Multiple Choice Questions In Engineering Mathematics By Jas Tordillo

Multiple Choice Question in Engineering Mathematics By JAS Tordillo

Encoded By: Dajano, Jose Mari T. Salavante, Marc-Ian

1. A man sold a book by mistake at 120% of the marked price instead of discounting the marked price by 20%. If he sold the book for P14.40, what was the price for which he have sold the book? a) P8.00 b) P8.50 c) P9.00 d) P9.60 2. In how many ways can 9 books be arranged on a shelf so that 5 of the books are always together? a) 30,200 b) 25,400 c) 15,500 d) 14,400 3. If one third of the air tank is removed by each stroke of an air pump, what fractional part of the total air is removed in 6 strokes? a) 0.7122 b) 0.6122 c) 0.8122 d) 0.9122 4. If 3^x = 9^y and 27^y = 81^z, find x/z? a) 3/5 b) 4/3 c) 3/8 d) 8/3 5. Determine x, so that x, 2x+7, 10x-7 will be geometric progression. a) 7,-5/6 b) 7, -14/5 c) 7, -7/12 d) 7, -7/6 6. A man invested part of P20,000 at 18% and the rest at 16%. The annual income from 16% investment was P620 less than three times the annual income from 18% investment. How much did he invest at 18%? a) P5,457.20 b) P6,457.20 c) P7,457.20 d) P8,457.20 7. The sum of four positive integers is 32. Find the greatest possible product of these four numbers. a) 5013 b) 645 c) 4069 d) 4913 8. A piece of paper is 0.05 in thick. Each time the paper is folded into half, the thickness is doubled. If the paper was folded 12 times, how much thick in feet the folded paper be? a) 10.1 ft b) 12.1 ft

c) 15.1 ft d) 17.1 ft 9. A seating section in a certain athletic stadium has 30 seats in the first row, 32 seats in the second row, 34 seats in the third row, and so on, until the tenth row is reached, after which there are ten rows each containing 50 seats. Find the total number of seats in the section. a) 1200 b) 980 c) 890 d) 750 10. One pipe can fill a tank in 6 hours and another pipe can fill the same tank in 3 hours. A drain pipe can empty the tank in 24 hours. With all three pipes open, how long will it take to fill in the tank? a) 5.18 hours b) 4.18 hours c) 3.18 hours d) 2.18 hours 11. The ten’s digit of a certain two digit number exceeds the unit’s digit by four and is one less than twice the unit’s digit. Find the number. a) 65 b) 75 c) 85 d) 95 12. The sum of two numbers is 35 and their product is 15. Find the sum of there reciprocal. a) 2/7 b) 7/3 c) 2/3 d) 5/2 13. The smallest natural number for which 2 natural numbers are factors. a) Least common divisor b) Least common denominator c) Least common factor d) Least common multiple 14. Ana is 5 years older than Beth. In 5 years, the product of their ages is 1.5 times the product of their present ages. How old is Beth now? a) 30 b) 25 c) 20 d) 15 15. The time required for the examinees to solve the same problem differ by two minutes. Together they can solve 32 problems in one hour. How long will it take for the slower problem solver to solve a problem? a) 2 minutes b) 3 minutes c) 4 minutes d) 5 minutes 16. Find the value of m that will make 4x^2 – 4mx + 4m ) 5 a perfect square trinomial.

a) 3 b) -2 c) 4 d) 5 17. How many liters of water must be added to 35 liters of 89% hydrochloric acid solution to reduce its strength to 75%? a) 3.53 b) 4.53 c) 5.53 d) 6.53 18. A purse contains $11.65 in quarters and dimes. If the total number of coins is 70, find how many dimes are there. a) 31 b) 35 c) 39 d) 42 19. Equations relating x and y that cannot readily be solved explicitly for y as a function of x or for x as a function of y. Such equations may nonetheless determine y as a function of x or vice versa, such function called _________. a) logarithmic function b) implicit function c) explicit function d) continuous function 20. A piece of wire of length 50 m is cut into two parts. Each part is then bent to form a square. It is found that the total area of the square is 100 sq. m. Find the difference in length of the two squares. a) 6.62 b) 7.62 c) 8.62 d) 9.62 21. A tank is filled with an intake pipe that fills it in 2 hours and an outlet pipe that empty in 6 hours. If both pipes are left open, how long will it take to fill in the empty tank? a) 1.5 hrs b) 2.0 hrs c) 2.8 hrs d) 3 hrs 22. Maria sold a drafting pen for P612 at a loss of 25% on her buying price. Find the corresponding loss or gain in percent if she had sold it for P635? a) 20.18% b) 11.18% c) 22.18% d) 28.18% 23. Divide 1/8 by 8. a) 1/64 b) 18 c) 1

d) 64 24. Given 2 x 2 matrix [

], find its determinant.

a) 31 b) 44 c) -20 d) 20 25. If the sum is 220 and the first term is 10, find the common difference if the last term is 30. a) 2 b) 5 c) 3 d) 2/3 26. Find the sum of the sequence 25, 30, 35, ..... a) (2/5)(n^2 + 9n) b) (5/2)(n^2 + 9n) c) (9/2)(n^2 + 9n) d) (9/2)(n^2 – 9n) 27. Solve for x: √ . a) 4, -5 b) -4, -5 c) -4, 5 d) no solution 28. Solve for x: 10x^2 + 10x + 1 =0. a) -0.113, -0.887 b) -0.331, -0.788 c) -0.113, -0.788 d) -0.311, -0.887 29. The number x, 2x + 7, 10x – 7 form a Geometric Progression. Find the value of x. a) 5 b) 6 c) 7 d) 8 30. Find the 30th term of A.P. 4,7,10,... a) 91 b) 90 c) 88 d) 75 31. Find the sum of the first 10 terms of the geometric progression 2, 4, 8, 16,... a) 1023 b) 2046 c) 225 d) 1596 32. Find the sum of the infinite geometric progression 6, -2, 2/3,... a) 9/2 b) 5/2 c) 11/2 d) 7/2

33. Find the ratio of an infinite geometric series if the sum is 2 and the first term is ½. a) 1/3 b)1/2 c) 3/4 d) 1/4 34. Find the 1987th digit in the decimal equivalent to 1785/9999 starting from the decimal point. a) 8 b) 1 c) 7 d) 5 35. What is the lowest common factor of 10 and 32. a) 320 b) 2 c) 180 d) 90 36. Ten less than four times a certain number is 14. Determine the number. a) 6 b) 7 c) 8 d) 9 37. Jolo bought a second hand betamax VCR and sold it to Rudy at a profit of 40%. Rudy then sold the VCR to Noel at a profit of 20%. If Noel paid P2856 more than it cost to Jolo, how much did Jolo paid the unit? a) P4000 b) 4100 c) 4200 d) P4300 38. A club of 40 executives, 33 likes to smoke Malboro, and 20 likes to smoke Philip Morris. How many like both? a) 13 b) 10 c) 11 d) 12 39. A merchant has three items on sale, namely a radio for P50, a clock for P30 and a flashlight for P1.00. At the end of the day, he has sold a total of 100 of the three items and has taken exactly P1000 on the total sales. How many radios did he sale? a) 16 b) 20 c) 18 d) 24 40. What is the sum of the coefficients of the expansion of (2x – 1)^20? a) 0 b) 1 c) 2 d) 3 41. Find the ratio of the infinite geometric series if the sum is 2 and the first term is 1/2.

a) 1/3 b) 1/2 c) 3/4 d) 1/4 42. A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer and sol until there are 10 bricks in the last layer. How many bricks are there together? a) 638 b) 637 c) 640 d) 639 43. Once a month a man put some money into the cookie jar. Each month he put 50 centavos more into the jar than the month before. After 12 years he counted his money; he had P5436. How much did he put in the jar in the last month? a) 73.5 b) P75.50 c) P74.50 d) P72.50 44. 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, 7/8 b) -1. 5/8 c) -1, 7/8 d) -2, 5/8 45. Find the value of x in the equation 24x^2 + 5x -1 = 0. a) (1/6, 1) b) (1/6, 1/5) c) (1/2, 1/5) d) (1/8, -1/3) 46. The polynomial x^3 + 4x^2 -3x +8 is divided by x – 5, then the remainder is: a) 175 b) 140 c) 218 d) 200 47. Find the rational number equivalent to repeating decimal 2.3524242424... a) 23273/9900 b) 23261/990 c) 23289/9900 d) 23264/9900 48. The sum of Kim’s and Kevin’s ages is 18. In three years, Kim will be twice as old as Kevin. What are their ages now? a) 4, 14 b) 5, 13 c) 7, 11 d) 6, 12

49. Ten liters of 25% salt solution and 15%liters of 35% solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the percent concentration in the mixture? a) 19.55% b) 22.15% c) 27.05 d) 26.72% 50. Determine the sum of the infinite series: S = 1/3 + 1/9 + 1/27 + .... (1/3)^n. a) 4/5 b) 3/4 c) 2/3 d) 1/2 51. Determine the sum of the positive valued solution to the simultaneous equations: xy = 15, yz = 35, zx = 21. a) 15 b) 13 c) 17 d) 19 52. The areas of two squares differ by 7 sq. ft. and their perimeters differ by 4 ft. Determine the sum of their areas. a) 25 ft^2 b) 27 ft^2 c) 28 ft^2 d) 22 ft^2 53. A bookstore purchased a bestselling book at P200 per copy. At what price should this book be sold so that, giving a 20% discount, the profit is 30%? a) P450 b) P500 c) P375 d) P400 54. In a certain community of 1,200 people, 60% are literate. Of the males, 50% are literate and of the females 70% are literate. What is the female population? a) 850 b) 500 c) 550 d) 600 55. Gravity causes a body to fall 16.1 ft. in the 1st second, 48.3 ft. in the 2nd second, 80.5 ft. in the 3rd second, and so on. How far did the body fall during the 10th second? a) 248.7 ft b) 308.1 ft c) 241.5 ft d) 305.9 ft 56. In a commercial survey involving 1,000 persons on brand reference, 120 were found to prefer brand x only, 200 prefer brand y only, 150 prefer brand z only. 370 prefer either x or y but not z, 450 prefer brand y or z but not x, and 420 prefer either brand z or x but not y. How many persons have no brand preference, satisfied with any of the 3 brands?

a) 280 b) 230 c) 180 d) 130 57. The electric power which a transmission line can transmit is proportional to the total product of its design voltage and current capacity, and inversely to the transmission distance. A 115 kilovolt line rated at 1000 amperes can transmit 150 Megawatts over 150 km. How much power, in Megawatts, can a 230 kilovolt line rated 1500 amperes transmit over 100km? a) 785 b) 485 c) 675 d) 595 58. Find the geometric mean of 64 and 4. a) 16 b) 34 c) 32 d) 28 59) Factor the expression x^2 + 6x + 8 as completely as possible. a) (x + 8)(x – 2) b) (x + 4)(x – 2) c) (x + 4)(x + 2) d) (x – 4)(x – 2) 60. A batch of concrete consisted of 200 lbs. Fine aggregate, 350 lbs coarse aggregate, 94 lbs cement, and 5 gallons water. The specific gravity of the sand and gravel may be taken as 2.65 and that of the cement as 3.10. What was the weight of concrete in place per cubic foot? a) 172 lb b) 236 lb c) 162 lb d) 153 lb 61. Dalisay’s Corporation gross margin is 45% sales. Operating expenses such as sales and administration are 15% of sales. Dalisay is in 40% tax bracket. What percent of sales is their profit after taxes? a) 18% b) 5% c) 24% d) 50% 62. A and B working together can finish painting a home in 6 days. A working alone, can finish it in five days less than B. How long will it take each of them to finish the work alone? a) 10, 15 b) 15, 20 c) 20, 25 d) 5, 10 63. Determine the sum of the progression if there are 7 arithmetic mean between 3 and 35. a) 171 b) 182 c) 232

d) 216 64. Find the sum of 1, -1/5, 1/25,... a) 5/6 b) 2/3 c) 0.84 d) 0.72 65. Find the remainder if we divide 4y^3 + 18y^2 + 8y -4 by (2y + 3). a) 10 b) 11 c) 15 d) 13 66. What time after 3 o’clock will the hands of the clock be together for the first time? a) 3:16.36 b) 3:14.32 c) 3:12.30 d) 3:13.37 67. 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 68. The boat travels downstream in 2/3 of the time as it 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 b) 50 kph c) 30 kph d) 60 kph 69. Given that w varies directly as the product of x and y and inversely as the square of z, and that w = 4, when x = 2, y = 6, and z = 3. Find the value of ―w‖ when x = 1, y = 4, and z = 2. a) 2 b) 3 c) 4 d) 5 70. The third term of a harmonic progression is 15 and 9th term is 6. Find the eleventh term? a) 4 b) 5 c) 6 d) 7 71. Solve for x for the given equation, 7.4 x 10^-4 = e^-9.7x. a) 0.7621 b) 0.7432 c) 0.7243 d) 0.7331 72. Find the 10th term of the geometric progression: 3, 6, 12, 24,....

a) 1536 b) 1653 c) 1635 d) 3156 73. Find the sum of odd integers from 1 to 31. a) 256 b) 526 c) 265 d) 625 74. Box A has 4 white balls, 3 blue balls, and 3 orange balls. Box B has 2 white balls, 4 blue balls, and 4 orange balls. If one ball is drawn from each box, what is the probability that one of the two balls will be orange? a) 27/50 b) 9/50 c) 23/50 d) 7/25 75. Solve: x^2 + y^2 = 5z and x^2 – y^2 = 3z. How many and what numerical values for x, y, and z will satisfy these simultaneous equations? a) if z = 3^2, then x = 6 and y = 3 b) if z = 2^2, then x =4 and y =2 c) if z = 1^2, then x =2 and y = 1 d) There are an infinite no. of values that will satisfy 76. Two people driving towards each other between two towns 160 km apart. The first man drives at the rate of 45 kph and the other drives at 35 kph. From their starting point, how long would it take that they would meet? a) 3 hr b) 4 hr c) 2 hr d) 1 hr 77. Solve x for the equation 6x – 4 = 2x + 6. a) 10 b) 5/2 c) 5 d) 2.5 78. The man has a total of 33 goats and chickens. If the total of their feet is 900, find the number of goats and chickens. a) 12 goats and 21 chickens b) 9 goats and 27 chickens c) 6 cats and 5 dogs d) 13 goats and 20 chickens 79. Express 5y – [3x – (5y + 4)] into polynomial. a) 10y – 3x +4 b) 5y + 5x – 4 c) 5y + 5x + 4 d) 5y – 5x +4 80. What is the exponential form of the complex number 3 + 4i?

a) e^i53.1° b) 5e^i53.1° c) 5e^i126.9° d) 7e^i53.1° 81. Simplify the complex numbers: (3 + 4i) – (7 – 2i) a) -4 + 6i b) 10 + 2i c) 4 – 2i d) 5 – 4i 82. Solve for x: x^2 + x -12 = 0 a) x = 6, x = -2 b) x = 1, x = 12 c) x = 3, x = -4 d) x = 4, x = -3 83. √ √ = a) 0 b) √ c) √ d) 10 84. What us the value of x in the expression: x – 1/x = 0? a) x = -1 b) x = 1, 1/2 c) x = 1 d) x = 1, -1 85. What is the value of A: A^-6/8 = 0.001? a) 10 b) 100 c) 0 d) 10000 86. Find the value of x: ax – b = cx + d a) x = (a – b)/(c + d) b) x = (b + d)/(a – c) c) x = (a – d)/(c – b) d) x = (c + d)/(a – c) 87. Divide: 15x^4 +6x^3 + 15x + 6 by 3x^3 + 3. a) 5x + 2 b) 5x^2 + 2 c) 5x^2 d) 5x – 4 88. Simplify: √ √ a) √ b) √ c) √ d) √ 89. Find the value of x in the equation: csc x + cot x = 3

a) π/5 b) π/4 c) π/3 d) π/2 90. If A is in the III quadrant and cos A = -15/17, find the value of cos (1/2)A. a) –(8/17)^1/2 b) –(5/17)^1/2 c) –(3/17)^1/2 d) –(1/17)^1/2 91. Simplify the expression: (sin B + cos B tan B)/cos B a) 2 tan B b) tan B + tan B c) tan B cos B d) 2 sin B cos B 92. If cot 2A cot 68° = 1, then tan A is equal to ________. a) 0.194 b) 0.419 c) 0.491 d) 0.914 93. A ladder 5 m long leans against the wall of an apartment house forming an angle of 50 degrees, 32 minutes with ground. How high up the wall does it reach? a) 12.7 m b) 10.5 m c) 3.86 m d) 1.55 m 94. The measure of 2.25 revolutions counterclockwise is: a) -810 deg b) -805 deg c) 810 deg d) 805 deg 95. If sin A = 2.5 x and cos A = 5.5x, find the value of A in degrees. a) 14.5 deg b) 24.5 deg c) 34.5 deg d) 44.5 deg 96. Solve angle A of an oblique triangle wit vertices ABC, if a = 25, b = 16 and C = 94 degrees and 6 minutes. a) 50 deg and 40 min b) 45 deg and 35 min c) 55 deg and 32 min d) 54 deg and 30 min 97. Given: x = (cos B tan B – sin B)/cos B. Solve for x if B = 30 degrees. a) 0.577 b) 0 c) 0.500 d) 0.866

98. (cos A)^4 – (sin A)^4 is equal to _________. a) cos 2A b) sin 2A c) 2tan A d) sec A 99. 174 degrees is equivalent to _________ mils. a) 3094 b) 2084 c) 3421 d) 2800 100. What is the resultant of a displacement 6 miles North and 9 miles East? a) 11 miles, N 56° E b) 11 miles, N 54° E c) 10 miles, N 56° E d) 10 miles, N 54° E 101. Which is identically equal to (sec A + tan A)? a) 1/(sec A + tan A) b) csc A – 1 c) 2/(1 – tan A) d) csc A + 1 102. Determine the simplified form of (cos 2A – cos A)/(sin A). a) cos 2A b) –sin A c) cos A d) sin 2A 103. Ifsec 2A = 1/sin 13A, determine the angle A in degrees. a) 5 deg b) 6 deg c) 3 deg d) 7 deg 104. Solve for x in the equation: arctan (x + 1) + arctan (x – 1) = arctan (12). a) 1.50 b) 1.34 c) 1.20 d) 1.25 105. Solve for x if tan 3x = 5tan x. a) 20.705 deg b) 30.705 deg c) 15.705 deg d) 35.705 deg 106. If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.939x, find the value of x. a) 0.265 b) 0.256 c) 0.562 d) 0.625 107. The angle of inclination of ascend of a road having 8.25% grade is ______.

a) 4.72 b) 4.27 c) 5.12 d) 1.86 108. A man finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower? a) 76. 31 m b) 73.31 m c) 73.16 m d) 73.61 m 109. 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 b) 10.37 c) 10.73 d) 10.23 110. What is the value of log2 5 + log3 5? a) 7.39 b) 3.79 c) 3.97 d) 9.37 111. Points A and B 1000 m apart are plotted on a straight highway running east and west. From A, the bearing of a tower C is 32 degrees W of N and from B the bearing of C is 26 degrees N of E. Approximate the shortest distance of tower C to the highway. a) 364 m b) 374 m c) 394 m d) 384 m 112. If log of 2 to base 2 plus log of x to the base of 2 is equal to 2, then the value of x is: a) 4 b) -2 c) 2 d) -1 113. Arctan [2cos (arcsin √ /2)] is equal to: a) π/3 b) π/4 c) π/6 d) π/2 114. Solve A for the given equations cos^2 A = 1 – cos^2 A. a) 45, 125, 225, 335 degrees b) 45, 125, 225, 315 degrees c) 45, 135, 115, 315 degrees d) 45, 150, 220, 315 degrees 115. If sin A = 2/5, what is the value of 1 – cos A? a) 0.083

b) 0.916 c) 0.400 d) 0.614 116. Sin A cos B – cos A sin B is equivalent to: a) cos (A – B) b) sin (A – B) c) tan (A – B) d) cos (A –B) 117. How many degrees is 4800 mils? a) 270 deg b) 90 deg c) 180 deg d) 215 deg 118. ln 7.18^xy equals a) 1.97xy b) 0.86xy c) xy d) 7.18xy 119. The log10 (8)(6) equal to: a) log10 8 + log10 6 b) log10 8 - log10 6 c) log10 8 log10 6 d) log10 8 / log10 6 120. 38.5 to the x power = 6.5 to the x – 2 power, solve for x using logarithms. a) 2.70 b) -2.10 c) 2.10 d) -2.02 121. Given the triangle ABC in which A = 30°30’, b = 100 m and c = 200 m. Find the length of the side a. a) 124.64 m b) 142.24 m c) 130.5 m d) 103.00 m 122. An observer wishes to determine the height of the tower. He takes sight at the top of the tower from A and B, which are 50 ft apart at the same elevation on a direct line with the tower. The vertical angle at point A is 30 deg and at point B is 40 deg. What is the height of the tower? a) 85.60 ft b) 110.29 c) 143.97 d) 92.54 ft 123. What is the value of log to the base of 1000^3.3? a) 9.9 b) 99.9 c) 10.9 d) 9.5

124. In a triangle, find the side c if angle C = 100 deg, side b = 20, and side a = 15. a) 28 b) 29 c) 27 d) 26 125. Given a triangle with an angle C = 28.7 deg, side a = 132 units and side b = 224 units. Solve for the side c. a) 95 units b) 110 units c) 125.4 units d) 90 units 126. 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 deg and 35 deg respectively. The height of the tower is 50 m. Find the height of the monument. a) 33.51 m b) 47.3 m c) 7.48 m d) 30.57 m 127. Find the value of x if log12 x = 2. a) 144 b) 414 c) 524 d) 425 128. If tan x = 1/2, tan y = 1/3. What is the value of tan (x + y)? a) 1 b) 2 c) 3 d) 4 129. The logarithm of the quotient M/N and the logarithm of the product MN is equal to 1.55630251 and 0.352182518 respectively. Find the value of M. a) 6 b) 7 c) 8 d) 9 130. The angle of elevation of the top tower B from the top of the tower A is 28 deg and the angle of elevation of the top tower A from the base of the tower B is 46 deg. The two towers lie in the same horizontal plane. If the height of the tower B is 120 m, find the height of tower A. a) 87.2 m b) 90.7 m c) 79.3 m d) 66.3 m 131. Evaluate the log6 845 = x. a) 3.76 b) 5.84 c) 4.48 d) 2.98

132. Find the value of log8 48. a) 1.86 b) 6.81 c) 8.61 d) 1.68 133. Find the value of sin 920 deg. a) 0.243 b) -0.243 c) 0.342 d) -0.342 134. Log (x)^n = a) log x b) n log x c) 1/n log x d) n 135. Sin 2θ is equal to: a) 2 sin θ cos θ b) 1/2 sin θ c) sin θ cos θ d) 1 – sin^2 θ 136. What is the interior angle (in radian) of an octagon? a) 2.26 rad b) 2.36 rad c) 2.8 rad d) 2.75 rad 137. The trigonometric function (1 + tan^2 θ) is also equal to: a) sec^2 θ b) cos^2 θ c) csc^2 θ d) sin θ 138. Derive the formula of each interior angle (in degrees). a) (no. of sides – 2)180 b) [(no. of sides – 2)180/no. of sides] c) [(no. of sides – 1)180/no. of sides] d) [no. of sides – 2]/180 139. What is the Cartesian logarithm of 402.9? a) 2.605 b) 2.066 c) 3.05 d) 3.60 140. What is the value of the following limit? a) 3 b) 6 c) 9 d) 0

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141. Given the three sides of a triangle: 2, 3, 4. What is the angle in radians opposite the side with length 3? a) 0.11 b) 0.41 c) 0.55 d) 0.81 142. Find the area of the geometric figure whose vertices are at (3, 0, 0), (3, 3, 0), (0, 0, 4) and (0, 3, 4). a) 12 sq. units b) 14 sq. units c) 15 sq. units d) 24 sq. units 143. A central angle of 45 degrees subtends an arc of 12 cm. What is the radius of the circle? a) 15.28 cm b) 18.28 cm c) 20.28 cm d) 30.28 cm 144. It is a part of circle bounded by a chord and an arc. a) slab b) segment c) section d) sector 145. What is the area (in sq. inches) of a parabola with a base of 15 cm and a height of 20 cm? a) 87 b) 55 c) 31 d) 11 146. Triangle ABC is a right triangle with right angle at C. CD is perpendicular to AB. BC = 4 and CD = 1. Find the area of the triangle ABC. a) 2.95 b) 2.55 c) 2.07 d) 1.58 147. The tangent and a secant are drawn to a circle from the same external point. If the tangent is 6 inches and the external segment of the secant is 3 inches, the length of the secant is ________ inches. a) 15 b) 14 c) 13 d) 12 148. If a regular polygon has 27 diagonals, then it is a, a) nonagon b) pentagon c) hexagon d) heptagon

149. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the dodecagon. a) 125 b) 135 c) 149 d) 169 150. An annulus is a plane figure, which is composed of two concentric circles. The area of the annulus can be calculated by getting the difference between the area of the larger circle and the area of the smaller circle. Also, it can be calculated by removing the hole. The method is called: a) Law of Extremities b) Law of Reduction c) Law of Deduction d) Sharp Theorem 151. The sides of a triangle are 195, 157, and 210 respectively. What is the area of the triangle? a) 73250 sq. units b) 14586 sq. units c) 10250 sq. units d) 11260 sq. units 152. Given a triangle of sides 10 cm and 15 cm an included angle of 60 degrees. Find the area of the triangle. a) 70 b) 80 c) 72 d) 65 153. The sides of a triangle are 8 cm, 10 cm, and 14 cm. Determine the radius of the inscribed and circumscribed circle. a) 3.45, 7.14 b) 2.45, 7.14 c) 2.45, 8.14 d) 3.45, 8.14 154. The sides of a cyclic quadrilateral are a = 3m, b = 3m, c = 4m and d = 4m. Find the radius of the inscribed and circumscribed circle. a) 1.71, 2.50 b) 1.91, 2.52 c) 2.63, 4.18 d) 2.63, 3.88 155. From the point inside a square the distance to three corners are 4, 5 and 6 m respectively. Find the length of the sides of a square. a) 7.53 b) 8.91 c) 6.45 d) 9.31 156. A regular pentagon has sides 20 cm. An inner pentagon with sides of 10 cm is inside and concentric to the larger pentagon. Determine the area inside and concentric to the larger pentagon but outside of the smaller pentagon. a) 430.70 cm^2

b) 573.26 cm^2 c) 473.77 cm^2 d) 516.14 cm^2 157. A rhombus has diagonals of 32 and 20 inches. Determine its area. a) 360 in^2 b) 280 in^2 c) 320 in^2 d) 400 in^2 158. In a circle with a diameter of 10 m, a regular five pointed star touching its circumference is inscribed. What is the area of the part not covered by the star? a) 60.2 m^2 b) 50.48 m^2 c) 45.24 m^2 d) 71.28^m 159. Find the area of a regular octagon inscribed in a circle of radius 10 cm. a) 186.48 cm^2 b) 148.91 cm^2 c) 282.24 cm^2 d) 166.24 cm^2 160. Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m. a) 846 m^2 b) 1090 m^2 c) 1075 m^2 d) 988 m^2 161. The area of a circle circumscribing a hexagon is 144π m^2. Find the area of the hexagon. a) 374.12 m^2 b) 275.36 m^2 c) 415.26 m^2 d) 225.22 m^2 162. Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides. a) 441.66 cm^2 b) 467.64 cm^2 c) 519.60 cm^2 d) 493.62 cm^2 163. Find each interior angle of a hexagon. a) 90 deg b) 120 deg c) 150 deg d) 180 deg 164. Find the length of the side of pentagon if the line perpendicular to its side is 12 units from the center. a) 8.71 b) 17.44 c) 36.93 d) 18.47 165. How many sides are in a polygon if each interior angle is 165 degrees.

a) 12 sides b) 24 sides c) 20 sides d) 48 sides 166. Find the area of triangle whose sides are: 25, 39 and 40. a) 468 b) 684 c) 486 d) 864 167. Find the area of a regular hexagon inscribed in a circle of radius 1. a) 2.698 b) 2.598 c) 3.698 d) 3.598 168. A goat is tied to a corner of a 30 ft by 35 ft building. If the rope is 40 ft long and the goat can reach 1 ft farther than the rope length. What is the maximum area the goat can cover. a) 4840 b) 4804 c) 8044 d) 4084 169. In triangle BCD, BC = 25 m, and CD = 10 m. The perimeter of the triangle maybe: a) 79 m b) 70 m c) 71 m d) 72 m 170. A quadrilateral have sides equal to 12 m, 20 m, 8 m and 16.97 m respectively. If the sum of the two opposite angles is equal to 225, find the area of the quadrilateral. a) 168 b) 100 c) 124 d) 158 171. The area of a circle inscribed in a hexagon is 144π m^2. Find the area of the hexagon. a) 498.83 m^2 b) 489.83 m^2 c) 439.88 m^2 d) 349.88 m^2 172. Each angle of the regular dodecagon is equal to _________ degrees. a) 135 b) 150 c) 125 d) 105 173. If an equilateral triangle is circumscribe about a circle of radius 10 cm, determine the side of the triangle. a) 34.64 cm b) 64.12 cm c) 36.44 cm

d) 32.10 cm 174. The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector. a) 59.8 cm^2 b) 58.9 cm^2 c) 89.5 cm^2 d) 85.9 cm^2 175. The distance between the center of the three circles which are mutually tangent to each other externally are 10, 12 and 14 units. Find the area of the largest circle. a) 72π b) 64π c) 23 π d) 16 π 176. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and the altitude of the other is 3 units less than its base. Find the altitude, if the areas of the triangles differ by 21 square units. a) 6 & 12 b) 5 &11 c) 3 & 9 d) 4 & 10 177. If the sides of a parallelogram and an included angle are 6, 10 and 100 degreess respectively, find the length of the shorter diagonal. a) 10.63 b) 10.73 c) 10.23 d) 10.37 178. In triangle ABC, angle C = 34 degrees, side a = 29 cm, b = 40 cm. Solve the area of the triangle. a) 324 cm^2 b) 342 cm^2 c) 448 cm^2 d) 484 cm^2 179. An oblique equilateral parallelogram. a) square b) rectangle c) rhombus d) recession 180. What is the interior angle (in radian) of an octagon a) 2.26 rad b) 2.36 rad c) 2.8 rad d) 2.75 rad 181. The circumference of a great circle of a sphere is 18π. Find the volume of the sphere. a) 3053.6 b) 4053.6 c) 5053.6 d) 6053.6

182. A pyramid whose altitude is 5 ft weighs 800 lbs. At what distance from its vertex must it be cut by a plane parallel to its base so that the two solids of equal weight will be formed? a) 3.97 ft b) 2.87 ft c) 4.97 ft d) 5.97 ft 183. Find the increase in volume of a spherical balloon when its radius is increased from 2 to 3 inches. a) 75. 99 cu. in. b) 74.59 cu. in. c) 74.12 cu. in. d) 79.59 cu. in. 184. If the lateral area of a right cylinder is 88 and its volume is 220, find its radius. a) 2 cm b) 3 cm c) 4 cm d) 5 cm 185. It is desired that the volume of the sphere be tripled. By how many times will the radius be increased? a) 2^1/2 b) 3^1/3 c) 3^1/2 d) 3^3 186. A cone and a cylinder have the same height and the same volume. Find the ratio of the radius of the cone to the radius of the cylinder. a) 0.577 b) 0.866 c) 1.732 d) 2.222 187. Compute the surface area of the cone having a slant height of 5 cm and a diameter of 6 cm. a) 47.12 cm^2 b) 25.64 cm^2 c) 38.86 cm^2 d) 30.24 cm^2 188. The ratio of the volume of the lateral area of a right circular cone is 2:1. If the altitude is 15 cm, what is the ratio of the slant height to the radius? a) 5:2 b) 5:3 c) 4:3 d) 4:2 189. 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 contents in cubic centimeter. a) 387.4 b) 381.7 c) 383.5 d) 385.2

190. A circular cylinder is circumscribed about a right prism having a square base one meter on an edge. The volume of the cylinder is 6.283 m^3. Find its altitude in m. a) 4.5 b) 5.5 c) 4 d) 5 191. The volume of water in a spherical tank having diameter of 4 m is 5.236 m^3. Determine the depth of the water in the tank. a) 1.6 b) 1.4 c) 1.2 d) 1.0 192. The corners of a cubical block touched the closest spherical shell that encloses it. The volume of the box is 2744 cm^3. What volume in cm^3 inside the shell is not occupied by the block? a) 4713.56 b) 3360.14 c) 4133.25 d) 5346.42 193. A circular cone having an altitude of 9 m is divided into 2 segments having the same vertex. If the smaller altitude is 6m, find the ratio of the volume of the small cone to the big cone. a) 0.296 b) 0.396 c) 0.186 d) 0.486 194. A frustum of a regular pyramid has an upper base of 8 m x 80 m and a lower base of 10 m x 100 m and an altitude of 5 m. Find the volume of the pyramid. a) 4066.67 m^3 b) 5066.67 m^3 c) 6066.67 m^3 d) 7066.67 m^3 195. The bases of a right prism is a hexagon with one each side equal to 6 cm. The bases are 12 cm apart. What is the volume of a right prism? a) 1211.6 cm^3 b) 2211.7 cm^3 c) 1212.5 cm^3 d) 1122.4 cm^3 196. The volume of the water in hemisphere having a radius of 2 m is 2.05 m^3. Find the height of the water. a) 0.602 b) 0.498 c) 0.782 d) 0.865 197. Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and a central angle of 150 deg. a) 7711.82 cm^3

b) 6622.44 cm^3 c) 5533.32 cm^3 d) 8866.44 cm^3 198. A cubical container that measures 2 in on a side is tightly packed with marbles and is filled with water. All the 8 marbles are in contact with the walls of the container and the adjacent marbles are the same size. What is the volume of water in the container? a) 0.38 in^3 b) 2.5 in^3 c) 3.8 in^3 d) 4.2 in^3 199. If one edge of a cube measures12 cm, calculate for the surface area of the cube and the volume of the cube. a) 864 cm^2; 1728 cm^3 b) 468 cm^2; 1728 cm^3 c) 863 cm^2; 8721 cm^3 d) 468 cm^2; 8721 cm^3 200. 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 cm^3 b) 1875 cm^3 c) 5178 cm^3 d) 5871 cm^3 201. If a right cone has a base radius of 35 cm and an altitude of 45 cm. Solve for the total surface area and the volume of the cone. a) 10,116.89 cm^2 and 57,726.76 cm^3 b) 9,116.89 cm^2 and 57,726.76 cm^3 c) 10,116.89 cm^2 and 67,726.76 cm^3 d) 9,116.89 cm^2 and 67,726.76 cm^3 202. If the volume of a sphere is 345 cm^3. Solve for its diameter. a) 8.70 cm b) 7.70 cm c) 6.70 cm d) 9.70 cm 203. A group of children playing with marbles placed 50 pieces of the marbles inside a cylindrical container with water filled to a height of 20 cm. If the diameter of each marble is 1.5 cm and that of the cylindrical container 6 cm. What would be the new height of water inside the cylindrical container after the marbles were placed inside? a) 23.125 cm b) 24.125 cm c) 22.125 cm d) 25.125 cm 204. A pipe lining material silicon carbide used in a conveyance of pulverized coal to fuel a boiler, has a thickness of 2 cm and inside diameter of 10 cm. Find the volume of the material with pipe length of 6 meters. a) 45,239 cm^3 b) 42,539 cm^3

c) 49,532 cm^3 d) 43,932 cm^3 205. Given of diameter x and altitude h. What percent is the volume of the largest cylinder which can be inscribed in the cone to the volume of the cone? a) 44% b) 56% c) 46% d) 65% 206. Each side of a cube is increased by 1%. By what percent is the volume of the cube increased? a) 23.4% b) 30.3% c) 34.56% d) 3.03% 207. Two vertical conical tanks are joined at the vertices by a pipe. Initially the bigger tank is full of water. The pipe valve is open to allow the water to flow to the smaller tank until it is full. At this moment, how deep is the water in the bigger tank? The bigger tank has a diameter of 6 ft and a height of 10 ft, the smaller tank has a diameter of 6 ft and a height of 8 ft. Neglect the volume of water in the pipeline. a) √ b) √ c) √ d) √ 208. A pyramid has a square base of 8 m on a side and an altitude of 10 m. How many liters of water will it hold when full and inverted? a) 223,330 b) 203,330 c) 213,330 d) 233,330 209. What solid figure that has many faces? a) octagon b) decagon c) polygon d) polyhedron 210. If the length of the latus rectum of an ellipse is three-fourth of the length of its minor axis, find its eccentricity. a) 0.15 b) 0.33 c) 0.55 d) 0.66 211. Find the equation of a line where x-intercept is 2 and y-intercept is -2. a) 2x + 2y +2 = 0 b) x – y – 2 = 0 c) -2x + 2y = -2 d) x – y – 1 = 0 212. A point (x, 2) is equidistant from the points (-2, 9) and (4, -7). The value of x is:

a) 11/3 b) 20/3 c) 19/3 d) 3 213. A parabola y = -x^2 – 6x – 9 opens ______________. a) to the right b) upward c) to the left d) downward 214. A line with a curve approaches indefinitely near as its tracing point passes off infinitely is called the: a) tangent b) asymptote c) directly d) latus rectum 215. Find the eccentricity of an ellipse when the length of the latus rectum is 2/3 of the length of the major axis. a) 0.58 b) 0.68 c) 0.78 d) 0.98 216. The directrix of a parabola is the line y = 5 and its focus is at the point (4, -3). a) 20 b) 18 c) 16 d) 12 217. The radius of a sphere is r inches at time t seconds. Find the radius when the rates of increase of the surface area and the radius are numerically equal. a) 1/(8π) in b) 1/(4π) in c) 2π in d) π^2 in 218. In general quadratic equation, if the discriminant is zero, the curve is a figure that represents ________. a) hyperbola b) circle c) parabola d) ellipse 219. The equation of the tangent to the curve y = x + 5/x at point P(1, 3) is: a) 4x – y + 7 = 0 b) x + 4y – 7 = 0 c) 4x + y -7 = 0 d) x – 4y + 7 = 0 220. A line 4x + 2y – 2 = 0 is coincident with the line: a) 4x + 4y – 2 = 0 b) 4x + 3y + 33 = 0

c) 8x + 4y – 2 = 0 d) 8x + 4y – 4 = 0 221. A locus of a point which moves so that it is always equidistant from a fixed point (focus) to a fixed line (directrix) is a _____________. a) circle b) ellipse c) parabola d) hyperbola 222. Find the equation of the line passing through (7, -3) and (-3, -5). a) x + 5y + 22 = 0 b) x + 5y – 22 = 0 c) x – 5y + 22 = 0 d) x – 5y – 22 = 0 223. Find the vertex of the parabola, x^2 = 8y a) (0, 0) b) (0, 4) c) (4, 0) d) (0, 8) 224. What type of conics is x^2 – 4y + 3x + 5 = 0. a) parabola b) ellipse c) hyperbola d) circle 225. Determine 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) b) (-2, -1) c) (-1, -2) d) (1, 1) 226. A line passing through a point (2, 2). Find the equation of the line if the length of the segment intercepted by the coordinate’s axes is equal to the square root of 5. a) 2x – y – 2 = 0 b) 2x + y + 2 = 0 c) 2x – y + 2 = 0 d) 2x + y – 2 = 0 227. Point P(x, y) moves with a distance from point (0, 1) one half of its distance from line y = 4, the equation of its locus is: a) 2x^2 – 4y^2 = 5 b) 4x^2 + 3y^2 = 12 c) 2x^2 + 5y^2 = 3 d) x^2 + 2y^2 = 4 228. The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth. a) 93,000,000 miles b) 94,335,000 miles

c) 91, 450,000 miles d) 94,550,000 miles 229. What is the equation of the asymptote of the hyperbola (x^2)/9 – (y^2)/4 = 1. a) 2x – 3y = 0 b) 3x – 2y = 0 c) 2x – y = 0 d) 2x + y = 0 230. Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x – 6y + 25 = 0. a) 2, 8 b) 4, 16 c) 16, 64 d) 1, 4 231. Find the equation of the axis of symmetry of the function y = 2x^2 – 7x + 5. a) 7x + 4 = 0 b) 4x + 7 = 0 c) 4x – 7 = 0 d) x – 2 = 0 232. Find the value of k for which the equation x^2 + y^2 + 4x – 2y – k = 0, represents a point circle. a) 5 b) 6 c) -6 d) -5 233. Find the equation of the circle whose center is at (3, -5) and whose radius is 4. a) x^2 + y^2 – 6x + 10y + 18 = 0 b) x^2 + y^2 + 6x + 10y + 18 = 0 c) x^2 + y^2 – 6x – 10y + 18 = 0 d) x^2 + y^2 + 6x – 10y + 18 = 0 234. Determine B such that 3x + 2y – 7 = 0 is perpendicular to 2x – By + 2 = 0. a) 5 b) 4 c) 3 d) 2 235. In a Cartesian coordinates, the coordinates of a square are (1, 1), (0, 8), (4, 5), and (-3, 4). What is the area? a) 25 b) 20 c) 18 d) 14 236. The segment from (-1, 4) to (2, -2) is extended three times its own length. Find the terminal point. a) (11, -24) b) (-11, -20) c) (11, -18) d) (11, -20)

237. Find the distance between A(4,-3) and B(-2, 5). a) 10 b) 8 c) 9 d) 11 238. Given three vertices of a triangle whose coordinates are A(1, 1), B(3, -3) and C(5, -3). Find the area of the triangle. a) 3 b) 4 c) 5 d) 6 239. The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3). Find the values of x and y. a) 33, 12 b) 5, 0 c) 6, 9 d) 14, 6 240. A line passes through (1, -3) and (-4, -2). Write the equation of the line in slope-intercept form. a) y – 4 = x b) y = -x – 2 c) y = x – 4 d) y – 2 = x 241. What is the x-intercept of the line passing through (1, 4) and (4, 1). a) 4.5 b) 5 c) 6 d) 4 242. Find the distance between the lines, 3x + y – 12 = 0 and 3x + y – 4 = 0. a) 16/√ b) 12/√ c) 4/√ d) 8/√ 243. Find the area of the circle whose equation is x^2 + y^2 = 6x – 8y. a) 25π b) 5π c) 15π d) 20π 244. Find the major axis of the ellipse x^2 + 4y^2 – 2x – 8y + 1 = 0. a) 2 b) 10 c) 4 d) 6 245. 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 246. Find the equation of the hyperbola whose asymptotes are y = 2x and which passes through (5/2, 3). a) 4x^2 – y^2 – 16 = 0 b) 2x^2 – y^2 – 4 = 0 c) 3x^2 – y^2 – 9 = 0 d) 5x^2 – y^2 – 25 = 0 247. Find the eccentricity of the curve 9x^2 – 4y^2 – 36x + 8y = 4. a) 1.80 b) 1.90 c) 1.70 d) 1.60 248. The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = - 6 is: a) 3x + 2y = 12 b) 2x – 3y = 12 c) 3x – 2y = 12 d) 2x – 3y = -12 249. What is the radius of a circle defined by the equation x^2 – 6x + y^2 – 4y – 12 = 0. a) 3.46 b) 7 c) 5 d) 6 250. Find the slope of the line defined by y – x = -5. a) 1 b) 1/4 c) -1/2 d) 5 + x 251. What conic section is represented by 4x^2 – y^2 + 8x + 4y = 15. a) parabola b) ellipse c) hyperbola d) circle 252. What conic section is represented by x^2 + y^2 – 4x + 2y – 20 = 0 a) circle b) parabola c) ellipse d) hyperbola 253. Find the equation of the straight line with a slope of 3 and a y-intercept of 1. a) 3x – y + 1 = 0 b) 3x + y + 1 = 0 c) 3x – y – 1 = 0 d) 3x + y – 1 = 0 254. 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 b) y – x – 4 = 0 c) x – y – 4 = 0 d) x + y – 4 = 0 255. Find the distance from the line 4x – 3y + 5 = 0 to the point (2, 1). a) 1 b) 2 c) 3 d) 4 256. What is the center of the curve x^2 + y^2 – 2x – 4y – 31 = 0. a) (-1, -2) b) (1, -2) c) (-1, 2) d) (1, 2) 257. Determine the equation of the curve such that the sum of the distances of any point on the curve from two points whose coordinates are (-3, 0) and (3, 0) is always equal to 8. a) 7x^2 + 16y^2 – 112 = 0 b) 16x^2 + 7y^2 – 112 = 0 c) 7x^2 + 16y^2 + 112 = 0 d) 16x^2 + 7y^2 + 112 = 0 258. The equation 9x^2 + 16y^2 + 54x - 64y = -1 describes: a) a hyperbola b) a sphere c) a circle d) an ellipse 259. The sum of the distances from the two foci to any point in a/an ______________ is a constant. a) a parabola b) any conic c) hyperbola d) ellipse 260. Determine the curve: 9x^2 + 6y^2 + 2x + 3y + 9 = 0. a) ellipse b) hyperbola c) parabola d) circle 261. Locus of points on a side which rolls along a fixed line: a) cardoid b) epicycloid c) cycloid d) hypocycloid 262. What is the radius of a circle with the following equation? x^2 – 6x + y^2 – 12 = 0 a) 2 b) 5 c) 7 d) 25

253. Find the slope of the line passing to the point (-3, -4) and (2, 4). a) 0 b) 5 c) 10 d) 1.6 254. What is the slope of the line perpendicular to y = (1/4)x + 6? a) 4 b) 1 c) -4 d) -1 255. Given the polar coordinates (4, 20°). Find the rectangular coordinates. a) -2, 3.46 b) -3.46, -2 c) 2, -3.46 d) -3.46, 4 256. Find the equation of the line which passes through the point (2, 1) and perpendicular to the line whose equation is y = 4x + 3. a) x – 4y + 6 = 0 b) y – 4x + 6 = 0 c) x + 4y – 6 = 0 d) y – 4x + 6 = 0 257.What is the second derivative of a function y = 5x^3 + 2x + 1? a) 25x b) 30x c) 18 d) 30 258. Find the height of a circular cylinder of a maximum volume, which can be inscribed in a sphere of radius 10 cm. a) 11.55 cm b) 12.55 cm c) 14.55 cm d) 15.55 cm 259. Find the maximum point of y = x + 1/x. a) (2, 5/2) b) (1, 2) c) (-1, -2) d) (2, 3) 260. Simplify the expression Lim(x^2 – 16)/(x – 4) as x approaches 2. a) 8 b) 6 c) 4 d) 2 261. Evaluate the Lim (x^2 + 3x – 4) as x approaches 3. a) 18 b) 12 c) 4

d) 2 262. The distance a body travels is a function of time t and is defined by: x(t) = 18t + 9t^2. What is its velocity at t = 3? a) 36 b) 45 c) 72 d) 92 263. Water running out a conical funnel at the rate of 1 cu. in per second. If the radius of the base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in from the top. a) -1/9 π in/sec b) -3/2 π in/sec c) -8/9 π in/sec d) -4/9 π in/sec 264. ________ is the concept of finding the derivative of composite functions. a) Logarithmic differentiation b) Chain rule c) Trigonometric differentiation d) Implicit differentiation 265. The volume of the sphere is increasing at the rate of 6 cm^3/hr. At what rate is its surface area increasing (in cm^2/hr) when the radius is 50 cm? a) 0.54 b) 0.44 c) 0.34 d) 0.24 266. A man on a wharf 3.6 m above sea level is pulling a rope tied to a raft at 0.60 m per second. How fast is the raft approaching the wharf when there are 6 m of rope out? a) -0.95 m/s b) -0.85 m/s c) -0.75 m/s d) -0.65 m/s 267. If the distance x from the point of departure at time t is defined by the equation x = -16t^2 + 5000t + 5000, what is the initial velocity? a) 2000 b) 0 c) 5000 d) 3000 268. Using two existing corner sides of an existing wall, what is the maximum rectangular area that can be fenced by a fencing material 30 ft long? a) 225 sq. ft b) 240 sq. ft c) 270 sq. ft d) 335 sq. ft 269. The radius of a sphere is r inches at time t seconds. Find the radius when the rates of increase of the surface area and the radius are numerically equal. a) 1/(8π) in

b) 1/(4π) in c) 2π in d) π^2 in 270. Three sides of a trapezoid are each 8 cm long. How long is the fourth side when the area of the trapezoid has the greatest value? a) 8 cm b) 12 cm c) 16 cm d) 20 cm 271. Find the change in y = 2x – 3 if x changes from 3.3 to 3.5. a) 0.1 b) 0.2 c) 0.3 d) 0.4 272. If y = arctan(ln x), find dy/dx at x = 1/e. a) e b) e/2 c) e/3 d) e^2 273. Evaluate the limit (ln x)/x as x approaches positive infinity. a) 1 b) 0 c) infinity d) -1 274. lim[(x^3 – 27)/(x – 3)] as x approaches 3. a) 0 b) infinity c) 9 d) 27 275. A box is to be constructed from a piece of zinc 20 in square by cutting equal squares from each corner and turning up zinc to form the side. What is the volume of the box that can so constructed? a) 599.95 in^3 b) 592.59 in^3 c) 579.50 in^3 d) 622.49 in^3 276. Given the function f(x) = x to the 3rd power – 6x + 2, find the value of the first derivative at x = 2, f(2). a) 6 b) 7 c) 3x^2 – 5 d) 8 277. 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) 7/6 gph b) 1/6 gph

c) 2/3 gph d) 1/2 gph 278. Evaluate Lim [(x^2 – 16)/(x – 4)] as x approaches 4. a) 1 b) 8 c) 0 d) 16 279. Evaluate Lim [(x - 4)/(x^2 – x – 12)] as x approaches 4. a) undefined b) 0 c) infinity d) 1/7 280. Evaluate Lim [(x^3 – 2x + 9)/(2x^3 – 8)] as x approaches infinity. a) 0 b) 2 c) 1/2 d) 1/4 281. If y = 1/(t + 1) and x = t/(t + 1), find dy/dx or y’. a) 1 b) -1 c) t d) –t 282. Differentiate: y = [(sin x)/(1 – 2cos x)]. a) (cos x – 1)/(1 – 2cos x)^2 b) (cos x – 2)/(1 – 2cos x)^2 c) (cos x)/(1 – 2cos x)^2 d) (-2)/(1 – 2cos x)^2 283. Given the curve y = 12 – 12x + x^3, determine its maximum, minimum and inflection points. a) (-2, 28), (2, -4), & (0, 12) b) (2, -28), (2, 4), & (0, 2) c) (-2, -28), (-2 -4) & (2, 12) d) (-2, 28), (-2, 4) & (1, 12) 284. Given the curve y^2 = 5x – 1 at point (1, -2), find the equation of tangent and normal to the curve. a) 5x + 4y + 3 = 0 & 4x – 5y – 14 = 0 b) 5x + 4y – 3 = 0 & 4x + 5y – 14 = 0 c) 5x – 4y + 3 = 0 & 4x + 5y + 14 = 0 d) 5x – 4y – 3 = 0 & 4x + 5y – 14 = 0 285. Find the radius of the curvature at any point on the curve, y + ln cos x = 0 a) cos x b) 1.5707 c) sec x d) 1 286. Find the minimum volume of a right circular cylinder that can be inscribed in a sphere having a radius r.

a) 1/√ volume of sphere b) √ volume of sphere c) 2/√ volume of sphere d) √ volume of sphere 287. Find the point in the parabola y^2 = 4x at which rate change of the ordinate and abscissa are equal. a) (1, 2) b) (-1, 4) c) (2, 1) d) (4, 4) 288. What is the allowable error in measuring the edge of cube that is intended to hold 8 m^3, if the error of the computed volume is not to exceed 0.03 m. a) 0.002 b) 0.003 c) 0.0025 d) 0.001 289. Find the slope of x^2 y = 8 at point (2, 2) a) 2 b) -1 c) -2 d) 1/2 290. Water is flowing into a conical vessel 15 cm deep and having a radius of 3.75 cm across the top. If the rate at which the water rises is 2 cm/sec, how fast is the water flowing into the conical vessel when the water is 4 cm deep? a) 6.28 m^3/s b) 2.37 m^3/s c) 4.57 m^3/s d) 5.73 m^3/s 291. Find the slope of the line having a parametric equation y = 4t + 6 and x = t + 1. a) 1 b) 2 c) 3 d) 4 292. Determine the diameter of a closed cylindrical tank having a volume of 11.3 m^3 to obtain a minimum surface area. a) 1.44 b) 2.44 c) 3.44 d) 4.44 293. Determine the velocity of progress with the given equation, D = 20t + 5/(t + 1) when t = 4 sec. a) 16.8 m/s b) 17.8 m/s c) 18.8 m/s d) 19.8 m/s 294. Find the slope of the curve x^2 + y^2 – 6x + 10y + 5 = 0 at point (1, 0).

a) 1/3 b) 3/4 c) 2/5 d) 1/5 295. Two posts 10 m high and the other is 15 m high stands 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) 12 m b) 14 m c) 18 m d) 16 m 296. Find the slope of the line having the parametric equations x = t – 1 and y = 2t. a) 1 b) 3 c) 2 d) 4 297. Find the second derivative of y with respect to x for: 4x^2 + 8y^2 = 36. a) 9/4y^3 b) 4y^3 c) -9/4y^3 d) -4y^3 298. Find the derivative of h with respect to u; for h = π^2u. a) π^2x b) 2u ln π c) 2π^2u ln π d) 2π^2u 299. Find y’ if y = x ln x – x. a) ln x b) x ln x c) (ln x)/x d) x/ln x 300. Differentiate, y = sec x^2. a) 2x sec x^2 b) 2sec x^2 c) 2xtan x^2 d) 2xsec x^2 tan x^2 301. What is the derivative of the function with respect to x of (x + 1)^3 – x^3? a) 3x + 3 b) 3x – 3 c) 6x – 3 d) 6x + 3 302. Evaluate the Lim [(x^2 – 1)/(x^2 + 3x – 4)] as x approaches 1. a) 3/5 b) 2/5 c) 4/5 d) 1/5

303. Evaluate: Lim [(1 – cos x)/x^2] as x approaches 0 a) 0 b) 1/2 c) 2 d) -1/2 304. Evaluate: Lim [(3x^4 – 2x^2 + 7)/(5x63 + x – 3)] as x approaches infinity. a) undefined b) 3/5 c) infinity d) 0 305. Differentiate: (x^2 + 2)^1/2 a) [(x^2 + 1)^1/2]/2 b) x/(x^2 + 2)^1/2 c) 2x/(x + 2)^1/2 d) (x^2 + 2)^2 306. Differentiate y = e^x cos x^2 a) –e^x sin x^2 b) e^x (cos x^2 – 2xsin x^2) c) e^x cos x^2 – 2xsin x^2 d) -2xe^x sin x 307. Differentiate: y = log (x^2 + 1)^ 2 a) log e (x)(x^2 + 1)^2 b) 4x(x^2 + 1) c) (4xlog e)/(x^2 +1) d) 2x(x + 1) 308. If y = 4cos x + sin 2x, what is the slope of the curve then x = 2. a) -2.21 b) -4.94 c) -3.25 d) -2.22 309. Find y’ = arcsin cos x. a) -1 b) -2 c) 1 d) 2 310. A poster is to contain 300 m^2 of printed matter with margins of 10 cm at the top and bottom and 5 cm at each side. Find the overall dimensions, if the total area of the poster is a minimum. a) 27.76 cm, 47.8 cm b) 20.45 cm, 35.6 cm c) 22.24 cm, 44.5 cm d) 25.55 cm, 46.7 cm 311. Water is flowing into a conical cistern at the rate of 8 m^3/min. If the height of the inverted cone is 12 m and the radius of its circular opening is 6 m. How fast is the water level rising when the water is 4 m deep? a) 0.74 m/min

b) 0.64 m/min c) 0.54 m/mid d) 0.84 m/min 312. An isosceles triangle with equal sides of 20 cm has these sides at variable equal angles with the base. Determine the maximum area attainable by the triangle. a) 250 cm^2 b) 200 cm^2 c) 180 cm^2 d) 300 cm^2 313. 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 cm^2 b) 18.71 cm^2 c) 14.03 cm^2 d) 17.15 cm^2 314. What is the limit value of y = (x^3 + x)/(x^2 + x) as x approaches zero? a) 1 b) indeterminate c) 0 d) 3 315. A fencing is limited to 20 ft high. What is the maximum rectangular area that can be fenced in using two perpendicular corner sides of an existing wall? a) 120 b) 100 c) 140 d) 190 316. Find the point on the curve x^2 = 2y which is nearest to the point (4, 1). a) (2, 4) b) (4, 2) c) (2, 2) d) (2, 3) 317. Find the largest area of a rectangle which can be inscribed in the ellipse, 4x^2 + 9y^2 = 36. a) 12 b) 24 c) 6 d) 48 318. The derivative with respect ot v of the function f(y) = √ is: a) (y^-2/3)/3 b) 3y^2/3 c) 3y^-2/3 d) (y^2/3)/3 319. If a is the simple constant, what is the derivative of y = x^a? a) ax – x b) ax c) ax to the a - 1 power d) x to the a – 1 power

320. The first derivative with respect to y of the function d(y) = 3√ is _____. a) 3(9/2) b) 3(9) to the 1/2 power c) 0 d) 9 321. Find the derivative of f(x) = [x to the 3rd power – (x – 1) to the 3rd power] to the 3rd power? a) 3x – 3 (x – 1) b) 3[x to the 3rd power – x – 1] to the 3rd power c) 9[x to the 3rd power – (x – 1) to the 3rd power]^2 [x –(x – 1)]^2 d) 9[x to the 3rd power – (x – 1) to the 3rd power]^2 [x^2 – (x – 1)^2] 322. Water from the filtering facility is pouring into a swimming pool. After n hours, there are n + √ gallons in the pool. At what rate is the water pouring into the pool when n = 16 hrs? a) 1/2 gph b) 9/8 gph c) 1 gph d) 7/6 gph 323. Find the slope of the equation y = x^2 when x = 2. a) 2 b) 6 c) 4 d) 1 324. What is the value of the following limit? Lim (x^2 – 9)/(x – 3) as x approaches 3. a) 3 b) 6 c) 9 d) 0 325. The position of an object as a function of time is describe by x = 4t^3 + 2t^2 – t + 3. What is the distance traveled by an object at t = -2 and t = 2? a) 44 b) 63 c) 78 d) 108 326. Lim (x^2 0 4)/(x – 2) as x approaches 2, compute the indicated limit. a) 4 b) 8 c) 6 d) 10 327. Evaluate the integral of [(3^x) /(e^x)]dx from 0 to 1. a) 1.510 b) 1.051 c) 1.105 d) 1.510 328. Evaluate the integral of tan^2 x dx. a) tan x – x + c b) sec^2 x + x + c

c) 2sec x – x + c d) (tan^2 x)/s + x + c 329. Evaluate the integral of sqrt(3t – 1) dt. a) (2/9)(3t – 1)^5/2 + c b) (2/9)(3t – 1)^3/2 + c c) (1/2)(3t – 1)^5/2 + c d) (1/2)(3t – 1)^3/2 + c 330. Evaluate the integral of (3t – 1)^3 dt. a) (1/12)(3t – 1)^4 + c b) (1/4)(3t – 1)^4 + c c) (1/3)(3t – 1)^4 + c d) (1/12)(3t – 1)^3 + c 331. Integrate the square root of (1 – cos x) dx. a) -2 sqrt(2) cos (x/2) + c b) -2sqrt(2) cos x + c c) 2sqrt(2) cos (x/2) + c d) -2sqrt(2) cos x+ c 332. Find the area bounded by the parabolas x^2 – 2y = 0 and x^2 + 2y – 8 = 0. a) 32/2 b) 20/3 c) 16/3 d) 64/3 333. Evaluate: integral of cos^8 3A dA from 0 to π/6. a) 35π/768 b) 45π/768 c) 125π/768 d) 5π/768 334. Evaluate: integral of 1/(4 + x^2)^3/2 dx. a) x/(4sqrt(x^2 + 4)) + c b) -1/(4sqrt(x^2 + 4)) + c c) - x/(4sqrt(x^2 + 4)) + c d) 1/(4sqrt(x^2 + 4)) + c 335. Evaluate: integral of (e^x)/(e^x + 1) dx a) ln(e^x + 1) + c b) ln(e^-x + 1) + c c) ln^2 (e^x + 1) + c d) ln^2 (e^x + 1) + c 336. Evaluate: integral of (e^x – 1)/(e^x + 1) a) ln (e^x -1)^2 + x + c b) ln (e^x + 1) + x + c c) ln (e^x + 1)^2 –x + c d) ln (e^x + 1)^2 –x + c 337. Evaluate integral of ln x dx from 1 to 0. a) infinity b) 1 c) 0

d) e 338. 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) 36 339. Find the area bounded by the curves x^2 + y^2 = 9 and 4x^2 + 9y^2 = 36, on the first quadrant. a) 2/3π b) 3/4π c) 1/2π d) 3/2π 340. Determine the integral of z sin z with respect to z, then r from r = 0 to r = 1 and from z = 0 to z = π/2. a) 1/2 b) 4/5 c) 1/4 d) 2/3 341. Integrate 1/(3x + 4) with respect to x and evaluate the result from x = 0 to x = 2. a) 0.278 b) 0.336 c) 0.252 d) 0.305 342. An area in the xy plane is bounded by the following lines: x = 0 (y-axis), y = 0 (x-axis), x + 4y = 20, and 4x + y = 20. The linear function z = 5x + 5y attains its maximum value within the bounded area only at one of the vertices (intersections of the above lines). Determine the maximum value of z. a) 40 b) 25 c) 50 d) 45 343. Find the area bounded by the parabola x^2 = 4y and y = 4. a) 21.33 b) 33.21 c) 31.32 d) 13.23 344. Find the area in the first quadrant bounded by the parabola y^2 = 4x, x = 1 ad x = 3. a) 9.555 b) 5.955 c) 5.595 d) 9.955 345. Evaluate integral of 12 sin^5 x cos^5 x dx from 0 to π/2. a) 0.20 b) 0.50 c) 0.25 d) 0.35

346. Evaluate integral of x(x – 5)^12 dx from 5 to 6. a) 0.456 b) 0.587 c) 0.708 d) 0.672 347. What is the area bounded by the curve y^2 = x and the line x – 4 = 0. a) 32/3 b) 34/7 c) 64/3 d) 16/3 348. Find the area bounded by the curve r = 8 cos 2θ. a) 16π b) 32π c) 12π d) 8π 349. The area bounded by the curve y = 2x^1/2, the line y = 6 and the y-axis is to be resolved at y = 6. Determine the centroid of the volume generated. a) 0.56 b) 1.80 c) 1.0 d) 1.24 350. Find the area of the region bounded by the polar curve r^2 = a^2 cos 2θ. a) 2a^2 b) 4a^2 c) 3a^2 d) a^2 351. The area bounded by the curve y^2 = 12x and the line x = 3 is resolved about the line x = 3. What is the volume generated? a) 185 b) 187 c) 181 d) 183 352. Find the moment of inertia with respect to the x-axis of the area bounded by the parabola y^2 = 4x and the line x = 1. a) 2.35 b) 2.68 c) 2.13 d) 2.56 353. Given the area in the first quadrant bounded by x^2 = 8y, the line y – 2 = 0 and the y-axis. What is the volume generated when the area is resolved about the line y – 2 = 0? a) 28.41 b) 27.32 c) 26.81 d) 25.83 354. Find the area of the horizontal differential rectangle xdy by the x-axis and the line y = 4. The parabola y = 4x. Rectangle area = (4 – x)dy.

a) 64/2 b) 32/3 c) 32/4 d) 32/2 355. What is the approximate area bounded by the curves y = 8 – x^2 and y = -2 + x^2? a) 22.4 b) 29.8 c) 44.7 d) 26.8 356. What retarding force is required to stop a 0.45 caliber bullet of mass 20 grams and speed of 200 m/s as it penetrates a wooden block to a depth of 2 inches? a) 17,716 N b) 19,645 N c) 15,500 N d) 12,500 N 357. A freely falling body is a body in rectilinear motion and with constant ________. a) velocity b) speed c) deceleration d) acceleration 358. A ball is thrown upward with an initial velocity of 50 ft/s. How high does it go? a) 39 ft b) 30 ft c) 20 ft d) 45 359. It takes an airplane one hour and forty-five minutes to travel 500 miles against the wind and covers the same distance in one hour and fifteen minutes with the win. What is the speed of the airplane? a) 342 mph b) 375 mph c) 450 mph d) 525 mph 360 When the total kinetic energy of a system is the same as before and after the collision of two bodies, it is called: a) static collision b) elastic collision c) inelastic collision d) plastic collision 361. An airplane travels from points A to B with a distance of 1500 km and a wind along its flight. If it takes the airplane 2 hours from A to B with the tailwind and 2.5 hours from B to A with the headwind, what is the velocity? a) 700 kph b) 675 kph c) 450 kph d) 750 kph

362. The periodic oscillations either up or down or back and forth motion in a straight line is known as ________. a) transverse harmonic motion b) resonance c) rotational harmonic motion d) translational harmonic motion 363. A flywheel of radius 14 inches is rotating at the rate of 1000 rpm. How fast does a poin on the rim travel in ft/sec? a) 122 b) 1456 c) 100 d) 39 364. Pedro started running at a speed of 10 kph. Five minutes later, Mario started running in the same direction and catches up with Pedro in 20 minutes. What is the speed of Mario? a) 12.5 kph b) 15.0 kph c) 17.5 jph d) 20.0 kph 365. A flywheel accelerates uniformly from rest to a speed of 200 rpm in one-half second. It then rotates at the same speed for 2 seconds before decelerating to rest in one-third second. Determine the total number of revolutions of the flywheel during the entire time interval? a) 8.06 rev b) 9.12 rev c) 6.90 rev d) 3.05 366. A ball is thrown upward with an initial velocity of 60 ft/s. Determine the velocity at the maximum height. a) 6.12 ft/s b) 2.61 ft/s c) 2.12 ft/s d) 0 ft/s 367. A bullet if fired vertically upward with a mass of 3 grams. If it reaches an altitude of 100 m, what is its initial velocity? a) 54.2 m/s b) 47.4 m/s c) 52.1 m/s d) 44.2 m/s 368. What is the acceleration of a point on a rim of a flywheel 0.8 m in diameter turning at the rate of 1400 rad/min? a) 214.77 m/s b) 217.77 m/s c) 220.77 m/s d) 227.77 m/s 369. Impulse causes ______________. a) the object’s momentum to change b) the object’s momentum to decrease

c) the object’s momentum to increase d) the object’s momentum to remain constant or to be conserve 370. A DC-9 jet with a takeoff mass of 120 tons has two engines producing average force of 80,000 N during takeoff. Determine the plane’s acceleration down the runway if the takeoff time is 10 seconds. a) 1.52 m/s^2 b) 1.33 m/s^2 c) 3.52 m/s^2 d) 2.45 m/s^2 371. In a hydraulic press, the small cylinder has a diameter of 8 cm, while the larger piston has a diameter of 2 cm. If the force of 600 N is applied to the small piston, what is the force of the large piston, neglecting friction? a) 3895 N b) 4125 N c) 4538 N d) 5395 N 372. A car accelerates uniformly from standstill to 80 mi/hr in 5 seconds. What is its acceleration? a) 23.47 ft/sec^2 b) 33.47 ft/sec^2 c) 43.47 ft/sec^2 d) 53.47 ft/sec^2 373. A stone is thrown vertically upward at the rate of 20m/s. It will return to the ground after how many seconds? a) 3.67 sec b) 5.02 sec c) 4.08 sec d) 2.04 sec 374. A plane is headed due east with airspeed of 240 mph. If a wind at 40 mph is blowing from the north, find the ground speed of the plane. a) 190 mph b) 210 mph c) 243 mph d) 423 mph 375. The study of motion without reference to the force that causes the motion is known as __________. a) statics b) dynamics c) kinetics d) kinematics 376. A car accelerates from rest and reached a speed of 90 kph in 2- seconds. What is the acceleration in meter per second? a) 0.667 b) 0.707 c) 0.833 d) 0.866

377. Momentum is a property related to the object’s __________. a) motion and mass b) mass and acceleration c) motion and weight d) weight and velocity 378. A gulf weighs 1.6 ounce. If its velocity immediately after being driven is 225 fps, what is the impulse of the bow in slug-ft/sec? a) 0.855 b) 0.812 c) 0.758 d) 0.699 379. A missile is fired with a speed of 100 fps in a direction 30 degrees above the horizontal. Determine the maximum height to which it rises? a) 60 ft b) 52 ft c) 45 ft d) 39 ft 380. When the total kinetic energy of a system is the same as before and after collision of two bodies, it is called: a) plastic collision b) inelastic collision c) elastic collision d) static collision 381. A man travels in a motorized banca at the rate of 15 kph from his barrio to the poblacion and come back to his barrio at the rate of 12 kph. If his total time of travel back and forth is 3 hours, the distance from the barrio to the poblacion is: a) 10 km b) 15 km c) 20 km d) 25 km 382. A 50,000 N car travelling with a speed of 150 km/hr rounds a curve whose radius is 150 m. Find the centripetal force. a) 70 kN b) 25 kN c) 65 kN d) 59 kN 383. A ball is dropped from a building 100 m high. If the mass of the ball is 10 grams, after what time will the ball strikes the earth? a) 5.61 s b) 2.45 s c) 4.52 s d) 4.42 s 384. A 900 N weight hangs on a vertical plane. A man pushes this weight horizontally until the rope makes an angle of 40° with the vertical. What is the tension in the rope? a) 1286 N b) 1175 N

c) 918 N d) 825 N 385. A plane dropped a bomb at an elevation 1000 meters from the ground intended to hit a target which is 200 m from the ground. If the plane was flying at a velocity of 300 kph, at what distance from the target must the bomb be dropped to hit the target? Wind velocity and atmospheric pressure to be disregarded. a) 1864.71 m b) 2053.20 m c) 1574.37 m d) 1064.20 m 386. What is the minimum distance can a truck slide on a horizontal asphalt road if it is travelling at 25 m/s? The coefficient of sliding friction between the asphalt and rubber tire is at 0.60. The weight of the truck is 8500 kg. a) 44.9 b) 58.5 c) 53.2 d) 63.8 387. A concrete highway curve with a radius of 500 ft is banked to give lateral pressure equivalent to f = 0.15. For what coefficient of friction will skidding impend for a speed of 60 mph. a) µ > 0.360 b) µ < 0.310 c) µ > 0.310 d) µ < 0.360 388. A circle has a diameter of 20 cm. Determine the moment of inertia if the circular area relative to the axis perpendicular to the area through the center of the circle in cm^4. a) 14,280 b) 15,708 c) 17,279 d) 19,007 389. An isosceles triangle has a 10 cm base and a 10 cm altitude. Determine the moment of inertia of the triangle area relative to a line parallel to the base and through the upper vertex in cm^4. a) 2,750 b) 3,025 c) 2,500 d) 2,273 390. Two electrons have speeds of 0.7c and x respectively. If their relative velocity is 0.65c, find x. a) 0.02c b) 0.12c c) 0.09c d) 0.25c 391. A baseball is thrown from a horizontal plane following a parabolic path with an initial velocity of 100 m/s at an angle of 30° above the horizontal. How far from the throwing point will the ball attain its original level?

a) 890 m b) 883 m c) 878 m d) 875 m 392. What is the speed of a synchronous earth’s satellite situated 4.5 x 10^7 m from the earth? a) 11,070 kph b) 12,000 kph c) 11,777.4 kph d) 12,070.2 kph 393. What is the inertia of a bowling ball (mass 0.50 kg) of radius 15 cm rotating at an angular speed of 10 rpm for 6 seconds. a) 0.001 kg-m^2 b) 0.002 kg-m^2 c) 0.0045 kg-m^2 d) 0.005 kg-m^2 394. The angle or inclination of ascend of a road having 8.25% grade is ____________ degrees. a) 4.72 b) 4.27 c) 5.12 d) 1.86 395. A highway curve has a super elevation of 7 degrees. What is the radius of the curve such that there will be no lateral pressure between the tires and the roadway at a speed of 40 mph? a) 265.71 m b) 438.34 m c) 345.34 m d) 330.78 m 396. A shot is fired at an angle of 30 degrees with the horizontal and a velocity of 120 m/s. Calculate the range of the projectile. a) 12.71 km b) 387.57 ft c) 0.789 mile d) 423.74 yd 397. A stone dropped from the top of a building 55 yd elevation will hit the ground with a velocity of: a) 37 ft/sec b) 33 ft/sec c) 105 ft/sec d) 103 ft/sec 398. What is the kinetic energy of a 4000 lb automobile which is moving at 44 ft/sec? a) 1.21 x 10^5 ft-lb b) 2.10 x 10^5 ft-lb c) 1.80 x 10^5 ft-lb d) 1.12 x 10^5 ft-lb 399. Find the rate of increase of velocity if a body increases its velocity from 50 m/sec to 130 m/sec in 16 sec. a) -4.0 m/sec^2

b) 80 m/sec^2 c) -80 m/sec^2 d) 5.0 m/sec^2 400. A 20 kg sack is raised vertically 5 meters in 0.50 sec. What is the change in Potential Energy? a) 98.1 J b) 981 J c) 200 J d) 490.5 J 401. A 350 lbf acts on a block at an angle of 15 degrees with the horizontal. What is the work done by this force if it is pushed 5 feet horizontally? a) 1350.3 ft-lb b) 1690 ft-lb c) 1980 ft-lb d) 2002 ft-lb 402. A 20 kg object moving at 10 m/sec strikes an unstretched spring to a vertical wall having a spring constant of 40 kN/m. Find the deflection of the spring. a) 111.8 mm b) 223.6 mm c) 70.7 mm d) 50.0 mm 403. A 300 kg box impends to slide down a ramp inclined at an angle of 25 degrees with the horizontal. What is the frictional resistance? a) 1243.76 N b) 9951.50 N c) 1468.9 N d) 3359.7 N 404. A marksman fires a rifle horizontally at a target. How much does the bullet drop in flight if the target is 150 m away and the bullet has a muzzle velocity of 500 m/sec? a) 0.34 m b) 0.44 m c) 0.64 m d) 0.54 m 405. A ball is thrown from a building at an angle of 60 degrees with the horizontal at an initial velocity of 30 m/sec. After hiting level ground at the base of the building, it has covered a total distance of 150 m. How tall is the building? a) 230.7 m b) 756.7 m c) 692.5 m d) 1089 m 406. A highway curve with radius 800 ft is to be banked so that a car travelling 55 mph will not skid sideways even in the absence of friction. At what angle should the curve be banked? a) 0.159 deg b) 75 deg c) 6.411 deg d) 14.2 deg

407. An airplane flying horizontally at a speed of 200 m/sec drops a bomb from an elevation of 2415 meters. Determine the time required for the bomb to reach the earth. a) 11.09 sec b) 22.18 sec c) 44.37 sec d) 8.20 sec 408. Find the banking angle of a highway curve of 100 m radius designed for cars travelling at 180 kph, if the coefficient of friction between the tires and the road is 0.58. a) 19.23 deg b) 38.5 deg c) 76.9 deg d) 45 deg 409. A pulley has a tangential speed of 14m/sec and an angular velocity of 6/5 rad/sec. What is the normal acceleration of the pulley? a) 91 m/sec^2 b) 99 m/sec^2 c) 105 m/sec^2 d) 265 m/sec^2 410. An elevator weighing 4000 kb attains an upward velocity of 4 m/sec in 3 sec with uniform acceleration. Find the apparent weight of a 40 kg man standing inside the elevator during its ascent. a) 339 N b) 245 N c) 446 N d) 795 N 411. A stone is dropped from a cliff and 2 sec later another stone is thrown downward with a speed of 22 m/sec. How far below the top of the cliff will the second stone overtake the first? a) 375 m b) 507 m c) 795 m d) 994 m 412. How much horizontal force is needed to produce an acceleration of 8 m/sec^2 on a 75 kg box? a) 600 N b) 500 N c) 400 N d) 200 N 413. An elevator with a mass of 1500 kg descends with a acceleration of 2.85 m/sec^2. What is the tension in the supporting cable? a) 10,440 N b) 12,220 N c) 15,550 N d) 20,220 N 414. A dictionary is pulled to the right at a constant velocity by a 25 N force pulling upward at 60 degrees above the horizontal. What is the weight of the dictionary if the coefficient of kinetic friction is 0.30?

a) 31 N b) 21 N c) 20 N d) 63 N 415. The breaking strength of a string is 500 N. Find the maximum speed that it can attain if a 1.5 kg ball is attached at one end while the other end is held stationary and is whirled in a circle. The string is 0.65 m long. a) 15.4 m/sec b) 55.2 m/sec c) 24.4 m/sec d) 14.7 m/sec 416. The position of a body weighing 72.6 kg is given by the expression S = 5t^2 + 3t + 4, where S is in meters and t is in seconds. What force is required for this motion? a) 625 N b) 695 N c) 726 N d) 985 N 417. Assuming a shaft output of 3,000 kW and a fuel rate of (JP-4) 34.2 lbs/min. What is the overall thermal efficiency of the machine? (HHV of JP-4 is 18,000 Btu/lb) a) 24.2% b) 28.3% c) 27.7% d) 29.1% 418. g = 32.2 ft/sec^2. How is it expressed in SI? a) 9.81 m/sec^2 b) 9.86 m/sec^2 c) 9.08 m/sec^2 d) 9.91 m/sec^2 419. A winch lifted a mass of 1600 kg through a height of 25 m in 30 sec. If the efficiency of the winch is 60%, calculate the energy consumed in kWh. a) 0.1718 kWh b) 0.1881 kWh c) 0.1817 kWh d) 0.218 kWh 420. Cast iron weighs 640 pounds per cubic foot. The weight of a cast iron block 14‖ x 12‖ x 18‖ is: a) 1120 lbs b) 1000 lbs c) 1200 lbs d) 1088 lbs 421. A solid disk flywheel (l = 2—kg-,^2) is rotating with a speed of 900 rpm. What is its rotational kinetic energy? a) 730 x 10 to the 3rd power J b) 680 x 10 to the 3rd power J c) 1100 x 10 to the 3rd power J d) 888 x 10 to the 3rd power J

422. The path of a projectile is a: a) ellipse b) parabola c) part of a circle d) hyperbola 423. What is the name for a vector that represent the sum of two vectors? a) moment b) torque c) scalar d) resultant 424. Determine the super elevation of the outer rail of a 4-ft wide railroad track on a 10 degrees curve. (A 10 degrees curve is one which a chord 100 ft long subtends an angle of 10 degrees at the center). Assumed velocity of 45 mph. a) 0.90 ft b) 2.80 ft c) 2.50 ft d) 1.15 ft 425. A 10‖ diameter helical gear carries a torque of 4000 in-lb. It has a 20 degree involute stub teeth and a helix angle of 30 degree. Determine the axial component of the load on the teeth. a) 451.4 lb b) 218 lb c) 471.5 lb d) 461.6 lb 426. A winch lifted a mass of 1600 kg through a height of 25 m in 30 sec. Calculate the input power in kW if the efficiency of the winch is 60%. a) 18.1 kW b) 21.8 kW c) 28.1 kW d) 13.08 kW 427. A diagram which shows only the forces acting on the body: a) free body diagram b) cash flow c) forces flow diagram d) motion diagram 428. One horse power is equivalent to: a) 746 watts b) 7460 watts c) 74.6 watts d) 7.46 watts 429. Which is a true statement about the vector? V1 = i + 2j + k and v2 = i + 3j – 7k a) the vectors coincide b) the angle between them is 17.4 degree c) the vectors are parallel d) the vectors are orthogonal 430. In a lifting machine, a load of 50 kN is moved by a distance of 10 cm using an effort of 10 kN which moves through a distance of 1 m, the efficiency of the machine is:

a) 20% b) 50% c) 10% d) 40% 431. What is the angle between two vectors A and B? A = (3, 2, 1) and B = (2, 3, 2) a) 24.8 deg b) 36.7 deg c) 42.5 deg d) 77.5 deg 432. What is the equivalent of one horsepower? a) 746 W b) 3141 kW c) 33,000 ft-lb/min d) 2545 Btu/lb 433. Two people are driving towards each other between two towns 160 km apart. The first man drives at the rate of 45 kph and the other drives at 35 kph. From their starting point how long would it take that they will meet. a) 3 hr b) 4 hr c) 2 hr d) 1 hr 434. Resistance to motion, caused by one surface rubbing against another. a) inertia b) resistance c) gravity d) friction 435. What happens to the acceleration if the mass is tripled and the force remains the same? a) it will be tripled b) it will be 1/3 of the original c) it will remain the same d) it will be 3 times the original 436. Which number has five significant digits? a)0.01410 b)0.00101 c)1.0140 d)0.01414 437. The prefix of a no. 10 raise ot the power minus 6 is: a) tera b)deci c) centi d) micro 438. The length of a bar is one million of a meter is called: a) omicron b) micron c) one bar d)one milli

439. 120 Giga Newton is how many Mega Newton? a) 12,000 b) 120 c) 1,200 d) 120,000 440. Factor the expression ( 289x^3 - 204x^2 + 36x ) a)4x( 17/2 x – 3)( 17/2 x – 3 ) b) 4x(17x-3)(17x-3) c) 4x(4x-3)(4x+3) d)4x(17x-3)(17x+3) 441. Factor the expression as completely as possible: (2x^3 -7x^2 +6x) a) x(x-2)(x-3) b) x(x-2)(x+3) c) x(x-2)(2x+3) d) x(x-2)(2x-3) 442. ( (xyz)^(1/n) )^n is equal to: a) (xyz)^(1/n) b) (xyz)^n c) xyz d) (xyz)^(n-1) 443. If x raise to the one half of one equals 4, x equal to: a) 24 b) 8 c) 12 d) 16 444. If the numbers one and above divided by zero the answer is: a) zero b) infinity c) indeterminate d) absurd 445. Solve for x and y: 4x + 3y = 11 and 8x^2 – 9y^2 = -7. a) x = 5/3 and y = 3/2 b) x = 3/2 and y = 3/2 c) x = 3/5 and y = 5/3 d) x = 3/2 and y = 5/3 446. If A can do the work in a days and B in b days, how long will it take to do the job working together? a) ( a + b ) / ab days b) ( a + b ) / 2 days c) ab / ( a + b ) days d) a + b days 447. Five hundred kg of steel containing 8% nickel to be made by mixing a steel containing 14% nickel with another containing 6% nickel. How much of each is needed? a) 125 kg and 375 kg b) 150 kg and 350 kg c) 200 kg and 300 kg

d) 250 kg and 250 kg 448. Logarithm of 10th root of, x raise to 10 equals to: a) log x b) ( log x^(1/10) ) / 10 c) 10 log x d) log x^10 449. What is the natural logarithm of e to the a plus b power? a) ab b) log ab c) a + b d) 2.718 ( a + b) 450. What is the logarithm of negative one hundred? a) No logarithm b) Zero c) Positive log d) Negative log 451. The logarithm of 1 to base e is: a) One b) 2.718 c) Infinity d) Zero 452. What is the value of (0.101)^(5/6)? a) antilog [ log 0.101/(5/6) ] b) antilog [ 6/5 log 0.101 ] c) 6/5 antilog [ log 0.101 ] d) antilog [ 5/6 log 0.101] 453. A box contains 8 black and 12 white balls. What is the probability of getting 1 black and 1 white ball in two consecutive draws from the box? a) 0.53 b) 0.45 c) 0.50 d) 0.55 454. What is the sum of the following finite sequence of terms? 28, 35, 42, ..., 84. a) 504 b) 525 c) 540 d) 580 455. Solve for x that satisfy the equation, x^2 + 36 = 9 – 2x^2 a) ±6i b) +9i c) ±3i d) -9i 456. 35.2 to the x power = 7.5 to the x-2 power, solve for x using logarithms. a) -2.06 b) -2.10 c) -2.60

d) +2.60 457. Solve algebraically: 4x^2 + 7y^2 = 32 and 11y^2 – 3x^2 = 41. a) y = 4, x = ±1 and y = -4, x = ±1 b) y = +2, x = ±1 and y = -2 , x = ±1 c) x = 2, y = 3 and x = -2, y = -3 d) x = 2, y = -2 and x = 2, y = -2 458. Factor the expression 16 – 10x + x^2. a) (x+8)(x-2) b) (x-8)(x+2) c) (x-8)(x-2) d) (x+8)(x+2) 459. What is the value of e^-4 = _____________. a) 0 b) 0.183156 c) 0.1381560 d) 0.0183156 460. A pump can pump out a tank in 15 hrs. Another pump can pump out the same tank in 20 hrs. How long will it take both pumps together to pump out the tank? a) 8.57 hrs b) 7.85 hrs c) 6.58 hrs d) 5.50 hrs 461. A tank can be filled by one pipe in 9 hrs and another pipe in 12 hrs. Starting empty, how long will it take to fill the tank if water is being taken out by a third pipe at a rate per hour equal to one-sixth the capacity of the tank? a) 36 hrs b) 25 hrs c) 30 hrs d) 6 hrs 462. A rubber ball was dropped from a height of 42 m and each time it strikes the ground it rebounds to a height of 2/3 of the distance from which it fell. Find the total distance travelled by the ball before it comes to rest. a) 180 m b) 190 m c) 210 m d) 220 m 463. From a box containing 8 red balls, 8 white balls and 12 blue balls, one ball is drawn at random. Determine the probability that it is red or white: a) 0.571 b) 0.651 c) 0.751 d) 0.0571 464. If 1/x, 1/y, 1/z are in A.P., then y is equal to: a) x-z b) ½(x+2z) c) (x+z)/2xz

d) 2xz/(x+z) 465. A class of 40 took examination in Algebra and Trigonometry. If 30 passed algebra, 36 passed Trigonmetry, and 2 failed in both subjects, the number of students who passed the two subjects is: a) 22 b) 28 c) 30 d) 60 466. Simplify: ( ab / (ab)^(1/3) )^(1/2) a) (ab)^(1/3) b) ab c) (ab)^(1/2) d) (ab)^(1/5) 467. Combine into a single fraction: (3x-1)/(x^2-1) – (x+3)/(x^2+3x+2) – 1/(x+2) a) x-1 b) x+1 c) 1/(x+1) d) 1/(x-1) 468. Two cars start at the same time from nearby towns 200 km apart and travel toward each other. One travel at 60 kph and the other at 40 kph. After how many hours will they meet on the road? a) 1 hour b) 2 hrs c) 3 hrs d) 2.5 hrs 469. A single engine airplane has an airspeed of 125 kph. A west wind of 25 kph is blowing. The plane is to patrol due to east and then return toa is base. How far east can it go if the round trip is to consume 4 hrs? a) 240 km b) 180 km c) 200 km d) 150 km 470. A car travels from A to B, a distance of 100 km, at an average speed of 30 kph. At what average speed must it travel back from B to A in order to average 45 kph for the round trip of 200 km? a) 70 kph b) 110 kph c) 90 kph d) 50 kph 471. Two trains A and B having average speed of 75 mph and 90 kph respectively, leave the same point and travel in opposite direstions. In how many minutes would they be 1600 miles apart? a) 533 b) 733 c) 633 d) 833

472. It takes Butch twice as long as it takes Dan to do a certain piece of work. Working together, they can do the work in 6 days. How long would it take Dan to do it alone? a) 12 days b) 10 days c) 11 days d) 9 days 473. A man leaving his office one afternoon noticed the clock at past two o’clock. Between two to three hours, he returned to his office noticing the hands of the clock interchanged. At what time did he leave the office? a) 2:26.01 b) 2:10.09 c) 2:30.01 d) 2:01.01 474. A company has a certain number of machines of equal capacity that produced a total of 180 pieces each working day. If two machines breakdown, the work load of the remaining machines is increased by three pieces per day to maintain production. Find the number of machines. a) 12 b) 18 c) 15 d) 10 475.A rectangular field is surrounded by a fence 548 meters long. The diagonal distance from corner to corner is 194 meters. Determine the area of the rectangular field. a) 18,270 m^2 b) 18,720 m^2 c) 18,027 m^2 d) 19,702 m^2 476. Solve for x: (x+2)^(1/2) + (3x-2)^(1/2) = 4 a) x = 1 b) x = 3 c) x = 2 d) x = 4 477. Solve for x: (1/x) + (2/x^2) = (3/x^3). a) x=1,x=-3 b) x=3,x=1 c) x=-1,x=3 d) x=2,x=3 478. Solve for x: x^(2/3) + x^(-2/3) = 17/4 a) x=-4,x=-1/4 b) x=8,x=-1/4 c) x=4,x=1/8 d) x=8,x=1/8 479. A rectangular lot has a perimeter of 120 meters and an area of 800 square meters. Find the length and width of the lot. a) 10m and 30m b) 30m and 20m c) 40m and 20m

d) 50m and 10m 480. A 24-meter pole is held by three guy wires in its vertical position. Two of the guy wires are of equal length. The third wire is 5 meters longer than the other two and is attached to the ground 11 meters farther from the foot of the pole than the other two equal wires. Find the length of the wires. a) 25m and 30m b) 15m and 40m c)20m and 35m d) 50 and 10m 481. In a racing contest, there are 240 cars which will have fuel provisions that will last for 15 hours. Assuming a constant hourly consumption for each car, how long will the fuel provisions last if 8 cars withdraw from race every hour after the first? a) 20 hours b)10 hours c) 15 hours d) 25 hours 482. A pile of boiler pipes contains 1275 pipes in layers so that the top layer contains one pipe and each lower layer has one more pipe than the layer above. How many layers are there in the pile? a) 50 b) 45 c) 40 d) 55 483. A production supervisor submitted the following report on the average rate of production of printed circuit boards(PCB) in an assembly line: ―1.5 workers produce 12 PCB’s in 2 hours‖. How many workers are employed in the assembly line working 40 hours each per week with a weekly production of 8000 PCB’s/ a) 50 workers b) 60 workers c) 55 workers d) 70 workers 484. A man bought 20 calculators for P20,000.00. There are three types of calculators bought, business type costs P3,000 each, scientific type costs P1,500 each and basic type costs P500 each. How many calculators of each type were purchased? a) 3, 6, 11 b) 2, 6, 12 c) 1, 4, 15 d) 2, 5, 13 486. A veterans organization in cebu city consists of men who fought in World War II and men who fought in Korea. The secretary noted that 180 members had fought in Korea and that 70% had taken part in World War II, while 10% of the members had fought in both World War II and Korea. How many members are there together? a) 400 b) 500 c) 450 d) 700

487. An angle greater than a straight angle and less than two straight angles is called: a) Right angle b) Obtuse angle c) Reflex angle d) Acute angle 488. A line segment joining two points on a circle is called: a) Arc b) Tangent c) Sector d) Chord 489. All circles having the same center but with unequal radii are called: a) encircle b) tangent circles c) concyclic d) concentric circles 490. A triangle having three sides equal is called: a) equilateral triangles b) scalene triangles c) isosceles triangles d) right triangles 491. In a regular polygon, the perpendicular line drawn from the center of the inscribed circle to any one of the sides is called: a) radius b) altitude c) median d) rhombus 492. A quadrilateral with two and only two sides of which are parallel is called: a) parallelogram b) trapezoid c) quadrilateral d) rhombus 493. A polygon with fifteen sides is termed as: a) dodecagon b) decagon c) pentedecagon d) nonagon 494. A statement the truth of which is admitted without proof is called: a) an axiom b) a postulate c) a theorem d) a corollary 495. A rectangle with equal sides is termed as: a) rhombus b) trapezoid c) square d) parallelogram

496. The sum of the sides of a polygon is termed as: a) circumference b) altitude c) apothem d) perimeter 497. A line that meets a plane but not perpendicular to it, in relation to the plane, is: a) parallel b) collinear c) coplanar d) oblique 498. A quadrilateral whose opposite sides are equal is generally termed as: a) a square b) a rectangle c) a rhombus d) a parallelogram 499. A part of a line included between two points on the line is called: a) a tangent b) a secant c) a sector d) a segment 500. Lines which pass through a common point are called: a) collinear b) coplanar c) concurrent d) congruent 501. Points which lie on the same plane is called: a) collinear b) coplanar c) concurrent d) congruent 502. In two intersecting lines, the angles opposite to each other are termed as: a) opposite angles b) vertical angles c) horizontal angles d) inscribed angles 503. A normal to a given plane is: a) perpendicular to the plane b) lying on the plane c) parallel to the plane d) oblique to the plane 504. Which of the following statements is correct? a) all equilateral triangles are similar b) all right-angled triangles are similar c) all isosceles triangles are similar d) all rectangles are similar

505. A polygon is ________ when no side, when extended, will pass through the interior of the polygon. a) equilateral b) isoperimetric c) congruent d) none of the above 506. The sum of the sides of a polygon: a) perimeter b) hexagon c) square d) circumference 507. What are the exact values of the cosine and tangent trigonometric functions of the acute angle A, given sin A = 5/8? a) cos A = 8 / 39^(1/2) and tan A = 39^(1/2) / 5 b) cos A = 39^(1/2) / 5 and tan A = 8 / 39^(1/2) c) cos A = 39/8 and tan A = 5/ 39^(1/2) d) cos A = 8/5 and tan A = 5/8 508. Given a triangle with angle C=290, side a =132 units and side b=233.32 units. Solve for angle B. a) B=1200 b) B=122.50 c) B=125.20 d) B=1300 509. Simplify: cos2 θ ( 1 + tan2 θ ) a) tan 2θ b) 1 c) sin 2θ d) cos θ 510. What is the cosine of 1200? a) -0.500 b) -0.450 c) -0.866 d) 0.500 511. What is the sine of 8400? a) -0.866 b) -0.500 c) 0.866 d) 0.500 512. If the sine of angle A is given as k, what would be then tangent of angle A? Symbol h for hypotenuse, o for opposite and a for adjacent. a) hk/o b) hk/a c) ha/k d) ok/a 513. Which is true regarding the signs of the natural functions for angles between 900 and 1800? a) The tangent is positive

b) The cotangent is positive c) The cosine is negative d) The sine is negative 514. What is the inverse natural function of the cosecant? a) secant b) sine c) cosine d) tangent 515. What is the sum of the squares of the sine and cosine of an angle? a) 0 b) 1 c) 3^(1/2) d) 2 516. What is an equivalent expression for sin 2x? a) ½ sin x cos x b) 2 sin x cos ½ x c) -2 sin x cos x d) 2 sin x/sec x 517. A transit set-up 112.1 feet from the base of a vertical chimney reads 32030’ with the crosshairs set on top of the chimney. With the telescope level, the vertical rod at the base of the chimney is 5.1 feet. How tall is the chimney? a) 66.3 ft b) 71.4 ft c) 76.5 ft d) 170.9 ft 518. If sin θ – cos θ = 1/3, what is the value of in 2θ? a) 1/3 b) 1/9 c) 8/9 d) 4/9 519. If cos θ = 3^(1/2)/2, then find the value of x if x = 1 – tan2 θ: a) -2 b) -1/3 c) 4/3 d) 2/3 520. Solve for x: x = 1-(sin θ-cos θ)^2 a) sin θcos θ b) -2cos θ c) cos 2 θ d) sin 2 θ 521. A mobiline tower and a Nipa Hut stand on a level plane. The angles of depression of the top and bottom of the Nipa Hut viewed from the top of the mobiline tower are 150 and 400, respectively. The height of the tower is 100m. Find the height of the Nipa hut. a) 78.08 m b) 87.08 m c) 68.07 m

d) 77.08 m 522. Ship A started sailing N40032’E at the rate of 3 mph. After 2 hours, ship B started from the same port going S45018’E at the rate of 4 mph. After how many hours will the second ship be exactly south of ship A? a) 2.25 hrs b) 2.97 hrs c) 3.73 hrs d) 4.37 hrs 523. Solve for the value of x in the equation: ln (2x+7) – ln (x-1) = ln 5 a) x=4 b) x=5 c) x=6 d) x=8 524. Two ships started sailing from the same point. One travelled N200E at 30 mph while the other travelled S500E at 20 mph. After 3 hrs, how far apart are the ships? a) 124 miles b) 129 miles c) 135 miles d) 145 miles 525. A quadrilateral ABCD is inscribed in a semi-circle such that one of the sides coincides with the diameter AD. AB = 10 meters, and BC = 20 meters. If the diameter AD of the semi-circle is 40 meters, find the area of the quadrilateral. a) 350 m^2 b) 420 m^2 c) 470 m^2 d) 530 m^2 526. Solve for x: Arcsin 2x - Arcsin x = 150 a) 0.1482 b) 0.2428 c) 0.3548 d) 0.4282 527. Solve for x: 2^x + 4^x = 8 ^x a) 0.694242 b) 0.692424 c) 0.964242 d) 0.742420 528. Given: Triangle ABC whose angle A is 320 and a = 75 m. The opposite side of angle B is 100m. Find angle C. a) 1000 b) 1030 c) 1100 d) 1150 529. Given triangle ABC with sides AB=210 m, BC=205 m, and AC=110 m. Find the largest angle. a) 72.7510 b) 75.7210

c) 77.1570 d) 82.5170 530. A pole which leans 10015’ from the vertical towards the sun casts a shadow 9.43m long on the ground when the angle of elevation of the sun is 54050’. Find the length of the pole. a) 12.5m b) 14.2m c) 15.4m d) 18.3m 531. Two points lie on a horizontal line directly south of a building 35 m high. The angles of depression to the points are 29010’ and 43050’, respectively. Determine the distance between the points. a) 26.3 m b) 28.7 m c) 30.2 m d) 36.4 m 532. Two points lie on a horizontal line directly south of a building 35 m high. The angles of depression to the points are 29010’ and 43050’, respectively. Determine the distance between the building and the farthest point. a) 62.7 m b) 36.5 m c) 26.5 m d) 72.6 m 533. Given triangle ABC with sides AB=210 m, BC=205 m, and AC=110 m. Find the largest angle. a) C = 1100 b) C = 85.20 c) C = 77.10 d) C = 43.50 534. Given triangle ABC whose angle A is 320 and opposite side of A is 75 meters. The opposite side of angle B is 100 m. find the opposite side of angle C. a) c = 137.8 m b) c = 181.2 m c) c = 117.7 m d) c = 127.8 m 535. A point P within an equilateral triangle has a distance of 4m, 5m, and 6m respectively from the vertices. Find the side of the triangle. a) 8.53m b) 6.78m c) 9.45m d) 17.8m 536. The diagonal of the floor of a rectangular room is 7.50 m. The shorter side of the room is 4.5 m. What is the area of the room? a) 36 sq. m b) 27 sq. m c) 58 sq. m d) 24 sq. m

537. A semi-circle of radius 14 cm is formed from a piece of wire. If it is bent into a rectangle whose length is 1 cm more than its width, find the area of the rectangle. a) 256.25 sq. cm b) 323.57 sq. cm c) 386.54 sq. cm d) 452.24 sq. cm 538. The length of the side of’ a square is increased by 100%. Its perimeter is increased by: a) 25% b) 100% c) 200% d) 300% 539. A piece of wire of length 52 cm is cut into two parts. Each part is then bent to form a square. It is found that total area of the two squares is 97 sq. cm. the dimension of the bigger square is: a) 4 b) 9 c) 3 d) 6 540. A sector has a radius of 12 cm. If the length of its arc is 12 cm, its area is: a) 66 sq. cm b) 82 sq. cm c) 144 sq. cm d) 72 sq. cm 541. The perimeter of a sector is 9 cm and its radius is 3 cm. What is the area of the sector? a) 4 sq. cm b) 9/2 sq. cm c) 11/2 sq. cm d) 27/2 sq. cm 542. An iron bar 20 cm long is bent to form a closed plane area. What is the largest area possible? a) 21.56 sq. m b) 25.68 sq. m c) 28.56 sq. m d) 31.83 sq. m 543. A swimming pool is to be constructed in the shape of partially-overlapping identical circles. Each of the circles has a radius of 9 cm, and each passes through the center of the other. Find the area of the swimming pool. a) 302.33 sq. m b) 362.55 sq. m c) 398.99 sq. m d) 409.44 sq. m 544. A circle of radius 5 cm has a chord which is 6 cm long. Find the area of the circle concentric to this circle and tangent to the given chord. a) 14 π b) 16 π c) 9 π d) 4 π

545. The diagonals of a rhombus are 10 cm and 8 cm, respectively. Its area is: a) 10 sq. cm b) 50 sq. cm c) 60 sq. cm d) 40 sq. cm 546. The diagonals of a parallelogram are 10 cm and 16 cm, respectively, if one of its side measures 6 cm, what is the area? a) 59.92 sq. cm b) 65.87 sq. cm d) 69.56 sq. cm d) 78.56 sq. cm 547. Given a cyclic quadrilateral whose sides are 4 cm, 5cm, 8cm and 11cm. its area is: a) 40.25 sq. cm b) 48.65 sq. cm c) 50.25 sq. cm d) 60.25 sq. cm 548 How many cubic meters is 100 gallons of liquid? a) 1.638 b) 37.85 c) 3.7850 d) 0.37854 549. How many cubic meters is 100 cubic feet of liquid? a) 3.785 b) 28.31 c) 37.85 d) 2.831 550. The volume of a sphere is 904.78 m^3. Find the volume of the spherical segment of height 4 m. a) 234.57 m^3 b) 256.58 m^3 c) 145.69 m^3 d) 124.58 m^3 551. A sector of radius of 6 cm and central angle of 600 is bent to form a cross. Find the volume of the cone. a) (35)^(1/2) π / 3 b) π (35)^(1/2) c) 35 π / 3^(1/2) d) 35 π / 3 552. A spherical wedge of a sphere of radius 10 cm has an angle of 400. Its volume is: a) 523.42 cm^3 b) 465.42 cm^3 c) 683.42 cm^3 d) 723.45 cm^3 553. If a solid steel ball is immersed in an eight cm diameter cylinder, if displaces water to a depth of 2.25 cm. The radius of the ball is: a) 3 cm

b) 6 cm c) 9 cm d) 12 cm 554. The volume of a cube is reduced by how much if all sides are halved? a) 1/8 b) 5/8 c) 6/8 d) 7/8 555. If 23 cm^3 of water are poured into a conical vessel, it reaches a depth of 12 cm. How much water must be added so that the depth reaches 18 cm? a) 95 cm^3 b) 100 cm^3 c) 54.6 cm^3 d) 76.4 cm^3 556. A cylindrical tank, lying horizontally, 0.90 m in diameter and 3 m long is filled to a depth of 0.60 m. How many gallons of gasoline does it contain? a) 250 b) 360 c) 300 d) 270 557. A closed cylindrical tank is 8 ft long and 3 ft in diameter. When lying in a horizontal position, the water is 2 feet deep. If the tank is in the vertical position, the depth of the water tank is: a) 5.67 m b) 5.82 m c) 5.82 ft d) 5.67 ft 558. The surface area of a sphere is 4πr^2. Find the percentage increase in its diameter when the surface area increases by 21%. a) 5% b) 10% c) 15% d) 20% 559. Find the percentage increase in volume of a sphere if its surface area is increased by 21%. a) 30.2% b) 33.1% c) 34.5% d) 30.9% 560. Determine the estimated weight of steel plate size ¼ x 4 x 8. a) 184.4 kg b) 148.7 kg c) 327 kg d) 841 kg 561. The no. of board feet in a plank 2 in. thick, 6 in. wide and 20 ft long is: a) 15 b) 30

c) 20 d) 25 562. Determine the volume of a right truncate triangle prism with the following dimensions: Let the corners of the triangular base be defined by A, B ad C. The length AB=11ft, BC=10ft and CA=13ft. The sides at A, B and C are perpendicular to the triangular base and have the height of 8.6ft, 7.1ft and 5.5ft, respectively. a) 377 ft^3 b) 337 ft^3 c) 358 ft^3 d) 389 ft^3 563. A right circular conical vessel is constructed to have a volume of 100,000 liters. Find the diameter if depth is to be 1.25 times the diameter. a) 6.736 m b) 7.632 m c) 8.24 m d) 9.45 m 564. A hollow sphere with an outer radius of 32 cm is made of a metal weighing 8 grams per cubic cm. The weight of the sphere is 150 kg so that the volume of the metal is 24,000 cubic cm. Find the inner radius. a) 30 cm b) 35 cm c) 40 cm d) 45 cm 565. A circular cylindrical tank, axis horizontal, diameter 1 meter, and length 2 meters, is filled with water to a depth of 0.75 meters. How much water is in the tank? a) 2.578 m^3 b) 2.125 m^3 c) 1.2638 m^3 d) 1.0136 m^3 566. A machine foundation has the shape of a frustrum of a pyramid with lower base 6m x 2m, upper base 5.5m x 1.8m, and altitude of 1.5m. Find the volume of the foundation. a) 12.5 m^3 b) 14.2 m^3 c) 15.6 m^3 d) 16.4 m^3 567. An elevated water tank is in the form a circular cylinder with diameter of 3 m and a hemispherical bottom. The total height of the tank is 5 m. Water is pumped into the tank at a rate of 30 gallons per minute. How long will it take to fully fill the tank starting empty? a) 4.668 hrs b) 5.468 hrs c) 7.725 hrs d) 9.245 hrs 568. The intercept form for algebraic straight equation: a) a/x + y/b = 1 b) y = mx + b c) Ax + By + C = 0

d) x/a + y/b = 1 569. Find the slope of the line y-x=5. a) 1 b) 5+x c) -1/2 d) ¼ 570. Find the equation of the line that passes through the points (0,0) and (2,-2). a) y=x b) y=-2x+2 c) y=-2x d) y=-x 571. Find the equation of the line with slope=2 and y-intercept=-3. a) y=-3x+2 b) y=2x-3 c) y=2/3x+1 d) y=2x+3 572. The equation y=a1+a2x is an algebraic expression for which of the following: a) A cosine expansion b) projectile motion c) a circle in polar form d) a straight line 573. In finding the distance, d, between two point, which equation is the appropriate one to use? a) d=((x1-x2)^2 + (y2-y1)^2)^(1/2) b) d=((x1-y1)^2 + (x2-y2)^2)^(1/2) c) d=((x1^2 – x2)^2 + (y1^2 - y2^2))^(1/2) d) d=((x2-x1)^2 + (y2-y1)^2)^(1/2) 574. The slope of the line 3x + 2y + 5 = 0 is: a) -2/3 b) -3/2 c) 3/2 d) 2/3 575. Find the area of the circle whose center is at (2,-5) and tangent to the lien 4x+3y-8=0. a) 6π b) 3 π c) 9 π d) 12 π 576. Given the equation of the parabola: y^2 – 8x -4y -20 =0. The length of its latus rectum is: a) 2 b) 4 c) 6 d) 8 577. Find the equation of the tangent to the circle x^2 + y^2 – 34 = 0 through point (3,5). a) 3x+5y-34=0 b) 3x-5y-34=0 c) 3x+5y+34=0 d) 3x-5y+34=0

578. If the distance between the points (8,7) and (3,y) is 13, what is the value of y? a) 5 b) -19 c) 19 or -5 d) 5 or -19 579. Which of the following is perpendicular to the line x/3 + y/4 =1? a) x-4y-8=0 b) 4x-3y-6=0 c) 3x-4y-5=0 d) 4x+3y-11=0 580. The two straight lines 4x-y+3=0 and 8x-2y+6=0 a) intersects at the origin b) are coincident c) are parallel d) are perpendicular 581. A line which passes through (5,6) and (-3,-4) has an equation of: a) 5x+4y+1=0 b) 5x-4y-1=0 c) 5x-4y+1=0 d) 5x+4y-1=0 582. The equation of the line through (1,2) parallel to the line 3x-2y+4=0. a) 3x-2y+1=0 b) 3x-2y-1=0 c) 3x+2y+1=0 d) 3x+2y-1=0 583. Find the area of the polygon which is enclosed by the straight lines x-y=0, x+y=0, x-y=2a and x+y=2a. a) 2a^2 b) 4a^2 c) 2a d) 3a^2 584. Find the equation of the circle with center at (2, -3) and radius of 4. a) x^2 + y^2 -6x + 4y + 3 = 0 b) x^2 + y^2 -4x + 6y - 3 = 0 c) x^2 + y^2 -6x + 4y - 3 = 0 d) x^2 + y^2 -2x + 3y - 1 = 0 585. Find the area of the curve whose equation is : 2x^2 – 8x + 2y^2 + 12y = 1. a) 35.4 sq. units b) 39.2 sq. units c) 42.4 sq. units d) 44.2 sq. units 586. Find the area of the curve whose equation is : 9x^2 – 36x + 25y^2 = 189. a) 41.7 sq. units b) 43.4 sq. units c) 46.2 sq. units d) 47.1 sq. units

587. Given the curve Ax^2 + By^2 + F = 0. It passes through the points (4,0) and (0,3). Find the value of A, B and F. a) 9,16,144 b) 9,16,121 c) 3,4,112 d) 3,4,144 588. A straight line passes through (2,2) such that the length of the line segment intercepted between the coordinate axis is equal to the square root of 5. Find the equation of the straight line. a) 4x-y-2=0 b) x-4y-2=0 c) 2x-y-2=0 d) 2y-x-4=0 589. Find the area of the circle whose equation is : 2x^2 – 8x + 2y^2 + 12y = 1. a) 24.4 sq. units b) 34.2 sq. units c) 42.4 sq. units d) 54.2 sq. units 590. Find the area of the curve whose equation is : 9x^2 – 36x + 25y^2 = 189. a) 27.2 sq. units b) 32.8 sq. units c) 47.1 sq. units d) 75.4 sq. units 591. What is the first derivative with respect to x of the function G(x) = 4 * 9^(1/2) ? a) 0 b) 4/9 c) 4 d) 4(9^(1/2)) 592. If a is a simple constant, what is the derivative of y = x^a? a) ax b) x^(a-1) c) a x^(a-1) d) (a-1)x 593. Find the derivative of F(x) = [x^3 – (x-1)^3]^3. a) 3x^2 – 3(x-1)^2 b) 3[x^3 – (x-1)^3]^2 c) 9[x^3 – (x-1)^3][x^2 – (x-1)^2] d) 9[x^3 – (x-1)^3]^2 [x^2 – (x-1)^2] 594. Differentiate f(x) = [2x^2 +4x +1]^(1/2) a) 2x+2 b) ½[2x^2 + 4x + 1]^(1/2) c) (2x + 2)/ [2x^2 +4x +1]^(1/2) d) (4x + 4)/ [2x^2 +4x +1]^(1/2) 595. Find the second derivative of y = (x^2 + x^-2)^(1/2) a) 1 - 2x^-3 b) 1 - 6x^4 c) 3

d) 6 / x^4 596. If y=cos x, what is dy/dx? a) sec x b) – sec x c) csc x d) – sin x 597. What is the slope of the graph y = -x^2 at the point (2,3)? a) -4 b) -2 c) 1 d) 3 598. Given the function f(x) = x^3 – 5x + 2, find the value of the first derivative at x=2. a) 2 b) 3x^2 – 5 c) 7 d) 8 599. Find the slope of the tangent to a parabola y = x^2, at a point on the curve where x=1/2. a) 0 b) 1/2 c) -1/2 d) 1 600. What is the slope of the curve y = x^2 -4x as it passes through the origin? a) 0 b) -3 c) -4 d) 4 601. Find the slope of the line tangent to the curve y = x^3 – 2x + 1 at the point (1,2). a) 1/4 b) 1/3 c) 1/2 d) 1 602. Determine the equation of the line tangent to the graph y = 2x^2 + 1, at the point (1,3). a) y = 2x + 1 b) y = 4x - 1 c) y = 2x - 1 d) y = 4x + 1 603. Given Y1 = 4x + 3 and Y2 = x^2 + C, find C such that Y2 is tangent to Y1. a) 2 b) 4 c) 5 d) 7 604. The distance of a body travels is a function of time and is given by x(t) = 18t + 9t^2. Find its velocity at t=2. a) 20 b) 24 c) 36

d) 54 605. If x increases uniformly at the rate of 0.001 feet per second, at what rate is the expression (1+x)^3 increasing when x becomes 9 feet? a) 0.001 b) 0.003 c) 0.3 d) 1.003 606. A spherical balloon is being filled with air at a rate of 1 cubic foot per second. Compute the time rate of rate of the surface area of the balloon at the instant when its volume is 113.1 cubic feet. a) 0.67 ft^2 / s b) 1.73 ft^2 / s c) 3.0 ft^2 / s d) 3.7 ft^2 / s 607. What is the maximum of the function y = -x^3 +3x for x=-1? a) -2 b) -1 c) 0 d) 2 608. The cost C of a product is a function of the quantity x, of the product: C(x) = x^2 – 4000x + 50. Find the quantity for which the cost is minimum. a) 1000 b) 1500 c) 2000 d) 3000 609. Compute the following limit Lim x+2 x →∞ x-2 a) 0 b) 1 c) 2 d) ∞ 610. Find the equation of the tangent to the ellipse: 4x^2 + 9y^2 = 40 at point (1,-2). a) 2x – 9y – 20 = 0 b) 9x + 5y + 2 = 0 c) 9x – 2y + 20 = 0 d) 2x + 9y +20 = 0 611. Find the equation of the tangents to the graph y = x^3 + 3x^2 – 15x – 20 at the points of the graph where the tangents to the graph have a slope of 9. a) 9x + y + 70 = 0 b) 9y + x + 60 = 0 c) 9x – y – 48 = 0 d) x - y - 9 = 0 612. A rectangular field to contain a given area is to be fenced off along a straight river. If no fencing is needed along the river, show that the least amount of fencing will be required when the length of the field is twice its width. a) L = 3W

b) L = 4W c) L = W d) L = 2W 613. Find the shape of the largest rectangle that can be inscribed in a given circle. a) Trapezoid b) Rectangle c) Parallelogram d) Square 614. Divide the number 60 into two parts so that the product P of one part and the square of the other is a maximum. a) 30 and 30 b) 25 and 35 c) 50 and 10 d) 40 and 20 615. What is the maximum volume of a box that is constructed from a piece of cardboard 16 inches square by cutting equal squares out of the corners and turning up the sides. a) 303.4 in^3 b) 404.5 in^3 c) 202.2 in^3 d) 101.1 in^3 616. A square sheet of galvanized iron, 100 cm x 100 cm will be used in making an open-top container by cutting a small square from each corner and bending up the sides. Determine how large the square should be cut from each corner in order to obtain the largest possible volume. a) 16 2/3 cm x 16 2/3 cm b) 11 ½ cm x 11 ½ cm c) 12 1/3 cm x 12 1/3 cm d) 14 ¼ cm x 14 ¼ cm 617. The sum of two positive numbers is 36. What are the numbers if their product is to be the largest possible? a) 10 and 10 b) 15 and 15 c) 12 and 12 d) 18 and 18 618. A bus company charges P85 per passenger from Manila to Baguio for 100 or less passengers. For group tours, the company allows for P0.50 discount of the ticket price for every passenger in excess of 100. How many passengers give the maximum income? a) 110 b) 150 c) 120 d) 135 619. A tinsmith wishes to make a gutter of maximum cross-section (carrying capacity) whose bottom and sides are each 6 inches wide and whose sides have the same slope. What will be the width at the top? a) 10 in b) 12 in c) 8 in

d) 14 in 620. A lot is in the shape of a quadrant of a circle of radius 100 meters. Find the area of the e largest rectangular building that can be constructed inside the lot. a) 2500 m^2 b) 7500 m^2 c) 5000 m^2 d) 9000 m^2 621. The cost of setting up a geothermal power plant is P10M for the first MW, P11M for the second MW, P12M for the third MW, etc., the other expenses (land rights, desing fee, etc.) amount to P50M. If the expected annual income per MW is 2M, find the plant capacity that will yield a maximum rate of return of investment. a) 8 MW b) 10 MW c) 9 MW d) 14 MW 622. If the fuel cost to run a boat is proportional to the square of her speed and is P25 per hour for a speed of 30 kph, find the most economical speed to run the boat, other expenses independent from the speed amount to P100 per hour and the distance is 200 km. a) 60 kph b) 100 kph c) 70 kph d) 30 kph 623. The strength of a rectangular beam is proportional to the breadth and the square of the depth. Find the dimensions of the strongest beam that can be cut from a log 30 cm in diameter. a) b = 17.32 cm, h = 24.49 cm b) b = 22.45 cm, h = 31.55 cm c) b = 12.45 cm, h = 19.85 cm d) b = 19.65 cm, h = 28.49 cm 624. Two posts, one 8 meters high and the other 12 meters high, stand 15 meters apart. They are to be stayed by wires attached to a single stake at ground level, the wires running to the tops of the posts. How far from the shortest post should the stake be placed, to use the least amount of wire? a) 6m b) 4m c) 8m d) 12m 625. A cylindrical glass jar has a metal top. If the metal costs three times as much as the glass per unit area, find the proportions of the least costly jar that holds a given amount. a) H = D b) H = ¼ D c) H = ½ D d) H = 2D 626. The parcel post regulations limit the size of a package to such a size that the length plus the girth equals 6 feet. Determine the volume of the largest cylindrical package that can be sent by the parcel post. a) 2.546 cu. ft

b) 3.846 cu. ft c) 4.234 cu. ft d) 6.870 cu. ft 627. A cylindrical steam boiler is to be constructed having a capacity of 30 cu. meters. The material for the sides costs P430 per sq. meter and for the ends P645 per sq. meter. Find the radius when the cost is least. a) 1m b) 1.47m c) 2.1m d) 1.7m 628. A boat is being towed toward a pier which is 20 feet above the water. The rope is pulled in at a rate of 6 ft/sec. How fast is the boat approaching the base of the pier when 25 feet of rope remain to be pulled in? a) 8 ft/sec b) 12 ft/sec c) 10 ft/sec d) 15 ft/sec 629. A water tank is in the form of a right circular cone with vertex down, 12 feet deep and 6 feet across the top. Water is being pumped into the tank at the rate of 10 cu. ft/min. How fast is the surface of the water in the tank rising when the water is 5 feet deep? a) 8 ft/min b) 4 ft/min c) 6 ft/min d) 2 ft/min 630. Water is flowing out of a conical funnel at a rate of 1 cu. in/sec. If the radius of the funnel is 2 inches and the altitude is 6 inches, find the rate at which the water level is dropping when it is 2 inches from the top. a) 0.179 in/sec b) 1.245 in/sec c) 0.889 in/sec d) 2.225 in/sec 631. A helicopter is rising vertically from the ground at constant rate of 15 ft per second. When it is 250 feet off the ground, a jeep passed beneath the helicopter travelling in a straight line at a constant speed of 50 mph. Determine how fast is the distance between them is changing after one second. a) 34 ft/sec b) 45 ft/sec c) 38 ft/sec d) 60 ft/sec 632. A plane flying north at 640 kph passes over a certain town at noon and a second plane going east at 600 kph is directly over he same town 15 minutes later. If the planes are flying at the same altitude, how fast will they be separating at 1:15 PM? a) 872 kph b) 287 kph c) 782 kph d) 728 kph

633. The height of a cylindrical cone is measured to be four meters which is equal to its radius with a possible error of 0.04. Determine the percentage error in computing the volume. a) 3% b) 10% c) 5% d) 1% 634. Divide 94 into three parts such that one-half the product of one pair, plus one-third the product of another pair, plus one-fourth the product of the third pair may seem to be a maximum value. a) 42,40,12 b) 35,40,19 c) 38,40,16 d) 30,50,14 635. Integrate (3x^4 + 2x^3 + x^2 + 1)dx a) (3x^3)/5 + (2x^2)/4 + x + 1 + c b) (3x^5)/5 + (x^4)/2 + (x^3)/3 + x + c c) (5x^5)/3 + 4x^2 + x + c d) 3x^3 + 2x^4 + x^3 + x^2 + c 636. The integral of cos x dx with respect to x: a) –sin x +c b) sin x +c c) cos x +c d) –cos x +c 637. Find the area under the curve y = 1/x between the limits y=2 and y=10. a) 1.61 b) 2.39 c) 3.71 d) 3.97 638. Fill in the blank in the following statement: The integral of a function between certain limits divided by the difference in abscissas between those limits gives the ___________ of the function. a) average b) middle c) intercept d) limit 639. Find the area bounded between y = 6x-1 and y = x/4 + 3 by x=0 and the intersection point. a) 32/529 b) 16/23 c) 32/23 d) 64/23 640. If it is known that y=1 when x=1, what is the constant of integration for the following integral? Y(x) = (e^(2x) - 2x)dx a) c = 2 – e^2 b) c = 3 – e^2 c) c = 4 – e^2 d) ½(4 – e^2)

641. Evaluate integral of Tan (ln x) dx x a) ln cos (ln x) + c b) ln sec (ln x) + c c) 1/2 Tan^2 (ln x) + c d) Tan (ln x) + c 642. Evaluate integral of cos x ln sin x dx a) sin x (1- ln sin x) + c b) sin x (1+ ln sin x) + c c) sin x (ln sin x - 1) + c d) ln sin x + c 643. Evaluate ∫ _e^x_dx_ 1 + e^(2x) a) 1/2 ln (1 + e^2x) + c b) ln (1 + e^2x) + c c) 1/2 (1 + e^2x)^2 + c d) Arctan (e^x) + c 644. Evaluate ∫ _______dx__________ ln x^x [(ln x)^2 -1]^(1/2) a) Arc sec (ln x) + c b) 2/3[(ln x)^2 -1]^(3/2) + c c) ln (ln x)^2 – 1 + c d) Arc sin (ln x) + c 645. Evaluate ∫ a) 2 b) -2 c) -3 d) 3 646. Evaluate ∫ a) ln (10x + 1) + c b) 1/10 ln(10x + 1) + c c) ln(10x) + c d) 10x + 1 + c 647. Evaluate ∫ 8dx / x^5 a) 8x^4 + c b) 2x^4 + c c) -2x^-4 + c d) 2x^-4 + c 648. Evaluate ∫ (x^2)[(8 - x^3)^(1/2)]dx a) -2/9 (8 – x^3)^(3/2) + c b) -8 (8 – x^3)^(3/2) + c c) 2/9 (8 – x^3)^(3/2) + c d) -2/3 (8 – x^3)^(3/2) + c 649. Evaluate ∫ x^2a dx

a)

+c

b) +c c) x^a / a + c d) x / 2a + c 650. Find the area bounded by the parabola y = x^2, the x-axis and the lines x=1 and x=3. a) 8 2/3 sq. units b) 7 1/2 sq. units c) 9 1/4 sq. units d) 12 sq. units 651. An ellipsoidal tank measuring 6 ft by 12 ft has its axis vertical, the axis of rotation being the major axis. It is filled with water to a depth of 7 feet. Find the amount of water in the tank. a) 111 cu. ft b) 121 cu. ft c) 141 cu. ft d) 161 cu. ft 652. Find the area enclosed by the curves: y^2 = 8x – 24 and 5y^2 = 16x. a) 20 sq. units b) 16 sq. units c) 18 sq. units d) 22 sq. units 653. An open cylindrical tank 3 feet in diameter and 4.5 feet high is full of water. It is then tilted until one-half of its bottom is exposed. How many gallons of water was spilled out? a) 187.4 gal b) 148.7 gal c) 178.4 gal d) 147.8 gal 654. The parabolic reflector of an automobile headlight is 12 inches in diameter and 4 inches depth. What is the surface area in square inches? a) 135.9 sq. in b) 195.3 sq. in c) 153.9 sq. in d) 159.3 sq. in 655. A cistern in the form of an inverted right circular cone is 20 meters deep and 12 meters diameter at the top. If the water is 16 meters deep in the cistern, find the work in kJ in pumping out the water to a height of 10 meters above the top of the cistern. a) 61,817 kJ b) 55,004 kJ c) 64,890 kJ d) 68,167 kJ 656. A flour bag originally weighing 60 kg is lifted through a vertical distance of 9 meters. While the bag is being lifted, flour is leaking from the bag at such a rate that the weight lost is proportional to the square root of the distance travelled. If the total loss is 12 kg, find the amount of work in kJ done in lifting the bag? a) 4.59 kJ b) 9.54 kJ

c) 5.94 kJ d) 4.95 kJ 657. What is the name for a vector that represents the sum of two vectors? a) scalar b) tensor c) resultant d) tangent 658. What is the acceleration of a body that increases its velocity from 60 m/s to 110 m/s? a) 5 m/s b) 3.0 m/s c) 4.0 m/s d) 5.0 m/s 659. A cyclists on a circular track of radius r = 250 m is travelling at 9 m/s. His speed in the tangential direction increases at a rate of 1.5 m/s^2. What is the cyclist’s total acceleration? a) -1.53 m/s^2 b) 1.53 m/s^2 c) 2.3 m/s^2 d) -2.3 m/s^2 660. A bus weighing 9000N is switched to a 2% upgrade with a velocity of 40 kph. If the train resistance is 950 N, how far up the grade will it go? a) 50 m on slope b) 5 m on slope c) 500 m on slope d) 75 m on slope 661. Moment of inertia on SI is described as: a) N-m b) N/m c) kg/m d) Farad/m 662. A solid disks flywheel (I=200 kg-m^2) is rotating with a speed of 900 rpm. What is the rotational KE? a) 730 x 10^3 J b) 680 x 10^3 J c) 888 x 10^3 J d) 1100 x 10^3 J 663. The weight of a mass 10 kg at a location where the acceleration of gravity is 9.7 m/s^2 is: a) 79.7 N b) 77.9 N c) 97.7 N d) 977 N 664. A standard acceleration due to gravity in SI unit: a) 32.2 ft/s^2 b) 35.5 m/s^2 c) 9.81 ft/s^2 d) 9.81 m/s^2 665. A 50 kg sack is raised vertically 5 meters. What is the change in potential energy?

a) 2452.5 kJ b) 2.4525 kJ c) 2452.5 N d) 2.4525 kN 666. A shot is fired at an angle of 300 with the horizontal and a velocity of 90 m/s. Calculate the range of the projectile. a) 715 km b) 715 cm c) 0.444 mi d) 250 ft 667. A ball dropped from the top of a building 60 meters elevation will hit the ground with a velocity of: a) 34.31 m/s b) 31.34 m/s c) 43.31 m/s d) 33.41 m/s 668. What horizontal force P can be applied to a 100 kg block in a level surface (µ = 0.20) that will cause an acceleration of 2.50 m/s^2? a) 343.5 N b) 224.5 N c) 53.8 N d) 446.2 N 669. Which of the following is not a vector quantity? a) mass b) torque c) displacement d) velocity 670. The product of force and the time during which it acts is known as: a) impulse b) momentum c) work d) impact 671. The property of the body which measures its resistance to changes in motion: a) acceleration b) weight c) mass d) rigidity 672. The study of motion without reference to the forces which causes motion is known as: a) kinetics b) dynamics c) statics d) kinematics 673. The branch of physical science which deals with state of rest or motion of bodies under the action of forces is known as: a) mechanics b) kinetics

c) kinematics d) statics 674. In physics, work is defined in terms of the force acting through a distance. The rate at which the work is done is called: a) force b) energy c) power d) momentum 675. The point through which the resultant of the distributed gravity force passes regardless of the orientation of the body in space is known as: a) center of inertia b) center of gravity c) center of attraction d) moment of inertia 676. The momentum of a moving object is the product of its mass(m) and velocity(v). Newton’s second law of motion says that the rate of change of momentum with respect to time is: a) power b) energy c) momentum d) force 677. A coin is tossed vertically upward from ground at a velocity of 12 m/s. How long will the coin touch the ground? a) 4.45 asec b) 3.45 sec c) 2.45 sec d) 1.45 sec 678. A bullet is fired at an angle of 750 with the horizontal with an initial velocity of 420 m/s. How high can it travel after 2 seconds? a) 840 m b) 792 m c) 750 m d) 732 m 679. A flywheel rotates at 150 rpm slowed down to 120 rpm during the punching portion of the cycle. Compute the angular acceleration of the flywheel in rad/sec^2, if time is 1 sec. a) 3.14 rad/sec/sec b) -3.14 rad/sec/sec c) 4.31 rad/sec/sec d) -4.31 rad/sec/sec 680. A shot is fired at an angle of 300 with the horizontal and a velocity of 400 ft per sec. Find the height of the projectile. a) 600 ft b) 622 ft c) 700 ft d) 680 ft 681. A projectile is fired with a velocity of 1600 fps and the target distance is 50,000 ft. Determine the angle of elevation of the projectile.

a) 38057’ b)32017’ c) 24032’ d) 19028’ 682. Given the component velocities Vsubx and Vsuby, what is the resultant velocity at t = 3. a) 19 b) 23 c) 21 d) 24 683. A 500 lbf acts on a block at an angle of 300 with respect to the horizontal. The block is pushed 5 feet horizontally. What is the work done by this force? a) 2.936 kJ b) 2,936 kJ c) 3.396 kJ d) 3,396 kJ 684. Traffic travels at 110 mph around a banked highway curve with a radius of 2000 ft and f = 0.3. What banking angle to resist the centrifugal force? a) 5.330 b) 5.990 c) 6.660 d) 7.770 685. A plane dropped a bomb at an elevation of 1000m from the ground intending to hit a target which elevation is 200 m from the ground. If the plane was flying at a velocity of 300 kph, at what distance from the target must the bomb be dropped to hit the target? a) 1064 m b) 1046 m c) 1275 m d) 1146 m 686. A projectile is launched from a level plane at 300 from the horizontal with an initial velocity of 1500 ft/sec. What is the maximum height and maximum range the projectile can reach? a) 2772 m ; 18,500 m b) 2727 m ; 18,885 m c) 2266 m ; 18,994 m d) 2663 m ; 18,449 m 687. A flywheel stops in 10 sec from a speed of 80 rpm. Compute the number of turns the flywheel makes before it stops. a) 6.56 rev b) 6.96 rev c) 5.56 rev d) 6.65 rev 688. An elevator weighing 4000 lb attains an upward velocity of 20 fps in 5 sec with uniform acceleration. What is the tension in the supporting cables? a) 4947 lbs b) 4974 lbs c) 4749 lbs d) 4497 lbs

689. A gun is fired horizontally at a 10 kg block of wood suspended at the end of a cord. The block with the bullet embedded in it rises vertically by 10 cm. Mass of bullet is 40 grams. Find the velocity of the bullet just before it hit the block. a) 354.1 m/s b) 351.4 m/s c) 341.5 m/s d) 315.4 m/s 690. A body weighing 100 kg is hanging at the end of a rope 5 m long. What horizontal force is needed to move the body a horizontal distance of 1m. a) F = 24.1 kg b) F = 22.4 kg c) F = 21.4 kg d) F = 20.4 kg 691. A light rail transit travels between two terminals 1 km apart in a minimum time of 1 min. If the LRT cart accelerates and decelerates at 3.4 m/s^2, starting from rest at the first terminal and coming to stop at the second terminal, find the maximum speed in km per hr. a) 63.9 kph b) 64.9 kph c) 65.9 kph d) 66.9 kph 692. A body weighing 2000 kg is suspended by a cable 20 meters and pulled 5 meters to one side by a horizontal force. Find the tension in the cable. a) 2066 kg b) 2660 kg c) 5166 kg d) 3020 kg 693. A body weighing 350 kg rests on a plane inclined 300 with the horizontal. The angle of static friction between the body and the plane is 15 degrees. What horizontal force P is necessary to hold the body from sliding down the plane? a) 93.7 kg b) 73.9 kg c) 97.3 kg d) 119 kg 694. A 200 kg crate is on a 300 ramp. The coefficient of friction between the crate and the ramp is 0.35. If a force is applied to the crate horizontally, calculate the force F to start the crate moving up the ramp. a) 244 kg b) 38 kg c) 232 kg d) 223 kg 695. A 600 N block rests on a 300 inclined plane. The coefficient of static friction is 0.30 and the coefficient of kinetic friction is 0.20. If a force P is applied to the block horizontally, find the value of P needed to keep the block moving up the plane. a) 257 N b) 750 N c) 275 N

d) 527 N 696. A steam pipe weighing 200 kg per meter will cross a road by suspension on a cable anchored between supports 6 meters apart. The maximum allowable sag of the cable is 50 cm, calculate the length of the cable. a) 2.5 m b) 3.6 m c) 6.1 m d) 9.5 m 697. A parabolic cable has a span of 400 feet. The difference in elevation of the supports is 10 feet and the lowest point of the cable is 5 feet below the lower support. If the load supported by the cable is 12 lbs per horizontal foot, find the maximum tension in the cable. a) 25,902 lbs b) 27,857 lbs c) 29,345 lbs d) 34,876 lbs 698. A tripod whose legs are each 4 meters long supports a load of 1000 kg. The feet of the tripod are the vertices of a horizontal equilateral triangle whose side is 3.5 m. Determine the load on each leg. a) 256 kg b) 386 kg c) 296 kg d) 458 kg 699. Two cars A and B accelerate from a stationary start. The acceleration of A is 4 ft/sec^2 and that of B is 5 ft/sec^2. If B was originally 20 feet behind A , how long will it take B to overtake A. a) 18.6 sec b) 10 sec c) 12.5 sec d) 6.32 sec 700. Two cars, A and B, are travelling at the same speed of 80 km/hr in the same direction on a level road, with car A 100 meters ahead of car B. Car A slows down to make a turn decelerating at 7 ft/sec^2. In how many seconds will B overtake A. a) 6.96 sec b) 5.55 sec c) 7.85 sec d) 9.69 sec 701. In a 25 storey office building, the elevator starting from rest at first floor, is accelerated at 0.8 m/sec^2 for 5 seconds then continues at constant velocity for 10 seconds more and is stopped in 3 seconds with constant deceleration. If the floors are 4 meters apart, at what floor does the elevator stop? a) 12th floor b) 14th floor c) 10th floor d) 15th floor

702. A stone is dropped from a cliff into the ocean. The sound of the impact of the stone on the ocean surface is heard 5 seconds after it is dropped. The velocity of sound is 1100 fps. How high is the cliff? a) 352.5 ft b) 255.5 ft c) 325.5 ft d) 335.5 ft 703. Water drips from a faucet at a rate of 8 drops per second. The faucet is 18 cm above the sink. When one drop strikes the sink, how far is the next drop above the sink? a) 15.8 cm b) 12.5 cm c) 18.5 cm d) 25.6 cm 704. Bombs from a plane drop at a rate of one drop per second. Calculate the vertical distance after two bombs after the first had dropped for 7 seconds. Assume freely falling body with g = 9.8 m/sec^2. a) 37.6 m b) 73.6 m c) 63.7 m d) 76.3 m 705. A weight is dropped from a helicopter that is rising vertically with a velocity of 6 m/sec. If the weight reaches the ground in 15 seconds, how high above the ground was the helicopter when the weight was dropped? a) 1100 m b) 1013 m c) 1580 m d) 1130 m 706. A bomber flying at a horizontal speed of 800 kph drops a bomb. If the bomb hits the ground in 20 seconds, calculate the vertical velocity of the bomb as it hit the ground. a) 169 m/sec b) 196 m/sec c) 175 m/sec d) 260 m/sec 707. A flywheel starting from rest develops a speed of 400 rpm in 30 seconds. How many revolutions did the flywheel make in 30 seconds it took to attain 400 rpm. a) 100 rev b) 150 rev c) 120 rev d) 360 rev 708. A 100 kg block of ice is released at the top of a 300 incline 10 meters above the ground. If the slight melting of the ice renders the surface frictionless, calculate the velocity at the foot of the incline. a) 30 m/sec b) 24 m/sec c) 14 m/sec d) 10 m/sec

709. What drawbar pull is required to change the speed of a 120,000 lb car from 15 mph to 30 mph on a half mile while the car is going up a 1.5% upgrade? Car resistance is 10 lb/ton. a) 3425 lbs b) 3542 lbs c) 3245 lbs d) 4325 lbs 710. A body weighing 200 kg is being dragged along a rough horizontal plane by a force of 45 kg. If the coefficient of friction is assumed to be 1/12 and the line pull makes an angle of 180 with the horizontal, what is the velocity acquired from rest in the first 3 meters. a) 2.8 m/sec b) 3.1 m/sec c) 3.5 m/sec d) 4.9 m/sec 711. A 50 kN Diesel Electric Locomotive (DEL) has its speed increased from 30 kph to 120 kph in a distance of 1 km while ascending a 3% grade. What constant trust (drawbar pull) parallel to the surface of the railway must be exerted by the wheel? The total frictional resistance is 30 N/kN of DEL weight. a) 5.655 kN b) 7.889 kN c) 6.556 kN d) 7.996 kN 712. Water is flowing through a cast iron pipe at the rate 3500 GPM. The inside diameter of pipe is 6 in. Find the flow velocity? a) 39.7 m/s b) 32.5 m/s c) 12.1 m/s d) 17.84 m/s 713. Find the water pressure reading if manometer is 0.45 m Hg. Mercury is 13.6 times heavier than water. a) 60 kPa b) 50 kPa c) 70 kPa d) 65 kPa 714. Determine the velocity of the fluid in a tank at the exit, given that surface h1 = 1m and h2 = 100 cm. a) 3.9 m/s b) 4.2 m/s c) 4.8 m/s d) 5.6 m/s 715. Water is flowing at a rate of 3500 GPM. The inside radius is 8cm and coefficient of friction is 0.0181. What is the pressure drop over a length of 50 m? a) 317 kPa b) 301 kPa c) 341 kPa d) 386 kPa 716. The unit of kinematic viscosity in SI is described as:

a) Newton per meter b) Watt per meter c) Pascal second d) Sq. m per sec 717. Which of the following is not a unit of viscosity? a) Pa-sec b) Poise c) stoke d) Dyne 718. Which of the following describes laminar flow? a) NR = 2180 b) NR = 1989 c) NR = 4100 d) NR = 2100 719. Water is flowing in a pipe with radius of 30 cm at a velocity of 12 m/s. The density and viscosity of water are: Density = 1000 kg/m^3 ; Viscosity = 1.12 Pa-s. What is the Reynold’s number? a) 6428 b) 6386 c) 4534 d) 2187 720. What is the density of a solid that weights 194 N (43.9 lbf) in air and 130 N (29.4 lbf) in water? a) 3534.50 kg/m^3 b) 3031.25 kg/m^3 c) 2989.34 kg/m^3 d) 3235.96 kg/m^3 721. What is the buoyant force of a body that weighs 100 kg in air and 70 kg in water? a) 234.17 N b) 329.68 N c) 285.6 N d) 294.3 N 722. A venturi meter with a 15 cm throat is installed in a 20 cm pipe which inclined upward at an angle of 300 to the horizontal. If the distance between pressure tape along the pipe is 1 m, the differential pressure is 65 kPA. What is the discharge of water in m^3/s? Assume coefficient of 0.995. a) 0.109 m^3/s b) b) 0.536 m^3/s c) 0.233 m^3/s d) 0.0123 m^3/s 723. What is the pressure of point A in the tank if h = 2 feet from the water level? (g = 32.2 ft/s^2 and ρ = 1.94 slug/ft^3). a) 75 lbf/ft^2 b) 85 lbf/ft^2 c) 100 lbf/ft^2 d) 125 lbf/ft^2

724. Steam with an enthalpy of 700 kcal/kg enters a nozzle and leaves with an enthalpy of 650 kcal/kg. Find the initial velocity if steam leaves with a velocity of 700 m/s, assuming the nozzle is horizontal and disregarding heat losses. a) 276 m/s b) 296 m/s c) 376 m/s d) 267 m/s 725. The flow of water through a cast iron pipe is 6000 GPM. The pipe is 1 ½ ft nominal diameter. What is the velocity of water? a) 8.56 ft/sec b) 7.56 ft/sec c) 6.56 ft/sec d) 5.56 ft/sec 726. A perfect venturi with throat diameter of 2 in is placed horizontally in a pipe with a 2 inches is placed horizontally in a pipe with a 6 inches inside diameter. What is the difference between the pipe and venturi throat static pressure if the mass flow rate of water is 100 lb/sec. a) 38.8 lb/in^2 b) 36.8 lb/in^2 c) 37.8 lb/in^2 d) 35.8 lb/in^2 727. A deposit of P1000 is made in a bank account that pays 8% interest compounded annually. Approximately how much money will be in the account after 10 years? a) P2160 b) P2345 c) P1860 d) P1925 728. You need P4000 per year for your college four year course. Your father invested P5000 in 7% account for your education when you were born. If you withdraw P4000 at the end of your 17th, 18th,19th, and 20th birthday, how much money will be left in the account at the end of the 21st year? a) P2500 b) P3400 c) P1700 d) P4000 729. What is the acid test ratio? a) The ratio of the owners equity to the total current liabilities b) The ratio of all assets to total liabilities c) The ratio of gross margin to operating sales and administrative expenses d) The ratio of current assets (exclusive of inventory) to total current liabilities 730. An interest rate is quoted as being 7 1/2 % compounded quarterly. What is the effective annual interest rate? a) 21.8 % b) 7.71% c) 7.22% d) 15.78%

731. Mr. Ayala borrows P100,000.00 at 10% effective annual interest. He must pay back the loan over 30 years with uniform monthly payments due on the first day of each month. What does Mr. Ayala pay each month? a) P870 b) P846 c) P878 d) P839 732. A steel drum manufacturer incurs a yearly fixed operating cost of P200,000. Each drum manufactured cost P160 to produce and sells for P200. What is the manufacturers break-even sales volume in drums per year? a) 1250 b) 2500 c) 1000 d) 5000 733. The length of time, usually in years, for the cumulative net annual profit to equal the initial investments is called: a) receivable turnover b) return on investment c) price earning ratio d) pay back period 734. A local firm is establishing a sinking fund for the purpose of accumulating a sufficient capital to retire its outstanding bonds at maturity. The bonds are redeemable in 10 years, and their maturity value is P150,000. How much should be deposited each year if the fund pays interest at the rate of 3%? a) P12,547.14 b) P13,084.58 c) P14,094.85 d) P16,848.87 735. What is the formula for a straight line depreciation rate? a) 100% - %net salvage value over estimated life b) 100% net salvage value over estimated service life c) 100% net salvage value over estimated service life d) average net salvage value over estimated service life 736. A machine is under consideration for investment. The cost of the machine is P25,000. Each year it operates, the machine will generate a savings of P15,000. Given an effective annual interest rate of 18%, what is the discounted payback period, in years, on the investment of the machine? a) 1.75 years b) 3.17 years c) 1.67 years d) 2.16 years 737. A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average rate of 42%, what minimum rate of return, before payment of taxes, must the investment offer to be justified? a) 12.1 % b) 10.7%

c) 11.1 % d) 12.7 % 738. Liquid assets such as cash and other assets that can be converted quickly into cash such as accounts receivable, and merchandise is called: a) current assets b) fixed assets c) total assets d) land and buildings 739. Instead of the profits being paid out to the stockholders or owners as dividends, they are retained in the business and used to finance expansion. This is called: a) retained earnings b) flow back c) bonds d) deposits 740. A term used to describe payment of an employee for time spent on the property of the employer though not actually working at the job, e.g. time spent changing clothes to get ready for work or time spent travelling from the plant entrance to the place of work. a) portal-to-portal pay b) down-time pay c) call-in pay d) lost time pay 741. A machine has an initial cost of P50,000 and a salvage value of P10,000 after 10 years. What is the straight-line method depreciation rate as a percentage of the initial cost? a) 10% b) 8% c) 12% d) 9% 742. Fifteen years ago, P1000 was deposited in a bank account, and today it is worth P2370. The bank pays interest semi-annually. What was the interest rate paid on this account? a) 4.9% b) 5.8% c) 5.0% d) 3.8% 743. Company A purchases P200,000 of equipment in year zero. It decides to use straight-line depreciation over the expected 20 year life of the equipment. The interest rate is 14%. If its average tax rate is 40%, what is the present worth of the depreciation tax held? a) P3,500 b) P26,500 c) P98,700 d) P4,000 744. A product has a current selling price of P325. If its selling price is expected to decline at the rate of 10% per annum because of obsolescence, what will be its selling price four years hence? a) P213.23 b) P202.75 c) P302.75 d) P156.00

745. You borrow P3500 for one year from a friend at an interest rate of 1.5% per month instead of taking a loan from a bank at a rate of 18% per year. Compare how much money will you save or lose on the transaction. a) You will pay P155 more than if you borrowed from the bank b) You will save P55 by borrowing from your friend c) You will pay P85 more than if you borrowed from the bank d) You will pay P55 less than if you borrowed from the bank 746. Instead of paying P100,000 in an annual rent for offices space at the beginning of each year for the next 10 years, an engineering has decided to take out a 10 year P1,000,000 loan for a new building at 6% interest. The firm will invest P100,000 of the rent save and earn 18% annual interest on that amount. What will be the difference between the firm’s annual revenue and expenses? a) The firm will need P17,900 extra. b) The firm will break even. c) The firm will have P21,500 left over. d) The firm will need P13,000 extra. 747. The peso amount as earned from an investment or project is called: a) ROI b) Interest c) ROR d) Surplus 748. Those funds that are required to make the enterprise or project a going concern: a) Working capital b) Accumulated amount c) Banking d) Principal or present worth 749. You borrowed the amount of P10,000 for 120 days at 30% per annum simple interest. How much will be due at the end of 120 days? a) P10,100 b) P11,000 c) P11,600 d) P12,000 750. You obtain a loan of P0.5 million at the rate of 12% compounded annually in order to build a house. How much must you pay monthly to amortize a loan within a period of five years? a) P10,968 b) P11,968 c) P12,968 d) P13,968 751. An asset is purchased for P25,000. Its estimated life is 10 years after which it will be sold for P500. Find the depreciation for the first three years using the sum of the years digit. a) P11,000.72 b) P13,007.72 c) P12,027.27 d) P13,027.72 752. If P10,000 is invested at the end of each year for 6 years, at an annual interest of 10%, what is the total amount available upon the deposit of the sixth payment?

a) P77,651 b) P80,156 c) P78,156 d) P77,156 753. The original cost of an equipment is P50,000, the salvage value after 5 years is P8,000, and the rate of interest on the investment is 10%. Determine the capital recovery per year. a) P11,879.50 b) P12,897.50 c) P10,879.50 d) P11,379.50 754. A small shop in Leyte fabricates portable threshers for palay producers in the locality. The shop can produce each thresher at a labor cost of P2000. The cost of materials for each unit is P4500. The variable costs amount to 800 per unit, while fixed charges incurred per annum totals to P90,000. If the portable threshers are sold at P14,000 per unit, how many units must be produced and sold per annum to break even? a) 14 units b) 17 units c) 19 units d) 21 units 755. You want to save an amount of P100,000 at the end of 10 years. You are given 8% interest compounded quarterly. How much would you have to save per month in order to accumulate the sum of P100,000 ten years from now. a) P864.50 b) P590.00 c) P648.50 d) P548.40 756. With an interest at 10% compounded annually, after how many years will a deposit now of P1000 become P1331? a) 3 years b) 4 years c) 5 years d) 6 years 757. What rate (%) compounded quarterly is equivalent to 6% compounded semi-annually? a) 5.93 b) 5.99 c) 5.96 d) 5.9 758. Determine the break-even point in terms of number of units produced per month using the following data: (the costs are in pesos per unit) Selling price per unit = 600 Total monthly overhead expenses = 428,000 Labor cost = 115 Cost of materials = 76 Other variable cost = 2.32 a) 1036

b) 1044 c) 1053 d) 1025 759. The present value of an annuity of ―R‖ pesos payable annually for 8 years, with the first payment at the end of 10 years, is P187,481.25. Find the value of R if money is worth 5%. a) P45,000 b) P44,000 c) P42,000 d) P43,000 760. The amount of P50,000 is deposited in a bank. How much money are you going to withdraw after 8 years at 8% compounded annually? a) P83,546 b) P85,456 c) P92,546 d) P97.856 761. A machine has an initial cost of P300,000. Its salvage value after 5 years is P30,000. What is the straight line depreciation rate of the machine? a) 25% b) 23% c) 18% d) 15% 762. An asset is purchased for P120,000 and it can be sold for P12,000. Its estimated life is 10 years. Find the depreciation for the second year using the sum-of-the-years digit method. a) P17,672 b) P17,850 c) P18,276 d) P19,636 763. A bank offers 2% effective monthly interest. What is the effective annual rate? a) 26.82% b) 25.28% c) 24.65% d) 22.45% 764. How much must you invest today in order to accumulate P20,000 at 8% after 6 years? a) P20,004.50 b) P18,450.80 c) P15,305.60 d) P12,603.40 765. A machine that cost P1000 will save P0.10 per unit produced. Maintenance cost will be P100 annually. 2000 units are produced annually. What is the payback period at 12% interest? a) 8 years b) 9 years c) 10 years d) 12 years 766. An item is purchased for P100,000. Annual cost is P18,000. Using 10%, what is the capitalized cost of the perpetual service? a) P220,000

b) P250,000 c) P265,000 d) P280,000 767. A car was bought at P549,492.13 with 14% down payment and the remaining balance will be paid on installment basis with a monthly payment of P12,000 for 60 months. Determine the interest rate compounded annually. a) 19.56% b) 18.25% c) 16.45% d) 14.35% 768. A businessman wishes to earn 9% on his capital after payment of taxes. If the minimum rate of return, before payment of taxes is 12.1 %. What is the available average taxed rate of the income from a businessman’s investment? a) 25.6 % b) 24.6% c) 22.4% d) 20.5% 769. A debt of P1000 is to be paid in five equal yearly payments, each payment combining an amortization installment an interest at 8% on the previously unpaid balance of the debt. What should be the amount of each payment? a) P365.50 b) P310.20 c) P290.60 d) P250.45 770. A father wishes to develop a fund for his new born son’s college education. The fund is to pay P5000 on the 18th, 19th 20th and the 21st birthdays of his son. The fund will be built up by the deposit of a fixed sum on the son’s first to seventeenth birthdays. If the fund earns 4%, what should the yearly deposit into the fund be? a) P985.44 b) P845.66 c) P795.65 d) P765.88 771. A man owns a building on which there is a P100,000 mortgage which earns 6% per annum. The mortgage is being paid for in 20 equal year-end payments. After making 8 payments, the man desires to reduce his payments by refinancing the balance of the debt with a 30-year mortgage at 8%, and to be retired by equal annual payments. What would be the reduction in the yearly payment? a) P2,225.70 b) P2,550.80 c) P2,985.30 d) P3,120.90 772. An engineer borrows P150,000 at 12% effective annual interest. He must pay back the loan over 25 years with uniform monthly payments due on the first day of each month. What is this monthly payment? a) P1126 b) P1265

c) P1398 d) P1498 773. Funds are deposited in a savings account at an interest rate of 8% per annum compounded semi-annually. What is the initial amount that must be deposited to yield a total of P10,000 in 10 years? a) P1458 b) P2550 c) P3875 d) P4564 774. A machinery has an initial cost of P40,000 and results in an increase in annual maintenance costs of P2000. If the machinery saves the company P10,000 per year, in how many years will the machine pay for itself if compounding is considered? (i = 7%) a) 8 years b) 9 years c) 7 years d) 11 years 775. How long will it take a sum of money to double at a 5% annual percentage rate? a) 14.2 years b) 15.9 years c) 18.4 years d) 19.3 years 776. A sum of P1000 is invested now and left for eight years, at which time the principal is withdrawn. The interest that has accrued is left for another eight years. If the effective annual interest rate is 5%, what will be the withdrawal amount at the end of the 16th year? a) P980 b) P830 c) P780 d) P706 777. How many horsepower is 746 kW? a) 1 HP b) 100 HP c) 74.6 HP d) 1000 HP 778. What is the origin of the energy conservation equation used in flow system? a) Newton’s First Law of Motion b) Newton’s Second Law of Motion c) First Law of Thermodynamics d) Second Law of Thermodynamics 779. A volume of 560 cc of air is measured at a pressure of 10 mm Hg vacuum and a temperature of 200C. What will be the volume at standard pressure and 00C? a) 6.9 cc b) 535.5 cc c) 437.5 cc d) 1071 cc 780. What is the specific weight of a liquid substance if it specific weight relative to water is 8.77 and the specific weight of water is 62.4 lb per cubic foot?

a) 86.03 kN/m^3 b) 82.20 kN/m^3 c) 102.56 kN/m^3 d) 89.90 kN/m^3 781. Steam at a pressure of 12.5 MPa has a specific volume of 1160 x 10^-6 m^3 per kg and a specific enthalpy of 2560 kJ/kg. Find the internal energy per mass of steam. a) 2574.5 kJ per kg b) 2545.5 kJ per kg c) 2634.17 kJ per kg d) 2560.50 kJ per kg 782. A heat engine (Carnot cycle) has its intake and exhaust temperature of 2100C and 1200C respectively. What is its efficiency? a) 42.86% b) 34.85% c) 16.34% d) 18.63% 783. One kilogram of water is heated by 2000 Btu energy. What is the change in temperature in 0 K? a) 55.6 0K b) 54.1 0K c) 50.4 0K d) 48.5 0K 784. A pressure reading of 35 psi in kPa abs is: a) 427.3 b) 724 c) 273.4 d) 342.72 785. What conditions exists in a adiabatic throttling process? a) Enthalpy is variable b) Enthalpy is constant c) Entropy is constant d) Volume is constant 786. The specific gravity of a substance is the ratio of its density to the density of: a) mercury b) gas c) air d) water 787. What do you call the weight of the column of air above the earth’s surface? a) air pressure b) aerostatic pressure c) wind pressure d) atmospheric pressure 788. An air bubble rises from the bottom of a well where the temperature is 200C, to the surface where the temperature is 320C. Find the percent increase int eh volume of the bubble if the depth of the well is 8.5 m. Atmospheric pressure is 101,325 Pascals. a) 45.5%

b) 72.5% c) 89.76% d) 91.34% 789. Gas being heated at constant volume is undergoing the process: a) isentropic b) adiabatic c) isometric d) isobaric 790. What is the required heating energy in raising the temperature of a given amount of water when the energy applied is 1000 kw-hr with heat losses at 25%? a) 1000 b) 1500 c) 1333 d) 1250 791. What is the process that has no heat transfer? a) reversible b) isothermal c) polytropic d) adiabatic 792. Heat normally flowing from a high temperature body to a low temperature body where in it is impossible to convert heat without other effects is called the: a) First Law of Thermodynamics b) Second Law of Thermodynamics c) Third Law of Thermodynamics d) Zeroth Law of Thermodynamics 793. What equation applies in the first law of thermodynamics for an ideal gas in a reversible open steady state system? a) Q – W = U2 – U1 b) Q + VdP = H2 – H1 c) Q - VdP = H2 – H1 d) Q - PdV = H2 – H1 794. Form of energy associated with kinetic energy of the random motion of large number of molecules: a) internal energy b) kinetic energy c) heat of fusion d) heat 795. Which of the following is a set of standard condition of atmospheric air? a) 1 atm, 255 0K, 22 cu./kg mole b) 101.325 kPa, 273 0K, 22.4 cu./kg mole c) 101.325 kPa, 273 0K, 23.66 cu./kg mole d) 1 atm, 10 0C, 22.41 cu./kg mole 796. Steam flows into a turbine at a rate of 20 kg/s and 21 kw of heat/ are lost from the turbine. Ignoring elevation and other energy effects, calculate the power output from the turbine if the energy input is 2850 kJ/kg and energy output is 2410 kJ/kg. a) 8800 kw

b) 8821 kw c) 8779 kw d) 8634 kw 797. What pressure of water is a column of 100 cm high equivalent to: a) 9807 dynes/cm^2 b) 9807 N/m^2 c) 0.1 bar d) 100 kPa 798. An engine has an efficiency of 26%. It uses 2 gallons of gasoline per hour. Gasoline has heating value of 20,500 Btu/lb and a specific gravity of 0.80. What is the power output of the engine? a) 41.7 kw b) 0.33 kw c) 26.0 kw d) 20.8 kw 799. A thermodynamic system which undergoes a cyclic process during a positive amount of work done by the system: a) reversed Rankine cycle b) heat pump c) reversible-irreversible process d) heat engine 800. In a constant temperature, closed system process, 100 Btu of heat is transferred to the working fluid at 1000F. What is the change in entropy of the working fluid? a) 0.18 kJ/0K b) 0.57 kJ/0K c) 0.25 kJ/0K d) 0.34 kJ/0K 801. If an initial volume of an ideal gas is compressed to one-half of its original volume and to twice its original temperature, the pressure: a) doubles b) quadruples c) remains constant d) halves 802. (u + pv) is a quantity called: a) flow energy b) shaft work c) enthalpy d) internal energy 803. What horsepower is required to isothermally compress 800 ft^3 per minute of air from 14.7 psia to 120 psia? a) 13,800 HP b) 28 HP c) 256 HP d) 108 HP 804. A pressure of one bar is equivalent to: a) 110 kPa

b) 14 psi c) 720 mm Hg d) 1,000,000 dynes/cm^2 805. A pressure reading of 4.5 kg/cm^2 is equal to: a) 441.40 kPaa b) 451.60 kPaa c) 542.72 kPaa d) 582.92 kPaa 806. A water temperature rise of 380F in the condenser is equivalent to: a) 3.33 0C b) 33.3 0C c) 21.1 0C d) 38.1 0C 807. A boiler installed where the atmospheric pressure is 752 mm Hg has a pressure of 12 kg/cm^2. What is the absolute pressure in MPa? a) 1.277 MPa b) 1.772 MPa c) 2.177 MPa d) 3.771 MPa 808. An oil storage tank contains oil with specific gravity of 0.88 and depth of 20 meters. What is the absolute pressure in kPa? a) 274 b) 247 c) 724 d) 742 809. A pressure tank for a water pump system contains 2/3 water by volume when the pressure is 10 kg/cm^2 gauge. What is the absolute pressure at the bottom of the tank if the water is 2 meters depth? a) 1012 kPa b) 1201 kPa c) 1102 kPa d) 1080 kPa 810. Convert 360F to temperature difference to 0C. a) 36 b) 40 c) 20 d) 25 811. At what temperature are the two temperatures scales 0C and 0F equal? a) -20 0C b) -40 0C c) -30 0C d) 40 0C 812. The temperature inside a furnace is 320 0C and the temperature of the outside/ is -100C. What is the temperature difference in 0F? a) 495 0F b) 549 0F

c) 594 0F d) 645 0F 813. Convert 60 lbs/ft^3 to kN/m^3: a) 9.426 b) 7.356 c) 8.956 d) 5.479 814. A boiler feed pump delivers 200,000 kg of water per hour at 10 MPa and 2300C. What is the volume flow rate in m^3/sec? a) 0.0666 b) 0.0888 c) 0.0777 d) 0.0999 815. The radiator of a heating system was filled with dry and saturated steam at 0.15 MPa after which the valves on the radiator were closed. As a result of heat transfer to the room, the pressure drops to 0.10 MPa. What percentage of steam has condensed? a) 31.6% b) 25.4% c) 36.1% d) 45.7% 816. A throttling calorimeter receives a sample of steam from a steam main in which the pressure is 1 MPa. After throttling, the steam is at 100 kPa and 120 0C. What is the quality of steam in the steam main? a) 96.9 % b) 95.5% c) 99.6% d) 92.4% 817. Steam at 2.5 MPa and 320 0C expands through a nozzle to 1.5 MPa at the rate of 10,000 kg/hr. If the process occurs isentropically and the initial velocity is low, calculate the exit area of the nozzle. a) 853 x 10^-6 m^2 b) 358 x 10^-6 m^2 c) 835 x 10^-6 m^2 d) 583 x 10^-6 m^2 818. Water at a pressure of 10 MPa and the temperature of 2300C is throttled to a pressure of 1 MPa in an adiabatic process. What is the quality after throttling? a) 11.3% b) 12.5% c) 14.5% d) 19.3% 819. An air compressor delivers air to an air receiver having a volume of 2 m^3. At the start, the air in the receiver is at atmospheric condition of 250C and 100 kPa. After 5 minutes, the pressure of the air in the tank is 1500 kPa and the temperature is 600C. What is the capacity of the compressor in m^3/min of free air? a) 4.97 b) 5.55

c) 6.95 d) 8.45 820. At the suction of an air compressor, in which the conditions are 97.9 kPa and 270C, the air flow rate is 10.3 m^3/min. What is the volume flow rate at the free air conditions of 100 kPa and 200C? a) 7.635 m^3/min b) 6.590 m^3/min c) 9.848 m^3/min d) 3.568 m^3/min 821. Steam at 5 MPa and 3500C enters a turbine and expands isentropically to 0.01 MPa. If the steam flow rate is 100,000 kg/hr, determine the turbine power. a) 28.5 kw b) 22.5 kw c) 25.8 kw d) 33.8 kw