engineering mathematics

MULTIPLE CHOICE QUESTIONS IN

MATHEMATICS

PERFECTO B. PADILLA JR

AND

DIEGO INOCENCIO TAPANG GILLESANIA

ENCODED BY: BAUTISTA, HEZZIELEEN F.

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 2nd row, 36 in the 3rd row, . . and 48 in the 9th row. From the 10th up to the 20th 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 units 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 30C. During El Nino drought, temperature increased to 40C. 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 36 cubic

meters. The rate of change in volume is 9 cubic meters per minute. Find the rate of change in area of the sphere. a. 6 m2/min b. 2 m2/min c. 3 m2/min d. 4 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=9406. 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 its 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?

. .2 .4 .3

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 cm2. 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. Varignons c. Castigllianos d. Pascals

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-y2-8x+4y-4=0 b. x2-4y2-8x+4y-4=0 c. 4x2-y2-8x-4y-4=0 d. x2-4y2+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+Cy2+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 sin4 = ? a. sin 2 b. cos 2 c. cos 4 d. cos 3

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. 301525

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(-)= sin b. tan(-)= tan c. cos(-)= cos d. csc(-)= csc

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 10C? 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 sons 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/m2 b. 8.33 x 104 N/m2

c. 8.33 x 105 N/m2 d. 8.33 x 106 N/m2

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 = /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. radian d. 1 quarter circle

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

container containing 2,000,000 cu. m of water at 0C. 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. Newtons law b. Inverse Square law c. Coulombs 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 earths 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. (3t-1)3 + c d. (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 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

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 b. 23 c. 64 d. 16

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 observers 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

+ 9y2 = 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. /3 b. /4 c. /6 d. /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/ n b. 500 00x/ n c. 500x/ n d. 5 000x/ 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 in3 c. 90 in3 d. 30.4 in3

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 . 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 =/3 to Cartesian equation

a. x=31/2x b. 3y=31/2x c. y=x d. y=31/2x

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 Moivres 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

72F. 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 cos=-15/17 and is in the third

quadrant, find cos /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 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 , 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+y2=z and below the cylinder x2+z=4

a. 2 cubic units

b. /4 cubic units c. cubic units d. 4 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 3sin 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/From

Damarinas

Canlubang

Batangas

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=b2+c2-bc cos A b. a2=b2+c2-2bc cos A

c. a2=b2+c2-2bc sin A d. a2=b2+c2-2bc 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 =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 =2, then angle (180-)= __________

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+ i3 cos 3x ++i sin x + i2 sin 2x+ i3 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


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, 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


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, 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-Q2=A2+B2 b. P2+Q2=A2-B2 c. P2-Q2=A2-B2 d. P2+Q2=A2+B2

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-x2

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 + sin22 + sin23 + .. + sin2 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


a. 3/2 b. 2 c. 3 d. 1/2


(

)

a. 25/48 b. 125/48 c. 125/16 d. 125/8

319. Find the value of 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+tanh2 x= ?

a. cosh2x-sech2x b. cosh2x+sech2x c. sech2x-cosh2x d. sech2x+cosh2x

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. 4/3ab2 b. 2/3 ab2 c. 4/3 ba2 d. 2/3 a2b

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-x2. 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 years 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

a8-17a4+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. Snells law on light incidence and

refraction gives us the following equation: n1sin1=n2sin2 where n1 and n2 denote the indexes on refraction 1 and 2 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. =33.6 b. =43.6 c. =53.6 d. =23.6

372. If

, y=?

a.

b.

c. -

d.

373. Sin215+sin275

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=?

a. 0.686 m b. 0.688 m c. 0.866 m d. 0.868 m

378. Differentiate the equation

a.

b.

c.

E

A D

4-r

4+r

45

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.

385. Obtain the differential equation of all circles with center on line and passing through the origin.

a.

b.

c.

d. ( )

( )

386. Obtain the differential equation 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.

393. Solve the equation

. 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.

MULTIPLE CHOICE QUESTIONS IN

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.

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 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 observers 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.

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.

D.

458. Evaluate .

A.

B.

C.

D.

459. Evaluate .

A.

B.

C.

D.

460. Evaluate

.

A.

B.

C.

D. arctan

461. Evaluate

.

A. arcsec

B.

[ ]

C.

D. arcsin

462. Evaluate

.

A.

B.

C.

D.

463. Evaluate

.

A.

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

470. Evaluate the integral of

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

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