Mathematics 1

MATHEMATICS 1. 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 7. 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 b. c. d. 5 and 11 3 and 9 6 and 12 8. 2. 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 9. 3. 4. 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 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 5. 6. 10 b. origin 28. Total momentum b. 4) with respect to the translated axis with origin at (1. How far from the throwing point will the ball attain its original level? a. 36π c. 2. 875 m 32. . 480 b. 1023 b.25 ft/s^2 31. d. Total potential energy c. 24π 35. 853. Use value c. 11 d. Y-axis b. The roots of a quadratic equation are 1/3 and 1/4. Determine the acceleration after the time interval of 10 sec. 1. 4 8/3 c. undefined 29. infinity d. P 12. 1) 37. 9. 881. What is the equation? a. (1.c. m is _______. –1) b. 1/4 c. 7. The phase difference is always zero b. 385. d. Find the ratio of an infinite geometric progression if the sum is 2 and the first term is 1/2. 11. Total kinetic energy d. 15. 540 41.32 36. 2 d.5 c.5 45. 12π d. 1/3 b. 8. …. The volume of a sphere is 36π cu. 16. 890 m b. Standing waves are produced d. a. 2 c. 4. the resulting fraction is 3/5. a.37 b.7 b. 12x^2 + 7x –1 = 0 d. π/3 d. 16. 880 m d. When the two waves of the same frequency speed and amplitude travelling in opposite directions are superimposed. Arctan[2cos(Arcsin(sqrt(3)/ 2))] is equal to a. 20 34. Fair value b. P 12. 2046 46.32 d. Evaluate the limit (x-4)/ (x^2 – x – 12) as x approaches 4 a.. 15% compounded semiannually will have an effective rate of _________. 16. 840 c. a. P 12.7 d. π/2 b. the bearing of tower C is 32° W of N and from B the bearing of C 26° N of E. 5/3 d. 12x^2 + 7x + 1 = 0 26. the curve is symmetric with respect to the __________ a. 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. The velocity of an automobile starting from rest is given by ds/dt = (90t) ⁄ (t+10) feet/sec. 680 d. The surface area of this sphere in sq. The denominator of a certain fraction is three more than twice the numerator.56% d. 13/5 33. Distractive waves are produced c.7 43. 10. 3/4 d. is a. (1.02% 27. Find the original fraction a. units) bounded by the parabolas x^2 – 2y = 0 and x^2 + 2 – 8=0 a. a. a.7 c. π/4 38. If all the y – terms have even exponents. 15. π/16 c. Constructive interference always results 39. 4. 883 m c. e 44. 5/13 c. A semiconductor company will hire 7 men and 4 women. 8/ 3 b. 12. Line 45° with the axis d. 1. a. a. In how many ways can the company choose from 9 men and 6 women who qualified for the position? a. Points A and B 1000 m apart are plotted on a straight highway running east and west. infinity b. 2. 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.93% c. If 7 is added to both terms of the fraction. How much must you invest today in order to withdraw P 2. 1596 d. What are the lengths of the bases? a.32 c. Its two bases have ratio of 4:5. a. –1) c. (–1. Find the coordinates of the point P(2. Find the area (in sq. 1 c. 1/7 d. A trapezoid has an area of 36 m^2 and altitude of 2 m. zero b. Market value 30.3). Evaluate the limit ln x/x as x approaches infinity. You find 7% and 12% solution on the shelves. 225 c. Approximate the shortest distance of the tower from the highway. X-axis c.10 ft/s^2 25. a. 835. The sum of the first 10 terms of a geometric progression 2.71 ft/s^2 b. P 12. Total mechanical energy 42. 18. 2.75 ft/s^2 2. Book value d. 12x^2 – 7x – 1 = 0 c. The work done by all forces except the gravitational force is always equal to the ________ of the system.78% b. 3 b. 1) d. 18π b. For a particular experiment you need 5 liters of a 10% solution. 1/2 40. 12x^2 – 7x + 1 = 0 b. 000 annually for 10 years if the interest rate is 9%? a. (–1.15 c. 8. 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. m. From A. Find the area of the triangle which the line 2x – 3y + 6 = 0 forms with the coordinate axes. 94. a. -2[sqrt(2)cos((1/2)x) + c d. Monopoly c. Reflex angle d.000 miles and the eccentricity of the ellipse is 1/60. origin d. II 67. 0.34 years b.axis c. What is the allowable error in measuring the edge of the cube that is intended to hold 8 cu.335. Determine the semi-annual payment.200 b. in d. 4 c.03 x^3 cu. 90 65. Maximize velocity c.02 cu. x = y^2 + c c. then the function is a. 10. 4 sq. X . If log of 2 to the base 2 plus log of x to the base 2 is equal to 2. nonagon 53. When will the girl receive the money if the fund is invested at 8% compounded quarterly? a. 0. -2[sqrt(2)cosx] + c b. 2 sq. 0. in c.193.1700 m c. heptagon c. Solve for x in the equation: Arc tan x = (π/2) – 45°.0710 m d. 0. 0. Find the value of (1 + i)^5.45 d. 91 57. 0. ……. linear c.45 years c. c. 7. 2 b. Find the angular velocity of the wheel. 10. Maximize the angle of elevation 60. Find the equation of the curve at every point of which the tangent line has a slope of 2x a. -2[sqrt(2)cos((1/2)x) + c 56. a. The tangent function of the angle of trajectory must be equal to one b. 0. 2 b. logarithmic 61. in 48. The major axis of the elliptical path in which the earth moves around the sun is approximately 186. 93.281 b. The first due in 6 months. Integrate the [sqrt(1 – cos x)]dx a. I d. If a regular polygon has 27 diagonals. 88 d. sinusoidal d. pentagon b. b. if sec A is positive and csc A is negative? a.295. 4(1 + i) b. 56% b. 46% c. which of the following applies? a. 94. Maximize the angle of elevation and velocity d. units 62. P 1. A debt of P 10. x = -y^2 + c d. Oligopsony b. Plane angle b. a.i d.218 c.1 x^3 cu.000 miles d. -2 d. 180 d.0170 m b.182 49.821 d. IV b. 0.05 c. y = -x^2+ c b.000. Given a cone of diameter x and altitude of H. 90 c. hexagon d. 364 384 394 374 m m m m 47. If the first derivative of a function is a constant. A rotating wheel has radius of 2 ft and 6 inches. P1. units d. 2 rad/s . 4 rad/s b. Monopsony d. What is the least common factor of 10 and 32? a. Find the approximate change in the volume of a cube of side “x” inches caused by increasing its side by 1%. 91. a. a. Find the 30th term of the arithmetic progression 4.000.000 miles b. where i is an imaginary number. 5 sq. Y . -4(1 + i) 58. Oligopoly 64.000. a. 6 rad/s d. its curve is symmetric with respect to the a..100 miles c. Dihedral angle c. P 1.90 55. then the value of x is _______ a.0017 m 59.57 years d. y = x^2 + c 68. a. If the equation is unchanged by the substitution of y for x.000 is left to a girl to be held in trust fund by her guardian until it amounts to P 50. units b. quadratic b. A point on the rim of the wheel moves 30 ft in 2 seconds. 0. 7. a. the amount of divergence between the two planes is expressed by measuring the __________. P 1. d. m. the sum of P 20. m? a. When two planes intersect with each other. a. By the condition of a will.000 miles 52. a. 0. 3 sq. 65% d. line 45° with the x axis b. 10. 0. 11. then it is a ________. -1 50. A market situation whereby there is only one buyer of an item for which there are no goods substitute.axis 66.400. if the error of the computed volume is not to exceed 0.3 x^3 cu. III c. 44% 51. Of what quadrant is A.a. units c. in b. What percent is the volume of the largest cylinder which can be inscribed in the cone to the volume of the cone? a. a. Determine the apogee of the earth. 1 + i c. 0. 1 . 75 b.000 with 10% interest compounded semiannually is to be amortized by semi-annual payment over the next 5 years. 5 rad/s c. 320 c.450.02 x^3 cu. To maximize the horizontal range of the projectile.550.. -2[sqrt(2)cosx] + c c.98 years 63. Polyhedral angle 54. Find the 100th term of the sequence 1. central tendency d.5 miles 78. 20 87. (-1. 3. -2 88. When the balloon is 40 ft from A. 89.84% b. 16.04 d. has a slope equal to ________.8 80. 17.5 x 107 m from the earth? csc(-T) = csc(T) sin(-T) = sin(T) cos(-T) = cos (T) tan(-T) = tan (T) 72. 12 c. 59. 297/452 70. Circular disk 90.01. The arithmetic mean of 6 numbers is 17. 2) a. Find the slope of x^2y = 8 at the point (2. A merchant has three items on sale namely: a radio for $50. What is the area of the sector in cm? a. circumference b.12 ft/sec^2 b. How far downstream should he go if he is to return in 7/4 hours after leaving? a. 16 b.4) b.000.-2) 75. ring b. (4. infinity d. Determine the coordinates of the point which is threefifths of the way from the point (2.75 mm c. certainty 74. The quartile deviation is a measure of ________. 15 ft/s b. The area of the region bounded by two concentric circles are called a. The angle of a sector is 30° and the radius is 15 cm.93 ft/sec^2 d. 13 ft/s 83.41 m c. 297/425 d.35% 77. -1/2 d. annulus d. What are the two numbers if their difference is 4? a. 4. A statue 3 m high is standing on base of 4 m high. 14. A man rows downstream at the rate of 5 mph and upstream at the rate of 2 mph. the new set of numbers will have an arithmetic mean of 19. 976/435 b. 3.39 ft/sec^2 73.2) c.05 c. 4 c. 80 d. 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.72% d. 12.99…. If two numbers are added to the progression. major axes c. 8. a. 1 b.00.41 m 76. Find the thickness of the wall if the allowable compressive stress is 10MPa a.36% c. 0. 2 d. 10 ft/s c. A horizontal line has a slope of a. 12 ft/s d. A balloon is rising vertically over a point A on the ground at the rate of 15 ft/s.00 ft/sec^2 c. radical axes 79. a.9 b.57 mm b. 58. a. 0.1) b. 5) a. luxuries d. dispersion b. How many radios did she sell? a. 3. 0. -1 c. 2.71 m d.00.49% 71.75 mm d. are known as _________. division c. necessity 86. 17. -5) to the point (-3. The effective rate of 14% compounded semi-annually is a.75 mm 92. 0. positive b. 2.9 d.1 miles b. while travelling in a straight line. 2. (2. A point B on the ground level with and 30 ft from A.1) d. (1. washer c.00 on the total sales.51 m b. (-1. The apothem of the polygon is the ________ of its inscribed circle. 2. A car accelerates at a constant rate from 15 mi/hr to 45 mi/hr in 15 seconds. 2. utility b. length d.94% d.02 91. 27 d. 15. 14. The cords of an ellipse. What is the speed of a synchronous earth’s satellite 4.00.8 c. infinity c. (-1. Which true? a. 3. 2. which is perpendicular to the x-axis. 16. a. (1. negative 84. b. An iron column of annular cross-section has an outer diameter of 200 mm and is subjected to a force of 75 kN. 12.1) d.88% b.7 miles c. What is the average acceleration? a. a. Evaluate cos [arctan(15/8) – arctan(7/24)] a. 17. she has sold a total of 100 of the three sale items and has taken exactly $1.-1) c. 14.4) 85. 792/525 c. 3. how far should he stand from the . of the following is base in order that the angle subtended by the statue is a maximum a. 2 b. d. At the end of the day. zero c.3 miles d. a clock for $30. 23. 85. 20 b.00 and a flashlight $1. diameters b. c. discount c. 21. radius 81. diameter c.03 b. e 89. which pass through the center. asymptote d. 12. 1. What is the effective rate corresponding to 18% compounded daily? Take 1 year = 365 days. It is defined to be the capacity of a commodity to satisfy human want. 19. 25 82.68% c. A line. 0. a. at what rate is its distance from B changing? a.69.5 m above the ground. If an observer’s eye is 1. (-2. a. d. A 50 kg block of wood rest on top of the smooth plane whose length is 3 m and whose altitude is 0. 2. 2.28 m/s c. Moment of inertia c. a.23 b. The midpoint of the line segment between P1(x1. They collide head on and stick together. a. –1). A paraboloid . 265 kN c.41 s 95. P 2500 b. a. 15 b. 2x^2 – 4y^2 = 5 c. zero b. Delayed Annuity c. 12 π/81 c.8 m. A man wishes his son to receive P 500. the operation of root extraction is called as _________. It is a series of equal payments occurring at equal interval of time where the first payment is made after several periods. revolution b. 6) d.35 x 10^19 N d. one c. 12 d.14 s c. A sinusoid c. P 2000 111. 805 degrees d.000 and an estimated life of 10 years with a salvage value of P 500. change d.14 m/s b. 2. force tending to move block down the ramp is a. If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve.000 ten years from now. y’ = y/2x 106. How long will it take for the block to slide to the bottom of the plane when released? a. – 810 degrees 105. In complex algebra.51 s d. De Moivre’s diagram b. multiplied by the ratio 101. Two bodies each having a mass of 450 milligrams are separated in space a distance of 10 km apart. 1. Their velocity after collision is a. 810 degrees b. –5) 96. 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. Point P(x. A measure of the resistance of a body it offers to any change in its angular velocity. An exponential d. Deferred Annuity b. 1. How long is the fourth side when the area of the trapezoid has the greatest value? a. relative error 113. The measure of 2.35 x 10^-25 N b. 172 m b. absolute error b. we use a diagram to present a complex plane commonly called _______.90 d. 0. 167 m 185 m 110.070. A cissoid b. 12. 1. π/5 c. The difference between an approximate value of a quantity and its exact value or true value is a. P 135. 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. b. What is its book value after 8 years? Using straightline method. –6) b. In Algebra. y’ = 2y/x d. P 134. π/2 108. (6. after the beginning of the payment. P 123. unknown c. Three sides of a trapezoid are each 8-cm long. P 145. x^2 + 2y^2 = 4 b. a. x = 3^(1/2) d. How far does an automobile move while its speed increases uniformly from 15 kph to 45 kph in 20 seconds? a. Progressive Annuity 112. a. 4x^2 + 3y^2 = 12 99. 35 π/768 107. 4) is P(2. 10 102. When the corresponding elements of two rows of a determinant are proportional. Evaluate the integral of (cos8A)^8dA whose limit is from 0 to π/6. A machine costs P 8. Angular acceleration 104.52 s b.19 114.07 m/s d. Funicular diagram c. what is the force exerted on each other due to gravitation? a. a. y = 3^(1/2)x b. 0.34 c. (5.4 kph 12. then the value of the determinant is a. (6.y) moves with a distance from point (0.000 kph 93. Find the value of x in the equation csc x + cot x = 3. 16 c. Find the coordinates of P1.678. one d. determine by its mass and distribution of its mass about the axis of 97. (0 correct answers) a. Convert the θ = π/3 Cartesian equation.777.35 x 10^9 N c.433.a. y1) and P2(–2. a. a. 200 m c.2 kph 11. Simple Annuity d. π/3 b. The equation of its locus is a.25 revolutions counterclockwise is _________. 450 kN d. –6) c. The equation y^2 = cx is the general equation of a.070 kph 11.35 x 10^-7 N 109. y = x c. P 4000 c. 23 π/765 d. 2x^2 + 5y^2 = 3 d. y’ = x/2y b. A block weighing 500 kN on a ramp inclined at with the horizontal. 1. 121 kN rest 25° The the 98. – 835 degrees c. 1. the curve is _________. (–6. evolution 94.345. 3y = 3^(1/2)x to rotation is known as _________ a. y’ = 2x/y c. d. Torsion d. π/4 d. involution d. Venn diagram 100. resolution c. 0.1) one-half of its distance from line y = 4.21 m/s 103. Friction b. 27 π/363 b. P 3000 d. 211 kN b. 0.868. c. a. 2. 238. 105° c.10 x 10^5 ft-lb 129. if the areas of the triangle differ by 21 sq.500 be in 15 years? a.2 d. Longitudinal strain b. 225° . 12 b. 4 c. 11 134. when will be the second be 1 ⁄ 2 the volume of the first? 125. 2 . Find the probability of drawing the balls in the order red. 225° .23 135. 4. Find the area of the octagon. 135° b. 11 d. How many like both? a. a. 150° d.00 d. 0. a. 315° b. 5 d. The line passing through the focus and is perpendicular to the directrix of a parabola.33 d. Each angle of dodecagon is _______ a. The sum of the interior angles of a polygon is 540 degrees. 45° . 6 and12 d. 5. How much is that money worth now considering interest at 8% compounded quarterly a. axis of the parabola 121. Three forces 20 N. 4x – 7 = 0 c. Solve for A in the equation: cos^2 A = 1 – cos^2 A a. 30°15’25” 124. P 6. P 13. 13 c.12 c. The function y = (x-4)/(x+2) is discontinuous at x = ? a. 1.234. Newton’s Law 131. Law of Universal Gravitation c. 1/2 d. At an interest rate of 10% compounded annually.100 b. 315° 45° . 2 122. a. Due to the load. 0. a.96° b. 1 3 -2 120. 25. latus rectum c. Find the altitudes. A club of 40 executives. Linear strain c. 173 lbs c. Shear strain d. Inverse Square Law b. d. “The force between two charges varies directly as the magnitude of each charge and inversely as the square of the distance between them. P 6. According to this law. Equal volumes of two different liquids evaporate at different. x – 2 = 0 133. d. and the second in 7 weeks. Determine the tension in the rope. 125° . A regular octagon is inscribed in a circle of radius 10. 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. a. 5 b. a.12 x 10^5 ft-lb c. Find the equation of the axis symmetry of the function y = 2x^2 – 7x + 5 a. Find the 1987th digit in the decimal equivalent to 1785/9999 starting from the decimal point. 288. If the first is totally evaporated in 6 weeks. P 13. a.03489 d. ln 3 c. 10 128.04289 118. which is stretched between two rigid walls 30 ft apart. 194 lbs b. a. 125° a regular equal to 127. 5 b. If ( x + 3) : 10 = ( 3x – 2) : 8. 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. Coulomb’s Law d. 282. sec x 132.sec x b. 3 and 9 c. 315° 45° . – tan x d. 7x + 4 = 0 d.2 c. 3 d.83 b. 6 yellow balls and 7 green balls. the rope sags 4 ft in the middle. 335° b. units. A load of 100 lb is hung from the middle of a rope. directrix b. 135° . but constant rates.d. 6. 0.437. Evaluate the integral of dx/ (x+2) whose limit is from -6 to -10. 8 c. 1 d.18 c. 4 and 10 116. 165 lbs d. a. 4 c. A man expects to receive P 25. 149 lbs 117. 28.3894 b. yellow and green. 45° .” a.09 d. P 13.958. a. 4). A person draws 3 balls in succession from a box containing 5 red balls. 8 136. 1 b. 40° c. 0.21 x 10^5 ft-lb b.0894 c.675. 1. Determine B such that 3x + 2y = 0 is perpendicular to 2x – By + 2=0 a. P 6. 2 126. a. tan x c. find ( 2x – 1). 150° .80 x 10^5 ft-lb d. 33 likes to smoke Marlboro and 20 like to smoke Philip Morris. P 6. 5 and 11 b. . ln 2 b. 3 d. 4x + 7 = 0 b. 115.50 123.00 b. c. 7 c.87 119.265.2 137. Tangent line d.265.8 b.90 c.97° d. 7. how much will a deposit of P1. Volume strain 138. 220° . 30 N and 40 N are in equilibrium. 1. which is moving at 44 ft/s? a. 225° . The derivative of ln cos x is a. Find the length of the vector (2. Find the angle between the 30 N and the 40 N forces. 125° . P 13. What is the kinetic energy of a 4000-lb automobile.859. 228. sqrt(2) 130.000 in 8 years. Argand diagram c. Two triangles have equal bases. 6 b. 8. Find the number of sides. then they are classified as a. What rate of interest compounded annually is the same as the rate of interest of 8% compounded quarterly? a. 40° 162. (-11 . F each side is doubled. Hypergolic solutions d. csc 20° b.79 c. Distribution 161. 320 c. 263 141. 281 mph b. 90 cu. 200 mph d. 8. Minor axis 149. A function F(x) is called _________ of f(x) if F’(x) = f(x) a. cos 20° d. 490 m^4 154. The sides of a right triangle are 8. 10° d. 243 mph 144. tan 45° c. 1974 c. P 10.90 d. Latus rectum d. y = ce^(2x) 143. 11/3 d. P 9248 c. Parameter d. If the interest is 12% compounded quarterly. P 10. d. Parallel lines d. P 10.39 d. 23 π d. 110 cu. csc 520° is equal to a. 295 b. Focal width b. Explicit function b. a. find the ground speed of the plane.97 b. a. sin 20° 152. parabola c. 7. P 9321 146. Find the angle in mils subtended by line 10 yards long a distance of 5000 yards a. extraneous solutions b. conditional solutions c. 2. 30. The area of the largest circle is a. 30° c. Money borrowed today is to be paid in 6 equal payments at the end of 6 quarters. 300 b. in c. 22/3 145. 16/3 b. P 10. 240 d. How much was initially borrowed if quarterly payment is P 2. elastic collision c. 15 and 17 units. If the roots of an equation are zero. In an ellipse. in d. A piece of wire is shaped to enclose a square whose area is 169 sq. What is the accumulated amount after three years of P 6500 invested at the rate of 12% per year compounded semi-annually? a. antiderivative c. (11 . 3. y = ce^(-x) b. Conjugate axis c. The terminal point is a.37 163. c. in b. find x. The segment from (-1 . 16 π b. Find the area bounded by the curve defined by the equation x^2 = 8y and its latus rectum. inelastic collision 147. -20) 156.25x).586.04 mils 158.88% c. P 9500 b. 420 157. A plane headed due east with airspeed of 240 mph.5 mils c. 9. a chord which contains a focus and is in a line perpendicular to the major axis is a _________. 1 mil b. ellipses b. What is the moment of inertia of a circle of radius 5 m with respect to its tangent? a. 2. It is then reshaped to enclose a 150. 7. (11 . 4 mils d. Frequency b.4x = Arc tan (cot 0.4 cu. Modulus Factor of safety Proportionality constant 151. -2) is extended three times its own length. 4x^2 – 256 = 0 equation ______________ a. implicit function 160. Strain . trivial solutions 155. If a wind at 40 mph is blowing from the north. What is this temperature expressed in degrees Kelvin? a. It is the ratio of the ultimate stress to the allowable stress a. 1964 d. Find the equation of the family of orthogonal trajectories of the system of parabolas y^2 = 2x + c. The volume of a gas under standard atmospheric pressure 76-cm of Hg is 200 cu. What is the value of log(sub 2)5 + log(sub 3)5? a. 4) to (2 . a.42% 153.200. 2454 m^4 b. It is the characteristics of a population which is measurable. If 84° – 0. 20° b.56 c. b.90% b. 290 d.834. off center collision b. 1994 148. (11 . The distance between the centers of the three circles which are mutually tangent to each other externally are 10. A collision in which the total kinetic energy after collision is less than before collision is called a.a. circle is the of b. y = ce^x d.-20) d.000? a. What is the volume when the pressure is 80 cm Hg if the temperature is unchanged? a. 275 c. 2054 m^4 d. A comfortable room temperature is 72°F. 32/3 c. 64 π c. 8. cm.99 b. derivative d. a. P 9221 d. 3. 1473 m^4 c.38 159. 72 π 140. 190 cu. d. c.24% d. MCMXCIV is a Roman numeral equivalent to a.5 weeks 139. 18) c. -24) b. Sample c. inches. 274 mph c. 6. how many square units will the area of the new triangle? a. 4 weeks 5 weeks 42 ⁄ 5 weeks 3. 1984 b. straight line collision d. a.382. a. 12 and 14 units. y = ce^(-2x) c. in 142. 2015 c.57% d. cm 164. A circle with a radius of 6 has half of its area removed by cutting a border of uniform width.rectangle whose length is 15 cm. cos 4y c. 10. orthocenter b. -6 c. it produces acceleration in the direction of the resultant force.09c b.5 kg-m^2 d. sin 4y 166. Find the numbers. 156 sq. 10° and 100° respectively. d. 3 b. 5 7 4 6 170. With what speed in meters per second does it strike the ground? Assume g = 10 m/s. 14 m/s d. Whenever a net force acts on a body. P 27. Is maximum at the centroidal axis d. 2027 b. Find the 30th term of the arithmetic progression 4. 10. How long will it take the money to triple itself if invested at 10% compounded semi-annually? a. 0. a. Ten less than four times a certain number is 14. sec 4y d. 9. centroid c. 380 kg-m^2 171. What will be the future worth of money after 12 months. 10. the potential energy per unit volume and the kinetic energy per unit volume has the same value. a. circumcenter 174. Bernoulli’s Energy Principle 178.9 yrs 179. Determine the distance between foci. 7. P 29. Latus rectum d. 170 sq. This theory is popularly known as a. 10…. If the sides of a parallelogram and an include angle are 6°.75% c. cm c. 9. the sum of the pressure. cm b. a.5 kg-m^2 b.3 yrs b. a.65c. Is zero at the centroidal axis c. ten times more b. d.7c and x respectively. It can be defined as the set of all points in the plane whose distances from two fixed points is a constant a. a.5 yrs d. 5 173. 9. Find the width of the border. Find the value of k for which the equation x^2 + y^2 + 4x . 120 kg-m^2 c. Given an ellipse ( x^2/36 ) + ( y^2/32 ) = 1. lesser d. 11.000 c. 9. Hydraulic theorem c.859 b. 8 m/s c. The moment of inertia of a plane figure. cm d. and one number is twice the other. b. -5 d. c. 62.” This concept is known as a. b.63 b. Fluid theory b. Faraday’s Law of Forces 180. 5 and 12 167. 2. Determine the number. P 30. 10 m/s 184.12c c. Newton’s First Law of Motion b.68% 169. 4 c. Decreases as the distance of the axis moves farther from the centroid b.000 is invested today at simple interest rate of 1% per month? a. c.73 168. Assuming the rate of population increase will remain the same.75 1. The area of the rectangle is __________. 71 . Increases as distance of the axis moves farther from the centroid 183. a. Convergent series is a sequence of decreasing numbers or when the succeeding term is _______ then the preceding term. 7 and 14 c. 8 and 13 b. 12. a. 2 176. find the length of the shorter diagonal. A mango falls from a branch 5 meters above the ground. 0. 18 d. The altitude of the sides of a triangle intersect at the point known as a. Focal width b. What interest rate compounded monthly is equivalent to 10% effective rate? a. 13. an acceleration that is directly proportional to the mass of the body.47% b. Hyperbola 182. in what year will the population triple? a. “At any point along the streamline in an ideal fluid in steady flow.000 d.37 c.2 1. 12 m/s b. a. if the sum of P 25. The population of the Philippines doubled in the last 30 years from 1967 to 1997. a. a. Ellipse d. 11. 72.3 yrs c. Pascal’s theorem d. 2021 185. 0. Conjugate axis 172. 2 and 12 d. 6 b. Newton’s Second Law of Motion d.35 3. The electrons have speeds of 0. Minor axis c. 175 sq.23 d. 2030 d. Circle b. Find x. tan 4y b. The sum of two numbers is 21. In an ellipse.25c d. greater c. a chord which contains a focus and is in a line perpendicular to the major axis is a ______ a. Simplify 4 cos y sin y (1 – 2 sin^2 y) a. 165 sq. equal 165. Parabola c.76 181.000 177. If their relative velocity is 0. a. Hooke’s Law of Equilibrium c. 0.02c 175. P 28.k=0 represents a point circles a.2y . What is the moment of inertia of a cylinder of radius 5 m and a mass of 5 kg? a. incenter d. 10. 25 ft/s^2 31. 15 and 29 b. with interest at 15% compounded annually? a. f”(a)=0 7. Find the sum of the infinite geometric progression 6.114. 883 m 32. 20 34. 116. 1) 37. h/4 d. Maximum and minimum points b.31 m 14. 61 91 81 186. Illuminance b.0025 m 17. -3/5 19. 126. 7/2 d. a.454. P 12. Market value 30. 5/2 200. Maximum points 197. P 40. how many ways can these 15 people win first. positive b. 360.5 191. Convergent series b. 57. The attitude of a cylinder of maximum volume which can be inscribed in a right circular cone of radius r and height h is ________. Rational 11. Voting stock 192. 36π 35.64 cm 8. P 41. the annual depreciation cost should not exceed 20% of the first cost at any time with no salvage value. infinite c. zero d. 835.12 c. if one leg is 14 cm longer than the other.32 36. 5/13 33.59 20. 34. 38. velocity 195. The hypotenuse of the right triangle is 34 cm. the numerical coefficient of the 5th term is. 2/3. X-axis 28. Lesser 15. What is the accumulated amount of five year annuity paying P 6. 5x^2 + 3x – 2 = 0 22. Depreciation 3. a. Determine the length of service life necessary if the depreciation used is the SYD method a. second. P 15. 253. time d. A sequence of numbers where the succeeding term is greater than the preceding term. Momentum is the product of mass and ________ a. 500x/(pi)n 24.614. 1. Limacon 18. 2. h/3 c. 18 and 32 199. In the expansion (x + 4y)^12. 12 years b. 506. Isometric series c. 4 and 10 13. 42.6 b. x=-4 23. d. 17 and 31 d. 3h/2 b. 1/7 29. Preferred stock d. 16 and 30 c. If 15 people won prizes in the state lottery (assuming that there are no ties). ……. Point of derivatives which do not exists (and so equals zero) are called a.544. 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. 2x – y – 2 = 0 10. 19 years d. fourth and fifth prizes? a. a.5 d. 19. π/4 . Divergent series 190.630 d. Stationary points d. 2.0045 kg-m^2 9. Luminance d. a. c. 0. Luminous intensity c.440 b. a. 8/3 25. 1/x 21. third. 0.29 c.845 187. If the two numbers namely 250 and 850 are removed. Acceleration b. 10 years ANSWER KEY 1.260 d. Dissonant series d.29 d. 4. 9 years c. ABC Corporation makes it a policy that for any new equipment purchased. The arithmetic mean of 80 numbers is 55. 15.720 189.29 198. 0.360 c.000 at the end of each year. P 41. -2. a. 2h/3 194. If sec^2 A is 5/ 2. 11/2 c. Radiance 188. (1. 12x^2 – 7x + 1 = 0 26.4 c..31 d. the quantity 1 – sin^2 A is equivalent to _________.72° 6. Minimum points c. Division 2. force c. 0. 16. a.003 b. 9/2 b.b. Common stock b. Non par value stock c. 50 196.454. 76. negative 193. what is the arithmetic mean of the remaining numbers? a. Find the length of the two legs. It describes the luminous flux incidence per unit area and is expressed in lumens per square meter.29 b. Frequency 12. 63. a. P 40.62 b. Monopsony 5. 19/27 16. At maximum point the value of y” is a.56% 27.3 4. 3. 4.880 c. 000 miles 52. 131.52 s 95. IV 67. 163.02 91. 10. 139. 148.9 80. Dispersion 178. –6) 96. In y = ce^(-x) 243 mph 32/3 P 9221 inelastic collision 1994 Latus rectum Parallel lines 150. 44% 51. P 1. 158. axis of the parabola 3 6. 58. 143. y = x^2 + c 68. 1.73 9. 174.72% 77. Newton’s Second Law of Motion 180.4 kph 93. 107. 0. 110. Infinity 89. -4(1 + i) 58. 145. 111. 153.93 ft/sec^2 73. 0. In 48. 149. 6 rad/s 69. 161. 136. 12 ft/s 83. 147.38. 166. 11. 167. 3.550. 157. Principle Factor of safety csc 20° 8.5 miles 78. 135.281 49. 165. 109. 114. y = 3^(1/2)x 100. 102.03 x^3 cu. Dihedral angle 54.71 m 76.05 55. 116. 2. 128.87 45° .75 mm 92. 135° .04 mils P 10. 2. 171.83 8 282. 137. 104. 16 87. 179.2) 85. 106. 91 57. 155.76 181. Monopsony 64.19 Argand diagram 4 and 10 194 lbs 0. 125.-20) 240 2.35 x 10^-25 N 167 m P 2500 Deferred Annuity 112. 11. 126. 173. units 62. 225° . 177. (-1. 156. 10 m/s 184. 14. Radius 81. 115. 152.21 x 10^5 ft-lb ln 2 Coulomb’s Law – tan x 4x – 7 = 0 5 P 13. Utility 86. 117. 12. (6. 0.777. Ellipse Increases as distance of the axis moves farther from the centroid 183. 105. Standing waves are produced 39. zero 101. 160.96° 150° 3 -2 13 1. 133. Linear must 74. 27 82. 140.42% 2454 m^4 trivial solutions (11 .0017 m 59. 151. 108.868.265.79 165 sq.000 Bernoulli’s 11. 169. 176. 2 65. 170. -2 88. 138. 127. 121.57% 6 62. 182. Annulus 90. 374 m 47. 4x^2 + 3y^2 = 12 99. 154. -2[sqrt(2)cos((1/2)x) + c 56.295.1) 75. Origin 66. cm Lesser sin 4y 7 and 14 10.04289 P 6.7 43. 141. A sinusoid 98. The tangent function of angle of trajectory equal to one 60. 540 41.834.3 yrs Energy 120. 23. 297/425 70. Zero 84. 0. 142.8 Longitudinal strain 42 ⁄ 5 weeks 64 π 295 190 cu.265. Evolution 94.00 28. 113. 162. (1. 211 kN 97. 129. 144.57 years 63. 118. 119. Diameters 79.5 kg-m^2 Latus rectum -5 Orthocenter 0.09c 4 P 28. 175. the be 61. 134. 2015 . 315° absolute error P 135. 2 45. ¾ 40. 168. 172. 124. 146. Zero 44. Total kinetic energy 42. cos(-T) = cos (T) 72.38 Antiderivative Frequency 40° 3. 16 0. 103. 164. 123. 132.49% 71.14 m/s Moment of inertia 810 degrees y’ = y/2x 35 π/768 π/5 1. 1. 122. 19. 159. Nonagon 53. 130. 2046 46. 94. 2 50. 3 sq. 4 Preferred stock Negative h/3 velocity 42.185. P 40.31 and Maximum minimum points 197. 188. 91 360. 195. 192. 199.29 16 and 30 9/2 9 years . 189. 193. 186. 190. 191.454. 200. 187.720 Divergent series 0.360 Illuminance 126. 196. 194. 198.