve, the curve

is:

A. a cissoid

B. a paraboloid

C. a sinusoid

D. an exponential


<PHYSICS>


GILLESANIA>


ADRIAN C.

592. It is defined as the motion of a rigid

body in which a straight line passing

through any two of its particles

always remains parallel to its initial

position.

A. translation

B. rotation

C. plane motion

D. kinetics

593. Which of the following is not a

vector quantity?

A. mass

B. torque

C. displacement

D. velocity

594. The product of force and the time

during which it acts is known as:

A. impulse

B. momentum

C. work

D. impact

595. The property of the body which

measures its resistance to changes in

motion.

A. acceleration

B. weight

C. mass

D. rigidity

596. The study of motion without

reference to the forces which causes

motion is known as:

A. kinetics

B. dynamics

C. statics

D. kinematics

597. A branch of physical science that

deals with state of rest or motion of

bodies under the action of forces is

known as:

A. mechanics

B. kinetics

C. kinematics

D. statics

598. In physics, work is defined in terms

of the force acting through a

distance. The rate at which the work

is done is called:

A. force

B. energy

C. power

D. momentum

599. The point through which the

resultant of the disturbed gravity

force passes regardless of the

orientation of the body in space is

called:

A. center of inertia

B. center of gravity

C. center of attraction

D. moment of inertia

600. The specific gravity of the substance

is the ratio of the density of the

substance to the density of water.

Another term for specific gravity is:

A. specific weight

B. unit weight

C. relative density

D. density

601. The momentum of a moving object

is the product of its mass ( ) and

velocity ( ). Newton’s Second Law

of Motion says that the rate of

change of momentum with respect to

time is:

A. power

B. energy

C. momentum

D. force

602. The acceleration due to gravity in the

English System or ft/s2 is:

A. 20.2

B. 32.2

C. 15.2

D. 62.4

603. Ivory soap floats in water because:

A. all matter has mass

B. the density of ivory soap is unity

C. the specific gravity of ivory soap

is greater than that of water

D. the specific gravity of ivory

soap is less than that of water

604. One (1) gram of ice at 0°C is placed

on a container containing 2,000,000

cu. m. of water at 0°C. Assuming no

heat loss, what will happen?

A. ice will become water

B. some part of the ice will not

change

C. the volume of the ice will not

change

D. all of the above

605. When two waves of the same

frequency, speed and amplitude

travelling in opposite directions

superimposed,

A. destructive interference always

results

B. constructive interference always

results

C. standing waves are produced

D. the phase difference is always

zero

606. Any two points along a steamline in

an ideal fluid in steady flow, the sum

of the pressure, the potential energy

per unit volume, and the kinetic

energy per unit volume has the same

value. This concept is known as the:

A. Pascal’s theorem

B. Bernoulli’s energy theorem

C. Fluid theory

D. Hydraulic theorem

607. Whenever a net force acts on a body,

it produces an acceleration in the

direction of the resultant force, an

acceleration which is directly

proportional to the resultant force

and inversely proportional to the

mass of the body. This theory is

popularly known as:

A. Newton’s first law of motion

B. Newton’s second law of motion

C. Faraday’s law of forces

D. Hooke’s law of equilibrium

608. Kinematic viscosity in SI derived

unit is described as:

A. watt per meter Kelvin

B. sq. m. per second

C. Pascal-second

D. Newton per meter

609. In a cantilever beam with a

concentrated load at the free end, the

moment is:

A. constant along the beam

B. maximum at the wall

C. ¼ maximum halfway out on the

beam

D. maximum at the free end

610. What is the name of the vector that

represents the sum of two vectors?

A. scalar

B. tangent

C. tensor

D. resultant

611. The loss of weight of a body

submerged in a fluid is:

A. proportional to the weight of the

body

B. proportional to the depth of

submergence

C. equal to the weight of the fluid

displaced

D. independent of the volume of the

body

612. A leak from a faucet comes out in

separate drops. Which of the

following is the main cause of this

phenomenon?

A. gravity

B. air resistance

C. viscosity of the fluid

D. surface tension

613. Inelastic collision in which the total

kinetic energy after collision is

_____ before collision.

A. equal to zero

B. equal

C. less than

D. greater than

614. The property by virtue of which a

body tends to return to its original

size or shape after a deformation and

when the deforming forces have

been removed.

A. elasticity

B. malleability

C. ductility

D. plasticity

615. A flowerpot falls off the edge of a

fifth-floor window. Just as it passes

the third-floor window someone

accidentally drops a glass of water

from the window. Which of the

following is true?

A. The flowerpot hits the ground at

the same time as the glass.

B. The glass hits the ground before

the flowerpot.

C. The flowerpot hits the ground

first and with a higher speed than

the glass.

D. The flowerpot and the glass hit

the ground at the same instant.

616. One Joule of work is done by a force

of one Newton acting through a

distance of:

A. one centimeter

B. one inch

C. one meter

D. one foot

617. Kinetic energy equals:

A. ½ velocity

B. mass velocity

C. mass acceleration

D. ½ mass velocity2

618. In an ideal gas where = pressure,

= volume, and = absolute

temperature in degrees Kelvin,

which of the following is constant?

A.

B.

C.

D.

619. The path of the projectile is:

A. a parabola

B. an ellipse

C. a part of a circle

D. a hyperbola

620. One mole of gas at standard

temperature and pressure (STP)

conditions occupies a volume equal

to:

A. 22.4 liters

B. 9.81 liters

C. 332 liters

D. 2274.5 liters

621. “Equal volume of all gases under the

same conditions of temperature and

pressure contain the same number of

molecules”. This hypothesis is

popularly known as:

A. Dalton’s hypothesis

B. Avogadro’s hypothesis

C. Debye-Sear’s hypothesis

D. Compton’s hypothesis

622. The ratio of the uniform triaxial

stresses, to the change in volume at

equal stress in all directions is:

A. modulus of flexure

B. modulus of rapture

C. bulk modulus of elasticity

D. coefficient of restitution

623. According to the laws of Johannes

Kepler, “The orbit of satellite is an

ellipse, the radius vector sweeps

equal areas in equal intervals of time

and the square of the periods of

revolution with respect to both the

satellite and planet is proportional to

the cubes of their mean distance

from each other.” The shape of the

ellipse depends upon its:

A. eccentricity

B. lengths of latera recta

C. apogee and perigee

D. ascending and descending nodes

624. This implies the resistance to shock

or difficulty of breaking and express

the work per unit volume required to

fracture a material.

A. toughness

B. malleability

C. hardness

D. ductility

625. The reciprocal of bulk modulus of

elasticity of any fluid is called:

A. compressibility

B. volume strain

C. volume stress

D. shape factor

626. “The resultant of the external force

applied to an object composed of a

system of particles, is equal to the

vector summation of the effective

forces acting on all particles”. This

principle is known as:

A. Archimedes’s principle

B. Bernoulli’s principle

C. D’Alembert’s principle

D. Gauss-Jordan principle

627. Calorie is the amount of heat

required to increase the temperature

of _____ of water by one degree

centigrade.

A. 1 kg

B. 1 lb

C. 1 mg

D. 1 gram

628. It describes the luminous flux

incidence per unit area and is

expressed in lumens per square

meter.

A. luminous intensity

B. illuminance

C. radiance

D. luminance

629. The moment of inertia of a plane

figure:

A. is zero at the centroidal axis

B. increase as the distance of the

axis moves farther from the

centroid

C. decrease as the distance of the

axis moves farther from the centroid

D. is maximum at the centroidal axis

630. The distance that the top surface is

displaced in the direction of the force

divided by the thickness of the body

is known as:

A. longitudinal strain

B. shear strain

C. volume strain

D. linear strain

631. To maximize the horizontal range of

the projectile, which of the following

applies?

A. maximize the angle of elevation

B. maximize velocity

C. maximize the angle of elevation

and velocity

D. the tangent function of the

angle of trajectory must be equal

to one

632. According to this law, “The force

between two charges varies directly

as the magnitude of each charge and

inversely as the square of the

distance between them.

A. law of universal gravitation

B. Newton’s law

C. Coulomb’s law

D. inverse square law

633. Formation of bubbles in a low-

pressure area in a centrifugal pump

and later their sudden collapse, is

called:

A. compression

B. corrosion

C. explosion

D. cavitation

644. The hardness of steel may be

increased by heating to

approximatelyv1500°F and

quenching in oil or water if

A. the carbon content is above 3.0%

B. the carbon content is from 0.2%

to 2.0%

C. the carbon content is below 0.2%

D. the steel has been hot rolled

instead of cast

645. Galvanized iron is a term referring to

iron coated with:

A. magnesium

B. aluminum

C. zinc

D. tin

646. A process of welding metals in

molten or in vaporous state without

application of mechanical pressure or

blow. Such welding may be

accomplished by the oxyacetylene or

by hydrogen flame or by electric arc.

It is called:

A. fusion welding

B. TIG welding

C. MIG welding

D. cold welding

647. A chemical method of feed water

treatment wherein water is passed

through a bed of sodium zeolite

Nesub2Z which reacts with calcium

and magnesium salts:

A. demineralization process

B. ion exchange treatment

C. lime soda treatment

D. thermal treatment

648. Used as a guide to selecting the most

efficient centrifugal pump:

A. specific speed

B. impeller type

C. Bernoulli’s equation

D. overall efficiency

649. The impulse and momentum

principle is mostly useful for

problems involving;

A. velocity, acceleration, and time

B. force, acceleration, and time

C. force, velocity, and time

D. force, velocity, and acceleration

650. Which of the following is not true

regarding the Blasius boundary layer

solution/

A. It permits one to calculate the skin

friction on a flat plate

B. It is valid for laminar flow

C. It is an approximate solution

D. It is valid only for potential flow

651. The greatest unit pressure the soil

can continuously withstand:

A. point of raptue

B. bearing strength

C. ultimate strength

D. yield point

652. Heat transmission carried by the

movement of heated fluids away

from a hot body, as in the heating of

water by a hot surface:

A. radiation

B. convection

C. conduction

D. absorption

653. The type of cooler extensively used

for medium and large size diesel

engines:

A. radiation cooler

B. shell and tube cooler

C. disk cooler

D. plate cooler

654. A closed vessel intended for use in

heating water or for application of

heat to generate steam or other vapor

to be used externally to itself is

called:

A. unfired pressure vessel

B. steam generator

C. boiler or steam generator

D. boiler

655. The sum of the three types of energy

at any point in the system is called:

A. Bernoulli’s theorem

B. enthalpy

C. internal energy

D. pressure heads

656. In energy transformation process in

which the resultant condition lacks

the driving potential needed to

reverse the process, the measure of

this loss is expressed as:

A. enthalpy increase of the system

B. specific bent ratio of the moment

C. entropy increase of the system

D. entropy decrease of the system

657. The system is safe to be in

thermodynamics equilibrium:

A. if it has no tendency to undergo

further chemical reaction

B. when there is no tendency

towards spontaneous change

C. when the system is not

accelerating

D. when all its parts are at the same

temperature

658. An instrument used for measuring

high temperature gas

A. plenometer

B. manometer

C. anemometer

D. pyrometer

659. The power output of the engine is

increased through:

A. turbo-charging

B. scavenging

C. all of these

D. super-charging

660. The equilibrium temperature that a

regular thermometer measures if

exposed to atmospheric air is:

A. dry bulb temperature

B. °C

C. wet bulb temperature

D. dew point

661. On the hoist or load block or some

equality visible space of every hoist

designed to lift its load vertically

shall be legibly marked:

A. its electrical voltage

B. its brand and model

C. its rated load capacity

D. its motor hp or kW

662. The hardness of water is given in

ppm (parts per million, i.e., pounds

per million pounds of water). This

hardness is

A. the total number of pounds of

dissolved solids in the water per

million pounds of water

B. the total number of pounds of

calcium and magnesium

bicarbonate in the water.

C. the total number of pounds of

sodium bicarbonate in the water per

million pounds of water.

D. the total number of pounds of salt

(sodium chloride) in the water per

million pounds of water

663. Momentum = Force _____

A. time

B. velocity

C. velocity2

D. ½ velocity

664. An instrument used for measuring

specific gravity of fluids:

A. hygrometer

B. flowmeter

C. psycrometer

D. hydrometer


<MECHANICS>


GILLESANIA>


ADRIAN C.

665. A 10-lbm object is acted upon by a

4-lb force. What is the acceleration in

ft/min2?

A. 8.0 10 to the 4th power ft/min

2

B. 9.2 10 to the 4th power ft/min

2

C. 7.8 10 to the 4th power ft/min

2

D. 4.637 10 to the 4th

power

ft/min2

666. What horizontal force P can be

applied to a 100-kg block in a level

surface with coefficient of friction of

0.2, that will cause an acceleration of

2.50m/s2?

A. 343.5 N

B. 224.5 N

C. 53.8 N

D. 446.2 N

667. A skier wishes to build a rope tow to

pull herself up a ski hill that is

inclined at 15° with the horizontal.

Calculate the tension needed to give

the skier’s 54-kg body an

acceleration of 1.2 m/s2. Neglect

friction.

A. 202 N

B. 403 N

C. 106 N

D. 304 N

668. A pick-up truck is travelling forward

at 25 m/s. The truck bed is located

with boxes, whose coefficient of

friction with the bed is 0.4. What is

the shortest time that the truck can be

brought to a stop such that the boxes

do not shift?

A. 4.75 sec

B. 2.35 sec

C. 5.45 sec

D. 6.37 sec

669. A 40-kg block is resting on an

inclined plane making an angle 20°

from the horizontal. If the coefficient

of friction is 0.60, determine the

force parallel to the incline that must

be applied to cause impending

motion down the plane.

A. 77

B. 82

C. 72

D. 87

670. A 50-kilogram block of wood rest on

top of the smooth plane whose length

is 3 m, and whose altitude is 0.8 m.

How long will it take for the block to

slide to the bottom of the plane when

released?

A. 1.51 seconds

B. 2.41 seconds

C. 2.51 seconds

D. 2.14 seconds

671. A body weighing 40 lbs. starts from

rest and slides down a plane at an

angle of 30° with the horizontal for

which the coefficient of friction

µ=0.3. How far will it move during

the third second?

A. 19.99 ft

B. 39.63 ft

C. 18.33 ft

D. 34.81 ft

672. A car and its load weighs 27 kN and

the center of gravity is 600 mm from

the ground and midway between the

front and rear wheel which are 3 m

apart. The car is brought to rest from

a speed of 54 kph in 5 seconds by

means of the brakes. Compute the

normal force on each of the front

wheels of the car.

A. 7.576 kN

B. 9.541 kN

C. 5.478 kN

D. 6 kN

673. An elevator weighing 2,000 lb

attains an upward velocity of 16 fps

in 4 sec with uniform acceleration.

What is the tension in the supporting

cables?

A. 1,950 lb

B. 2,150 lb

C. 2,495 lb

D. 2,250 lb

674. A block weighing 200 N rests on a

plane inclined upwards to the right at

a slope of 4 vertical to 3 horizontal.

The block is connected to a cable

initially parallel to the plane, passing

through the pulley and connected to

another block weighing 100 N

moving vertically downward. The

coefficient of kinetic friction

between the 200 N block and the

inclined plane is 0.10. Which of the

following most nearly gives the

acceleration of the system?

A.

B.

C.

D.

675. A car travels on the horizontal

unbanked circular track of radius .

Coefficient of friction between the

tires and track is 0.3. If the car’s

velocity is 10 m/s, what is the

smallest radius it may travel without

skidding?

A. 50 m

B. 60 m

C. 15 m

D. 34 m

676. If a car travels at 15 m/s and the

track is banked 5°, what is the

smallest radius it can travel so that

the friction will not be necessary to

resist skidding?

A. 262.16 m

B. 651.23 m

C. 278.14 m

D. 214.74 m

677. A vertical bar of length with a

mass of 40 kg is rotated vertically

about one end at 40 rpm. Find the

length of the bar if it makes an angle

45° with the vertical?

A. 1.58 m

B. 2.38 m

C. 3.26 m

D. 1.86 m

678. The seats of a carousel are attached

to a vertical rotating shaft by a

flexible cable 8 m long. The seats

have a mass of 75 kg. What is the

maximum angle of tilt for the seats if

the carousel operates at 12 rpm?

A. 30°

B. 35°

C. 45°

D. 39°

679. A highway curve is superelevated at

7°. Find the radius at the end of the

cable that will break if there is no

lateral pressure on the wheels of a

car at a speed of 40 mph.

A. 247.4 m

B. 265.6 m

C. 229.6 m

D. 285.3 m

680. A 2-N weight is swung in a vertical

circle of 1-m radius at the end of a

cable that will break if the tension

exceeds 500 N. Find the angular

velocity of the weight when the cable

breaks.

A. 49.4 rad/s

B. 37.2 rad/s

C. 24.9 rad/s

D. 58.3 rad/s

681. Traffic travels at 65 mi/hr around a

banked highway curve with a radius

of 3000 ft. What banking angle is

necessary such that friction will not

be required to resist the centrifugal

force?

A. 5.4°

B. 18°

C. 3.2°

D. 2.5°

682. A concrete highway curve with a

radius of 500 feet is banked to give a

lateral pressure equivalent to

. For what coefficient of

friction will skidding impend for a

speed of 60 mph?

A. < 0.360

B. < 0.310

C. > 0.310

D. > 0.360

683. A 3500 lbf car is towing a 500 lbf

trailer. The coefficient of friction

between all tires and the road is 0.80.

How fast can the car and the trailer

travel around an unbanked curve of

radius 0.12 mile without either the

car or trailer skidding?

A. 87 mph

B. 72 mph

C. 26 mph

D. 55 mph

684. A cast-iron governor ball 3 inches in

diameter has its center 18 inches

from the point of support. Neglecting

the weight of the arm itself, find the

tension in the arm if the angle with

the vertical axis is 60°.

A. 7.63 lb

B. 6.36 lb

C. 7.56 lb

D. 7.36 lb

685. An object is placed 3 feet from the

center of a horizontally rotating

platform. The coefficient of friction

is 0.3. The object will begin to slide

off when the platform speed is

nearest to:

A. 17 rpm

B. 12 rpm

C. 22 rpm

D. 26 rpm

686. A force of 200 lbf acts on a block at

an angle of 28° with respect to the

horizontal. The block is pushed 2

feet horizontally. What is the work

done by this force?

A. 320 J

B. 540 J

C. 480 J

D. 215 J

687. A 10-kg block is raised vertically 3

meters. What is the change in

potential energy. Answer in SI units

closest to:

A. 350N-m

B. 294 J

C. 350 kg-m2/s

2

D. 320 J

688. At her highest point, a girl on the

swing is 7 feet above the ground, and

at her lowest point, she is 3 feet

above the ground. What is her

maximum velocity?

A. 10 fps

B. 12 fps

C. 14 fps

D. 16 fps

689. An automobile has a power output of

1 hp. When it pulls a cart with a

force of 300 N, what is the cart’s

velocity?

A. 249 m/s

B. 24.9 m/s

C. 2.49 m/s

D. 0.249 m/s

690. The weight of a mass of 10

kilograms at a location where g=9.77m/s2 is:

A. 79.7 N

B. 77.9 N

C. 97.7 N

D. 977 N

691. What is the resultant velocity of a

point of -component ,

and -component at

time ?

A. 63.1326

B. 62.1326

C. 64.1326

D. 74.1326

692. A boat has a speed of 8 mph in still

water attempts to go directly across a

river with a current of 3 mph. What

is the effective speed of the boat?

A. 8.35 mph

B. 8.54 mph

C. 7.42 mph

D. 6.33 mph

693. A ship moving North at 10 mph. A

passenger walks Southeast across the

deck at 5 mph. In what direction and

how fast is the man moving, relative

to the earth’s surface.

A. N 28°40’W; 7.37 mph

B. N 61°20’E; 7.37 mph

C. N 61°20’W; 7.37 mph

D. N 28°40’E; 7.37 mph

694. A man wishes to cross due west on a

river which is flowing due north at

the rate of 3 mph. if he can row 12

mph in still water, what direction

should he take to cross the river?

A. S 14.47°W

B. S 75.52°W

C. S 81.36°W

D. S 84.36°W

695. A plane is headed due east with air

speed of 240 kph. If a wind of 40kph

is blowing from the north, find the

ground speed of the plane.

A. 243 kph

B. 423 kph

C. 200 kph

D. 240 kph

696. Three forces 20N, 30N, and 40N are

in equilibrium. Find the angle

between the 30-N and 40-N forces.

A. 30°15’25’’

B. 28.96°

C. 40°

D. 25.97°

697. A 10-kg weight is suspended by a

rope from a ceiling. If a horizontal

force of 5.80 kg is applied to the

weight, the rope will make an angle

with the vertical equal to:

A. 60°

B. 30°

C. 45°

D. 75°

698. A 100kN block slides down a plane

inclined at an angle of 30° with the

horizontal. Neglecting friction, find

the force that causes the block to

slide.

A. 86.6 kN

B. 80 kN

C. 20 kN

D. 50 kN

699. What tension must be applied at the

ends of a flexible wire cable

supporting a load of 0.5 kg per

horizontal meter in a span of 100 m

if the sag is to be limited to 1.25 m?

A. 423.42 kg

B. 584.23 kg

C. 500.62 kg

D. 623.24 kg

700. The allowable spacing of towers to

carry an aluminum cable weighing

0.03 kg per horizontal meter if the

maximum tension at the lowest point

is not to exceed 1150 kg at sag of

0.50 m is:

A. 248 m

B. 390 m

C. 408 m

D. 422 m

701. A wooden plank meters long has

one end leaning on top of a vertical

wall 1.5 m high and the other end

resting on a horizontal ground.

Neglecting friction, find if a force

(parallel to the plank) of 100 N is

needed to pull a 400 N block up the

plank.

A. 6 m

B. 5 m

C. 4 m

D. 3 m

702. A block of wood is resting on a level

surface. If the coefficient of friction

between the block and the surface is

0.30, how much can the plane be

inclined without causing the block to

slide down?

A. 16.7°

B. 30.2°

C. 21.2°

D. 33.3°

703. A 500-kg block is resting on a 30°

inclined plane with a µ=0.3 Find the

required force acting horizontally

that will prevent the block from

sliding.

A. 1020 N

B. 1160 N

C. 4236 N

D. 5205 N

704. A 500-kg block is resting on a 30°

inclined plane with a µ=0.3 Find the

required force acting horizontally

that will start the block to block up

the plane.

A. 4236 N

B. 1160 N

C. 5205 N

D. 2570 N

705. What is the acceleration of the body

that increases in velocity from 20

m/s to 40 m/s in 3 seconds? Answer

in S.I. units.

A. 8 m/s2

B. 6.67 m/s2

C. 5 m/s2

D. 7 m/s2

706. From a speed of 75 kph, a car

decelerates at the rate of 500 m/min2

along a straight path. Howw far in

meters, will it travel in 45 sec?

A. 795

B. 791

C. 797

D. 793

707. With a starting speed of 30 kph at a

point , a car accelerates uniformly.

After 18 minutes, it reaches point ,

21 km from . Find the acceleration

of the car in m/s2.

A. 0.126 m/s2

B. 0.0562 m/s2

C. 0.0206 m/s2

D. 3.42 m/s2

708. A train upon passing point at a

speed of 72 kph accelerates at 0.75

m/s2 for one minute along a straight

path then decelerates at 1.0 m/s2.

How far in kilometers from point

will it be in 2 minutes after passing

point .

A. 4.95

B. 4.75

C. 4.85

D. 4.65

709. A car starting from rest moves with a

constant acceleration of 10 km/hr2

for 1 hour, then decelerates at a

constant -5 km/hr2 until it comes to a

stop. How far has it travelled?

A. 10 km

B. 20 km

C. 12 km

D. 15 km

710. The velocity of an automobile

starting from rest is given by

/ / ft./sec.

Determine its acceleration after an

interval of 10 seconds (in ft/sec2).

A. 2.10

B. 1.71

C. 2.25

D. 2.75

711. A train running at 60 kph decelerated

at 8 m/min2 for 14 minutes. Find the

distance traveled, in kilometers

within this period.

A. 12.2

B. 13.2

C. 13.8

D. 12.8

712. An automobile accelerates at a

constant rate of 15 mi/hr to 45 mi/hr

in 15 seconds, while travelling in a

straight line. What is the average

acceleration?

A. 2 ft/s2

B. 2.39 ft/s2

C. 2.12 ft/s2

D. 2.93 ft/s2

713. A car was travelling at a speed of 50

mph. The driver saw a road block 80

m ahead and stepped on the brake

causing the car to decelerate

uniformly at 10 m/s2. Find the

distance from the roadblock to the

point where the car stopped. Assume

perception reaction time is 2

seconds.

A. 12.48 m

B. 6.25 m

C. 10.28 m

D. 8.63 m

714. A man driving his car at 45 mph

suddenly sees an object in the road

60 feet ahead. What constant

deceleration is required to stop the

car in this distance?

A. -36.3 ft/s2

B. -45.2 ft/s2

C. -33.4 ft/s2

D. -42.3 ft/s2

715. Determine the outside diameter of

hallow steel tube that will carry a

tensile load of 500 kN at a stress of

140 MPa. Assume the wall thickness

to be one-tenth of the outside

diameter.

A. 123 mm

B. 113 mm

C. 103 mm

D. 93 mm

716. A force of 10 Newtons is applied to

one end of a 10 inches diameter

circular rod. Calculate the stress.

A. 0.20 kPa

B. 0.05 kPa

C. 0.10 kPa

D. 0.15 kPa

717. What force is required to punch a 20-

mm diameter hole through a 10-mm

thick plate. The ultimate strength of

the plate material is 450 MPa.

A. 241 kN

B. 283 kN

C. 386 kN

D. 252 kN

718. A steel pipe 1.5m in diameter is

required to carry am internal

pressure of 750 kPa. If the allowable

tensile stress of steel is 140 MPa,

determine the required thickness of

the pipe in mm.

A. 4.56

B. 5.12

C. 4.25

D. 4.01

719. A spherical pressure vessel 400-mm

in diameter has a uniform thickness

of 6 mm. The vessel contains gas

under a pressure of 8,000 kPa. If the

ultimate tensile stress of the material

is 420 MPa, what is the factor of

safety with respect to the tensile

failure?

A. 3.15

B. 3.55

C. 2.15

D. 2.55

720. A metal specimen 36-mm in

diameter has a length of 360 mm. A

force of 300 kN elongates the length

by 1.20 mm. What is the modulus of

elasticity?

A. 88.419 GPa

B. 92.564 GPa

C. 92.658 GPa

D. 95.635 GPa

721. A steel wire 5-m long hanging

vertically supports a weight of 1200

N. Determine the required wire

diameter if the stress is limited to

140 MPa and the total elongation

must not exceed 4mm. Neglect the

weight of the wire and assume

GPa.

A. 3.09 mm

B. 3.56 mm

C. 3.33 mm

D. 2.89 mm

722. During a stress-strin test, the unit

deformation at a stress of 35 MPa

was observed to be m/m

and at a stress of 140 MPa it was

m/m. If the proportional

limit was 200 MPa, what is the

modulus of elasticity. What is the

strain corresponding to the stress of

80 MPa?

A. MPa;

m/m

B. MPa;

m/m

C. MPa;

m/m

D. MPa;

m/m

723. An axial load of 100 kN is applied to

a flat bar 20 mm thick, tapering in

width from 120 mm to 40 mm in a

length of 10 m. Assuming

GPa, determine the total elongation

of the bar.

A. 3.43 mm

B. 2.125 mm

C. 4.33 mm

D. 1.985 mm

724. Steel bar having a rectangular cross-

section 15 mm 20 mm and 150 m

long is suspended vertically from

one end. The steel has a unit mass of

7850 kg/m3 and a modulus of

elasticity of 200 GPa. If a loaf of

20 kN is suspended at the other end

of the rod, determine the total

elongation of the rod.

A. 43.5 mm

B. 54.3 mm

C. 35.4 mm

D. 45.3 mm

725. A steel bar 50 mm in diameter and 2

m long is surrounded by a shell of

cast iron 5 mm thick. Compute the

load that will compress the bar a

total of 1 mm in the length of 2 m.

Use GPa and

GPa.

A. 200 kN

B. 240 kN

C. 280 kN

D. 320 kN

726. A 20-mm diameter steel rod, 250

mm long is subjected to a tensile

force of 75 kN. If the Poisson’s ratio

µ is 0.30, determine the lateral strain

of the rod. Use GPa.

A. mm/mm

B. mm/mm

C. mm/mm

D. mm/mm

727. A solid aluminum shaft of 100-mm

diameter fits concentrically in a

hollow steel tube, determine the

minimum internal diameter of the

steel tube so that no contact pressure

exists when the aluminum shaft

carries an axial compressive load of

600 kN. Assume Poisson’s ratio

µ=1/3 and the modulus of elasticity

of aluminum be 70 GPa.

A. 100.0364 mm

B. 100.0312 mm

C. 100.0303 mm

D. 100.0414 mm

728. The maximum allowable torque, in

kN-m, for a 50-mm diameter steel

shaft when the allowable shearing

stress is 81.5 MPa is:

A. 3.0

B. 1.0

C. 4.0

D. 2.0

729. The rotation of twist in degrees of a

shaft, 800 mm long subjected to a

torque of 80 N-m, 20 mm in

diameter and shear modulus of

80,000 MPa is:

A. 3.03

B. 4.04

C. 2.92

D. 1.81

730. Compute the value the shear

modulus of steel whose modulus

of elasticity is 200 GPa and

Poisson’s ratio µ is 0.30.

A. 72,456 MPa

B. 76,923 MPa

C. 79,698 MPa

D. 82,400 MPa

731. Determine the length of the shortest

2-mm diameter bronze wire, which

can be twisted through two complete

turns without exceeding a stress of

70 MPa. Use GPa.

A. 6.28 m

B. 5.23 m

C. 6.89 m

D. 8.56 m

732. A hollow steel shaft 2540 mm long

must transmit torque of 35 kN-m.

The total angle of twist must not

exceed 3 degrees. The maximum

shearing stress must not exceed 110

MPa. Find the inside diameter and

the outside diameter of the shaft that

meets these conditions.

A. mm; mm

B. mm; mm

C. mm; mm

D. mm; mm

733. Determine the maximum shearing

stress in a helical steel spring

composed of 20 turns of 20-mm

diameter wire on a mean radius of 80

mm when the spring is supporting a

load of 2 kN.

A. 110.6 MPa

B. 101.1 MPa

C. 120.6 MPa

D. 136.5 MPa

734. A load is supported by two springs

arranged in series. The upper spring

has 20 turns of 29-mm diameter wire

on a mean diameter of 150 mm. The

lower spring consist of 15 turns of

10-mm diameter wire on a mean

diameter of 130 mm. Determine the

value of that will cause a total

deflection of 80 mm. Assume

GPa for both springs.

A. 223.3 N

B. 228.8 N

C. 214.8 N

D. 278.4 N

735. A 10-meter long simply supported

beam carries a uniform load of 8

kN/m for 6 meters from the left

support and a concentrated load of

15 kN 2 meters from the right

support. Determine the maximum

shear and moment.

A. kN;

kN-m

B. kN;

kN-m

C. kN;

kN-m

D. kN;

kN-m

736. A simple beam, 10 m long carries a

concentrated load of 500 kN at the

midspan. What is the maximum

moment of the beam?

A. 1250 kN-m

B. 1050 kN-m

C. 1520 kN-m

D. 1510 kN-m

737. A small square 5 cm by 5 cm is cut

out of one corner of a rectangular

cardboard 20 cm by 30 cm long.

How far, in cm from the uncut longer

side, is the centroid of the remaining

area?

A. 9.56

B. 9.35

C. 9.48

D. 9.67

738. What is the inertia of a bowling ball

(mass = 0.5 kg) of radius 15 cm

rotating at an angular speed of 10

rpm for 6 seconds?

A. 0.0045 kg-m2

B. 0.001 kg-m2

C. 0.005 kg-m2

D. 0.002 kg-m2

739. What is the moment of inertia of a

cylinder of radius 5 m and a mass of

5 kg?

A. 62.5 kg-m2

B. 80 kg-m2

C. 72.5 kg-m2

D. 120 kg-m2

740. The mass of air in a room which is

3m 5m 20m is known to be 350 kg.

Find its density.

A. 1.167 kg/m3

B. 1.176 kg/m3

C. 1.617 kg/m3

D. 1.716 kg/m3

741. One hundred (100) grams of water

are mixed with 150 grams of alcohol

( kg/ cu m). What is the

specific gravity of the resulting

mixtures, assuming that the two

fluids mix completely?

A. 0.96

B. 0.82

C. 0.63

D. 0.86

742. 100 g of water are mixed with 150 g

of alcohol ( kg/ cu m). What

is the specific volume of the

resulting mixtures, assuming that the

two fluids mix completely?

A. 0.88 cu cm/g

B. 1.20 cu cm/g

C. 0.82 cu cm/g

D. 0.63 cu cm/g

743. The pressure 34 meters below the

ocean is nearest to:

A. 204 kPa

B. 222 kPa

C. 344 kPa

D. 362 kPa

744. What is the atmospheric pressure on

a planet where the absolute pressure

is 100kPa and the gage pressure is 10

kPa?

A. 90 kPa

B. 80 kPa

C. 100 kPa

D. 10 kPa

745. If the pressure at a point in the ocean

is 60 kPa, what is the pressure 27

meters below this point?

A. 256.3 kPa

B. 521.3 kPa

C. 332.8 kPa

D. 185.4 kPa

746. A pressure gage 6 m above the

bottom of the tank containing a

liquid reads 90 kPa; another gage

height 4 m reads 103 kPa. Determine

the specific weight of the liquid.

A. 6.5 kN/m3

B. 5.1 kN/m3

C. 3.2 kN/m3

D. 8.5 kN/m3

747. The weight density of a mud is given

by , where is in

kN/m3 and is in meters. Determine

the pressure, in kPa, at a depth of

5m.

A. 89.36 kPa

B. 56.25 kPa

C. 62.5 kPa

D. 78.54 kPa

748. What is the resulting pressure when

one pound of air at 15 psia and

200°F is heated at constant volume

to 800°F?

A. 28.6 psia

B. 52.1 psia

C. 36.4 psia

D. 15 psia

749. The volume of a gas under standard

atmospheric pressure 76 cm Hg is

200 in3. What is the volume when

the pressure is 80 cm Hg, if the

temperature is unchanged?

A. 190 in3

B. 90 in3

C. 110 in3

D. 30.4 in3

750. A two-meter square plane surface is

immersed vertically below the water

surface. The immersion is such that

the two edges of the square are

horizontal. If the top of the square is

1 meter below the water surface,

what is the total water pressure

exerted on the plane surface?

A. 43.93 kN

B. 52.46 kN

C. 64.76 kN

D. 78.48 kN

751. Find the total water pressure on a

vertical circular gate, 2 meters in

diameter, with its top 3.5 meters

below the water surface.

A. 138.7 kN

B. 107.9 kN

C. 169.5 kN

D. 186.5 kN

752. An iceberg having specific gravity of

0.92 is floating on salt water of sp.

gr. 1.03. If the volume of ice above

the water surface is 1000 cu. m.,

what is the total volume of the ice?

A. 8523 m3

B. 7862 m3

C. 9364 m3

D. 6325 m3

753. A block of wood requires a force of

40 N to keep it immersed in water

and a force of 100 N to keep it

immersed in glycerin (sp. gr. = 1.3).

Find the weight and sp. gr. Of the

wood.

A. 0.7

B. 0.6

C. 0.9

D. 0.8

754. Reynolds number may be calculated

from:

A. diameter, density, and absolute

viscosity

B. diameter, velocity, and surface

tension

C. diameter, velocity, and absolute

viscosity

D. characteristic length, mass flow

rate per unit area, and absolute

viscosity

755. The sum of the pressure head,

elevation head, and the velocity head

remains constant, this is known as:

A. Bernoulli’s Theorem

B. Boyle’s Law

C. Archimedes’ Principle

D. Torrecelli’s Theorem

756. What is the expected head loss per

mile of closed circular pipe (17-in

inside diameter, friction factor of

0.03) when 3300 gal/min of water

flow under pressure?

A. 38 ft

B. 0.007 ft

C. 3580 ft

D. 64 ft

757. What is the rate of flow of water

passing through a pipe with a

diameter of 20 mm and speed of 0.5

m/sec?

A. m3/s

B. m3/s

C. m3/s

D. m3/s

758. An orifice has a coefficient of

discharge of 0.62 and a coefficient of

contraction of 0.63. Determine the

coefficient of velocity for the orifice.

A. 0.98

B. 0.99

C. 0.97

D. 0.96

759. The theoretical velocity of flow

through an orifice 3 m below the

surface of water in a tall tank is:

A. 8.63 m/s

B. 9.85 m/s

C. 5.21 m/s

D. 7.67 m/s

760. Water having kinematic viscosity

m2/s flows in a 100-

mm diameter pipe at a velocity of 4.5

m/s. the Reynolds number is:

A. 346,150

B. 258,250

C. 387,450

D. 298,750

761. Oil having specific gravity of 0.869

and dynamic viscosity of 0.0814 Pa-s

flows through a cast iron pipe at a

velocity of 1 m/s. The pipe is 50 m

long and 150 mm in diameter. Find

the head lost due to friction.

A. 0.73 m

B. 0.45 m

C. 0.68 m

D. 1.25 m

762. What commercial size of new cast

iron pipe shall be used to carry 4490

gpm with a lost of head of 10.56 feet

per mile? Assume .

A. 625 mm

B. 576 mm

C. 479 mm

D. 352 mm

763. Assume that 57 liters per second of

oil ( kg/m3) is pumped

through a 300 mm diameter pipeline

of cast iron. If each pump produces

685 kPa, how far apart can they be

placed? (Assume )

A. 23.7 m

B. 32.2 m

C. 12.6 m

D. 19.8 m

764. A 20-mm diameter commercial steel

pipe, 30 m long is used to drain an

oil tank. Determine the discharge

when the oil level in the tank is 3 m

above the exit of the pipe. Neglect

minor losses and assume .

A. 0.000256 m3/s

B. 0.000179 m3/s

C. 0.000113 m3/s

D. 0.000869 m3/s


<ENGINEERING ECONOMICS>


GILLESANIA>


ADRIAN C.

765. The recorded current value of an

asset is known as:

A. scrap value

B. book value

C. salvage value

D. present worth

766. The ratio of the interest payment to

the principal for a given unit of time

and is usually expressed as a

percentage of the principal is known

as:

A. investment

B. nominal interest

C. interest

D. interest rate

767. A method of depreciation whereby

the amount to recover is spread over

the estimated life of the asset in

terms of the periods or units of

output is called:

A. SOYD method

B. declining balance method

C. straight line method

D. sinking fund method

768. The interest rate at which the present

worth of cash flow on a project is

zero, or the interest earned by an

investment.

A. rate of return

B. effective rate

C. nominal rate

D. yield

769. The lessening of the value of an asset

due to the decrease in the quantity

available. This refers to the natural

resources such as coal, oil, and

timber in the forest.

A. depreciation

B. depletion

C. inflation

D. incremental cost

770. 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

total depreciation of an asset at the

end of the asset’s estimated life is

known as:

A. straight line method

B. SYD method

C. declining balance method

D. sinking fund method

771. The term used to express the series

of uniform payments occurring at

equal interval of time is:

A. compound interest

B. annuity

C. perpetuity

D. depreciation

772. The profit derived from a project or

business enterprise without

consideration of obligations to

financial contributors and claims of

others based on profit is known as:

A. yield

B. earning value

C. economic return

D. expected yield

773. As applied to capitalized asset, the

distribution of the initial cost by

periodic changes to operation as in

depreciation or the reduction of the

depth by either periodic or irregular

prearranged program is called:

A. amortization

B. annuity

C. depreciation

D. capital recovery

774. Those funds that are required to

make the enterprise or project a

going concern.

A. banking

B. accumulated amount

C. working capital

D. principal or present worth

775. These are product or services that are

desired by humans and will be

purchased if money is available after

the required necessities have been

obtained.

A. utilities

B. necessities

C. luxuries

D. producer goods and services

776. These are product or services that are

required to support human life and

activities, that will be purchased in

somewhat the same quantity even

though the price varies considerably.

A. utilities

B. necessities

C. luxuries

D. producer goods and services

777. A condition where only few

individuals produce a certain product

and that any action of one will lead

to almost the same action of the

others.

A. oligopoly

B. semi-oligopoly

C. monopoly

D. perfect competition

778. This occurs in a situation where a

commodity or service is supplied by

a number of vendors and there is

nothing to prevent additional vendors

entering the market.

A. perfect competition

B. monopoly

C. oligopoly

D. elastic demand

779. It is the amount that a willing buyer

will pay to a willing seller for a

property where each has equal

advantage and is under no

compulsion to buy or sell.

A. fair value

B. use value

C. market value

D. book value

780. It is defined to be the capacity of a

commodity to satisfy human want.

A. discount

B. luxuries

C. utility

D. necessity

781. A form of summary of assets,

liabilities, and net worth:

A. balance method

B. break-even point

C. balance sheet

D. production

782. The worth of a property, which is

equal to the original cost less

depreciation, is known as:

A. earning value

B. scrap value

C. book value

D. face value

783. When using net present worth

calculations to compare two projects,

which of the following could

invalidate the calculations?

A. mutually exclusive projects

B. evaluation over different

periods

C. non-conventional cash flows

D. difference in the magnitude of the

projects

784. Which of the following is a form of

business/company ownership?

A. partnership

B. corporation

C. single proprietorship

D. all of these

785. What must two investments with the

same present worth and unequal lives have?

A. identical salvage value

B. different salvage values

C. identical equivalent uniform

annual cash flows

D. different equivalent annual cash

flows

786. Find the interest on P6800.00 for 3 years

at 11% simple interest.

A. P1,875.00

B. P1,987.00

C. P2,144.00

D. P2,244.00

787. A man borrowed P10,000.00 from his

friend and agrees to pay at the end of 90

days under 8% simple interest rate.

What is the required amount?

A. P10,200.00

B. P11,500.00

C. P9,500.00

D. P10,700.00

788. Annie buys a television set from a

merchant who offers P25,000.00 at the

end of 60 days. Annie wishes to pay

immediately and the merchant offers to

compute the required amount on the

assumption that the money is worth 14%

simple interest. What is the required

amount?

A. P20,234,87

B. P19,222.67

C. P24,429.97

D. P28,456.23

789. What is the principal amount if the

amount of interest at the end of 2½ year

is P4500 for a simple interest of 6% per

annum?

A. P35,000.00

B. P30,000.00

C. P40,000.00

D. P45,000.00

790. How long must a P40,000 note bearing

4% simple interest to run to amount to

P41,350.00?

A. 340 days

B. 403 days

C. 304 days

D. 430 days

791. If P16,000 earns P480 in 9 months, what

is the annual rate of interest?

A. 1%

B. 2%

C. 3%

D. 4%

792. A man lends P6000 at 6% simple

interest for 4 years. At the end of this

time he invests the entire amount

(principal plus investment) at 5%

compounded annually for 12 years. How

much will he have at the end of the 16-

year period?

A. P13,361.20

B. P13,633.20

C. P13,333.20

D. P16,323.20

793. A time deposit of P110,000 for 31 days

earns P890.39 on maturity date after

deducting the 20% withholding tax on

interest income. Find the rate of interest

per annum.

A. 12.5%

B. 11.95%

C. 12.25%

D. 11.75%

794. A bank charges 12% simple interest on a

P300.00 loan. How much will be repaid

if the load is paid back in one lump sum

after three years?

A. P408.00

B. P551.00

C. P415.00

D. P450.00

795. The tag price of a certain commodity is

for 100 days. If paid in 31 days, there is

a 3% discount. What is the simple

interest paid?

A. 12.15%

B. 6.25%

C. 22.32%

D. 16.14%

796. Accumulate P5,000.00 for 10 years at

8% compounded quarterly.

A. P12,456.20

B. P13,876.50

C. P10,345.80

D. P11,040.20


8% compounded semi-annually.

A. P10,955.61

B. P10,233.67

C. P9,455.67

D. P11,876.34


8% compounded monthly.

A. P15,456.75

B. P11,102.61

C. P14,768.34

D. P12,867.34


8% compounded annually.

A. P10,794.62

B. P8,567.98

C. P10,987.90

D. P7,876.87

800. How long will it take P1,000 to amount

to P1,346 if invested at 6% compounded

quarterly?

A. 3 years

B. 4 years

C. 5 years

D. 6 years

801. How long will it take for an investment

to double its amount if invested at an

interest rate of 6% compounded bi-

monthly?

A. 10 years

B. 12 years

C. 13 years

D. 14 years

802. If the compound interest on P3,000.00

in 2 years is P500.00, then the

compound interest on P3,000.00 in 4

years is:

A. P956.00

B. P1,083.00

C. P1,125.00

D. P1,526.00

803. The salary of Mr. Cruz is increased by

30% every 2 years beginning January

1,1982. Counting from that date, at what

year will his salary just exceed twice his

original salary?

A. 1988

B. 1989

C. 1990

D. 1991

804. If you borrowed P10,000 from a bank

with 18% interest per annum, what is

the total amount to be repaid at the end

of one year?

A. P11,800.00

B. P19,000.00

C. P28,000.00

D. P10,180.00

805. What is the effective rate for an interest

rate of 12% compounded continuously?

A. 12.01%

B. 12.89%

C. 12.42%

D. 12.75%

806. How long will it take for an investment

to fivefold its amount if money is worth

14% compounded semiannually?

A. 11

B. 12

C. 13

D. 14

807. An interest rate of 8% compounded

semiannually is how many percent if

compounded quarterly?

A. 7.81%

B. 7.85%

C. 7.92%

D. 8.01%

809. A man is expecting to receive

P450,000.00 at the end of 7 years. If

money is worth 14% compounded

quarterly, how much is it worth at

present?

A. P125,458.36

B. P147,456.36

C. P162,455.63

D. P171,744.44

810. A man has a will of P650,000.00 from

his father, If his father deposited an

amount of P450,000.00 in a trust fund

earning 8% compounded annually, after

how many years will the man receive his

will?

A. 4.55 years

B. 4.77 years

C. 5.11 years

D. 5.33 years

25. Mr. Adam deposited P120,000.00 in a

bank who offers 8% interest

compounded quarterly. If the interest is

subject to a 14% tax, how much will he

receive after 5 years?

A. P178,313.69

B. P153.349.77

C. P170,149.77

D. P175,343.77

Multiple Choice Questions in Engineering Mathematics by Perfecto b. Padilla Jr

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