MATHEMATICS 1.
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Which of the following cannot be an operation of matrices? a. Division b. Subtraction c. Multiplication d. Addition _________ is the loss 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. extracted b. loss c. depreciation d. extracted One side of a regular octagon is 2. Find the area of the region inside the octagon. a. 19.3 b. 13.9 c. 21.4 d. 31 A market whereby there is only one buyer of an item for when there are no goods substitute a. Monopoly b. Monopsony c. Oligopsony d. Oligopoly The angle or inclination of ascend of a road having a 8.25% grade is _ degrees a. 1.86° b. 5.12° c. 4.27° d. 4.72° At the inflection point where x=a a. f”(a)=0 b. f”(a) is not equal to zero c. f”(a)<0 d. f”(a)>0
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If an equilateral triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle. a. 34.64 cm b. 32.10 cm c. 64.12 cm d. 36.44 cm 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. 0.005 kg-m^2 b. 0.001 kg-m^2 c. 0.0045 kg-m^2 d. 0.002 kg-m^2 A line passes through point (2, 2). Find the equation of the line if the length of the line segment intercepted by the coordinate axes is the sqrt(5) a. 2x – y + 2 = 0 b. 2x + y – 2 =0 c. 2x – y – 2 = 0 d. 2x + y + 2 = 0
10. The number 0.123123123…… is a/an _________ number. a. transcendental b. surd c. rational d. irrational 11. It is the characteristic of a population which is measurable. a. Parameter b. Sample c. Frequency d. Distribution 12. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base while the altitude of the other is 3 units less than its base. Find the altitudes if the areas of the triangle differ by 21 square units. a. 4 and 10
b. c. d.
5 and 11 3 and 9 6 and 12
13. A man finds the angle of elevation of the top of a tower to be 30°. He walks 85 m nearer the tower and finds its angle of elevation to be 60°. What is the height of the tower? a. 76.31 m b. 73.31 m c. 73.16 m d. 73.61 m 14. Convergent series is a sequence of decreasing numbers or when the succeeding term is _______ than the preceding term. a. equal b. greater c. lesser d. none of these 15. The probability of getting a credit in an examination is 1/3. If three students are selected at random, what is the probability that at least one of the students got credit? a. 2/3 b. 1/3 c. 8/27 d. 19/27 16. What is the allowable error in measuring the edge of the cube that is intended to hold 8 cu. meter, if the error of the computed volume is not exceed 0.03 cu. m.? a. 0.0025 m b. 0.003 m c. 0.002 m d. 0.001 m 17. The graph of r = a + b cos θ is a ________ a. lemniscate b. limacon c. lituus d. cardoid
18. If sin A = 3/5 and A is in quadrant II while cons B = 7/25 and B is in quadrant I, find sin(A+B). a. 4/5 b. -3/5 c. 3/5 d. 3/4 19. The amount of P 12,800 in 4 years at 5% compounded quarterly is a. P 15,847.83 b. P 14,785.34 c. P 16,311.26 d. P 15,614.59 20. If y = x a. b. c. d.
ln x, find d^y/dx^2. 1/x 1/x^2 – 1/x – 1/x^2
21. The equation whose roots are the reciprocals of the roots of the equation, 2x^2 – 3x -5 = 0. a. 5x^2 + 3x – 2 = 0 b. 2x^2 – 5x -3 = 0 c. 5x^2 – 2x – 3 = 0 d. 3x^2 – 5x - 2 = 0 22. Find the equation of the directrix of the parabola y^2=16. a. x=-4 b. x=8 c. x=4 d. x=-8 23. The wheel of a car revolves “n” times, while the car travels “x” km. The radius of the wheel in meters is _________. a. 5000x/(pi)n b. 500x/(pi)n c. 10000x/(pi)n d. 500000x/(pi)n 24. The diameter of a circle described by 9x^2 + 9y^2 = 16 is a. 4/3 b. 16/9
c. d.
4 8/3
25. The roots of a quadratic equation are 1/3 and 1/4. What is the equation? a. 12x^2 – 7x + 1 = 0 b. 12x^2 – 7x – 1 = 0 c. 12x^2 + 7x –1 = 0 d. 12x^2 + 7x + 1 = 0 26. 15% compounded semiannually will have an effective rate of _________. a. 18.78% b. 15.93% c. 15.56% d. 16.02% 27. If all the y – terms have even exponents, the curve is symmetric with respect to the __________ a. Y-axis b. X-axis c. Line 45° with the axis d. origin 28. Evaluate the limit (x-4)/ (x^2 – x – 12) as x approaches 4 a. infinity b. 2 c. 1/7 d. undefined 29. It is the amount which a willing buyer will pay to a willing seller for the property where each has equal advantage and is under compulsion to buy or sell. a. Fair value b. Use value c. Book value d. Market value 30. The velocity of an automobile starting from rest is given by ds/dt = (90t) ⁄ (t+10) feet/sec. Determine the acceleration after the time interval of 10 sec. a. 1.71 ft/s^2 b. 2.25 ft/s^2
c. d.
2.75 ft/s^2 2.10 ft/s^2
31. 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 will the ball attain its original level? a. 890 m b. 883 m c. 880 m d. 875 m 32. The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction a. 8/ 3 b. 5/13 c. 5/3 d. 13/5 33. A trapezoid has an area of 36 m^2 and altitude of 2 m. Its two bases have ratio of 4:5. What are the lengths of the bases? a. 8, 10 b. 12,15 c. 7, 11 d. 16, 20 34. The volume of a sphere is 36π cu. m. The surface area of this sphere in sq. m is _______. a. 18π b. 36π c. 12π d. 24π 35. How much must you invest today in order to withdraw P 2, 000 annually for 10 years if the interest rate is 9%? a. P 12, 881.37 b. P 12, 385.32 c. P 12, 853.32 d. P 12, 835.32
36. 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) 37. Arctan[2cos(Arcsin(sqrt(3)/ 2))] is equal to a. π/2 b. π/16 c. π/3 d. π/4 38. When the two waves of the same frequency speed and amplitude travelling in opposite directions are superimposed, a. The phase difference is always zero b. Distractive waves are produced c. Standing waves are produced d. Constructive interference always results 39. Find the ratio of an infinite geometric progression if the sum is 2 and the first term is 1/2. a. 1/3 b. 1/4 c. 3/4 d. 1/2 40. 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. 480 b. 840 c. 680 d. 540 41. The work done by all forces except the gravitational force
is always equal to the ________ of the system. a. Total momentum b. Total potential energy c. Total kinetic energy d. Total mechanical energy 42. Find the area (in sq. units) bounded by the parabolas x^2 – 2y = 0 and x^2 + 2 – 8=0 a. 10.7 b. 11.7 c. 9.7 d. 4.7 43. Evaluate the limit ln x/x as x approaches infinity. a. zero b. 1 c. infinity d. e 44. 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 5 liters of a 10% solution? a. 3 b. 1.5 c. 2 d. 2.5 45. The sum of the first 10 terms of a geometric progression 2, 4, 8, 16, ….. is a. 1023 b. 225 c. 1596 d. 2046 46. Points A and B 1000 m apart are plotted on a straight highway running east and west. From A, the bearing of tower C is 32° W of N and from B the bearing of C 26° N of E. Approximate the shortest distance of the tower from the highway.
a. b. c. d.
364 384 394 374
m m m m
47. Find the approximate change in the volume of a cube of side “x” inches caused by increasing its side by 1%. a. 0.1 x^3 cu. in b. 0.03 x^3 cu. in c. 0.02 x^3 cu. in d. 0.3 x^3 cu. in 48. Solve for x in the equation: Arc tan x = (π/2) – 45°. a. 0.281 b. 0.218 c. 0.821 d. 0.182 49. If log of 2 to the base 2 plus log of x to the base 2 is equal to 2, then the value of x is _______ a. 2 b. 4 c. -2 d. -1 50. 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. 56% b. 46% c. 65% d. 44% 51. The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth. a. 94,550,000 miles b. 94,335,100 miles c. 93,000,000 miles d. 91,450,000 miles
52. If a regular polygon has 27 diagonals, then it is a ________. a. pentagon b. heptagon c. hexagon d. nonagon 53. When two planes intersect with each other, the amount of divergence between the two planes is expressed by measuring the __________. a. Plane angle b. Dihedral angle c. Reflex angle d. Polyhedral angle 54. A debt of P 10,000 with 10% interest compounded semiannually is to be amortized by semi-annual payment over the next 5 years. The first due in 6 months. Determine the semi-annual payment. a. P 1,200 b. P 1,295.05 c. P1,400.45 d. P 1,193.90
58. What is the allowable error in measuring the edge of the cube that is intended to hold 8 cu. m., if the error of the computed volume is not to exceed 0.02 cu. m? a. 0.0170 m b. 0.1700 m c. 0.0710 m d. 0.0017 m 59. To maximize the horizontal range of the projectile, which of the following applies? a. The tangent function of the angle of trajectory must be equal to one b. Maximize velocity c. Maximize the angle of elevation and velocity d. Maximize the angle of elevation 60. If the first derivative of a function is a constant, then the function is a. quadratic b. linear c. sinusoidal d. logarithmic
55. Integrate the [sqrt(1 – cos x)]dx a. -2[sqrt(2)cosx] + c b. -2[sqrt(2)cosx] + c c. -2[sqrt(2)cos((1/2)x) + c d. -2[sqrt(2)cos((1/2)x) + c
61. Find the area of the triangle which the line 2x – 3y + 6 = 0 forms with the coordinate axes. a. 4 sq. units b. 3 sq. units c. 5 sq. units d. 2 sq. units
56. Find the 30th term of the arithmetic progression 4, 7, 10, …….. a. 75 b. 90 c. 88 d. 91
62. By the condition of a will, the sum of P 20,000 is left to a girl to be held in trust fund by her guardian until it amounts to P 50,000. When will the girl receive the money if the fund is invested at 8% compounded quarterly? a. 10.34 years b. 10.45 years c. 11.57 years d. 7.98 years
57. Find the value of (1 + i)^5, where i is an imaginary number. a. 4(1 + i) b. 1 + i c. 1 - i d. -4(1 + i)
63. A market situation whereby there is only one buyer of an item for which there are no goods substitute. a. Oligopsony b. Monopoly c. Monopsony d. Oligopoly 64. What is the least common factor of 10 and 32? a. 2 b. 320 c. 180 d. 90 65. If the equation is unchanged by the substitution of y for x, its curve is symmetric with respect to the a. line 45° with the x axis b. X - axis c. origin d. Y - axis 66. Of what quadrant is A, if sec A is positive and csc A is negative? a. IV b. III c. I d. II 67. Find the equation of the curve at every point of which the tangent line has a slope of 2x a. y = -x^2+ c b. x = y^2 + c c. x = -y^2 + c d. y = x^2 + c 68. A rotating wheel has radius of 2 ft and 6 inches. A point on the rim of the wheel moves 30 ft in 2 seconds. Find the angular velocity of the wheel. a. 4 rad/s b. 5 rad/s c. 6 rad/s d. 2 rad/s
69. Evaluate cos [arctan(15/8) – arctan(7/24)] a. 976/435 b. 792/525 c. 297/425 d. 297/452 70. The effective rate of 14% compounded semi-annually is a. 14.88% b. 12.36% c. 14.94% d. 14.49% 71. Which true? a. b. c. d.
of
the
following
is
csc(-T) = csc(T) sin(-T) = sin(T) cos(-T) = cos (T) tan(-T) = tan (T)
72. A car accelerates at a constant rate from 15 mi/hr to 45 mi/hr in 15 seconds, while travelling in a straight line. What is the average acceleration? a. 2.12 ft/sec^2 b. 2.00 ft/sec^2 c. 2.93 ft/sec^2 d. 2.39 ft/sec^2 73. The quartile deviation is a measure of ________. a. dispersion b. division c. central tendency d. certainty 74. Determine the coordinates of the point which is threefifths of the way from the point (2, -5) to the point (-3, 5) a. (-2,1) b. (1,-1) c. (-1,1) d. (-1,-2) 75. A statue 3 m high is standing on base of 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. 3.51 m b. 4.41 m c. 3.71 m d. 3.41 m 76. What is the effective rate corresponding to 18% compounded daily? Take 1 year = 365 days. a. 17.84% b. 16.68% c. 19.72% d. 17.35% 77. A man rows 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 in 7/4 hours after leaving? a. 3.1 miles b. 2.7 miles c. 3.3 miles d. 2.5 miles 78. The cords of an ellipse, which pass through the center, are known as _________. a. diameters b. major axes c. asymptote d. radical axes 79. The angle of a sector is 30° and the radius is 15 cm. What is the area of the sector in cm? a. 85.9 b. 89.8 c. 58.9 d. 59.8 80. The apothem of the polygon is the ________ of its inscribed circle. a. circumference b. diameter c. length d. radius
81. The arithmetic mean of 6 numbers is 17. If two numbers are added to the progression, the new set of numbers will have an arithmetic mean of 19. What are the two numbers if their difference is 4? a. 16, 20 b. 8, 12 c. 23, 27 d. 21, 25 82. A balloon is rising vertically over a point A on the ground at the rate of 15 ft/s. A point B on the ground 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. 15 ft/s b. 10 ft/s c. 12 ft/s d. 13 ft/s 83. A horizontal line has a slope of a. positive b. zero c. infinity d. negative 84. Find the point in the parabola y^2 = 4x at which the rate of change of the ordinate and abscissa are equal (0 correct answers) a. (4,4) b. (1,2) c. (2,1) d. (-1,4) 85. It is defined to be the capacity of a commodity to satisfy human want. a. utility b. discount c. luxuries d. necessity 86. A merchant has three items on sale namely: a radio for $50.00, a clock for $30.00 and a flashlight $1.00. At the
end of the day, she has sold a total of 100 of the three sale items and has taken exactly $1,000.00 on the total sales. How many radios did she sell? a. 16 b. 4 c. 80 d. 20 87. Find the slope of x^2y = 8 at the point (2, 2) a. 2 b. -1 c. -1/2 d. -2 88. A line, which is perpendicular to the x-axis, has a slope equal to ________. a. 1 b. infinity c. 2 d. e 89. The area of the region bounded by two concentric circles are called a. ring b. washer c. annulus d. Circular disk 90. Find the 100th term of the sequence 1.01, 1.00, 0.99…. a. 0.03 b. 0.05 c. 0.04 d. 0.02 91. An iron column of annular cross-section has an outer diameter of 200 mm and is subjected to a force of 75 kN. Find the thickness of the wall if the allowable compressive stress is 10MPa a. 12.57 mm b. 15.75 mm c. 17.75 mm d. 12.75 mm 92. What is the speed of a synchronous earth’s satellite 4.5 x 107 m from the earth?
a. b. c. d.
12,070.2 kph 11,070 kph 11,777.4 kph 12,000 kph
93. In Algebra, the operation of root extraction is called as _________. a. revolution b. resolution c. involution d. evolution 94. A 50 kg 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. 1.52 s b. 2.14 s c. 2.51 s d. 2.41 s 95. The midpoint of the line segment between P1(x1, y1) and P2(–2, 4) is P(2, –1). Find the coordinates of P1. a. (5, –6) b. (6, –6) c. (–6, 6) d. (6, –5) 96. A block weighing 500 kN on a ramp inclined at with the horizontal. force tending to move block down the ramp is a. 211 kN b. 265 kN c. 450 kN d. 121 kN
rest 25° The the
97. 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 sinusoid c. An exponential d. A paraboloid
98. Point P(x,y) moves with a distance from point (0,1) one-half of its distance from line y = 4. The equation of its locus is a. x^2 + 2y^2 = 4 b. 2x^2 – 4y^2 = 5 c. 2x^2 + 5y^2 = 3 d. 4x^2 + 3y^2 = 12 99. Convert the θ = π/3 Cartesian equation. a. y = 3^(1/2)x b. y = x c. x = 3^(1/2) d. 3y = 3^(1/2)x
to
100. When the corresponding elements of two rows of a determinant are proportional, then the value of the determinant is a. zero b. unknown c. one d. multiplied by the ratio 101. Three sides of a trapezoid are each 8-cm long. How long is the fourth side when the area of the trapezoid has the greatest value? a. 15 b. 16 c. 12 d. 10 102. A 16 gram mass is moving at 30 cm/sec while a 4 gram mass is moving in an opposite direction at 50 cm/sec. They collide head on and stick together. Their velocity after collision is a. 0.14 m/s b. 0.28 m/s c. 0.07 m/s d. 0.21 m/s 103. A measure of the resistance of a body it offers to any change in its angular velocity, determine by its mass and distribution of its mass about the axis of
rotation is known as _________ a. Friction b. Moment of inertia c. Torsion d. Angular acceleration 104. The measure of 2.25 revolutions counterclockwise is _________. a. 810 degrees b. – 835 degrees c. 805 degrees d. – 810 degrees 105. The equation y^2 = cx is the general equation of a. y’ = x/2y b. y’ = 2x/y c. y’ = 2y/x d. y’ = y/2x 106. Evaluate the integral of (cos8A)^8dA whose limit is from 0 to π/6. (0 correct answers) a. 27 π/363 b. 12 π/81 c. 23 π/765 d. 35 π/768 107. Find the value of x in the equation csc x + cot x = 3. a. π/3 b. π/5 c. π/4 d. π/2 108. Two bodies each having a mass of 450 milligrams are separated in space a distance of 10 km apart, what is the force exerted on each other due to gravitation? a. 1.35 x 10^-25 N b. 1.35 x 10^9 N c. 1.35 x 10^19 N d. 1.35 x 10^-7 N 109. How far does an automobile move while its speed increases uniformly from 15 kph to 45 kph in 20 seconds? a. 172 m b. 200 m
c. d.
167 m 185 m
110. A machine costs P 8,000 and an estimated life of 10 years with a salvage value of P 500. What is its book value after 8 years? Using straightline method. a. P 2500 b. P 4000 c. P 3000 d. P 2000 111. It is a series of equal payments occurring at equal interval of time where the first payment is made after several periods, after the beginning of the payment. a. Deferred Annuity b. Delayed Annuity c. Simple Annuity d. Progressive Annuity 112. The difference between an approximate value of a quantity and its exact value or true value is a. absolute error b. one c. change d. relative error 113. A man wishes his son to receive P 500,000 ten years from now. What amount should he invest today if it will earn interest of 12% compounded annually during the first 5 years and 15% compounded quarterly during the next 5 years? a. P 123,433.23 b. P 145,345.34 c. P 134,678.90 d. P 135,868.19 114. In complex algebra, we use a diagram to present a complex plane commonly called _______. a. De Moivre’s diagram b. Funicular diagram c. Venn diagram
d.
Argand diagram
115. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other is 3 units less than its base. Find the altitudes, if the areas of the triangle differ by 21 sq. units. a. 5 and 11 b. 3 and 9 c. 6 and12 d. 4 and 10 116. A load of 100 lb is hung from the middle of a rope, which is stretched between two rigid walls 30 ft apart. Due to the load, the rope sags 4 ft in the middle. Determine the tension in the rope. a. 194 lbs b. 173 lbs c. 165 lbs d. 149 lbs 117. A person draws 3 balls in succession from a box containing 5 red balls, 6 yellow balls and 7 green balls. Find the probability of drawing the balls in the order red, yellow and green. a. 0.3894 b. 0.0894 c. 0.03489 d. 0.04289 118. At an interest rate of 10% compounded annually, how much will a deposit of P1,500 be in 15 years? a. P 6,100 b. P 6,437.90 c. P 6,234.09 d. P 6,265.87 119. Solve for A in the equation: cos^2 A = 1 – cos^2 A a. 45° , 135° , 225° , 315° b. 45° , 150° , 220° , 315°
c. d.
45° , 125° , 225° , 315° 45° , 125° , 225° , 335°
b. c. d.
1 3 -2
120. The line passing through the focus and is perpendicular to the directrix of a parabola. a. directrix b. latus rectum c. Tangent line d. axis of the parabola
127. A club of 40 executives, 33 likes to smoke Marlboro and 20 like to smoke Philip Morris. How many like both? a. 12 b. 13 c. 11 d. 10
121. Determine B such that 3x + 2y = 0 is perpendicular to 2x – By + 2=0 a. 5 b. 4 c. 3 d. 2
128. What is the kinetic energy of a 4000-lb automobile, which is moving at 44 ft/s? a. 1.21 x 10^5 ft-lb b. 1.12 x 10^5 ft-lb c. 1.80 x 10^5 ft-lb d. 2.10 x 10^5 ft-lb
122. Find the length of the vector (2, 4, 4). a. 7.00 b. 5.18 c. 6.00 d. 8.50
129. Evaluate the integral of dx/ (x+2) whose limit is from -6 to -10. a. ln 2 b. ln 3 c. 1/2 d. sqrt(2)
123. Three forces 20 N, 30 N and 40 N are in equilibrium. Find the angle between the 30 N and the 40 N forces. a. 28.96° b. 40° c. 25.97° d. 30°15’25” 124. Each angle of dodecagon is _______ a. 135° b. 105° c. 150° d. 125°
a regular equal to
125. If ( x + 3) : 10 = ( 3x – 2) : 8, find ( 2x – 1). a. 1 b. 4 c. 3 d. 2 126. The function y = (x-4)/(x+2) is discontinuous at x = ? a. 2
130. 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. Inverse Square Law b. Law of Universal Gravitation c. Coulomb’s Law d. Newton’s Law 131. The derivative of ln cos x is a. - sec x b. tan x c. – tan x d. sec x 132. Find the equation of the axis symmetry of the function y = 2x^2 – 7x + 5 a. 4x + 7 = 0 b. 4x – 7 = 0 c. 7x + 4 = 0 d. x – 2 = 0
133. The sum of the interior angles of a polygon is 540 degrees. Find the number of sides. a. 6 b. 8 c. 5 d. 11 134. A man expects to receive P 25,000 in 8 years. How much is that money worth now considering interest at 8% compounded quarterly a. P 13,265.83 b. P 13,859.12 c. P 13,958.33 d. P 13,675.23 135. Find the 1987th digit in the decimal equivalent to 1785/9999 starting from the decimal point. a. 5 b. 7 c. 1 d. 8 136. A regular octagon is inscribed in a circle of radius 10. Find the area of the octagon. a. 282.8 b. 288.2 c. 238.2 d. 228.2 137. 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 138. 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 1 ⁄ 2 the volume of the first?
a. b. c. d.
4 weeks 5 weeks 42 ⁄ 5 weeks 3.5 weeks
139. The distance between the centers 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. 16 π b. 64 π c. 23 π d. 72 π 140. A comfortable room temperature is 72°F. What is this temperature expressed in degrees Kelvin? a. 295 b. 275 c. 290 d. 263 141. The volume of a gas under standard atmospheric pressure 76-cm of Hg is 200 cu. inches. What is the volume when the pressure is 80 cm Hg if the temperature is unchanged? a. 190 cu. in b. 110 cu. in c. 90 cu. in d. 30.4 cu. in 142. Find the equation of the family of orthogonal trajectories of the system of parabolas y^2 = 2x + c. a. y = ce^(-x) b. y = ce^(-2x) c. y = ce^x d. y = ce^(2x) 143. A plane headed due east with airspeed of 240 mph. If a wind at 40 mph is blowing from the north, find the ground speed of the plane. a. 281 mph b. 274 mph c. 200 mph d. 243 mph
144. Find the area bounded by the curve defined by the equation x^2 = 8y and its latus rectum. a. 16/3 b. 32/3 c. 11/3 d. 22/3 145. What is the accumulated amount after three years of P 6500 invested at the rate of 12% per year compounded semi-annually? a. P 9500 b. P 9248 c. P 9221 d. P 9321 146. A collision in which the total kinetic energy after collision is less than before collision is called a. off center collision b. elastic collision c. straight line collision d. inelastic collision 147. MCMXCIV is a Roman numeral equivalent to a. 1984 b. 1974 c. 1964 d. 1994 148. In an ellipse, a chord which contains a focus and is in a line perpendicular to the major axis is a _________. a. Focal width b. Conjugate axis c. Latus rectum d. Minor axis 149. 4x^2 – 256 = 0 equation ______________ a. ellipses b. parabola c. Parallel lines d. circle
is
the of
150. It is the ratio of the ultimate stress to the allowable stress a. Strain
b. c. d.
Modulus Factor of safety Proportionality constant
151. csc 520° is equal to a. csc 20° b. tan 45° c. cos 20° d. sin 20° 152. What rate of interest compounded annually is the same as the rate of interest of 8% compounded quarterly? a. 7.90% b. 6.88% c. 8.24% d. 8.42%
157. Find the angle in mils subtended by line 10 yards long a distance of 5000 yards a. 1 mil b. 2.5 mils c. 4 mils d. 2.04 mils 158. Money borrowed today is to be paid in 6 equal payments at the end of 6 quarters. If the interest is 12% compounded quarterly. How much was initially borrowed if quarterly payment is P 2,000? a. P 10,586.99 b. P 10,200.56 c. P 10,382.90 d. P 10,834.38
153. What is the moment of inertia of a circle of radius 5 m with respect to its tangent? a. 2454 m^4 b. 1473 m^4 c. 2054 m^4 d. 490 m^4
159. A function F(x) is called _________ of f(x) if F’(x) = f(x) a. Explicit function b. antiderivative c. derivative d. implicit function
154. If the roots of an equation are zero, then they are classified as a. extraneous solutions b. conditional solutions c. Hypergolic solutions d. trivial solutions
160. It is the characteristics of a population which is measurable. a. Frequency b. Sample c. Parameter d. Distribution
155. The segment from (-1 , 4) to (2 , -2) is extended three times its own length. The terminal point is a. (11 , -24) b. (11 , 18) c. (11 ,-20) d. (-11 , -20)
161. If 84° – 0.4x = Arc tan (cot 0.25x), find x. a. 20° b. 30° c. 10° d. 40°
156. The sides of a right triangle are 8, 15 and 17 units. F each side is doubled, how many square units will the area of the new triangle? a. 300 b. 320 c. 240 d. 420
162. What is the value of log(sub 2)5 + log(sub 3)5? a. 3.97 b. 3.79 c. 7.39 d. 9.37 163. 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. 156 sq. cm b. 175 sq. cm c. 170 sq. cm d. 165 sq. cm 164. Convergent series is a sequence of decreasing numbers or when the succeeding term is _______ then the preceding term. a. ten times more b. greater c. lesser d. equal 165. Simplify 4 cos y sin y (1 – 2 sin^2 y) a. tan 4y b. cos 4y c. sec 4y d. sin 4y 166. The sum of two numbers is 21, and one number is twice the other. Find the numbers. a. 8 and 13 b. 7 and 14 c. 2 and 12 d. 5 and 12 167. If the sides of a parallelogram and an include angle are 6°, 10° and 100° respectively, find the length of the shorter diagonal. a. 10.63 b. 10.37 c. 10.23 d. 10.73 168. What interest rate compounded monthly is equivalent to 10% effective rate? a. 9.47% b. 9.75% c. 9.57% d. 9.68% 169. Ten less than four times a certain number is 14. Determine the number.
a. b. c. d.
5 7 4 6
170. What is the moment of inertia of a cylinder of radius 5 m and a mass of 5 kg? a. 62.5 kg-m^2 b. 120 kg-m^2 c. 72.5 kg-m^2 d. 380 kg-m^2 171. In an ellipse, a chord which contains a focus and is in a line perpendicular to the major axis is a ______ a. Focal width b. Minor axis c. Latus rectum d. Conjugate axis 172. Find the value of k for which the equation x^2 + y^2 + 4x - 2y - k=0 represents a point circles a. 6 b. -6 c. -5 d. 5 173. The altitude of the sides of a triangle intersect at the point known as a. orthocenter b. centroid c. incenter d. circumcenter 174. The electrons have speeds of 0.7c and x respectively. If their relative velocity is 0.65c. Find x. a. 0.09c b. 0.12c c. 0.25c d. 0.02c 175. Given an ellipse ( x^2/36 ) + ( y^2/32 ) = 1. Determine the distance between foci. a. 3 b. 4 c. 18 d. 2
176. What will be the future worth of money after 12 months, if the sum of P 25,000 is invested today at simple interest rate of 1% per month? a. P 27,859 b. P 30,000 c. P 28,000 d. P 29,000 177. “At any point along the streamline 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 a. Fluid theory b. Hydraulic theorem c. Pascal’s theorem d. Bernoulli’s Energy Principle 178. How long will it take the money to triple itself if invested at 10% compounded semi-annually? a. 11.3 yrs b. 13.3 yrs c. 12.5 yrs d. 11.9 yrs 179. Whenever a net force acts on a body, it produces acceleration in the direction of the resultant force, an acceleration that is directly proportional to the mass of the body. This theory is popularly known as a. Newton’s First Law of Motion b. Hooke’s Law of Equilibrium c. Newton’s Second Law of Motion d. Faraday’s Law of Forces 180. A circle with a radius of 6 has half of its area removed by cutting a border of uniform width. Find the width of the border.
a. b. c. d.
2.2 1.35 3.75 1.76
181. It can be defined as the set of all points in the plane whose distances from two fixed points is a constant a. Circle b. Parabola c. Ellipse d. Hyperbola 182. The moment of inertia of a plane figure, a. Decreases as the distance of the axis moves farther from the centroid b. Is zero at the centroidal axis c. Is maximum at the centroidal axis d. Increases as distance of the axis moves farther from the centroid 183. 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 = 10 m/s. a. 12 m/s b. 8 m/s c. 14 m/s d. 10 m/s 184. The population of the Philippines doubled in the last 30 years from 1967 to 1997. Assuming the rate of population increase will remain the same, in what year will the population triple? a. 2027 b. 2015 c. 2030 d. 2021 185. Find the 30th term of the arithmetic progression 4, 7, 10…. a. 71
b. c. d.
61 91 81
186. If 15 people won prizes in the state lottery (assuming that there are no ties), how many ways can these 15 people win first, second, third, fourth and fifth prizes? a. 3,003 b. 360,360 c. 116,260 d. 4,845 187. It describes the luminous flux incidence per unit area and is expressed in lumens per square meter. a. Illuminance b. Luminous intensity c. Luminance d. Radiance 188. In the expansion (x + 4y)^12, the numerical coefficient of the 5th term is, a. 253,440 b. 506,880 c. 63,630 d. 126,720 189. A sequence of numbers where the succeeding term is greater than the preceding term. a. Convergent series b. Isometric series c. Dissonant series d. Divergent series 190. If sec^2 A is 5/ 2, the quantity 1 – sin^2 A is equivalent to _________. a. 0.6 b. 0.4 c. 2.5 d. 1.5 191. It is a stock that has prior right to dividends. It usually does not bring voting rights to the owners and the dividend is fixed and cannot
be higher than the specified amount. a. Common stock b. Non par value stock c. Preferred stock d. Voting stock
each year, with interest at 15% compounded annually? a. P 41,454.29 b. P 41,114.29 c. P 40,454.29 d. P 40,544.29
192. At maximum point the value of y” is a. positive b. infinite c. zero d. negative
198. The hypotenuse of the right triangle is 34 cm. Find the length of the two legs, if one leg is 14 cm longer than the other. a. 15 and 29 b. 16 and 30 c. 17 and 31 d. 18 and 32
193. The attitude of a cylinder of maximum volume which can be inscribed in a right circular cone of radius r and height h is ________. a. 3h/2 b. h/3 c. h/4 d. 2h/3 194. Momentum is the product of mass and ________ a. Acceleration b. force c. time d. velocity 195. The arithmetic mean of 80 numbers is 55. If the two numbers namely 250 and 850 are removed, what is the arithmetic mean of the remaining numbers? a. 38.62 b. 57.12 c. 42.31 d. 50 196. Point of derivatives which do not exists (and so equals zero) are called a. Maximum and minimum points b. Minimum points c. Stationary points d. Maximum points 197. What is the accumulated amount of five year annuity paying P 6,000 at the end of
199. Find the sum of the infinite geometric progression 6, -2, 2/3, …….. a. 9/2 b. 11/2 c. 7/2 d. 5/2 200. ABC Corporation makes it a policy that for any new equipment purchased; the annual depreciation cost should not exceed 20% of the first cost at any time with no salvage value. Determine the length of service life necessary if the depreciation used is the SYD method a. 12 years b. 9 years c. 19 years d. 10 years
ANSWER KEY
1. Division 2. Depreciation 3. 19.3 4. Monopsony 5. 4.72° 6. f”(a)=0 7. 34.64 cm 8. 0.0045 kg-m^2 9. 2x – y – 2 = 0 10. Rational 11. Frequency 12. 4 and 10 13. 76.31 m
14. Lesser 15. 19/27 16. 0.0025 m 17. Limacon 18. -3/5 19. P 15,614.59 20. 1/x 21. 5x^2 + 3x – 2 = 0 22. x=-4 23. 500x/(pi)n 24. 8/3 25. 12x^2 – 7x + 1 = 0 26. 15.56% 27. X-axis 28. 1/7 29. Market value 30. 2.25 ft/s^2 31. 883 m 32. 5/13 33. 16, 20 34. 36π 35. P 12, 835.32 36. (1, 1) 37. π/4
38. Standing waves are produced 39. ¾ 40. 540
74. (-1,1) 75. 3.71 m 76. 19.72% 77. 2.5 miles 78. Diameters 79. 58.9 80. Radius
41. Total kinetic energy 42. 10.7 43. Zero 44. 2 45. 2046 46. 374 m 47. 0.03 x^3 cu. In 48. 0.281 49. 2 50. 44% 51. 94,550,000 miles 52. Nonagon 53. Dihedral angle 54. P 1,295.05 55. -2[sqrt(2)cos((1/2)x) + c 56. 91 57. -4(1 + i) 58. 0.0017 m 59. The tangent function of angle of trajectory equal to one 60. Linear
61. 3 sq. units 62. 11.57 years 63. Monopsony 64. 2 65. Origin 66. IV 67. y = x^2 + c 68. 6 rad/s 69. 297/425 70. 14.49% 71. cos(-T) = cos (T) 72. 2.93 ft/sec^2 73. Dispersion
must
81. 23, 27 82. 12 ft/s 83. Zero 84. (1,2) 85. Utility 86. 16 87. -2 88. Infinity 89. Annulus 90. 0.02
the be
112. 113. 114. 115. 116. 117. 118. 119.
absolute error Argand diagram 4 and 10 194 lbs 0.04289 P 6,265.87 45° , 135° , 225° ,
315°
91. 12.75 mm 92. 11,777.4 kph 93. Evolution 94. 1.52 s 95. (6, –6) 96. 211 kN 97. A sinusoid 98. 4x^2 + 3y^2 = 12 99. y = 3^(1/2)x 100. zero 101. 102. 103. 104. 105. 106. 107. 108. 109. 110.
16
111.
Deferred Annuity
0.14 m/s Moment of inertia 810 degrees y’ = y/2x 35 π/768 π/5 1.35 x 10^-25 N 167 m P 2500
150.
Factor of safety
151. 152. 153. 154. 155. 156. 157. 158. 159. 160.
csc 20°
161. 162. 163. 164. 165. 166. 167. 168. 169. 170.
40°
171. 172. 173. 174. 175. 176. 177.
Latus rectum
P 135,868.19
120.
axis of the parabola
121. 122. 123. 124. 125. 126. 127. 128. 129. 130.
3
131. 132. 133. 134. 135. 136. 137. 138. 139. 140.
– tan x
141. 142. 143. 144. 145. 146. 147. 148. 149.
190 cu. In
6.00 28.96° 150° 3 -2 13 1.21 x 10^5 ft-lb ln 2 Coulomb’s Law
4x – 7 = 0 5 P 13,265.83 8 282.8 Longitudinal strain 42 ⁄ 5 weeks 64 π 295
y = ce^(-x) 243 mph 32/3 P 9221 inelastic collision 1994 Latus rectum Parallel lines
8.42% 2454 m^4 trivial solutions (11 ,-20) 240 2.04 mils P 10,834.38 Antiderivative Frequency
3.79 165 sq. cm Lesser sin 4y 7 and 14 10.73 9.57% 6 62.5 kg-m^2
-5 Orthocenter 0.09c 4 P 28,000 Bernoulli’s
Energy
Principle
178. 179.
11.3 yrs
181. 182.
Ellipse
184.
2015
Newton’s Second Law of Motion 180. 1.76
Increases as distance of the axis moves farther from the centroid 183. 10 m/s
185. 186. 187. 188. 189. 190.
91
191. 192. 193. 194. 195. 196.
Preferred stock
198. 199. 200.
16 and 30
360,360 Illuminance 126,720 Divergent series 0.4
Negative h/3 velocity 42.31
Maximum minimum points 197. P 40,454.29 9/2 9 years
and
