40. What is the equation of the line that passes through (4, 0) and is parallel to the line x - y - 2 = 0. A. y x + 4 = 0 C. I/ - x - 4 = 0 B. y x + 4 = 0 D. y + x 4 =0

41. If the sides of the parallelogram and an included angle are 6, 10 and 100° respectively, find the length of the shorter diagonal. A. 10.53 C. 10.73 B. 10.43 D. 10.63

42. The sides of a quadrilateral are 10m, 8m, 16m and 20m, respectively. Two opposite interior angles have a sum of 225°. Find the area of the quadrilateral in sq. m. A. 143.33 C. 151.33 B. 145.33 D. 148.33

43. The sum of the interior angles of a polygon of n sides is 1080°. Find the value of n. A. 4 C. 6 B. 7 D. 8

44. A circle whose area is 453 square centimeters is cut into two segments by a chord whose distance from the center of the circle is 6 cm. Find the area of the larger segment in square cm. A. 377.8 C. 367.5 B. 363.6 D. 372.4

45. The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector? A. 85.9 sq. cm. C. 59.8 sq. cm. B. 58.9 sq. cm. D. 89.5 sq. cm.

46. What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm.?3 A. 13.52 B. 14.06 C. 12.73 D. 11.94

47. If the edge of a cube is increased by 30%, by how much is the surface area increased? A. 13 C. 10 B. _69 D. 7

48. The base edge of a regular hexagon prism is 6 cm and its bases are 12 cm apart. Find its volume in cu. cm. A. 1569.20 C. 1432.77 B. 1331.29 D. 1122.37

49. A trough has an open top 0.30 m by 6 m closed vertical ends which are equilateral triangles 30 cm on each side. It Is filled with water to half its depth. Find the volume of the water in cu. m. A. 0.058 C. 0.038 B. 0.049 D. 0.061

50. A frustum of a pyraMid has an upper base 100m by •10m and a lower base of 80m by 8m. If the altitude of the frustum is 5m, find its volume. A. 5144.44 cu. m. C. 4066.67 cu. m. B. 5244.44 cu. m. D. 4166.67 cu. m.

51. A conical vessel has a height of 24 cm and a base diameter of 12 Cm. It holds water to a depth of 18 cm above its vertex. Find the volume of its content in cc. A. 387.4 C. 383.5B. 381.7 D. 385.2

52. A solid has a circular base of radius r. Find the volume of the solid if every plane perpendicular to a given diameter is a square. A. 16 r3/3 C. 6 r3 B. 10 r3/3 D. 6 r3/3

53. Find the radius of the spherical wedge whose volume is 12 cu. m. with central angle of 1.8 radians.A. 2.13m C. 2.21 m B. 2.14 m D. 2.15 m

54. How many terms of progression 3, 5, 7, 9 must be taken in order that their sum will be 2600?A. 51 C. 50

B. -52 D. 52

55. There are 4 geometric between 3 and 729. Find the sum of the G.P. 3x x xx 729 A. 91 C. 999 B. 1092 D. 1001

56. Find the 12th term of the series 6, 3, 2. A. 1/3 ' C. • 1/6 B. 1 D. 1/2

57. In how many ways can you choose 5 out of 10 friends to invite to a dinner party?,t A. 262 • C. 30240 B. 252 D. 30220

58. How many ways can you arrange 10 books on a bookshelf that has space for only 5 books? A. 262 C. 30240 _ B. 252 D. 30220,

59. What are the odds of rolling a 6 when rolling a standard 6-sided number cube?A. 1/2 C. 1/6 B. 1/18 D. 1/9

60. What is the probability of rolling a sum of 7 when rolling a pair of dice? A. 1/2 C. 1/6 B. 1/18 D. 1/9

61. Two times the mother's age is 8 more than six times her daughter's age. Ten years ago, the sum of their ages was 44. The age of the daughter is: A. 16 C. 19 B. 15 D. 21

62. A mother is three times as old as her son. Four years ago, she was four times as old as her son was at that time. How old is her son? A. 18 years old C. 24 years old B. 10 years old D. 12 years old

63. Two thousand kilogram of steel containing 8% nickel is to be made by mixing steel containing 14% nickel with steel containing 6% nickel? How much of the steel containing 14% nickel is needed? A. 25% C. 35% 'B. 43% D. 45%

64. A pump can pump out a tank in 11 hours. Another pump can pump out the same tank in 20 hours. How long will it take both pumps together to pump out the tank? A. 5 hours C. 6 hours B. 4 hours D. 7 hours

65. One pipe can fill a tank in 5 hours and another pipe can fill the same tank in 4 hours. A drainpipe can empty the full content of the tank in 20 hours. With all the three pipes open, how long will it take to fill the tank? A. 2.9 hours C. 3.1 hours B. 2.5 hours D. 3.7 hours

66. A father and his son can dig a well if the father works 6 hours and his son works 12 hours or they can do it if the father works 9 hours and the son works 8 hours. How long will it take for the son to dig the well alone? A. 15 hours C. 12 hours B. 14 hours D. 20 hours

67. How many minutes after 10:00 o'clock will the hands of the clock be opposite each other for the first time?A. 21.18 C. 21.81 B. 18.21 D. 28.11

68. The sum of the reciprocals of two numbers is 11. Three times the reciprocal of one of the numbers is three more than twice the reciprocal of the other number. Find the numbers. A. 6 and 5 C. 1/5 and 1/6

B. 7 and 4 D. 1/4 and 1/7

69. In a two-digit number, the unit's digit is 3 greater than the ten's digit. Find the number if it is 4 times as large as the sum of its digits? A. 69 C. 3.6 B. 65 D. 59

70. The product of three consecutive integers is 9240. Find the third integers. A. 21 C. 22 B. 20 D. 23

71. The sum of the digits of a three-digit number is 14. The hundreds digit being 4 times the units digit. If 594 are subtracted from the number, the order of the digits will be reversed. Fi41c1 the number. A. 687 C. 492 B. 555 D. 842

72. If log,(3) = 1/4, then x = A. 81 C. 82 B. 80 D. 83

73. Simplify: x 2 X 3 A. x5 C. 1 B. 0 D. x

74. Simplify: a -2 a -3A. 1 / a-5 C. 1 / a 10B. 1 / a5 D. 1 / a

75. Simplify:a-3/a7A. 1 / a -5 C. 1 / a 1° B. 1 /a5 D. 1 / a

76. Water freezes at in SI unit. A. 0°C C. 32°F B. 100°C D. 212°F

77. Water boils at in SI unitA. 0°C C. C. 32°F B. 100° D. 212°F

78. 80 psi is equivalent to how many meters of water? A. 56.24 C. 54.26.B. 80.01 D. 81.01

79. The person who proved the millennial "Last Fermat's Theorem" is from what school? A. Cambridge University B. Harvard University C. Princeton University D. Massachusetts Institute of Technology

80. Among the biggest Universities in the U.S., which among the school below produced the largest pool of Billionaires? A. Cambridge University B. Harvard University C. Princeton University D. Massachusetts Institute of Technology

81. When you combine Matter and Antimatter what will happen? A. It will increase its charges B. It will produce new type of matter C. It will undergo decomposition D. It will explode

82. also known as slope. A. Slope C. Integral B. Derivative D. Angle of repose

83. What is the eccentricity of ellipse? A. Less than one C. Greater than one B. Equal to one D. Equal to zero

84. Derivative of a constant is equal to A. Zero C. Two B. One D. Infinite

85. Derivative of x is equal to A. Zero C. Two B. One D. Infinite

86. One over curvature is equal to A. Zero C. Circle B. One D. Radius of Curvature

87. Maxima and Minima are examples of applications of A. Differential Calculus B. Integral Calculus C. Differential Equation D. Linear Algebra

88. Other name for linear algerbra: A. Algebra C. Matrix B. complex D. Calculus

89. The derivative of e exp u: A. In e • C. a exp u B. e exp u D. log e

90. A type of rectangle with maximum area that can be cut from,a circle: A. Rectangle • C. Parallelogram B. Square D. Rhombus

91. Evaluate: I sinh u du A, cosh u + C C. tanh u + C B. sinh u + C D. —sech u + C .

92. EvalOdte: I cosh u du A. cosh u + C C. tanh u + C B. sinh u + C D. —sech u C

93. Type of integration, once evaluate, has a definite value: A. Equation C. Indefinite Integral B. Complex No. D. Definite Integral

94. The following are the applications of integration. techniques, except for A. Slope C. Length of arc B. Plane areas D. Solid of revolution

95. What is the Mass Moment of Inertia of a solid right circular cylinder? A. 1/3 Mr2 C. 1/$ Mr2 B. 1/2 Mr? D. 2/5 Mr2

96. What is the Mass Moment of Inertia of a solid sphere? A. 1/3 Mr2 C. mr2 B. 1/2 Mr2 D. 2/5 Mr2

97. 1 lambert is equal to

A. 3,183.099 cd/r-Tri C. 997.561 cd/m2 B. 1889.045 cd/m2 D. 981.048 cd/m2

98. He is the mathematician who invented Cartesian plane. Who is he? A. Rene Descartes C. MichiuKaku B. Isaac Newton D. John Smith

99. Speed is a quantity. A. scalar C. real B. vector D. imaginary

100. A Greeivhilosopher known for shouting "Eureka" after naMdly went out his house. A. Archimedes C. Hercules B. Plato D. Zeus

1. Which number has three significant digits? A. 0.0014 C. 0.01414 B. 1.4141 D. 0.0141

2. Resolve (x+2)I(x2 - 7x + 12) into partial fraction A. 6 / (x 4) - 2 / (x - 3) B. 6 / (x 4) - 5 / (x - 3) C. 6 / (x - 4) + 7 / (x-3) D. 6 / (x 4) + 5 / (x -- 3)

3. Solve the value of x if x = .\11- - A. 0.618 C. 0.852 B. 0.723 D. 0.453

4. Solve the value of x from the following equation xxx = 10 A. 1.258925 C. 1.932525 B. 1.543255 . D. 1.839352

5. A batch of concrete consisted of 200 lbs fine aggregate, 350 lbs coarse aggregate, 94 lbs cement and 5 gallons of water. The specific gravity of sand and gravel may be taken as 2.65 and that of the cement as 3.10. What was the weight of the concrete in pounds per cubic foot? A. 153 lbs C. 162 lbsB. 263 lbs D. 172 lbs

6. In a pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there? A. 14 layers C. 10 layers B. 12 layers D. 15 layers

7. What is the sum of the following finite sequence of terms? 18, 25, 32, 39... 67. A. 234 C. 213 B. 181 D. 340

8. How many permutations can be made out of the letters of the word ENGINEERING? A. 39 916 800 C. 55 440 B. 277 200 D. 3 326400

9. How many line segments can be formed by 13 distinct points no three of which are collinear? A. 78 C. 1716 B. 286 D. 156

10. In how many ways can you invite one or more of your five friends in a party? A. 31 B. 32 C. 36 D. 25

11. Seventy Electrical Engineers and 100 Mechanical Engineers attended a convention. Each Mechanical Engineer shook hands once with every Electrical Engineer and Mechanical Engineer at the convention, but no Electrical Engineer shook hands with other Electrical Engineer. How many handshakes occurred? A. 7000 C. 4950 B. 11950 D. 24500

12. Four Engineer and four Nurses form a circle with Engineers and Nurses alternating. In how many ways can they form a circle? A. 144 C. 288 B. 576 D. 1152

13. From the digits ( 1, 2, 3, 4, 5, 6, 7 ) how many odd numbers of three different digits can be formed? A, 5040 C. 343 B. 120 D. 121

14. How many numbers of 4 different digits each greater than 5000 can be formed from the digits 1, 2, 3, 4, 5, 6, 7? A. 30 B. 60 C. 90 D. 360

15. A prospective automobile buyer,can select a car from the following: Ten different body styles Eight different colors (Two tone or solid colors) Twelve different interior color schemes Four different transmissions An air conditioning option A white wall option How many automobiles are represented? A. 92 160 C. 368 6,40B. 23 040 D. 184 320

16. Which of the following is a happy number? A. 70 B. 143 C. 69 D. 12

17. Log x = In x A. 0.434* C. 2.303 B. 10 D. e

18. Find the middle term of the expansion ( x2- 2y )10? A. -8864 x12y5 C. -9064 xwysB. -8064 x10y6 D.a -8064 x12y5

19. Determine the absolute value of the complex number 3 + 4i.A. 3 B. 4 C. 5 D. 6

20. Solve the value of x of the given equations: (x+y)(x+y+z)= 384 (y+z)(x+y+z)= 288 (x+z)(x+y+z)= 480 A. 12 B. 4 C. 8 D. 10

21. Mary is 24 years old. Mary was twice as old as Ann was when Mary was as old as Ann is now. How old is Ann? A. 18 B. 16 C. 24 D. 36

22. In how many different ways can 4 persons be seated in consecutive seats in a row of 7 seats? A. 72 B. 120 C. 96 D. 168

23. Determine the sum of the positive value solution to simultaneous equations: xy = 15, yz = 35, zx = 21. A. 15 B. 13 C. 17 D. 19

24. Find the constant term in the expression of g (2x2 + A. 648 C. 672 B. 682 D. 664

25. Find the value of A and B in the given equation: (x+10) - A + B x2-4.) x-2 x+2 A. A = 3 and B = - 2 C. A = 5 and B = - 2 B. A = 2 and B = - 3 D. A = 3 and B = - 1

26. The triangle defined by the points A (6,1), B (2,4) and C (-2,1) i what? A. Right C. Isosceles B. Obtuse D. Scalene

27. Whays, the distance between line x + 2y + 8 = 0 and the points (5,-2)? A. 4.025 C. 4.250

B. 4.502 D. 4.052

28. A triangle having vertices at (0;0), (6,30°), and (9,70°). What is the perimeter of the triangle? ' A. 20.853* C. 29.456 B. 23'.754 D. 26.754

29. The equation of a line that intercepts the x - axis • at x = 4 and the y - axis at y = - 6 is: A. 2x 3y = 12 C. .3x - 2y = 12 B. 3x + 2y = 12 D. 2x + 3y = 12

30. The general second degree equation has the form of Ax + Bxy + Cy2 + Dx + Ey + F = 0. If B2 - 4AC = 0 , the equation describes: A. A circle C. A hyperbola B. An ellipse D. A parabola

31. The equation x2 + y2 4x + 2y - 20 = 0 describes: A. An ellipse centered at (2, - 1) B. A circle of radius 5 centered at (2, - 1) C. A circle of radius 5 centered at the origin D. A sphere centered at the origin

32. Which of the following points (1,0), (-1,0), (4,4) and (9,7) belong to the graph of the equation y = X2 — X? A. (-1,0) C. (4,4) B. (9,7) D. (1,0) .

33. A circle is described by the equation X2 + y2 - 16x = 0. What was the length of the chord that is 4 units from the center of the circle? A. 12.536 C. 8.536 B. 13.856 D. 9.63

34. Find the area of bounded by the parabola 4y = x2 - 2x + 1 and Itslatus rectum. A. 8/3 C. 2/3 B. 4/3 D. 10/3

35. An arch 18 m high has a form of a parabola with a vertical axis. The length of a horizontal beam placed across the arch is 8 m from the top is 64 m. Find the width at the bottom. A. 81 B. 96 C. 48 D. 64

36. Find the axis of symmetry of the function y = 2x2 7x + 5. A. 7x + 4 = 0 C. 4x + 7 = 0 B. 4x - 7 = 0 D. x - 2 = 0

37. Find the center of the conic whose equation. is 16X2— 9y2 — 128x 90y 113 0. • A. (-4,-5) C. (4,-5) B. (2,5) D. (2,-5) '

38. Compute the ratio of the area of the circle x2 + y2 -10x - 24y + 25 = 0 and the circle x2 + y2 - 10x + 4y - 7 -x-= 0 A. 4 B. 5 C. 3 D. 6

39. Find the area of the polygon whose vertices are (2,-6), (4,0), (2,4), (-3,2) and (-3,-3). A. 45.2 C. 55.3 B. 47.5. D. 574

40. Find the equation of the line passing through the points of intersection of the circles x2 + y2 + 4x = 0 and x2 + y'a - 4x + 2y 4 = 0 A. x + 4y + 2 = 0 C. 3x - 2y + 3 = 0 B. 2x - 3y ± 4 = 0 D. 4x y 4- 2 = 0

41.'Deterr,line the coordinates of the point which is three - fifths of the way from the point (2,-5) to the point (-3,5). A. (-1,1) C. (-2,-1) B. (0,-2) D. (1,1)

42. Transform the polar equation r2cos 0 sin 0 = 4 to rectangular coordinates. A. xy = 4 C. x + y = 4 B. 2xy = 4 D. x2 + y2 = 4

43. G numbers are generated recursively as follows: G(n) = 1 for n = 0, 1 G(n) = 2G(n - 2) + G(n - 1) for n = 2, 3, 4 .... Find G(6)? A. 11 B. 5 C. 43 D. 21

44. Given the polar equation r = 3 / ( 1 + 3 cosO ). This is a graph of a/an A. Ellipse C. Circle B. Parabola D. Hyperbola

45. Edmound plans to rotate the five tires of his new Ford Expedition so that each tire will have the same number of kilometers. when the odometer reads 50 000 km. How many kilometers will each tire travels? A. 10000 C. 30000 B. 20000 D. 40000

46. Differentiate f(x) = V2x2 + 4x + 1 A. 2x + 1 B. % V2x2 + 4x + 1 2x+2 C. 2x2+4x+1 4x+4 D. 1-2x2+4x+1

47. Find the second derivative of y = -\/}{7 + x-2 A. 1 - 2x-3 B. 1 - 6x-4 C. 3 D. 6/x4

48. The function is defined as f(x) = 1 / ( 1 + x ). For what value of x that f(f(x)) undefined? A. { -1 , -1/2 ) C. { -1 , 0 ) B. { -1 , - 2} D. { 0 }

49. If f(x) = (3V - 4)2 , then how does f(x) much increase as x goes from 2 to 3? A. 1.372 C. 1.273 B. 1.732 D. 1.723

50. Given the function f(x) = x3 - 5x + 2, find the value of the first derivative at x = 2, f(2). A. 6 C. 7 B. 3x2 - 5 D. 8

51. Evaluate the x+ :A. 1 C. 0 B. In-definite D. 2

52. Evaluate the limx.0 1—cos x A. 0*X2 B. 1/2 C. 2 D. -1/2

53. Find the derivative with respect to x of the function 3x2 A.2x2 2-...3c2 -3x B. 3x2 -2x2C. 2+3x2 -3x D. 2-TiTc2

54. What is the first derivative of (xy)x = e? A. y( 1 + In xy) / x C. - y( 1 - In xy) / x2 B. 0 D. y/x

55. The distance a body travels is a function of time and is given by x(t) = 18t + 9t2. Find the velocity at t = 2. A. 20 B. 24 C. 36 D. 54 56.

56. Two cities A and B are 8 km and 12 km respectively, north of a river which runs due to east. City B is being 15*km east of A. A pumping station can be • constructed (along the river) to supply water from two cities, Where should be the station be located so that the amount of pipe is minimum? A. 6 km east of A C. .3 km east of A B. 4 km east of A • D. 8 km east of A

57. A box is 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 can be constructed? A. 592.5 C. 432.5 B. 529.5 D. 475.3

58. Water is pouring into a swimming pool. After t hours, there are t + gallons in the pool. At what rate is the water pouring into the pool when t = 9 hours? A. 1 gph C. 1/2 gphB. 7/6 gph D. 1/6 gph

59. Find the approximate radius of curvature of f(x) at point (8,16) of f(x) = x2 + 6x 92. A. 5456 C. 5340 B. 5565 D, 3408

60. Find the area bounded by the curve r2 = 4 cos 20. A. 8 B. 2 C. 4 D. 6

61. Find the volume generated by the circle x2 + y2 = 25 if rotated about the line 4x + 3y = 40. A. 400 Tr2 C. 150 -rr2 B. 200 Tr2 D. 380 Tr2

62. The equation y2 = cx is the general solution of: A. ry' = 2x/y C. y' = y/2x B. y' = 2y/x D. y' = x/2y

63. Find dy/dt given the following two simu;6neous differential equations dx dy 2 -dt - 3 -dt + x - y k dx dy 3-+ 2--x = cost dtdt 2 ( 5 3 3 cos t - 2 -x - 2 -y - 2 . 1 6 ( 5 3 sin t + 2 -x - 2 -y - .21k) ( 5 3 COS t- - -X + y - ) 13 2 2 2 (COS - SX - 3y - 3k) A. B. C. D.

64. Determine the solution of the following differential equation y' + 5y = 0 A. y = 5x + C C. y = Ce5x B. y = Ce-5x D. y=AorC

65. The differential equation' dc-Txi. + 4x = 0 has initial condition x(0) = 12. What is the value of x(20=)? A. 3.35 x 10-4 C. 3 B. 4.03 x 104 D. 22

66. Determine the constant of integration for the separable differential equations xdx + 6y5dy = 0. It is known that when x = 0 , y•= 2? A. 64 B. 4 C. 32 D. 16

67. The rate of population growth of a country proportional to the number of inhabitants. If the population of a certain country now is 40 million and expected to double in 25 years, in hOw many years will the population be three times the present? A. 36.62 years C. 39.62 years B. 28.62 years D. 42.53 years

68. The population of a certain city is 50 000 and increasing at a rate numerically equal to the square root of the population. What will be the population 20 years hence? A. 57 980 C. 54 567 B. 67 687 D. 55 987

69. A certain radioactive substance• has a half-life of 38 hours. Find how long it takes for 90% of the • radioactivity to be dissipated. A. 145.7 hours C. 126.5 hours B. 135.7 hours D. 130.7 hours

70. A thermometer reading 75 °F is taken out where the temperature is 20 °F. The reading is 30 °F after 4 minutes. Find the thermometer reading 7 minutes after the thermometer was brought outside. • A. 23 °F C. 43 °F B. 25 °F D. 39 °F

71. Solve ('D2 - 2D + 5)y = 0 A. y = ex (C1cos 2x + C2sin 2x) B. y = e-x (Cictis 2x + C2sin 2x) C. y = ex (C1cos 3x + C2sin 3x) D. y = ex (C1cos lx + C2sin 2x)

72. Which of the following is the algebraic form of 2(cos 30° + isin30°)? A. v +i C. V2 + B. V5-- i D. Arf-i

73. Simplify number11997 + 11999 here is i is an imaginary A. 0 B. 2 + 1 C. 2i D. 1 - I

74. What is the complex expression of In ( 3 + 4j )? A. 1.2 + j 0.65 C. 1.5 + j 0.75 B. 1.609 + j 0.927 D. 1.2 + j 0.75

75 Compute the value of x by determinant 4 -1 2 3 2 0 2 1 10 3 0 1 14 2 4 5 A. -29 B. -28 C. -26 D. -27

76. Evaluate the Inverse Matrix A. A. B. C. D.

77. A number between 1 to 10000 inclusively is selected at random. What is the probability that it is a perfect square? A. .01 B. .015 C. .02 D. .025

78. An urn contoins four black balls and six white balls. What is the probability of getting one black ball and one white ball in two consecutive draws from the urn? A. .04' B. 24 C. 27 D.53

79, The arithmetic mean of 80 numbers is 55. If two numbers namely 250 and 850 are removed, what is the arithmetic mean of the remaining numbers? A. 42.31 C. 38.62 B. 50.03 D. 57.12

80. What is the standard deviation of 1, 4 and 7? A. 3.25 C. 4.51 B. 5.24 D. 2.45

81. Simplify cos( 30 - A ) - cos ( 30 + A ) as a function of angle A only A. Sin A C. Cos A B. Tan A D. Sec A

82. The number of board feet in a plank3 inches thick, 1 foot wide and 20 feet long is A. 30 C. 120 B. 60 D. 90

83. The area,of a triangle whose sides are 25, 39 and 40 is A. 486 C. 648 B. 846 D. 468

84. Find the radius of the circle inscribed in a triangle with sides of 5, 7 and 10 is: A. 1.7'74 C. 1.747 B. 1.744 D. 1.477

85. Given a triangle with angle C = 28.7°, side a = 132 units and side b = 224 units. Solve for the angle B. A. 130° C. 120° B. 110° D. 90°

86. Find the area of the spherical triangle ABC having the following parts: angle A = 140°, angle B = 75°, angle C = 86° and the radius of the sphere is 4m. A. 38.78 m2 C. 33.79 m" B. 41.41 m2 D. 34.56 m2

87. How many sides have a polygon if the sum of the measures of the angles is 900 degrees. A. 9 B. 6 C. 8 D 7

88. What is the value of each interior angle of a regular pentagon? A. Tr/5 C. 2T-r/5 B. Tr/3 D. 3rr/5

89. If the total number of diagonal of an n gon polygon is 77, then what is the value of n? A. 14 B. 13 C. 12 D. 15

90. Find the area of regular hexagon inscribed in a circle of radius 1 is: A. 2.689 C. 3.698 B. 2.598 D. 3.598

91. A circle has a circumference that is numerically equal to its area. If a certain square has the same area as the circle, what would be the length of the !side? A. 3 JTI C. it12- B. 11\/73- D. 2-Nfri

92. The perimeter of a circular sector whose central angle is 60° is 14 feet. Find the radius of the circle. A. 3.68 feet . 6.32 feet B. 4.59feet D. 8.74 feet

93. A solid spherical steel ball 20 cm in diameter is placed into a tall vertical cylinder containing water causing the water level to raise by 10 cm. What is the radius of the cylinder? A. 12.14 cm C. 10.28 cm B. 9.08 cm D. 11.55 cm

94. A cubical container that measures 2 in on a side is tightly packed with 8 marbles and is filled with water. All the 8 marbles are in contact with walls of the container and the adjacent marbles. All the marbles are the same in size. What is the volume of water in the container? A. 0.38 in3 • C. 2.5 in3 B. 3.8 in3 D. 4.2 in3

95. The slant height of a right circular cone is 5 m long. The base diameter is 6 cm. What is the lateral area in sq. m? A. 37.7 C. 44 B. 47 , D. 48.4 96.

96. A right circular cone with circular base down is h. If it contains water to a depth of 2h/3 the ratio of the volume of water to that of the cone is: A. 1:27 C. 8:27 B. 2:3 D. 26:27

97. The volume of a regular pyramid whose base is a square is 551.67 cu. m. If the altitude of the pyramid is 16.55 m, find the slant height of the lateral sides, A. 12.79 cm C. 19.27 cm B. 17.29 cm D. 17.92 cm

98. The volume of water in a spherical tank having a diameter of 4 m is 5.236 cu. m. Determine the depth of the water on the tank. A. 1.6m C. 1.2m B. 1.0 m D. 1.4 m

99. Find the volume of spherical wedge of radius 10 cm if the central angle is 50 degrees. A. 581.78 C. 654.5 B. 435.76 D. 680.5

100. A solid has a circular base of radius r; find the volume of the solid if every plane perpendicular to a given diameter is a square. A. 16/3 r3 C. 19/3 r3 B. 5r3 D. 16/5r3

1. Find the distance from the point A( 3, 4) and B( 4,3) along the arc x2 + y2 = 25 A. 2.21 B. 1.42 C. 1.89 D. 2.57

2. Find the amplitude and period in that order of y = 5-4 cos( x/3 + Tr) . A. 4, 6.rr B. 5, 5rr C. 8, 2Tr D. 7, 4-rr

3. The square root of negative numbers and is denoted by I or j which represents q-1. A. Imaginary numbers C. Complex numbers B. Real numbers D. None of these

The vertices of a triangle are A(1,0) , B( 9,2) & C(3, 6) 4. Find the equation of the median from A to BC A. 2x - y = 4 C. 4x+y= 5 B. -2x + y = 4 D. -4x + y = 5

5. Find the smallest interior angle. A. 47.73° C. 36.41° B. 50.21° D. 28.15°

6. Find the distance between the line 3x + 4y = 7 and the point ( 3,5) A. 2.5 B. 5.7 C. 4.4 D. 7.8

Given a regular nonagon whose side is 14 cm, 7. Find the area of the noganon. A. 1146.21 cm2 C. 2519.22 cm2 B. 1211.64 cm2 D. 2848.33 cm2

8. Find the difference between the area of the circumscribed and inscribed circle. A. v. 143.5 C. v. 168.9 B. v. 154.3 D. v. 199.2

9. Find the principal value of ( 1 + 2j) A. -11.11 +112.331 C. -22.34 B. -14.41 + 103,34i D. -26.25

10. Find the principal value of 1\i-j. A. 0.208 C. 0.144 B. 0.193 D. 0.294

11. What is the angle between - 2.5 + j4.33 and 4.33 2.5? A. 110 deg C. 180 deg B. 150 deg D. 270 deg

12. Find the coefficient of a12 b21 in the expansion of (a4 b3)10? A. 100 B. 110 C. 120 D. 140

13. Find the coefficient of x15 in the expansion of (x4 - 3/x)1 ? A. 153,090 C- 111,101 B. 190,135 D. 239,194

14. Two currents described as I1 = 20 sin ( 377t) and 12 = 30 cos ( 377t). What is the instantaneous current at t = 0.002 s? A. 36.055 C. 43.201 B. 31.029 D. 27.894

15. The space diagonal of a cube is 20 cm. What is the surface area of the cube? A. 750 cm2 C. 825 cm2 B. 800 cm2 D. 900 cm2

16. Find the area bounded by the curve y2 - 3x + 3 = 0 and x = 4. A. 9 B. 18 C. 12 D. 28

Given the graph of x2 + 3xy + y2 = 5 at the point ( 1,1) 17. Find the equation of the normal line at ( 1,1)A. . x-y=0 C, x - y = 2 B. x y 0 D. x - y = 5

18. Find the x intercept of the tangent line to ( 1,1) A. 5 B. 2 C. 9 D. 3

A hemispherical tank is being filled by water such a way that the surface is rising at rate of 0.001 m/s when the depth is 1.3 m. If the radius of the hemisphere is 2.4 m 19. What is the inflow rate of water in the tank? A. 0.01244 m3/s C. 0.02942 m3/s B. 0.01429 m3/s D. 0.01872 m3/s

20. What is the volume of water in the tank when the depth is 1.3 m? A. 10.442 m3 C. 21.892 m3 B. 11.392 m3 D. 16.514 m3

21. A conical tank is being filled with water at the constant rate of 0.1 m3/s. The radius of the cone Is 4 in and the height is 8 m. At what rate is the depth changing when the height of water in the tank is 1.25 m? A. 0.0921 m/s C. 0.0763 m/s B. 0.0815 m/s D. 0.0511 m/s

22. Find the x intercept of the line tangent to y = el° at x e. A. 2.113 B. 3.291 C. 1.359 D. 1.888

23. If i(s) = 10(2s-4-5)find 1(0.1). S2+3S+2 A. 19,22 C. 23.24

B. 18.96 D. 30.18

24. Three geometric means are inserted between 6 and 14,406. Determine their product, A. 24,210,897 C. 21,201,134 B. 25,412,184 D. 30,879,675

25. For a high voltage-transmission line, Er = DEs + B1s. If the per phase sending end voltage and current are: Es = 70,000 Volts at 0 deg, Is = 100 Amperes at 30 deg. Determine the receiving end per phase voltage Er if D = 0.95 at 0 deg and B = 100 ohms at 90 deg. A. 62,106.76 V C. 55,343.01 V B. 60,294.99 V D. 69,214.66 V

26. What is the volume of a regular tetrahedron if one side is 10 cm? A. 117.85 cm2 C. 130.25 cm2 B. 189.22 cm2 D. 108.14 cm2

27. A water tank is a horizontal cylinder 10 ft long and 10 ft in diameter. If water inside is 7.5 ft deep, determine the volume of water contained. A. 631.87 ft3 C. 524.79 ft3 B. 783.01 ft3 D. 713.88 ft3

28. The eccentricity of y2 = 4x + 1 A. 1 B. 0 D. 8 D. 3

29. The Angle of elevation of the top of the tree is 30°. If you walk 12 m nearer, the angle of elevation is 34°. What is the height of the tree? A. 48.1 m C. 61.5 m B. 52,3 m D. 42.4 m

30. How many triangles are determined by 10 non collinear points? A. 110 B. 120 C. 154 D. 178 3

31. Evaluate the fourier series 2e + 2e ( ) at t - 0.2 A. 1.39 B. 3.91 C. 5.15 D. 7.92 -

32. What is the angle between the planes 4x + 5y - 3z = 2 and 3x + 5y - 4z = 5? A. 74.13° C. 81.23° B. 78.44° D. 86.77°

33, Determine the divergence of V•= i ( x2y ) j( -xy ) R( xyz ) at ( 3, 2, 1). A. 11 B. 15 C. 17 D. 19

34. Evaluate,In,(3 + j4) A. 1.61 + 0.93i B. 1.16 + 0.801 C. 1.75 + 0.98i D. 2.22 + 0.87i

The sides of a triangle are 195, 157 and 210 35. What is the Area of the triangle? .A. . 14,687.75. . C...19,114.55 B. 15,829.41 D. 22,879.76-

36. What is the length of the biggest median? A. 186.81 C. 175.43 B. 117.92 D. 210.25

Given the ellipse x2 + 4y2 - 2x - 8y i- 1 = 0 37. Find the Area of the ellipse. A. 6.28 C. 9.13 B. 8.62 D. 4.05

38. Find the eccentricity. A. 0.924 C. 0.731

B. 0.866 D. 0.657

A coin is tossed 10 times. 39. What is the probability of getting exactly 5 heads? A. 0.143, B. 0.179 C. 0.246 D. 0.369

40. What is the probability of getting between 3 to 8 tails inclusive? A. 0.9346 C. 0.6754 B. 0.8721 D. 0.7321

41. Solve the particular solution is dy/dx - 3y/x = x3 y(1) = A. y = x4 + 3x3 C. y = x2 + 2x3 B. y = x3 + 3x4 D. y = x2 + 5x4

42. Two linespass trough (5,5) and separate tangents to circle C: + y2 = 9. Determine the distance between the x intercepts of the 2 lines. A. 12 B. 18 C. 25 D. 21

43. Solve the DE. dy/dy + 4y = cos 3x A. v = ce4: + 4/25 cos 3x + 3/25 sin 2x B. y = ce2x + 4/25 cos 4x + 5/25 sin 3x C. y = Ceix + 3/25 cos 3x + 3/25 sin 6x D. y = ce-3x + 6/25 cos 2x + 7/25 sin 4x

44. Maximize z = x + y subject to x2 + y2 = 25 A. 6.21 C. 7.07 B. 5.32 D. 4.89

45. Determine the cube roots of 81-120 A. 2L40. 2L160 2L_ 280 B. 3L50, 4L160 , 5L 280 C. 4L.40, 4 L 160 , 6L 280 D. 5L40, 3L160 , 21_ 280

A 10 ohms resistance R and a 1 henry inductance L is in series. An AC voltage e(t) = 100 sin ( 377t) is applied across the circuit. The Applicable D.E. is Ri + L di/dt = e(t) 46. Find the solution of the DE. \A. i = + 6.231 x 10'6 cos( 377t) -0.0561 sin 377t) B. i = cie1" + 7.036 x 10'6 cos (377t) -0.0265 sin 377t) C. i = cle'" + 5.369 x 1043 cos ( 377t) -0.0987 sin ( 377t) D. i = + 4.123 x 10'6 cos ( 377t) -0.1234 sin 377t)

47. Determine the amplitude of .the resulting sinusoidal current. A. 0.0265 A C. 0.0387 A B. 0.0148 A D. 0.0678 A

48. In a spherical tank having a diameter of 4 m , the volume is 5.236 m3. Find the depth of water. A. 1 m B. 3 m C. 7 m D. 5 m

49. A line passes thru (1, -3) and (-4, 2). Find the equation of the line in slope intercept form. A. y = -2 - x C. y = -4 - x B. y=-3 +x D. y = 3 + x

Given the D.E. y" + 3y' + 2y = 1, y(0) = 1 y1(0) = 1 50. Using Laplace Transform, Find L( y) A. s(s + 1)(s + 2) s(s + 2)(s + 1) C. 52+ 45 +1 52+ 35 +2 B. s2+ Ss +2 D s2+ 4s +2 s(s- 1)(s + 2) s(s- 3)(s + 4)

51. Find y A. y = 3e4 ++ % C. y = 2e4 + 1.5&21+%

B. y = 2e + +1/2 D. y = 4e4 + 4.2e-2t + 1/4

52. A balloon is rising vertically over a point A on the ground at the rate of 20 m/s. A point B is level with and 30 m from A. When the balloon is 40 m from A, at what rate is its distance from B changing. A. 16 fm/s C. 23 fm/s B. 19 fm/s D. 31 fm/s

53. If sin 0 = -1/3 and 0 is in the 3rd, find cos (20) + sec (0) + cot (0) A. 4.5223 C. 2.5455 B. 3.8476 D. 2.2186

54, A funnel in the form of a cone is 10 m across the top and 8-cm deep. Water is flowing into the funnel at the rate of 12 cm Is and out at the rate of 4 cm3ls. How fast is the surface of the water rising when it is 5 cm deep? A. 0.19 cm/s C. 0.33 cm/s B. 0.26 cm/s D. 0.41 cm/s

55. Evaluate cosh (0.942 + j0.429) A. 1.442 + 0.5221 C. 2.369 + 0.123i B. 1.268 + 0.4761 D. 5.684 + 0.786j

56. The second derivative of function f(x) is the same as -f(x). The characteristic of the function is A. Exponential C. Algebraic B. Logarithmic D. Nota

57. Determine the area bounded by the curves y = 6x - x2 and y = x2 - 2x A. 21.33 C. 37.38 B. 19.65 , D. 41.56

Given the vectors A = i xy + j 2yz + k 3zx and B = i yz + j 2zx + k 3xy 58. Find the magnitude of the vector sum (A + B) A. 33.29 - C. 29.88 B. 41.25 D. 21.04

59. Find the area bounded by the curve r = 2 cos( 0)

Given y = x3 - 2x2 60. Find the radius of curvature at (1, -1) A. 2.321 C. 3.569 B. 1.414 D. 1.873

61. Locate the center of curvature at ( 1, -1) A. (2, 0) B. (3, 1) C. (4, 5) D. (2, 2)

62. Find the inverse function f(x) = 2x - 6 A. x/2 + 3 C. x/2 + 5 B. x/3 + 2 D. xJ3 + 7

63. Find the Laplace Transform of t3I2e-41

A. -J3Tc 4(s + 4)3/2 B. 4(s + 5)3/2 C. Ni3it 3(s + 2)3/2 D. V31t 5(s + 4)3/2

A line passes thru the points A(1, 2, 4) and B(3, 7, -1). 64. Find equation of line AB. A. x= 1 + 2t ,y= 2+ 5t, z= 4+ -5t B. x= 1 + 3t , y = 4+ 3t, z= 3+ C. x= 1 + 4t , y = 2+ 5t, z= 4+ -3t D. x= 1 + 2t , y = 3+ 4t, z= 4+ -2t

65. Find the distance of line AB to C (9, 1, 8).. A. 8.916 C. 7.351 B. 6.224 D. 5.492

66. Find the equation of plane ABC. A. -5x + 16y + 14z = 83 C. -8x + lOy + 14z = 92. B -4x + 11y + 15z = 76 D. -3x + 21y + 13z = 57

67. Find y(0.0174) given the D.E (D2 4- 144)(D + 12) y(x) =0 1 1-x 2-x A. 0.97830 + 0.2073C2 + 0.81156C B. 0.824901 + 0.201402 + 0.7365703 C. 0.903501 + 0.159802 + 0.96341 C2-D. 0.6128C, + 0.564702 + 0.4398503 68. Evaluate xyzdzdydx o oo A. 0.054 C. 0.235 B. 0.101 D. 0.179

69. Find the, magnitude of the gradient of F at (1, 2, 3). f(x, y, z) = x2 + y2 + z2 A. 7.48 B. 8.32 C. 9.19 D. 5.66

70. Determine the radius of the sphere whose equation is x2 + y2 + Z2 - 2x + 8y + 16z 65 = 0 A. 10.921 C. 22.391 B. 12.083 D. 31.678

71. are the expanded set of numbers and the negative numbers. A. Whole numbers C. Absolute value B. Integers D. none of these

72. It is used to imply a relation of identity between two quantities. A. Significant digits C. Probability B. Equality D. none of these

73. An algebraic expression consisting of more than two terms. A. Monomial C. Polynomial B. Binomial D. none of these

74. Two or more events are said to be independent if the happening of one does not affect the probability of the happening of the others. A. Independent events B. Dependent events C. Mutually exclusive events D. None of these

75.______ angles are two angles whose sum is 90°

A. Supplementary C. Complementary B. Explementary D. none of these

76. angles are two angles whose sum is 360°. A. Supplementary C. Complementary B. Explementary D. none of these

77. The angle of the line of sight on a stationary object referred from the standard directions. A. Bearing C. Elevation B. Direction D. Depression

78. Spherical Defect (D) - the amount at which the sum of the sides differs from . A. 90° B. 180° C. 270° D. 360°

79. A straight line which meets a curve only at one point.A. Tangent C. Apothem

B. Trapezoid D. none of these

80. A figure containing all the points, and only those point, which fulfill a given requirements. A. Rhomboid C. Polygon B. Corollary D. Locus

81. length of a circle projected by the central angle. A. Chord C. Radius B. Arc D. Sector

82. A line joining any two points on a circle. A. Chord C. Radius B. Arc D. Sector

83. 7 +0 is: A. Irrational number C. Imaginary number B. Real number D. A variable

84. The micro or p means: A. 10.2 B. 10.6 C. 10-3 D. 10-1 -20

85. If eccentricity is less than one, then the curve is: A. Parabola C hyperbola B. Ellipse D. circle e x

86. The expression ex- r T-, is equal to: v• A. Cosh x C. coth x B. Tani.) x D. sinh x

87. If all the y-terms have even exponents, the curve is symmetric with respect to the A. X-axis C. y-axis B. Origin D. line 45° with the x-axis

88. Each angle of a regular dodecagon is equal to A. 135° B. 150° C. 125° D. 105°

89. What is the value of the work done for a closed, reversible, isometric system? A. Positive or negative C. Positive B. Negative D. Zero

90. The geometric mean of 64 and 4 is? A. it- B. 34 C. 32 D. 28

91. The logarithm of 1 to any base is: A. Indeterminate C. infinity B. One D. zero

92. The sum of the squares of the sine and cosine of an angle. A. 0 B. 1 C. 2 D. 3

93. What is the graph of the equation Axe +Bx + Cy2 + Dy + E = 0? A. Circle C. parabola B. Ellipse D. Hyperbola

94. Integral of sin x dx is: A. Sec x + C C. cos x + C B. -cos x C D. csc x + C

95. Locus of points on a side which rolls along a fixed line.

A. Cardioid C. cycloid B. Epicycloid D. hyposycloid

96. What is the sine of 820°? A. 0.984 C. -0.866 B. 0.866 D. -0.500

97. The length of the latus rectum of the parabola y = 4px2 is: A. p B.-4p C. 4p D. 2p

98. The number several of several outcomes divided by the number of possible outcomes js: A. Change C. Probability B. Combination D. permutation

99. Hexahedron has faces. A. 6 faces C. 4 faces B. 20 faces D. 8 faces

100.The unit prefix nanc is opposite to: A. Mega C. Tera B. Gina D. Hexa

1. Find the 30'h term of an A.P. 4, 7, 10...A. 91 B. 90 C. 88 D. 75

2. The seventh term is 56 and the 12th term is -1792 of the geometric progression. Find the ratio and the first term. Assume the ratios are equal. A. -2, 5/8 C. -1, 7/8 B. -1, 5/8 D. -2, 7/8

3. The difference of the squares of the digits of a two digit positive number is 27. If the digits are reversed in order and the resulting number subtracted from the original number, the difference is also 27. What is the original number? A. 63 B. 54 C. 48 D. 73

4. The boat travels downstream in 2/3 of the time as if does going upstream. If the velocity of the river current is 8 kph, determine the velocity of the boat in still water. A. 40 kph C. 50 kph B. 30 kph D. 60 kph

5. The number x, 2x + 7, 10x - 7 forms a Geometric Progression. Find the value of x. A. -5 & -3/7 C. 7 & -7/6 B. 7 & 7/6 D. 8 & 3/7

6. In how many ways can 3 MARINES and 4 ARMIES be seated on a bench if the ARMIES must be seated together? A. 640 B. 720 'C. 576 D. 144

7. Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal consists of the display of one or more flags. A. 64 B. 66 C. 68 D. 62

8. There are 5 main roads between the cities A and B, and four between B and C. In how many ways can a person drive from A to C and-return, ,going through B on both trips without ,drivirg or thc; same road twice? A. 260 B. 240 C. 120 D. 160

9. In Mathematics examination, a student may select 7 problems from a set of 10 problems, In how many ways can he make his choice? A. 120 B. 530 C. 720 D.' 320

10. How many line segments can be formed with 6 distinct points, no three of which are collinear? A. 10 B. 15 C. 20 D. 25

11. How many triangles are determined by the vertices of a regular hexagon? A. 10 B. 15 C. 20 D. 25

12. If an alloy containing 30% silver is mixed with a 55% silver alloy to get 800 pounds of 40% alloy, how much of the 30% silver alloy must be used? A, 450 pounds C. 460 pounds B. 420 pounds D. 480 pounds

13. If sin A = 2.5.11x ,cos A = 3.06x and sin 2A = 3.939x, find the value of x? A. 0.265 C. 0.562 B. 0.256 D. 0.625

14. A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top Of the PLDT tower are 13° and 35° respectively. The height of the tower is 50 m. find the height of the monument. A. 33.51 m C. 7.58 m B. 47.3 m D. 30.57 m

15. If the sides of a parallelogram and an included angle are 6, 10 and 100 degrees respectively, find the length of the shorter diagonal. A. 10.63 C. 10.73 B. 10.37 D. 10.23

16. Given a triangle of sides 10 cm and 16 cm an included angle of 60°. Find the area of the triangle. A. 70 B. 72 C. 80 D. 65

17. The side of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the inscribed and circumscribing circle. A. 3.45, 7.14 C. 2.45, 8.14 B. 2.45, 7.14 D. 3.45, 8.14

18. A rhombus has diagonals of 32 and 20 inches. Determine its area. A. 360 in2 B. 280 in2 C. 320 in2 D. 400 in2

19. Find the a; ea of a regular circle of radius 10 cm. A. 186.48 cm2 B. 148.91 cm2 C. 282.24 cm2 D. 166.24 cm2

20. Each angle of the regular dodecagon is equal to A. 135° B. 150° C. 1 25° D. 105°

21. If an equilateral is circumscribe about a circle of radius 10 cm, determine the side of the triangle. A. 34.64 cm C. 36.44 cm B. 64.12 cm D. 32.10 cm

22. The angle of a sector is 30° and the radius is 15 cm. What is the area of a sector?. A. 59.8 cm2 C. 89.5 cm2 B. 58.9 cm2 D. 85.9 cm2

23. A cubical container that measures 2 in. on a side is tightly packed with 8 marbles and is filled with water. All the 8 marbles are in ,contact with the walls of the container and the adjacent marbles. All the marbles are the same in size. What is the volume of water in the container? A. 0.38 in3 B. 2.5 in3 C. 3.8 in3 D. 4.2 in3

24. A pyramid with a square base has an altitude of 25 cm. If the edge of the base is 15 cm. Calculate the volume of the pyramid. A. 1785 cm3 C. 5178 cm3 B. 1875 cm3 D. 5871 cm3

25. Each side of a cube is increased by 1%. By what percent is the volume of the cube increased? A. 23.4% C. 34.56% B. 30.3% D. 3.03%

26. A circular cone having an altitude of 9 m is divided into 2 segments having the same vertex. If the smaller altitude is 6 m. Find the ratio of the volume of small cone to the big cone. A. 0.296 B. 0.386 C. 0.186 D. 0.486

27. What is the x-intercept of the line passing through (1, 4) and (4, 1)? A. 4.5 B. 5 C. 6 D. 4

28. Find the distance from the line 4x - 3y + 5 = 0 to the point (2, 1). A. 1 B. 2 C. 3 D. 4

29. Find the distance between the lines, 3x + y -12 = 0 and 3x + y - 4 = 0. A. 16W10 B. 12b/10 C. 4/V1.0 D.. 8/V10

30. Find the major axis of the ellipse x2 + 4y2 - 2x - 8y +1 = 0. A. 2 B. 10 C. 4 D. 6

31. Compute the focal length and the length of latus. rectum of parabola y2 + 8x - 6y + 25 = 0. A. 2, 8 B. 4, 16 C. 16, 64 D. 1, 4

32. An arch 18 m high has the form of parabola with a vertical axis. The length of a horizontal beam placed across the arch 8 m from the top is 64 m. find the width of the arch at the bottom. A. 86 m B. 96 m C.106 m D. 76 m

33. What is the equation of the asymptote of the hyperbola -x2 9 4 ---y2 = 1? A. 2x - 3y = 0 C. 2x - y = 0 B. 3x 2y = 0 D. 2x + y = 0

34. What is the volume of the solid bounded by the plane 3x + 4y + 6z = 12 and the coordinates axes. A. 4 B. 6 C. 9 D. 12

35. Evaluate: A. 1

36. Evaluate: Lim x3- 2x-F9 x -> 00 2x3-8A. 0 B. ½ C. 2 D. ¼

LIX11 3x4-2x2+ 7

37. Evaluate: LIX11 3x4-2x2+ 7 x co sx3+A. Undefined C. 3/5 B. Infinity D. 0

38. Differentiate: A. B. C. D.

39. If y = 4cos x = + sin 2x what is the slope of the curveA. 2.21 B. 3.25 C. 4.94 D. 2.21

40. Two post s one is 10 m high and the other 15 m high stand 30 m apart. They are to be stayed by transmission wires attached to a single state at ground level the wires running to the top of the posts. Where should tha stake be placed to use the least amount of wire?A. 12m B. 14m C. 18m D. 16m

41. The lower edge of a picture is 3m the upper edge is 5m above eye of an observer at what horizontal distance should he stand if the vertical angle subtended by the picture is to be greatest?A. 15m B. 3/5 C. 5/3 D. /15m

42. A triangle has variable sides x,y,z subject to constraint such that the perimeter P is fixed to 18 cm. What is the maximum possible area for the triangle.A. 15.15 cm2 C. 14.03 cm2

B. 18.71 cm2 D. 17.15 cm2

43. What is the allowable error in measuring the edge of a cube that is intended to hold 8 m3, if the error of the computed volume is not to exceed 0.03 m3? A. 0.002 B. 0.0025 C. 0.003 D. 0.001

44. Evaluate: ex-1 -dx e.4. 1 A. In (ex - 1)2 + x + C C. In (ex + 1) - x + C B. In (ex + 1) + x + C D. In (ex + 1)2- x + C

45. Evaluate: fofoY (3.2 + 9y2) dxdy A. 40 B. 20 C. 30 D. 50

46. Find the area bounded by the line x - 2y + 10 = 0, the x - axis, the y - axis and x = 10. A. 75 B. 45 C. 18 D. 36

47. Determine the integral of z sin z with respect to z, then r with respect to r from r = 0 to r = 1 and from z = 0 to z = 7r/2. A. 1/2 B. 4/5 C. 1/4 D. 213

48. Evaluate the integral of (3t - 1)3 dt. A. -1}-2.(3t-1)4+ C C. (3f - 1)4 + C B. -4' (3t 1)4 + D..1-.2- (3t - 1)3 + C

49. Evaluate the integral of 3t - 1 cit. A. 9 (3t - 1)5/2 + C C. 2 (3t 1)5/2 + C B. 3 (3f - 1)3/2 + C D. 22- (3t 1)3/2 C

50. The equation y2 = cx is the general solution of: A. y' C. y' = 2x B. y, = 2x D. y =

51. Solve xy' (2y 1) = y (1 - x) A. In (xy) = 2(x y) + C. In (xy) = x 2y + C B. In O<y) = 2y - x + C D. In (xy) = x + 2y + C

52. Find the general solution of the equation y' = x - 2xy. A. 2y = 1 + C e-x2 C. 2y = 1 - C e-X2 . 2y = 1 C ex' D. 2y = 1 + C e-x2 39. If y = 4cos + sin 2x, what Is the slope of the curve when x = 2. A. -2.21 B. -3.25 C. -4.94 D. -2.21 40. Two posts one is 10 m high and the other 15 m high stand 30 m apart. They are to be stayed by transmission wires attached to a single stake at ground level, the wires running to the top of the posts. Where should the stake be placed to use the least amount of wire? A. 12m B. 14m C. 18m D. 16 m 41. The lower edge of a picture is 3 m, the upper edge is 5 m above the eye of an observer, At what horizontal distance should he stand if the vertical angle subtended by the picture is to be greatest? A. 15m B. 3,/5 m C. 5 -\/.3 m D. '/15m 42. A triangle has variable sides x, y, z subject to the constraint such that the perimeter P is fixed to 18 cm. What is the maximum possible area for the triangle? A. 15.59 cm2 C. 14.03 cm2 B. 18.71 cm2 D. 17,15 cm2 53. A thermometer reading 18°F is brought into a room where the temperature is 70°F; a minute later, the thermometer reading is 31°F. Determine the 'temperature reading 5 minutes after the thermometer is first brought into the room. A. 57.68°F C. 64.10°F B. 45.68°F D. 60.61°F 54. Solve (D2 + 5D + 4) (2D2 + 5D + 2) y = 0 A. y = Cie-4x + C2e-x + C3e-2x + Coe-w2 B. y = + C2e2x + C3e2x + Coe >J2 C. y = Cie" + C2e2x + C3ex + C4e-x/2 D. y = Cie-4x + C2e-2x + C3ex + C4e-'12 55. Solve (D2 - 2D + 5)y = 0. A. y = ex (Cicos2x + C2sin2x) B. y = e-x(C1cos3x + C2sin3x) C. y = e-x(C1cos2x C2s1n2x) D. y = e-x(Cicos3x C2sin3x) 56. Solve for the general solution of the differential equation: (D + 100) y = 0. A. y = C e-1°I3x C. 100x + y = C B. y = C elc" D. 100x - y =C _ 57. WrlttettInItte form a + bl expression 13217 - 1427 + 118. A. 21+ 1 B. -1+ 1 C. 2i 1 D. 1 + i

81. A five pointer star is also known as: A. Pentagon C. Pentagram B. Pentatron D. quintagram82. When two planes intersect with each other, the amount of divergence between the two planes is expressed by measuring the: A. Dihedral angle C.polyhedral angle B. Plane angle D. reflex angle

83. If the product of the slopes of any two straight lines is negative 1, one of these lines are said to be: A. Parallel C. perpendicular B. Skew D. non-intersecting 84. The altitudes of the sides of the triangle intersect at the point known as: A. ,Orthocenter C. centroid B. Circumcenter D. incenter85. The median of a triangle is the line connecting the vertex and the midpoint of the opposite side. For a given triangle, these medians intersects at a point which is called the, A. Orthocenter C. centroid B. Circumcenter D. incenter86. What is the point where the second derivative is zero? A. Maxima C. inflection point B. Minima D.point of intersection 87. The characteristic is equal to the exponent 10, when the number is written in: A. Exponential C. logarithmic B. Scientific notation D. irrational 88. It is polyhedron of which two faces are equal polygons in parallel planes and th.: other faces are parallelograms. A. Tetrahedron C, frustum B. Prism D. prismatoid89. The ratio or product of two expression is direct or, inverse relation with each other is called. A. Ratio and proportion B. Constant of variation C. Means D. Extremes 90. The logarithm of a number to the base e(2.718281821....) is called. A. Naperian logarithm B. Characteristic C. Mantissa D. Briggsian logarithm 91. is a sequence of terms whose reciprocals from an arithmetic progression. A. Geometric progression B. HarrriotlicprogfeSsioh C. Alge061c progreipri D. Ratio linctproporticrl92. At the minimum point, the slope of the tangent line is: A. Negative C. positive B. Infinity D. zero 93. What is the angle of and less than 2? A. Straight angle C. Oblique angle B. Obtuse angle D. acute angle 94. The apothem of a polygon is the of its inscribe circle. A. Radius C. diameter B: CircumferenceD. length95. The volume of a circular cylinder is equal to the product of its base and altitude. A. Axiom C. theorem B. Postulate D. corollary 96. Points that lie in the same plane. A. Coplanar C. oblique B. Parallel D. collinear 97. In an ellipse a chord which contains a focus and is in a line perpendicular to the major axis is a: A. Latus rectum C. Conjugate axis B. Minor axis D. focal with 98. is the locus of a point that moves in a plane of that the difference of the distances from two fixed points of the plane is constant. A. Hyperbola C. circle B. Ellipse D. parabola 99. The inverse Laplace transform of is: s2+w-A. Sin wt r B. W D. coswt100. If n is any positive integer, then (n-1)(n-2) (n-3) (3)(2)(1). A. en-1 C. B. (n-1)1 D. (n.-nl)t:"