Mathematic Question for Board Exam

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

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

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

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. 17.1 1 fftt 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

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) d) 8 8//3 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 6. A man invested part of P20,000 at 18%

seats in the section. a) 1200 b) 980 c) 89 890 0 d) 750 10. One pipe can fill a tank in 6 hours an d another pip e can fill th e 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

and restinvestment at 16%. The annual fromthe 16% was P620 income less than

d) 11.2.18 The hours ten’s digit of a certain two digit

three times the annual investment. How muchincome did he from invest18% at 18%? a) P5,457.20 b) P6,457.20 c) P7,457.20 d) P8,457.20

number exceeds the unit’s digit digit. by four and is one less than twice the unit’s Find the number. a) 65 b) 75 c) 85 d) 95

12. The sum of two numbers is 35 and their product is 1 5. Find the sum of there reciprocal. a) 2/7 b) 7/3 c) 2/3 d) 5/2

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

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

19. Equations rel ating 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 le ngth 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 10 0 sq. m. Find the diff erence in length of the two squares.

solve the same problem differ by two minutes. Together they can solve 32 problems in one hour. How long will it t ake 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

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

c) 45 d)

22. sold drafting for P61 at a lossMaria of 25% on aher buyingpen price. Find2the

17. How many liters of water must be added to 35 liters of 89% hydrochloric acid solution to reduce its str ength to 75%? a) 3.53 b) 4.53 c) 5.53 d) 6.53

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 determinant. a) 31 b) 44

[ ], find its

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

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)

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

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) -0.11 -0.113, -0.8 -0.88 87 7 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

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%.

b) 76 c)

Rudy then sold the to Noel a profit of 20%. If Noel paidVCR P2856 moreat than it cost

d) 30.8Find 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

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

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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

the ratio and the first term. Assume the ratios are equal. a) --2 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

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

+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 equiva lent to repeating decimal 2.3524242424... a) 23273/9900 b) 23261/990

b) 1/2 c) 3/4 d) 1/4 42. A stack of bri cks 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

c) 23289/9900 d) 23264/9900

into the cookie jar. Each he put 50 centavos more into the jarmonth t han the month

concentration a) 19.55% 19.55% in the mixture?

before. After 12P5436. years he counted money; he had How muchhis 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

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

48. The sum of Kim’s and Kevin’s ages is 18. In three years, Kim will be twice as ol d 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 srcinally containing 30 liters of 10% salt solution. What is the percent

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

brand preference, satisfied with any of the 3 brands? a) 280 b) 230 c) 180 d) 130 57. The electric power which a transmission

52. The areas of tw o squares differ by 7 sq. ft. and their perimeters differ by 4 ft. Determine the sum of their areas. a) 25 ft^2 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

line can transmit is pro portional to the total product of its des ign voltage and current capacity, and inversely to the transmission distance. A 115 kilovolt line rated at 100 0 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

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

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

b) 308.1 ftft c) 241.5

3.10. What wasfoot? the weight of conc rete in pla ce per cubic

d) ft 56.305.9 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

a) 236 172 lb lb b) 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

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

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) 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 =

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 of the clock be together for the first time? a) 3:16.36 b) 3:14.32

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 0.7432 c) 0.7243 d) 0.7331 72. Find the 10th term of the geometric progression: 3, 6, 12, 24,.... a) 1536

c) d) 3:12.30 3:13.37

b) 1653 c) 1635

67. The the squares of the digits ofdifference a two digitofpositive number is 27. If the digits are reversed in order and the resulting number subtracted from the srcinal number, the difference is also 27. What is the srcinal number? a) 63 b) 54 c) 48

d) 73.3156 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,

66. What time after 3 o’clock will the hands

6, and z = 3. Find the value of ―w‖ when x = 1,y=4,andz=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?

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

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

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 are an aninf infinite inite no. no. of value values s that 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?

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) 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:

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

x –x 1/x a) = -1= 0? b) x = 1, 1/2 c) x = 1 d 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: a x – b = cx + d a) x = (a – b)/(c + d) b) x = = (b + d)/(a – c) c) x = (a – d)/(c – b)

b) and527 chickens c) 96 goats cats and dogs

d) x = (c + d)/(a – c) 87. Divide:15 x^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)

d) goats and chickens 79.13 Express 5y –20[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?

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 c)  d) 89. Find the value of x in the equation: csc x + cot x = 3 a) π/5

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b) /4 c) π/3 d) π/2

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

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

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

a) 0.194 to ________. 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 wit h 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

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

counterclockwise is: a) -810 deg

c) 2/(1 tan1 A) d) csc A– +

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

102. 2A –Determine cos A)/(sinthe A).simplified form of (cos 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: arc tan (x + 1) + arctan (x – 1) = arctan (12). a) 1.50 b) 1.34

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

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 ofx. 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 ______.

shortest distance of tower C to the highway. a) 364 m b) 374 m 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

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

114. Solve A for t he 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 deg ree reess 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

109. If theangle sidesare of a6,parallelogram and an included 10, and 100 degrees

116. Sin A cos B to:

respectively, find the length of the shorter diagonal. a) 10.63 b) 10.37 c) 10.73 d) 10.23 110. What is t he value of log 2 5 + log 3 5? a) 7.39 b) 3.79

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

– cos A sin B is equivalent

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 / log 10 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 =

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

length of the side a. a) 124.64 m b) 142.24 m c) 130.5 m

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 th e 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) 103.00 m 122. An observer wishes to determine the height of the tower. He takes sight at the top of th e tower fr om 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 lo g to the base of

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

1000^3.3? a) 9.9

c) 89 d)

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

130. Thethe angle of the elevation ofis the B from top of tower A 28top degtower 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 plan e. If the height of the tower B is 120 m, find the height of tower A. a) 87.2 m b) 90.7 m

30°30’, b = 100 m and c = 200 m. Find the

c) 79.3 m d) 66.3 m 131. Evaluate the log 6 845 = x. a) 3.76 b) 5.84 c) 4.48 d) 2.98

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

132. Find the value of lo g 8 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

limit?

135. Sin 2θ is equal to: a) 2 sin θ cos θ

b) 1/2 sin c) sin cos 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

) is also equal to: a) sec^2 b)cos^2

θ

c) d) csc^2 sin θ 138. Derive the formula of each interior angle (in degrees). a) (no. of sides – 2)180 b) [(no. of si sides des – 2)180/no. of sides] c) [(no. of sides – 1)180/no. of sides] d) [no. of sides – 2]/180

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b) 6 c) 9 d) 0 141. Given the three sides of a triangle: 2, 3, 4. What is th e angle in radians oppos ite 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 ar e at (3 , 0, 0), (3, 3, 0), (0, 0,

4) and (0,units 3, 4). a) 12 sq. b)14 sq. units c) 15 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 tri angle with right angle at C. CD is perpendicular to AB. BC = 4 and CD = 1. Find the area of th e triangle ABC. a) 2.95 b) 2.55 c) 2.07

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

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

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

d) heptagon 149. A regular dodecagon is ins cribed 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

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.

circle. Also, can be calculated removing theithole. The method isbycalled:

Determine the area inside and to the larger pentagon but outs ideconcentric of the

a) Law ofReduction Extremities b) Lawof 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. sq. units

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 to uching its circumference is inscribed. What is the area of the part not covered by the star? a) 60.2 m^2

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

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

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

161. The area of a circle circumscribing a

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

the goat can reach 1 ft farther than the rope length. What is th e 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

d) 493.62 163. Find cm^2 each interior angle of a hexagon.

170. quadrilateral havemsides equal to 12 m, 20Am, 8 m and 16.97 respectively. If

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

the sumfind of the angles is e qual to 225, thetwo areaopposite of the quadrilateral. a) 168 b) 100 c) 124 d) 158 171. The area of a circle inscribed in a

hexagon is 144

m^2. Find the area of the

hexagon is 144 hexagon.

m^2. Find the area of the

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

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.

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 3 0 degrees and the radius is 15 cm. What is the area of the sector. a) 59.8 cm^2 b) 58.9 cm^2

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

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 circ le.

181. The circumference of a great circle of a

sphere is 18π. Find the volume of the sphere.

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

a) 3053.6 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 b e cut by a plane parallel to its base so that the two solids of equal weight will be formed? a) 3.97 ft ft b) 2.87 ft

units lessof than base. Find the if the areas theits triangles differ byaltitude, 21 square

c) d) 4.97 5.97 ft ft

units. a) 6 & 12 b) 5 &11 c) 3 & 9 d) 4 & 10 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.

183. Find balloon the increase volume spherical wheninits radiusofisa increased from 2 to 3 inches. a) 75. 99 cu. in. b) 74.59 cu. in. c) 74.12 cu. in. d) 79 79.59 .59 ccu. u. in. 184. If the lateral area of a right cylinder is 88 and its volume is 220, find its radius.

a) 72π b) 64π c) 23 π

d) 16 π

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?

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

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.

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 no t occupied by the block? a) 4713.56 b) 3360.14 c) 4133.25 d) 5346.42

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

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.

and baseof diameter of 12 cm. It holdsFind water to a adepth 18 cm above its vertex.

a) 4066.67m^3 m^3 b)5066.67

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

c) d) 6066.67 7066.67 m^3 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

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

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

marbles placed 50 pieces of th e 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 pul verized coal to fuel a boiler, has a thickness of 2 cm and

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 th e base is 15 cm. Calculate the volume of the pyramid.

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 th e cone? a) 44% b) 56% c) 46%

a) 1785 b) 1875 cm^3 cm^3

d) 65% 206. Each side of a cube is in creased by 1%.

c) d) 5178 5871 cm^3 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

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 w ater. The pipe valve is open

to allow the water to flow to the smaller tan k until it is fu ll. 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.

b) upward c) to the left d) downward 214. A line with a curve approaches indefinitely near as its tracing point passes off infi nitely is called the: a) tangent

a)  b)   c)  d) 208. A pyramid has a square base of 8 m on a side and an altitude of 1 0 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) 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 th e line y = 5 and its focus is at the point (4, -3). a) 20 b) 18 c) 16

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 xintercept 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

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/(4 ) in c) 2 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) parabola circle c) 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

227. Point P(x, y) moves with a distance from point (0, 1) one half of its di stance 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

_____________. 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)

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

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)

230. Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x – 6y+25=0. a) 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

c) -2) d) (-1, (1, 1)

232. Findx^2 the +value of4x k for which the equation y^2 + – 2y – k=0,

226. passing (2, 2).of Find A theline equation ofthrough th e line aifpoint th e length

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 i s 4. a) x^2 x^2 + y^2 – 6x + 10 0y y + 18 = 0 b) x^2 + y^2 + 6x + 10y + 18 = 0

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

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 is perpendicular to 2x – By+2=0. a) 5 b) 4 c) 3

–7=0

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

d) 2 235. In a Cartesian coordinates, the coordinates of a square are (1, 1), (0, 8), (4, 5), and (-3, 4). What is t he 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)

c) 6 d) 4 242. Find the distance between the lines, 3x + y – 12=0and3x+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

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

244. Find major axis of the ellipse x^2 + 4y^2 – 2x the – 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 6 4 m. Find the width of th e 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

239. line segment 6) and (9, y)The is bisected by theconnecting point (7, 3).(x,Find the values of x and y. a) 33, 12 b) b) 5 5,, 0 c) 6, 9 d) 14, 6 240. A line passes through (1, -3) and (-4, 2). Write the equation of the line insl opeintercept form. a) y – 4 = x

√ √ √ √

b) 5 c) 15π d) 20π



b) 1.90 c) 1.70 d) 1.60 248. The equation of a line that int ercepts the x-axis at x = 4 and the y-axis at y = - 6 is: a) 3x + 2y = 12

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

b) 2x – 3y = 12 c) 3x – 2y 2y = 12 12 d) 2x – 3y = -12 249. What is th e 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

256. What is the center of th e 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

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 lin e

258. The equation 9x^2 + 16y^2 + 54x 64y = -1 describes: a) a hyperbola b) asphere 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

with a) 3xa–slope y + 1of =3 0 and a y-intercept of 1.

260. Determine the curve: 9x ^2 + 6y^2 + 2x +3y+9=0.

b) c)3x+y+1=0 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

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

259. Find the maximum point o f 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.

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

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

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?

c) 72 d) 92 263. Water running out a conical funnel at the rate of 1 cu. in per second. If th e 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 dr opping 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

a) 25x b) 30x

derivative of composite functions. a) Logarithmic differentiation

c) d) 18 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

b) Chain rule differentiation c) Trigonometric d) Implicit differentiation 265. The volume of the sphere is inc reasing 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 p ulling 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

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

b) -0.85 m/s c) -0.75 m/s d) -0.65 m/s 267. If th e 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?

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

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

270. Three sides of a trapezoid are each 8

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

cm How long is thehas fourth side when the long. area of the trapezoid t he greatest

277. Water is pouring into a swimming pool. After t hours there are t + gallons in the

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

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) 1/(4 ) in c) 2 in d) π^2 in

√

b) 8 c) 0 d) 16 279. Evaluate Lim [(x - 4)/(x^2 as x approaches 4. a) undefined b) 0

– x – 12)]

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 maximu m, minimum and inflection points. a) (-2, 28), (2, -4), & (0 (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 tan gent and normal a) 5x + to 4ythe + 3curve. = 0 & 4x – 5y – 14 = 0 b) 14=0 c) 5x 5x +– 4y 4y+– 3= 3= 0& 0& 4x 4x +5 +5 y y –+1 4= 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. Findrate the change point inofthe at which theparabola ordinatey^2 and= 4x



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

b) 2u ln

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

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

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

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) d) 24

c) d) infinity 0

297. Find the second of y with respect to x for: 4x^2 derivative + 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

305. Differentiate: a) [(x^2 + 1)^1/2]/2(x^2 + 2)^1/2 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

u; for h = a) ^2x

^2u.

c) 2π^2u ln π

d) 2 ^2u 299. Find y’ if y = x ln x – x.

a) ln x b) x ln x c) (ln x)/x

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

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 +

of the curve then x = 2. a) -2.21 b) -4.94 c) -3.25 d) -2.22 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.

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 pointon the curve x^2 = 2y which is nearest to the point (4, 1).

a) 27.76 cm, 47.8 cm b) 20.45 cm, 35.6 cm c) 22.24 cm 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 th e 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

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:

d) 0.84 312. Anm/min isosceles triangle with equal sides

a) (y^-2/3)/3 b) 3y^2/3

of 20 cm hasthe these sides at variable angles with base. Determine the equal 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

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

309. Find y’ = arcsin cos x.



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 rd d) 9[x to the 3rd power – (x – 1) to the 3 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?

√

√

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 xx – 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

b) 9/8 gph gph a) 1/2 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

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 sqrt(2) (2) cos cos ((x/2) 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.

b) 6 c) 9

a) 32/2 b) 20/3

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

c) d) 16/3 64/3 333. Evaluate: integral of cos^8 3A dA from

0 to

/6.

a) 35π/768

b) 45 /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

342. An area in the xy plane is bounded by the following lines: x = 0 (y-axis), y = 0 (xaxis), 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

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 e^x + 1)^ 1)^2 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

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) 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.

b) 5.955 c) 5.595 d) 9.955 345. Evaluate integral of 12 sin^5 x cos^5 x

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

fromz=0toz=

/2.

dx from 0 to

/2.

a) 0.20 b) 0.50 c) 0.25 d) 0.35 346. Evaluate integral of x(x from 5 to 6. a) 0.456 b) 0.587

– 5)^12 dx

a) 1/2 b) 4/5

c) d) 0.708 0.672

c) d) 1/4 2/3 341. Integrate 1/(3x + 4) with respect to x and evaluate the result fr om x = 0 to x = 2. a) 0.278 b) 0.336 c) 0.252 d) 0.305

347. the line areaxbounded y^2 =What x andis the – 4=0. by the curve a) 32/3 b) 34/7 c) 64/3 d) 16/3 348. Find the area bounded by the curve r =

8 cos 2 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 ofthe region bounded by

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

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

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

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=0and the y-axis. What is the volume generated when the area is resolved about the line y –

d) acceleration 358. A ball is thrown upward with an initial velocity of 50 ft/s. How high does it go? a) 39 ft ft b) 30 ft c) 20 ft d) 45 359. It takes an airplane one hour and fortyfive 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

the polar curve r^2 = a^2 cos 2 .

2=0? a) 28.41

b) c) 375 450 mph mph

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

d) 525 mphthe total kinetic energy of a 360 When system is the same as before and after the collision of two bodies, it is cal led: 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

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

b) 675 kph c) 450 kph d) 750 kph 362. The periodic oscillations either up or down or ba ck 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

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 th e 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 ______________.

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

b) the object’s momentum to decrease c) the object’s momentum to increase d) the object’s momentum to remain

second. It then rotates at the same speed for 2 seconds before decelerating to rest in one-

d) 2.45 371. In m/s^2 a hydraulic press, the small cylinder

third second.ofDetermine theduring total number of revolutions the flywheel the entire time interval? a) 8.06 rev b) 9.12 rev c) 6.90 rev d) 3.05

has a diameter of 8 cm, larger piston has a diameter of while 2 cm. the 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

a) the object’s momentum to change

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

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

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

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

to which it ris es? 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 cal led: 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

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

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) 0.866 377. Momentum is a property related to the

d) 59AkN kN 383. ball is dropped from a building 100

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 slugft/sec?

m high. If time the mass of the is 10the grams, after what will the ballball strikes earth? a) 5.61 s b) 2.45 s c) 4.52 s d) 4.42 s 384. A 900 N weight ha ngs 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

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

385. A plane dropped a bomb atan elevation 1000 meters from the ground intended to hit a target wh ich is 2 00 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 th e minimum distance can a truck slide on a horizontal asphalt road if it is travelling at 25 m/s? The coefficient of

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 thro wn 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 srcinal

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

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

b) 0.310 c) µµ >< 0.310

(mass kg)of of10 radius rotating at an angular0.50 speed rpm 15 forcm 6 seconds.

d) µ
level? a) 890 m b) 883 m 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

a) 0.001 kg-m^2 kg-m^2 b)0.002 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?

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 p ushed 5 feet horizontally? a) 1350.3 ft-lb b) 1690 ft-lb c) 1980 ft-lb

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 th e ground with a velocity of: a) 37 ft/sec

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

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

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

b) 80 m/sec^2 c) -80 m/sec^2

level groundaattotal the distance base of the building, it has covered of 150 m. How

d) 5.0 400. Am/sec^2 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 JJ c) 200 J d) 490.5 J

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 tra velling 55 mph will not skid sideways even in the absence

of friction. At what angle should the curve bebanked? a) 0.159 deg b) 75 deg c) 6.411 deg d) 14.2 deg 407. An airplane flying horizontally at a

b) 507 m 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 N

speed of 20 0 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

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

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

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

elevator a) 339 Nduring its ascent.

d) 14.7 416. Them/sec position of a body weighing 72.6

b) 245 NN 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

kg is given themeters expression S= + 3t + 4, where S by is in and t is in 5t^2 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

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 ft

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 cubi c

foot. The weight of a cast iron block 14‖ x

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

12‖1120 x 18‖lbsis: a) 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:

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 equi valent to: a) 746 watts watts

a) ellipse b) parabola

b) 7460 watts watts c) 74.6

c) of a circle d) part hyperbola 423. What is the name for a vector that represent the sum of two vectors? a) moment b) torque c) scalar d) resultant

d) 7.46 wattsis a true statement about the 429. Which 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%

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

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

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 ho w many Mega Newton? a) 12,000 b) 120 c) 1,200 d) 120,000 440. Factor the expression ( 289x^3 204x^2 + 36x )

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

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

435. happens to the acceleration if the massWhat is tripled and the force remains the

c) d) xyz (xyz)^(n-1)

same? a) it will be tripled b) it will be 1/3 of the srcinal c) it will remain the same d) it w ill be 3 times the srcinal 436. Which number has five significant digits? a)0.01410 b)0.00101

443. If xto: raise to the one half of one equals 4, x equal a) 24 b) 8 c) 12 d) 16 444. If the numbers one and above divided byzero 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) 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]

c) x = 3/5 and y = 5/3 d) x = 3/ 3/2 2 aand nd y = = 5/ 5/3 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

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 th e 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 sa tisfy the equation,

b) 150 kg and 350 kg c) 200 kg and 300 kg d) 250 kg and 250 kg 448. Logarithm of 10 th root of, x raise to 10 equals to: a) log x b) ( logx^(1/10) ) / 10 c) 10 log x d) log x^10 449. What is th e natural logarithm of e to the a plus b power? a) ab b) log ab

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.

c) + b ( a + b) d) a 2.718

a)yy == 4, y y= =-4,-2 ±1±1 b) +2x, x= =±1±1and and -2x, = x=

450. What is the logarithm of negative one hundred? a) No logarithm b) Zero c) Positive log d) Negative log 451. The logarithm of1 to base e is: a) One b) 2.718

c) = 2, y = 3 and x = -2, y = -3 d) xx=2,y=-2andx=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

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

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

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: (3x1)/(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

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

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 km

that0.571 it is red or white: a)

b) c) 180 200 km km

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)

d) 150 470. A km 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 be1600 miles apart? a) 533

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

b) 733 c) 633 d) 833 472. It takes Butch twice as long as it takes Dan to do a certain piece of wo rk. 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

Between two to three hours, he returned to his office noticing the hands of the clock

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 ha s a perimeter of 12 0 meters and an area of 800 square meters. Find the length and width of th e lot. a) 10m and 30m b) 30m and 20m

interchanged. At wha t 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.

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 fart her from the foot of the pole than the other two equal wire s. Find the length of the wires. a) 25m and 30m b) 15m and 40m c)20m and 35m d) 50 and 10m

a) 12 b) 18

481. Inwill a racing there are 240 cars which have contest, fuel provisions that will last

c) d) 15 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

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

noticed the clock at past two o’clock.

482. A pile of boile r 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

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

c) 40 d) 55 483. A production supervisor submitted the following report on the average rate of production of printed circuit boards(PCB) in

a) 50 workers b) 60 workers c) 55 workers d) 70 workers 484. A man bought 20 calculators for

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

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

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

noted that 180had members had in fought in War Korea and that 70% taken part World II,

493. as: A polygon with fifteen sides is termed

whileWorld 10% of theIImembers hadHow fought in both War and Korea. many members are there together? a) 400 b) 500 c) 450 d) 700 487. An angle greater t han a straight angle and less than two straight angles is called:

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

an assembly line: ―1.5 workers produce 12 PCB’s in 2 hours‖. How many wor kers are employed in the assembly line working 40 hours each per week with a weekly

production of 8000 PCB’s/

d) a corollary 495. A rectangle with equal sides is termed as: a) rhombus b) trapezoid c) square d) parallelogram

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

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:

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 thro ugh the interior of the polygon. a) equilateral b) isoperimetric c) congruent d) none of the above

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

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 and ta tan n A = 5/ 39 39^ ^(1/2 (1/2))

b) c) coplanar concurrent

d) cosGiven A = 8/5 and tanwith A = angle 5/8 C=29 0, side 508. a triangle

d) congruent 501. Points wh ich 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:

afor =132 units angle B. and side b=233.32 units. Solve a) B=1200 0 b) B=122.5 0 c) B=125.2 d) B=1300 509. Simplify: cos2 ( 1+tan 2 θ )

a) tan 2 b) 1

c) sin 2 d) cos θ

517. A transit set-up 112.1 feet from the base of a vertical chimney reads 32 030’ with the crosshairs set on top of the chimney. With the telescope level, the vertical rod at the base of th e chimney is 5. 1 feet. How tall is the chimney? a) 66.3 ft

511. What is the sine of 840 0? 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 90 0 and

b) 71.4 ft c) 76.5 ft d) 170.9 ft 518. If sin θ – cos θ = 1/3, what is the value

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?

520. Solve for x: x = 1- (sin θ-cos θ)^2

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 15 0 and 400, respectively. The height of the tower is 100m. Find the height of the Nipa hut. a) 78.08 m

a) 01 b)

b) c) 87.08 68.07m m

c) d) 3^(1/2) 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

d) 77.08 522. ShipmA started sailing N40 032’E at the rate of 3 mph. After 2 hours, ship B started from the same port going S45 018’E at the rate of 4 mph. After how many hours will the second ship be exactly south of shi p A? a) 2.25 hrs b)2.97 hrs c) 3.73 hrs

510. What is the cosine of 120 0? a) -0.500 b) -0.450 c) -0.866 d) 0.500

of in 2 θ?

a) 1/3 b) 1/9 c) 8/9 d) 4/9

519. If co s of x if x = 1 a) -2 b) -1/3 c) 4/3 d) 2/3

= 3^(1/2)/2, then find the value – tan2 θ:

a) sin cos b) -2cos θ c) cos 2

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

b) 75.7210 0 c) 77.157 d) 82.5170 530. A pole which leans 10 015’ from the vertical towards the sun casts a shadow 9.43m long on the ground when the angle of elevation of the sun is 54 050’. Find the

524. Two ships started sailing from the same 0E at 30 mph while point. One travelled N20 the other travelled S50 0E 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

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 29 010’ 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

b)420 m^2 c) 470 m^2 d) 530 m^2 526. Solve for x: Arcsin 2x - Arcsinx = 15 0 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

directly south of a building 35 m high. The angles of depression to the points are 29 010’ 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 = 110 0

528. Given: Triangle whose angle A is 320 and a = 75 m. TheABC opposite side of angle

0 b) C C= = 85.2 c) 77.1

0 B 100m. Find angle C. a) is 100 0 b) 103 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

d) C= 43.5 triangle ABC whose angle A is 534. Given 320 and opposite side of A is 75 meters. The opposite side of a ngle B is 1 00 m. find the opposite side of ang le C. a) c = 137.8 m b) c = 181.2 m c) c = 117.7 m d) c = 127.8 m

0

0

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

541. The perimeter of a sector i s 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

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) 2 27 7 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) 32 323.5 3.57 sq. 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 31.8 .83 3 ssq. q. 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) 386.54 sq. cm d) 452.24 sq. cm

c) 398.99 sq. m d) 40 409.4 9.44 sq. 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.

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 le ngth 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

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

bigg a) 4er square is:

b) c) 50 60 sq. sq. cm cm

b) c) 39 d) 6 540. A sector has a radius o f 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. sq. cm

d) 40 40The sq. sq. diagonals cm 546. 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

d) 12 cm 554. The volume of a cube is re duced by how much if all sides are halved? a) 1/8 b) 5/8 c) 6/8 d) 7/8

548 How many cubic meters is 10 0 gallons of liquid? a) 1.638 b) 37.85 c) 3.7850 d) 0.37854 549. How many cubic meters is 1 00 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.

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

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 60 0 is bent to form a cross. Find the volume of the cone. a) (35)^(1/2) π / 3

552. A spherical wedge of a sphere of radius 10 cm has an angle of 40 0. Its volume is:

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 ft 558. The surface area of a sphere is 4 r^2. Find the percentage increase in its diameter when the surface area increases by 21%.

a) 523.42 b) 465.42cm^3 cm^3

a) 5% b) 10%

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

c) d) 15% 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%

b) (35)^(1/2) c) 35 / 3^(1/2) d) 35 / 3

560. Determine the estimated weight of st eel 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 b oard feet in a plank 2 in.

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 bas e 5.5m x 1.8m, and altitude of 1.5 m. Find the volume of the foundation.

thick, 6 in. wide and 20 ft l ong 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

a) 12.5 m^3 b) 14.2 m^3 c) 15.6 m^3 d) 16.4 m^3 567. An elevated water ta nk 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 t ake to fully fill the tank starting empty? a) 4.668 hrs b) 5.468 hrs c) 7.725 hrs d) 9.245 hrs

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 de pth 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

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).

150 kg so thatcm. the Find volume the radius. metal is 24,000 cubic the of inner

a) y=x b) y=-2x+2

a)35 30cm cm b) c) 40 cm d) 45 cm 565. A circular cylin drical 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

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 y=2x-3 c) y=2/3x+1 d) y=2x+3

572. The equation y=a1+a2 x is an algebraic expression for whic h 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

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 srcin b) are coincident

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 - y 2^2))^(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.

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

a) 6π b) 3 c) 9 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

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

c) d) 3x+5y+34=0 3x-5y+34=0

equation : 2x^2 – 8x + 2y^2 + 12y = 1. a) 35.4 sq.isunits

d) 12 π

578. If theisdistance the points and (3,y) 13, whatbetween is the value of y? (8,7) a) 5 b) -19 c) 19 or -5 d) 5 or -19 579. Which of th e following is perpendicular to the line x/3 + y/4 =1? a) x-4y-8=0

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

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^ [2x^2 2 +4x +4x +1]^ +1]^(1/2) (1/2) d) (4x + 4)/ [2x^2 +4x +1]^(1/2) 595. Find the second derivative of y = (x^2

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

+ 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

590. Find the area of th e 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

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 th e 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

derivative of y = x^a? a) ax

d) 1 What is the slope of the curve y = x^2 600.

b) x^(a-1) c) aa x^(a-1) x^(a-1) d) (a-1)x 593. Find the derivative of F(x) = [x^3 – (x1)^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^2– (x-1)^2]

4x a) 0as it passes through the srcin? 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

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

c) y = 2x - 1 d) y=4x+1 603. Given Y1 =4x+3andY 2 = x^2 + C, find C such that Y 2 is tangent to Y 1. 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

d) 3000 609. Compute the following limit x+2

610. Find the equation of th e tangent to the ellipse: 4x^2 + 9y^2 = 40 at poi nt (1,-2). a) 2x – 9y – 20 = 0 b) 9x+5y+2=0 c) 9x – 2y+20=0 d) 2x + 9y +20 = 0

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.

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

a)1.73 0.67ft^2 ft^2/ s/ s b)

its a) Lwidth. = 3W

c) d) 3.0 3.7 ft^2 ft^2 //ss 607. What is the maximum of the function y = -x^3 +3x for x=-1? a) -2 b) -1 c) 0 d) 2

b) c) L L == 4W 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

Lim

x →∞ x-2 a) 0 b) 1 c) 2

d) ∞

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

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

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.

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

a) 16 2/3 cm cm x 16 2/3 cm b) 11 ½ cm x 11 ½ cm c) 12 1/3 cmx 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

maximum rate of return of investment. a) 8 MW b) 10 MW 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 spe ed to run the boat, other expenses independent from the speed amount to P100 per hour an d the distance is 200 km. a) 60 kph

less passengers. tours, theof the company allows For for group P0.50 discount

b) kph c) 100 70 kph

ticket pricemany for every passenger excess of 100. How passengers giveinthe maximum income? a) 110 b) 150 c) 120 d) 135 619. A tinsmith wishes to make a gutter of maximum cross-section (carrying capacity)

d) 30The kphstrength of a rectangular beam is 623. 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 sho uld the stake be

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

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 uni t 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

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 flow ing 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 le vel 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

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 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.

631. A helicopter is rising vertically from the ground at constant rate of 15 ft per second. When it is 2 50 feet off th e 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 at640 kph passes over a certain town at noon and a second

a) 1m b) 1.47m

plane going east 600 kphlater. is directly over he same town 15atminutes If the planes

c) d) 2.1m 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

are at the same altitude, theyflying be separating at 1:15 PM?how fast will 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

c) 32/23 d) 64/23 640. If it i s 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

one-half the product of one pair, plus onethird the product of anoth er 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 3x^5 ^5))//5 5 + (x (x^ ^4 4)/ )/2 + + (x (x^ ^3 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 c os x dx with respect to x:

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 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_

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 betw eenfunction. those limits gives the ___________ of the a) average b) middle c) intercept d) limit 639. Find the area bounded between y = 6x1 and y = x/4 + 3 by x=0 and the intersection point. a) 32/529 b) 16/23

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 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 x^3))^( ^(3/2 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

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) 15 3.9 sq. in

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

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 dee p 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 srcinally 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 su ch a rate that the

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 s q. units

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

c) d) 18 22 sq. sq. units units

d) tangent 658. What is the acceleration of a body that

653. An open cylindrical 3 feet in diameter and 4.5 feet hightank is full of water. It is then tilted until one-half of its bottom is exposed. How many gallons of wate r was spilled out? a) 187.4 gal gal b) 148.7 gal c) 178.4 gal d) 147.8 gal

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

649. Evaluate ∫ x^2a dx   + c  b)  + c

a)

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

d) 2.4525 kN 666. A shot is fired at an angle of 30 0 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

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

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 hor izontal 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

the rotational KE? a) 730 x 10^3 J b) 680 x 10^3 J c) 888 xx 10^3 10^3 JJ 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

d) 446.2 N 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

in SI unit: a) 32.2 ft/s^2

671. The property of thetobody which measures its resistance changes in motion:

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

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

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

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

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 30 0 with the horizontal and a velocity of 400 ft per sec. Find the height of the projectile. a) 600 ft b) 622 ft 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’

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). 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

b)320017’ c) 24 32’ 0 d) 19 28’ 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

will theasec coin touch the ground? a) 4.45

work done a) 2.936 kJby this force?

b) 3.45 sec c) 2.45 sec d) 1.45 sec 678. A bullet is fired at an angle of 75 0 with the horizontal with an initial velocity of 420 m/s. How high can it tra vel afte r 2 seconds? a) 840 m b) 792 m m c) 750 m

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 20 00 ft and f = 0.3. What banking angle to resist the centrifugal force? 0 a) 5.33 b) 5.990

Newton’s second law of motion says that the

c) 6.660 d) 7.770 685. A plane dropped a bomb atan 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

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

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 alevel plane at 30 0 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

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

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

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 30 0 with the horizontal. The angle of stat ic 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

d) 4497 lbsis fired horizontally at a 10 kg 689. A gun

c) kg d) 97.3 119 kg

block of wood at the embedded end of a in cord. The blocksuspended with the bullet 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

694. A 200of kgfricti crateonisbetween on a 30 the ramp. The coefficient 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

0

695. A 600 N block rests on a 30 0 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) 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

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

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

10 feet and the lowest point of th e 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 ar e 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.

th floor b) 14th c) 10 floor th d) 15 floor 702. A stone is dr opped from a cliff into the ocean. The sound of the impact of th e 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

Determine a) 256 kg the load on each leg.

drops perWhen second. The faucet is 18 above the sink. one drop strikes thecm sink,

b) 386 kg kg c) 296 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 srcinally 20 feet behind A , how long will it take B to overtake A. a) 18.6 sec

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 dro pped from a helicopter

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

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

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 ma kes an angle of 18 0 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

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 30 0 incline 10 meters above 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

ground. If the slightfrictionless, melting of the ice the renders the surface calculate

c) 12.1 m/s d) 17.84 m/s

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

713. Find the p ressure reading manometer is water 0.45 m Hg. Mercury is if 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 h 1 = 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

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

715. Water is flo wing 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 kin ematic viscosity in SI is described as: a) Newton per meter b) Watt per meter c) Pascal second d) Sq Sq.. m per s ec 717. Which of the following is not a unit of

b) 329.68 N c) 285.6 N d) 294.3 N N 722. A venturi meter with a 15 cm throat is installed in a 20 cm pipe which inclined upward at an angle of 30 0 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

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 f lowing in a pipe with radius of 30 cm at a velocity of 12 m/s. The density

tank if h = 2 feet from the water level? (g = 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 vel ocity if steam leaves with a velocity of 700 m/s, assuming the nozzle is horiz ontal and disregarding heat losses. a) 276 m/s

and viscosity of water are: Pa-s. Density = 1000 kg/m^3 ; Viscosity = 1.12 What is t he

b) c) 296 376 m/s m/s

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

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

32.2 ft/s^2 and ρ = 1.94 slug/ft^3).

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.

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

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

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:

education when you were born. If youth withdraw P4000 at the end of your 17 , 18th,19th, and 20th birthday, how much money will be left in the account at th e end of the 21 st 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

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

c) Theand ratio of gross margin to operating sales administrative expenses

b) P13,084.58 c) P14,094.85

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%

d) P16,848.87 735. What is t he formula for a straight line depreciation rate? a) 100% - %net %net salva salvage ge value value over over estimated life b) 100% net salvage value over estimated service life c) 100% net salvage value over estim ated 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

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

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%

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%

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

743. Company A purchases P200,000 of equipment in year zero. It decid es to use straight-line depreciation over the expected 20 year lif e 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

finance expansion. This is called: a) retained earnings

decline rate of 10%what per annum because at ofthe obsolescence, will be its

b) c) flow bondsback 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.

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

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

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 office s 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 expenses? a) The firm will need P17,900 extra. b) The firm will break even.

751. An asset is purchased for P25,000. Its estimated life is 10 years after which it will besold 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) 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

c) P78,156 d) P77,156 753. The srcinal 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

d) Principal or present 749. You borrowed theworth amount of P10,000

locality. can00. produce each at a laborThe costshop of P20 The cost of thresher

for 120 days 30% will per annum interest. Howatmuch be due simple 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 th e rate of 12% compounded annually in order

materials for each unitto is 800 P4500. variable costs amount per The 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

between the firm’s annual revenue and

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.

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) 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 semiannually? a) 5.93

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%

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

762. An asset is purchased for P120,000 and it can be sold for P1 2,000. Its es timated 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% 26.82% b) 25.28%

Cost = 76 of materials Other = 2.32variable cost 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

c) d) 24.65% 22.45% 764. much mustP20,000 you invest today in 6 orderHow to accumulate at 8% after 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

fund is to pay P5000 on the 18 th, 19th 20th and the 21st birthdays of his son. The fund will be built up by the deposit of a fixed sum

766. An item is purchased for P100,000. Annual cost is P1 8,000. 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%

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 beretired by equal annual payments. What would be the reduction in the yearly payment? a) P2,225.70 b) P2,550.80

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 a) 25.6 % b) 24.6% c) 22.4% d) 20.5% 769. A debt of P1000 is to be paid in five

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 mont hly 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

equal yearlyanpayments, eachinstallment payment an combining amortization

compounded What is the initial amountsemi-annually. that must be deposited to

interest of at 8% on theWhat previously balance the debt. shouldunpaid 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

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

businessman’s investment?

on the son’s first to seventeenth birthdays. If the fund earns 4%, what sho uld the yearly deposit into the fund be? a) P985.44

year, in how many years will th e machine payfor itself if compounding is considered? (i = 7%) a) 8 years b)9 years c) 7 years d) 11 years

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

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

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 210 0C 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

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 srcin of the energy conservation equation used in flow system?

c) First Law of Thermodynamics d) Second Law of Thermodynamics

2000 Btu energy. What is th e change in temperature in 0K? 0 a) 55.6 K b) 54.1 0K 0 c) 50.4 K d) 48.5 0K 784. A pressure reading of 35 psi in kPa abs is: a) 427.3 b) 724 c) 273.4 d) 342.72 342.72 785. What conditions exists in a adiabatic

779. A volume air is measured at a pressure of of 10560 mmcc Hgofvacuum and a

throttling process? a) Enthalpy is variable

temperature of 20 C. What will volume at standard pressure andbe 0 0the C? 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

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

a) Newton’s First Law of Motion b) Newton’s Second Law of Motion

0

787. What do you call the weight of the a) air pressure b) aerostatic pressure c) wind pressure d) atmospheric pressure 788. An air bubble rises from the bottom of

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 = H 2 – H1 c) Q - VdP = H 2 – H1 d) Q - PdV = = H 2 – H1

a well where the temperature is 20 0C, to the surface where the temperature is 32 0C. 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

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 0 b) 10 101 1.32 .325 5 kPa, kPa, 273 K, 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

790. What is the required heating energy in raising the temperature of a given amount o f water when the energy applied is 1000 kwhr 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

turbine. Ignoring elevation and other energy effects, calculate the power output from the turbine if the energy input is 285 0 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) adiabatic 792. Heat normally flowing from a high

d) 100 798. AnkPa engine has an efficiency of 26%. It

temperature to a low where in it isbody impossible to temperature convert heatbody without other effects is calle d the: a) First Law of Thermodynamics b) Second Law of Thermodynamics c) Third Law of Thermodynamics d) Zeroth Law of Thermodynamics

uses 2 gallons of gasoline hour.and Gasoline has heating value of 20,500per Btu/lb 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 kw

column of air abo ve the earth’s surface?

799. A thermodynamic system which undergoes a cyclic process during a positive amount of wo rk done by the system: a) revers ed Rankine cycle b) heat pump c) reversible-irreversible process d) heat engine

d) 582.92 kPaa 806. A water temperature rise of 38 0F in the condenser is equivalent to: a) 3.33 0C b) 33.3 0C c) 21.1 0C d) 38.1 0C

800. In a constant temperature, closed system process, 100 Btu of hea t is transferred to the working fluid at 100 0F. What is t he change in entropy of the working fluid? a) 0.18 kJ/ 0K b) 0.57 kJ/ 0K c) 0.25 kJ/ 0K 0 d) 0.34 kJ/ K 801. If an initial volume of an ideal gas is compressed to one-half of its srcinal volume and to twice its srcinal temperature, the pressure: a) doubles b) quadruples

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

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 fr om 14.7 psia to 120 psia? a) 13,800 HP b)28 HP c) 256 HP

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

d) 108 HP 804. A pressure of one bar is equivalent to:

b) 40 c) 20

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) 25At what temperature are the two 811. temperatures scales 0C and 0F equal? a) -20 0C 0 b) -40 C c) -30 0C d) 40 0C 812. The temperature inside a furnace is 320 0 C and the temperature of the outside/ is -

100C. What is the temperature difference in 0 F? a) 495 0F b) 549 0F 0 c) 594 F d) 645 0F 813. Convert 60 lbs/ft^3 to kN/m^3:

a) 853 x 10^-6 m^2 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 230 0C is throttled to a pressure of 1 MPa in an adiabatic process.

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 230 0C. What is th e 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 whic h the valves on the radiator were closed. As a result of hea t transfer to

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 atmo spheric condition of 25 0C and 100 kPa. After 5 minutes, the pressure of the air in the tank is 1500 kPa and the temperature is 60 0C. What is the capacity of the compressor in m^3/min of free air? a) 4.97 b) 5.55

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 ste am 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) 6.95 d) 8.45 820. At the suction of an air com pressor, in which the conditions are 97.9 kPa and 27 0C, the air flow rate is 10.3 m^3/min. What is the volume flow rate at th e free air conditions of 100 kPa and 20 0C? 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 350 0C enters a turbine and expands isentropically to 0.01

c) d) 99.6% 92.4%

MPa. If thethe steam flowpower. rate is 100,000 kg/hr, determine turbine

0

817. Steam at 2.5to MPa C rate expands through a nozzle 1.5 and MPa320 at the of 10,000 kg/hr. If the process occurs isentropically and the initial velocity is low, calculate the exit area of the nozzle.

a) 28.5kw kw b)22.5 c) 25.8 kw d) 33.8 kw