1. How many degrees Celsius is 100 degrees Fahrenheit.A. 37.8 B. 35.6 C. 40.3 D. 39.1

2. What is the absolute temperature of the freezing point of water in degrees Rankine?A. 275 B. 460 C. 487 D. 492

3. Express 45 digress in mills?A. 80mils C. 8000milsB. 800mils D. 80000

4. An angular unit equivalent to 1/400 of the circumference of a circle is called.A. Mil C. degreeB. Grad D. Radian

5. Carry out the following multiplication and express the answer in cubic meters: 3cm x 5mm x 2m.A. 3 x 10^(-3) C. 3 x 10^(2)B. 3 x 10^(-4) D. 3 x 10^(4)

6. How many square feet is 100 square metersA. 328.10 C. 1075.84B. 951.43 D. 1003.68

7. How many cubic feet is equivalent to 100 gallons of water.A. 7.45 B. 8.00 C. 13.37 D. 133.7

8. The number of board feet in a plank 3 inches thick 1 foot wide and 20 feet long is.A. 20 B. 60 C. 80 D. 30

9. The acceleration due to gravity in English unit is equivalent to:A. 32.2 B. 3.22 C. 9.81 D. 98.1

10. 10 to the 12th power is the value of the prefix.A. Giga C. TeraB. Pico D. Tetra

11. Convert 60 degrees to its value in centesimal systemA. 750 grade C. 800 gradeB. 779 grade D. 850 grade

12. When rounded-off to four signification figures, 102.35690 becomes.A. 102.4 B. 102.0 C. 102.3 D. 102.5

13. Which of the following is correct:A. 0.001 has three significant figuresB. 107.0 has three significant figuresC. 100.0 has four significant figuresD. O.0012 has five significant figures

14. Which of the following is correct:A. 1horse power = 746 KwB. 1horse power = 0.746WC. 1horse power = 0.746 KwD. 1horse power = 748 W

15. A line on a map was drawn at a scale of 5:100,000. If a line in the map is 290 mm long, the actual length of the line is:

A. 2.8 km B. 5.8 km C. 3.6 km D. 4.8 km

16. If the beating of A from B is S 400 W. then the bearing of B from A is:A. N 400 E C. N 500 EB. N 400 W D. N 500 W

17. The area of a triangle is 8346 sq. m. and two of its angles are 370 25’ and 560 17’ what is the length of the longest side?

A. 98.70 B. 182.05 C. 181.54 D. 150.45

18. The side of a triangle is 18cm, 24cm, and 34cm respectively. Find the length of the median to the 24cm side in cm

A. 24.4 B. 21.9 C. 23.4 D. 20.3

19. The sides of a triangle are 45 m and 55 m long. If its area is 785.45 sq. m. Find the sum of the sides.A. 135m B. 145 m C. 125 m D. 115 m

20. In triangle ABC, AB 8m and BC = 20m. One possible dimension of CA is:A. 13 B. 9 C. 11 D. 17

21. In triangle BCD, BC = 25m CD =10m. The perimeter of the triangle may be.A. 72 B. 71 C. 69 D. 70

22. The sides of a triangle ABC are AB = 25cm, BC = 39cm, and AC = 40cm. Find its area.A. 488 sq. cm. B. 648 sq. cm. C. 846 sq. cm. D. 468 sq. cm.

23. Two triangles has equal basis. 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 its altitudes, if the areas of the triangle differ by 21 square units.

A. 6 & 9 B. 4 & 10 C. 5 & 12 D. 7 & 11

24. The sides of a triangle are a = 23.9 m, b = 36.3 m, c = ___. The angle opposite side b is 102.7®. Determine the length of side C.

A. 23 m B. 25.5 m C. 24 m D. 30 m

25. In triangle ABC, angle A = 45® and angle C = 70®. Find the opposite angle A.A. 12 m B. 30 m C. 28 m D. 25.3 m

26. What is the smallest interior angle of the triangle whose sides are 18 cm, 24, cm, and 26 cm long?A. 37® B. 29® C. 42® D. 41®

27. The sum of the side of triangle ABC is equal to 400 m. A = 38®, B = 58®. Find the side AC in meters.A. 139 m B. 140 m C. 128 m D. 138 m

28. What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. m.A. 10 cm B. 11 cm C. 12 cm D. 13 cm

29. cos2 x+sin2 x=¿¿¿A. 1 – cos x B. – sin x C. 1 D. – 1

30. In spherical trigonometry, sides are in ______.A. nautical miles B. degrees C. meters D. miles

31. Determine the area enclosed by the curve x2−10 x+4 y+ y2=196.A. 144π B. 225π C. 200π D. 255π

32. What is the length of the latus rectum of the curve x2 = -12y? A. 12 B. -3 C. 3 D. -12

33. Find the length of the latus rectum of the following ellipse: 25x2 + 9y2 - 300x - 144y + 1251 = 0. A. 3.2 B. 3.3 C. 3.6 D. 3.5

34. Find the ratio of the major axis to the minor axis of the ellipse: 9 x2+4 y2−72x−24 y−144=0. A. 1.08 B. 1.23 C. 1.50 D. 1.67

35. The graph y=(x – 1) /(x+2) is not defined at: A. 0 B. 2 C. -2 D. 1

36. Determine the equation of the line tangent to the graph y = 2x2 + 1, at the point (1, 3). A. y = 2x + 1 B. y = 4x - 1 C. y= 4x+ 1 D. y =2x - 3

37. Convert θ = u/3 to Cartesian equation. A. y = √2x B. y = √−3 x C. y = −√2x D. y = √3 x

38. Find the polar coordinates for the point whose rectangular coordinate of (-6, -8). A. (10, -233.23°) B. (10, 233.23°) C. (10, 126.87°) D. (10, -53,13°)

39. One knot is equivalent to A. 1 mile B. 6080 feet C. 1 degree D. 5280 feet

40. One minute is equivalent to A. 1 mile B. 6080 feet C. 1 degree D. 5280 feet

41. If a regular polygon has 27 diagonals, then it is a: A. heptagon B. nonagon C. decagon D. octagon

42. One side of a regular octagon is 2. Find the area of the region inside the octagon. A. 19,3 sq. units B. 17.5 sq. unitsC. 11.9 sq. units D. 14.4 sq. units

43. A regular octagon is inscribed in a circle of radius 10. Find the area of the octagon. A. 228.2 sq. units B. 288.2 sq. units C. 282.8 sq. units D. 238.2 sq. units

44. A circle having an area of 224 sq. m. Is inscribed in an octagon. Find the area of the octagon. A. 362.7 sq. m. B. 300.2 sq. m.C. 236.3 sq. m. D. 247.6 sq. m.

45. Determine the area of a regular hexagon inscribed in a circle having an area of 170 sq. cm. A. 169.3 B. 128.1 C. 148.2 D. 140.6

46. What is the formula for the area of ellipse?

A. π=(a2+b2) B. π=(a2+b2)/2 C. πab D. π (a+b)

47. The slant height of a right circular cone is 5m long.. The base diameter is 6m. What is the lateral area in sq. m? A. 37.7 B. 47 C. 43 D. 40.2

48. How far from a vertex is the opposite face of a tetrahedron if an edge is 50 cm long? A. 37.771 cm B. 40.825 cm C. 39.064 cm D. 41.118 cm

49. A solid spherical steel ball 20 cm in diameter is placed into a tall vertical cylinder containing water, causing the water level to rise by 10 Cm. What is the radius of the cylinder? A. 12.99 B. 9.57 C. 10.46 D. 11.55

50. The surface area of a regular tetrahedron is 173.2 square centimeters. What is its altitude? A. 8.2 cm B. 9.6 cm . C. 7.2 cm D. 6.5 cm

51. What is the surface are of a sphere whose volume is 36 cu. m.? A. 52.7 sq. m. B. 59.3 sq. m. C. 48.7 sq. m. B D. 46.6 sq. m.

52. How much will the surface area of a sphere be increased if its radius is increased by 5%? A. 25.00% B. 15.50% C. 12.50% D. 10.25%

53. Find P(5,3): A. 5 B. 60 C. 15 D. 41

54. Find C(8,5): A. 56 B. 40 C. 80 D. 26

55.'' Find Ci8,8): A. 64 B. 40 C. 1 D. 80

56. A certain state lottery consists of selecting a set of 6 numbers randomly from a set of 49 numbers. To win the lottery, you must select the correct set of six numbers. How many possible lottery tickets are there? A. 10,000 B. 5,000,000 C. 13,983,816 D. 1.0068 x1010

57. What is the probability of rolling a sum of 3 when rolling a pair of dice? A. 1/2 B. 1/18 C. 1/6 D. 1/9

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

59. The ages of the father and his son are 45 and 5 years, respectively. How many years will the father be three times as old as his son? A. 5 B. 25 C. 15 D. 17

60. Mary is 24 years old. Mary is twice as old as Ana was when Mary was as old as Ana is now. How old is Ana? A. 16 B. 18 C. 20 D. 21

61. A 100-kilogram brine solution originally 4% by weight. Salt in water is boiled to reduce water content until the concentration is 5% by weight salt. How much water is evaporated? A. 5 B. 10 C. 20 D. 15

62. A pipe can fill up a tank with the drain open in three hours. If the pipe runs with the drain open for one hour and then the drain is closed, It will take 45 more minutes for the pipe to fill the tank. If the drain will be closed right at the start of filling, how long will It take for the pipe to fill the tank? A. 1.325 hours B. 1.125 hours C. 1.115 hours D. 1.215 hours

63. A and B can do a piece of work in 42 days, B and C in 31 days, & A and C in 20 days. Working together, how many days can all of them finish the work? A. 18.9 B. 19.4 C. 17.8 D. 20.9

64. Eight men can dig 150 feet of trench in 7 hours. Three men can backfill 100 feet of the trench in 4 hours. The time that it will take 10 men to dig and fill 200 feet of the trench is: A. 9.867 hours B. 9.687 hours C. 8.967 hours D. 8.697 hours

65. From the time 6:15 PM to the time 7:45 PM of the same day, the minute hand of a standard clock • describe an arc of: A. 360 B. 120 C. 540 D. 720

66. The sum of two numbers is 21, and one number is twice the other. Find the numbers. A. 7 and 14 B. 6 and 15 C. 8 and 13 D. 9 and 12

67. Ten less than four times a certain number is 14. Determine the number? A. 4 B. 5 C. -1 D. 7

68. 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. 8/5 B. 5/13 C. 13/5 D. 3/5

69. 9 log9(4) A. 1 B. 4 C. 2 D. 10

70. 3 log3−(5¿)¿ A. 1 B. 0 C. -1 D. undefined

71. Simplify:(x2 y3)3

A. x6 y9 B. 0 C. x D. xy

72. Simplify: (a−2 )5

A. 1 / a−5 C. 1/a10

B. 1 / a5 D. 1/a

73. Water freezes at ________in English unitA. 0°C C. 32F B. 100° D. 212f

74. Water boils at ________ in English unitA. 0°C C. 32°FB. 100°C D. 212°F

75. Who is the inventor of Calculus? A. Isaac Newton B. L. Da VinciC. Albert Einstein D. Archimedes

76. What is the formula of Surface Area of Sphere?

A. 4 πr 2 B. 43πr

3

C. 2πr 2 D. 4 πrd

77. What is the formula of Volume of Sphere?

A. 4 πr 2 B. 43πr

3

C. 2πr 2 D. 4 πrd

78. What is the area of bases of a cylinder?

A. 4 πr 2 B. 43πr

3

C. 2πr 2 D. 4 πrd

79. How many diagonals does a triangle have? A. 1 B. 2 C. 3 D. None

80. How many diagonals does a parallelogram have? A. 1 B. 2 C. 3 D. None

81. What is the altitude of a right circular cone with known lateral area whose volume is maximum? A. r (cube root of 3) B. r divided by 12 C. r (square root of 2) D. r divided by 2

82. Evaluate: ∫sinuduA. -cos u + C B. cos u + C C. -sin u + C D. sin u + C

83. Evaluate: ∫cos uduA. -cos u + C B. cos u C C. -sin u + C D. sin u + C

84. The sum of the Moment of Inertia about x-axis and about y-axis is A. I xy B. 1 C. Product of Inertia D. Polar moment of Inertia

85. Which among the following is the correct formula in determining the work done by a force? A. W=F∗d C. W=ma B. W=mg D. W=0.5mv

86. Which among the following is the correct formula in determining the work done by a spring? A. W = mg B. W = 0.5 kx C. W=0.5k x3 D. W=0.5k x2

87. Any number divided by Infinity is equal to A. 0 B. 1 C. Imaginary D. Infinity

88. One angle is the supplement of another if their sum equals two right angles: A. Complementary angles B. Supplementary angles C. Right angles D. Acute angles

89. A quadrilateral whose opposite sides are parallel: A. Trapezoid B. Parallelogram C. Trapezium D. Circle

90. The circle: of a polygon is the radius pfits inscribed A. Apex B. Arc C. Apothem D. Edge

91. The altitudes of a triangle meet in a point called Orthocenter. A. True B. False C. Trulse D. Both

92. Solids whose faces are plane polygons: A. Prisms B. Prismatoids C. Parallelepiped D. Polyhedrons

93. Polyhedrons whose bases are equal polygons in parallel planes and whose sides are parallelogram: A. Prisms B. Prismatoids C. Parallelepiped D. Polyhedrons

94. What is the nationality of Albert Einstein? A. Filipino B. American C. German D. Serbian95. Polygon on the surface of a sphere whose sides are arcs of great circle: A. Transforms B. Arc polygon C. Sphemgons D. Spherical polygon

96. One-half the volume of a cylinder is equal to: A. Paraboloid B. Cone C. Pyramid D. Sphere

97. Identify the polar curve: r = a (1 - sin 0) A. Cycloid B. Cardioid C. Bowtie D. Epicyloid

98. The probability that you will win the lottery is more likely to happen than the probability you will be stricken by lightning. True or False.A. True B. False C. Trulse D. All of the above

99. Which of the following is not a vector quantity? A. Force B. Work C. displacement D. velocity

100. Tony lifts vertically an object and walk to a certain point in his room. Provided that the floor is horizontal, did he do work in transferring the object? A. Yes B. No C. Maybe D. None of the above

SITUATION 1: At 2:00 A.M. an airplane takes off at a speed of 340 mph on an aircraft carrier. The aircraft carrier moves due south at the speed of 25 mph in the same direction as the plane. At 4:05 A.M. the communication between the plane and the aircraft carrier was cut off.

1. Compute the distance travelled by the aircraft carrier after 2 hours and 5 minutes travel. A. 52 miles B. 708 miles C. 656 miles D. 645 miles

2. Compute the distance traveled by the plane after 2 hours and 5 minutes travel.. A. 52 miles B. 708 miles C. 656 miles D. 645 miles

3. Compute the communication range between the aircraft carrier and the plane. A. 52 miles B. 708 miles C. 656 miles D. 645 miles

SITUATION 2: A job could be done by 25 workers in a target time of 90 days. There were 25 workers in the beginning but 5 workers quit after 30 days. Three more workers resigned after 60 days.

4. How many days did the remaining workers take to finish the job? A. 23 days B. 203 days C. 113 days D. 53 days

5. How many days did the workers finish the job? A. 23 days B. 203 days C. 113 days D. 53 days

6. How many days the project was delayed? A. 23 days B. 203 days C. 113 days D. 53 days

SITUATION 3: Two planes parallel to the base of a pyramid (12-m in altitude) cut the pyramid into three parts. The upper and lower planes are 4 m and 8 m away from the top of the pyramid.

7. Find the ratio of the volume of the middle part to the volume of the whole pyramid.

A. 0.259 B. 3.861 C. 0.704 D. 0.037

8. Find the ratio of the volume of the largest part to the volume of the whole pyramid. A. 0.259 B. 3.861 C. 0.704 D. 0.037

9. Find the ratio of the volume of the smallest part to the volume of the whole pyramid. A. 0.259 B. 3.861 C. 0.704 D. 0.037

SITUATION 4: An amount of P1, 000.00 becomes P1, 608.44 after 4 years compounded bi-monthly.

10. Find the nominal rate of interest. A. 12.00% B. 12.62% C. 12.06% D. 12.37%

11. Find the effective rate of interest. A. 12.00% B. 12.62% C. 12.06% D. 12.37%

12. Find the effective rate of interest if it is compounded quarterly. A. 12.00% B. 12.62% C. 12.06% D. 12.37%

SITUATION 5: An engineer is entitled to receive P25, 000 at the beginning of each year for 18 years. If the rate of interest is 4% compounded annually.

13 What is the present value of this annuity at the time he us supposed to receive the first payment. A. P111, 111 B. P25, 645 C. P666, 781 D. P325, 142

14. What is the sum of this annuity at the end of the 18th year?A. P111, 111 B. P25, 645 C. P666, 781 D. P325, 142

15. Find the difference between the sums of this annuity which is paid at the beginning of each year (annuity due) and ordinary annuity (annuity paid at the end of each year). A. P111, 111 B. P25, 645 C. P666, 781 D. P325, 142

16. The measure of 2.25 revolutions counterclockwise is, A. -810 degrees B. -800 degrees C. 800 degrees D. 810 degrees

17. Csc 270 degree = ?A. -42 B. -1 C. 1 D. 1.

18. If coversine θ is 0.134, find the value of θ? A. 60° B. 30° C. 90° D. 45°

19. If sin 3A = cos 6B then: A. A + B = 30° B. A + 2B = 30° C. A - B = 180° D. A 2B = 30°

20. Find the value of x in the equation csc x + cot x = 3. A. π /2 B. π /4 C. π /6 D. π /5

21. If sin A = 2.571x, cos A = 3.06x, and sin 2A = 3.939x, find the value of x. A. 0.20 B. 0.25 C. 0.05 D. -0.15

22. Solve for x from the given trigonometric equation: arctan (1 - x) + arctan (1 + x) = arctan 1/8 A. 4 B. 7 C. 6 D. 5

23. Find the value of y=(1 + cos 2θ) tan θA. cos θ B. tan θ C. sin 2 θ D. sin θ

24. Simplifying the equation sin2θ(1+cos 2θ) gives: A. 1 B. sin θ C. cos θ D. -1

25. The angle or inclination of ascends of a road having 8.25% grade is degrees.A. 7.43 B. 4.72 C. 4.27 D. 7.34

26. The hypotenuse of a right triangle is 34 cm. Find the length of the shortest leg if it is 14 cm shorter than the other leg. A. 15 cm B. 16 cm C. 17 cm D. 18 cm

27. Given angle A = 32°, angle B = 70°, and side c = 27 units. Solve for side a of the triangle. A. 24.94 units B. 13.65 units C. 14.63 units D. 11.05 units

28. If AB = 15 m, BC = 18 m and CA =.24 m, find the point of intersection of the angular bisector from the vertex C. A. 12.1 B. 11.9 C. 13.4 D. 14.3

29. A statue 2 meters high stands on a column that is 3 meters high. An observer in level with the top of the statue observed that the column and the statue subtend the same angle. How far is the observer from the statue? A. 5√2 B. 2√5 C. 15√2 D. −5√2

30. A 50-meter vertical tower casts a 62.3-meter shadow When the angle of elevation of the sun is 41.6°. The inclination of the ground is. A. 4.72° B. 4.33° C. 5.63° D. 5.17°

31. Calculate the area of a spherical triangle whose radius is 5m and whose angles are 40°, 65° and 110°. A. 12.34 sq. m. B. 14.89 sq. m. C. 16.45 sq. m. D. 15.27 sq. m.

32. A right spherical triangle has an angle C = 90°, a 50°, and c = 80°. Find the side b. A. 45.33° B. 78.66° C. 74.33° D. 75.89°

33, If the time is 8:00 AM GMT, what is the time in the Philippines, which is located at 120° East longitude? A. 6 PM B. 4 AM C. 4 PM D. 6 AM

34, The segment from (-1, 4) to (2, -2) is extended three times its own length. The terminal point is: A. (-11, 20) B. (-11, -20) C. (11, -20) D. (11, 20)

35. Find the coordinates of the points 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)

36. Find the area of triangle whose vertices are A (-3, -1), B (5, 3) and C (2, -8). A. 36 B. 31 C. 38 D. 37

37. Find the distance from the point (5, -3) to the line 7x 4y 28 = O. A. 2.61 B. 2.36 C. 2.43 D. 2.32

38. Find the slope of the line whose parametric equations are y = 5 - 3t and x = 2 + t. A. 3 B. -3 C. 2 D. -2

39. Find the angle that the line 2y - 9x - 18 = 0 makes with the x-axis.

A. 74.77° B. 45.21° C. 47.77° D. 77.47°