Multiple Choice
Question
in
Engineering Mathematics
By JAS Tordillo
Encoded By:
Dajano, Jose Mari T.
Salavante, Marc-Ian
1. A man sold a book by mistake at 120% of the marked price instead of discounting the marked
price by 20%. If he sold the book for P14.40, what was the price for which he have sold the
book?
a) P8.00
b) P8.50
c) P9.00
d) P9.60
2. In how many ways can 9 books be arranged on a shelf so that 5 of the books are always
together?
a) 30,200
b) 25,400
c) 15,500
d) 14,400
3. If one third of the air tank is removed by each stroke of an air pump, what fractional part of
the total air is removed in 6 strokes?
a) 0.7122
b) 0.6122
c) 0.8122
d) 0.9122
4. If 3^x = 9^y and 27^y = 81^z, find x/z?
a) 3/5
b) 4/3
c) 3/8
d) 8/3
5. Determine x, so that x, 2x+7, 10x-7 will be geometric progression.
a) 7,-5/6
b) 7, -14/5
c) 7, -7/12
d) 7, -7/6
6. A man invested part of P20,000 at 18% and the rest at 16%. The annual income from 16%
investment was P620 less than three times the annual income from 18% investment. How much
did he invest at 18%?
a) P5,457.20
b) P6,457.20
c) P7,457.20
d) P8,457.20
7. The sum of four positive integers is 32. Find the greatest possible product of these four
numbers.
a) 5013
b) 645
c) 4069
d) 4913
8. A piece of paper is 0.05 in thick. Each time the paper is folded into half, the thickness is
doubled. If the paper was folded 12 times, how much thick in feet the folded paper be?
a) 10.1 ft
b) 12.1 ft
c) 15.1 ft
d) 17.1 ft
9. A seating section in a certain athletic stadium has 30 seats in the first row, 32 seats in the
second row, 34 seats in the third row, and so on, until the tenth row is reached, after which there
are ten rows each containing 50 seats. Find the total number of seats in the section.
a) 1200
b) 980
c) 890
d) 750
10. One pipe can fill a tank in 6 hours and another pipe can fill the same tank in 3 hours. A drain
pipe can empty the tank in 24 hours. With all three pipes open, how long will it take to fill in the
tank?
a) 5.18 hours
b) 4.18 hours
c) 3.18 hours
d) 2.18 hours
11. The ten’s digit of a certain two digit number exceeds the unit’s digit by four and is one less
than twice the unit’s digit. Find the number.
a) 65
b) 75
c) 85
d) 95
12. The sum of two numbers is 35 and their product is 15. Find the sum of there reciprocal.
a) 2/7
b) 7/3
c) 2/3
d) 5/2
13. The smallest natural number for which 2 natural numbers are factors.
a) Least common divisor
b) Least common denominator
c) Least common factor
d) Least common multiple
14. Ana is 5 years older than Beth. In 5 years, the product of their ages is 1.5 times the product of
their present ages. How old is Beth now?
a) 30
b) 25
c) 20
d) 15
15. The time required for the examinees to solve the same problem differ by two minutes.
Together they can solve 32 problems in one hour. How long will it take for the slower problem
solver to solve a problem?
a) 2 minutes
b) 3 minutes
c) 4 minutes
d) 5 minutes
16. Find the value of m that will make 4x^2 – 4mx + 4m ) 5 a perfect square trinomial.
a) 3
b) -2
c) 4
d) 5
17. How many liters of water must be added to 35 liters of 89% hydrochloric acid solution to
reduce its strength to 75%?
a) 3.53
b) 4.53
c) 5.53
d) 6.53
18. A purse contains $11.65 in quarters and dimes. If the total number of coins is 70, find how
many dimes are there.
a) 31
b) 35
c) 39
d) 42
19. Equations relating x and y that cannot readily be solved explicitly for y as a function of x or
for x as a function of y. Such equations may nonetheless determine y as a function of x or vice
versa, such function called _________.
a) logarithmic function
b) implicit function
c) explicit function
d) continuous function
20. A piece of wire of length 50 m is cut into two parts. Each part is then bent to form a square. It
is found that the total area of the square is 100 sq. m. Find the difference in length of the two
squares.
a) 6.62
b) 7.62
c) 8.62
d) 9.62
21. A tank is filled with an intake pipe that fills it in 2 hours and an outlet pipe that empty in 6
hours. If both pipes are left open, how long will it take to fill in the empty tank?
a) 1.5 hrs
b) 2.0 hrs
c) 2.8 hrs
d) 3 hrs
22. Maria sold a drafting pen for P612 at a loss of 25% on her buying price. Find the
corresponding loss or gain in percent if she had sold it for P635?
a) 20.18%
b) 11.18%
c) 22.18%
d) 28.18%
23. Divide 1/8 by 8.
a) 1/64
b) 18
c) 1
d) 64
24. Given 2 x 2 matrix [
9 4
], find its determinant.
7 8
a) 31
b) 44
c) -20
d) 20
25. If the sum is 220 and the first term is 10, find the common difference if the last term is 30.
a) 2
b) 5
c) 3
d) 2/3
26. Find the sum of the sequence 25, 30, 35, .....
a) (2/5)(n^2 + 9n)
b) (5/2)(n^2 + 9n)
c) (9/2)(n^2 + 9n)
d) (9/2)(n^2 – 9n)
27. Solve for x: √20 − 𝑥 = 𝑥.
a) 4, -5
b) -4, -5
c) -4, 5
d) no solution
28. Solve for x: 10x^2 + 10x + 1 =0.
a) -0.113, -0.887
b) -0.331, -0.788
c) -0.113, -0.788
d) -0.311, -0.887
29. The number x, 2x + 7, 10x – 7 form a Geometric Progression. Find the value of x.
a) 5
b) 6
c) 7
d) 8
30. Find the 30th term of A.P. 4,7,10,...
a) 91
b) 90
c) 88
d) 75
31. Find the sum of the first 10 terms of the geometric progression 2, 4, 8, 16,...
a) 1023
b) 2046
c) 225
d) 1596
32. Find the sum of the infinite geometric progression 6, -2, 2/3,...
a) 9/2
b) 5/2
c) 11/2
d) 7/2
33. Find the ratio of an infinite geometric series if the sum is 2 and the first term is ½.
a) 1/3
b)1/2
c) 3/4
d) 1/4
34. Find the 1987th digit in the decimal equivalent to 1785/9999 starting from the decimal point.
a) 8
b) 1
c) 7
d) 5
35. What is the lowest common factor of 10 and 32.
a) 320
b) 2
c) 180
d) 90
36. Ten less than four times a certain number is 14. Determine the number.
a) 6
b) 7
c) 8
d) 9
37. Jolo bought a second hand betamax VCR and sold it to Rudy at a profit of 40%. Rudy then
sold the VCR to Noel at a profit of 20%. If Noel paid P2856 more than it cost to Jolo, how much
did Jolo paid the unit?
a) P4000
b) 4100
c) 4200
d) P4300
38. A club of 40 executives, 33 likes to smoke Malboro, and 20 likes to smoke Philip Morris.
How many like both?
a) 13
b) 10
c) 11
d) 12
39. A merchant has three items on sale, namely a radio for P50, a clock for P30 and a flashlight
for P1.00. At the end of the day, he has sold a total of 100 of the three items and has taken
exactly P1000 on the total sales. How many radios did he sale?
a) 16
b) 20
c) 18
d) 24
40. What is the sum of the coefficients of the expansion of (2x – 1)^20?
a) 0
b) 1
c) 2
d) 3
41. Find the ratio of the infinite geometric series if the sum is 2 and the first term is 1/2.
a) 1/3
b) 1/2
c) 3/4
d) 1/4
42. A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in
the third layer and sol until there are 10 bricks in the last layer. How many bricks are there
together?
a) 638
b) 637
c) 640
d) 639
43. Once a month a man put some money into the cookie jar. Each month he put 50 centavos
more into the jar than the month before. After 12 years he counted his money; he had P5436.
How much did he put in the jar in the last month?
a) 73.5
b) P75.50
c) P74.50
d) P72.50
44. The seventh term is 56 and the 12th term is -1792 of the geometric progression. Find the ratio
and the first term. Assume the ratios are equal.
a) -2, 7/8
b) -1. 5/8
c) -1, 7/8
d) -2, 5/8
45. Find the value of x in the equation 24x^2 + 5x -1 = 0.
a) (1/6, 1)
b) (1/6, 1/5)
c) (1/2, 1/5)
d) (1/8, -1/3)
46. The polynomial x^3 + 4x^2 -3x +8 is divided by x – 5, then the remainder is:
a) 175
b) 140
c) 218
d) 200
47. Find the rational number equivalent to repeating decimal 2.3524242424...
a) 23273/9900
b) 23261/990
c) 23289/9900
d) 23264/9900
48. The sum of Kim’s and Kevin’s ages is 18. In three years, Kim will be twice as old as Kevin.
What are their ages now?
a) 4, 14
b) 5, 13
c) 7, 11
d) 6, 12
49. Ten liters of 25% salt solution and 15%liters of 35% solution are poured into a drum
originally containing 30 liters of 10% salt solution. What is the percent concentration in the
mixture?
a) 19.55%
b) 22.15%
c) 27.05
d) 26.72%
50. Determine the sum of the infinite series: S = 1/3 + 1/9 + 1/27 + .... (1/3)^n.
a) 4/5
b) 3/4
c) 2/3
d) 1/2
51. Determine the sum of the positive valued solution to the simultaneous equations: xy = 15, yz
= 35, zx = 21.
a) 15
b) 13
c) 17
d) 19
52. The areas of two squares differ by 7 sq. ft. and their perimeters differ by 4 ft. Determine the
sum of their areas.
a) 25 ft^2
b) 27 ft^2
c) 28 ft^2
d) 22 ft^2
53. A bookstore purchased a bestselling book at P200 per copy. At what price should this book
be sold so that, giving a 20% discount, the profit is 30%?
a) P450
b) P500
c) P375
d) P400
54. In a certain community of 1,200 people, 60% are literate. Of the males, 50% are literate and
of the females 70% are literate. What is the female population?
a) 850
b) 500
c) 550
d) 600
55. Gravity causes a body to fall 16.1 ft. in the 1st second, 48.3 ft. in the 2nd second, 80.5 ft. in
the 3rd second, and so on. How far did the body fall during the 10th second?
a) 248.7 ft
b) 308.1 ft
c) 241.5 ft
d) 305.9 ft
56. In a commercial survey involving 1,000 persons on brand reference, 120 were found to prefer
brand x only, 200 prefer brand y only, 150 prefer brand z only. 370 prefer either x or y but not z,
450 prefer brand y or z but not x, and 420 prefer either brand z or x but not y. How many persons
have no brand preference, satisfied with any of the 3 brands?
a) 280
b) 230
c) 180
d) 130
57. The electric power which a transmission line can transmit is proportional to the total product
of its design voltage and current capacity, and inversely to the transmission distance. A 115
kilovolt line rated at 1000 amperes can transmit 150 Megawatts over 150 km. How much power,
in Megawatts, can a 230 kilovolt line rated 1500 amperes transmit over 100km?
a) 785
b) 485
c) 675
d) 595
58. Find the geometric mean of 64 and 4.
a) 16
b) 34
c) 32
d) 28
59) Factor the expression x^2 + 6x + 8 as completely as possible.
a) (x + 8)(x – 2)
b) (x + 4)(x – 2)
c) (x + 4)(x + 2)
d) (x – 4)(x – 2)
60. A batch of concrete consisted of 200 lbs. Fine aggregate, 350 lbs coarse aggregate, 94 lbs
cement, and 5 gallons water. The specific gravity of the sand and gravel may be taken as 2.65
and that of the cement as 3.10. What was the weight of concrete in place per cubic foot?
a) 172 lb
b) 236 lb
c) 162 lb
d) 153 lb
61. Dalisay’s Corporation gross margin is 45% sales. Operating expenses such as sales and
administration are 15% of sales. Dalisay is in 40% tax bracket. What percent of sales is their
profit after taxes?
a) 18%
b) 5%
c) 24%
d) 50%
62. A and B working together can finish painting a home in 6 days. A working alone, can finish
it in five days less than B. How long will it take each of them to finish the work alone?
a) 10, 15
b) 15, 20
c) 20, 25
d) 5, 10
63. Determine the sum of the progression if there are 7 arithmetic mean between 3 and 35.
a) 171
b) 182
c) 232
d) 216
64. Find the sum of 1, -1/5, 1/25,...
a) 5/6
b) 2/3
c) 0.84
d) 0.72
65. Find the remainder if we divide 4y^3 + 18y^2 + 8y -4 by (2y + 3).
a) 10
b) 11
c) 15
d) 13
66. What time after 3 o’clock will the hands of the clock be together for the first time?
a) 3:16.36
b) 3:14.32
c) 3:12.30
d) 3:13.37
67. The difference of the squares of the digits of a two digit positive number is 27. If the digits
are reversed in order and the resulting number subtracted from the original number, the
difference is also 27. What is the original number?
a) 63
b) 54
c) 48
d) 73
68. The boat travels downstream in 2/3 of the time as it does going upstream. If the velocity of
the river current is 8 kph, determine the velocity of the boat in still water.
a) 40 kph
b) 50 kph
c) 30 kph
d) 60 kph
69. Given that w varies directly as the product of x and y and inversely as the square of z, and
that w = 4, when x = 2, y = 6, and z = 3. Find the value of “w” when x = 1, y = 4, and z = 2.
a) 2
b) 3
c) 4
d) 5
70. The third term of a harmonic progression is 15 and 9th term is 6. Find the eleventh term?
a) 4
b) 5
c) 6
d) 7
71. Solve for x for the given equation, 7.4 x 10^-4 = e^-9.7x.
a) 0.7621
b) 0.7432
c) 0.7243
d) 0.7331
72. Find the 10th term of the geometric progression: 3, 6, 12, 24,....
a) 1536
b) 1653
c) 1635
d) 3156
73. Find the sum of odd integers from 1 to 31.
a) 256
b) 526
c) 265
d) 625
74. Box A has 4 white balls, 3 blue balls, and 3 orange balls. Box B has 2 white balls, 4 blue
balls, and 4 orange balls. If one ball is drawn from each box, what is the probability that one of
the two balls will be orange?
a) 27/50
b) 9/50
c) 23/50
d) 7/25
75. Solve: x^2 + y^2 = 5z and x^2 – y^2 = 3z. How many and what numerical values for x, y,
and z will satisfy these simultaneous equations?
a) if z = 3^2, then x = 6 and y = 3
b) if z = 2^2, then x =4 and y =2
c) if z = 1^2, then x =2 and y = 1
d) There are an infinite no. of values that will satisfy
76. Two people driving towards each other between two towns 160 km apart. The first man
drives at the rate of 45 kph and the other drives at 35 kph. From their starting point, how long
would it take that they would meet?
a) 3 hr
b) 4 hr
c) 2 hr
d) 1 hr
77. Solve x for the equation 6x – 4 = 2x + 6.
a) 10
b) 5/2
c) 5
d) 2.5
78. The man has a total of 33 goats and chickens. If the total of their feet is 900, find the number
of goats and chickens.
a) 12 goats and 21 chickens
b) 9 goats and 27 chickens
c) 6 cats and 5 dogs
d) 13 goats and 20 chickens
79. Express 5y – [3x – (5y + 4)] into polynomial.
a) 10y – 3x +4
b) 5y + 5x – 4
c) 5y + 5x + 4
d) 5y – 5x +4
80. What is the exponential form of the complex number 3 + 4i?
a) e^i53.1°
b) 5e^i53.1°
c) 5e^i126.9°
d) 7e^i53.1°
81. Simplify the complex numbers: (3 + 4i) – (7 – 2i)
a) -4 + 6i
b) 10 + 2i
c) 4 – 2i
d) 5 – 4i
82. Solve for x: x^2 + x -12 = 0
a) x = 6, x = -2
b) x = 1, x = 12
c) x = 3, x = -4
d) x = 4, x = -3
83. 2√50 − 5√8 =
a) 0
b) √8
c) √50
d) 10
84. What us the value of x in the expression: x – 1/x = 0?
a) x = -1
b) x = 1, 1/2
c) x = 1
d) x = 1, -1
85. What is the value of A: A^-6/8 = 0.001?
a) 10
b) 100
c) 0
d) 10000
86. Find the value of x: ax – b = cx + d
a) x = (a – b)/(c + d)
b) x = (b + d)/(a – c)
c) x = (a – d)/(c – b)
d) x = (c + d)/(a – c)
87. Divide: 15x^4 +6x^3 + 15x + 6 by 3x^3 + 3.
a) 5x + 2
b) 5x^2 + 2
c) 5x^2
d) 5x – 4
3
3
88. Simplify: 4√16 + 2√54
𝟑
a) 𝟏𝟒 √𝟐
2
b) 12 √3
3
c) 10√2
3
d) 8 √2
89. Find the value of x in the equation: csc x + cot x = 3
a) π/5
b) π/4
c) π/3
d) π/2
90. If A is in the III quadrant and cos A = -15/17, find the value of cos (1/2)A.
a) –(8/17)^1/2
b) –(5/17)^1/2
c) –(3/17)^1/2
d) –(1/17)^1/2
91. Simplify the expression: (sin B + cos B tan B)/cos B
a) 2 tan B
b) tan B + tan B
c) tan B cos B
d) 2 sin B cos B
92. If cot 2A cot 68° = 1, then tan A is equal to ________.
a) 0.194
b) 0.419
c) 0.491
d) 0.914
93. A ladder 5 m long leans against the wall of an apartment house forming an angle of 50
degrees, 32 minutes with ground. How high up the wall does it reach?
a) 12.7 m
b) 10.5 m
c) 3.86 m
d) 1.55 m
94. The measure of 2.25 revolutions counterclockwise is:
a) -810 deg
b) -805 deg
c) 810 deg
d) 805 deg
95. If sin A = 2.5 x and cos A = 5.5x, find the value of A in degrees.
a) 14.5 deg
b) 24.5 deg
c) 34.5 deg
d) 44.5 deg
96. Solve angle A of an oblique triangle wit vertices ABC, if a = 25, b = 16 and C = 94 degrees
and 6 minutes.
a) 50 deg and 40 min
b) 45 deg and 35 min
c) 55 deg and 32 min
d) 54 deg and 30 min
97. Given: x = (cos B tan B – sin B)/cos B. Solve for x if B = 30 degrees.
a) 0.577
b) 0
c) 0.500
d) 0.866
98. (cos A)^4 – (sin A)^4 is equal to _________.
a) cos 2A
b) sin 2A
c) 2tan A
d) sec A
99. 174 degrees is equivalent to _________ mils.
a) 3094
b) 2084
c) 3421
d) 2800
100. What is the resultant of a displacement 6 miles North and 9 miles East?
a) 11 miles, N 56° E
b) 11 miles, N 54° E
c) 10 miles, N 56° E
d) 10 miles, N 54° E
101. Which is identically equal to (sec A + tan A)?
a) 1/(sec A + tan A)
b) csc A – 1
c) 2/(1 – tan A)
d) csc A + 1
102. Determine the simplified form of (cos 2A – cos A)/(sin A).
a) cos 2A
b) –sin A
c) cos A
d) sin 2A
103. Ifsec 2A = 1/sin 13A, determine the angle A in degrees.
a) 5 deg
b) 6 deg
c) 3 deg
d) 7 deg
104. Solve for x in the equation: arctan (x + 1) + arctan (x – 1) = arctan (12).
a) 1.50
b) 1.34
c) 1.20
d) 1.25
105. Solve for x if tan 3x = 5tan x.
a) 20.705 deg
b) 30.705 deg
c) 15.705 deg
d) 35.705 deg
106. If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.939x, find the value of x.
a) 0.265
b) 0.256
c) 0.562
d) 0.625
107. The angle of inclination of ascend of a road having 8.25% grade is ______.
a) 4.72
b) 4.27
c) 5.12
d) 1.86
108. A man finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m
nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the
tower?
a) 76. 31 m
b) 73.31 m
c) 73.16 m
d) 73.61 m
109. If the sides of a parallelogram and an included angle are 6, 10, and 100 degrees respectively,
find the length of the shorter diagonal.
a) 10.63
b) 10.37
c) 10.73
d) 10.23
110. What is the value of log2 5 + log3 5?
a) 7.39
b) 3.79
c) 3.97
d) 9.37
111. Points A and B 1000 m apart are plotted on a straight highway running east and west. From
A, the bearing of a tower C is 32 degrees W of N and from B the bearing of C is 26 degrees N of
E. Approximate the shortest distance of tower C to the highway.
a) 364 m
b) 374 m
c) 394 m
d) 384 m
112. If log of 2 to base 2 plus log of x to the base of 2 is equal to 2, then the value of x is:
a) 4
b) -2
c) 2
d) -1
2
113. Arctan [2cos (arcsin √3/2)] is equal to:
a) π/3
b) π/4
c) π/6
d) π/2
114. Solve A for the given equations cos^2 A = 1 – cos^2 A.
a) 45, 125, 225, 335 degrees
b) 45, 125, 225, 315 degrees
c) 45, 135, 115, 315 degrees
d) 45, 150, 220, 315 degrees
115. If sin A = 2/5, what is the value of 1 – cos A?
a) 0.083
b) 0.916
c) 0.400
d) 0.614
116. Sin A cos B – cos A sin B is equivalent to:
a) cos (A – B)
b) sin (A – B)
c) tan (A – B)
d) cos (A –B)
117. How many degrees is 4800 mils?
a) 270 deg
b) 90 deg
c) 180 deg
d) 215 deg
118. ln 7.18^xy equals
a) 1.97xy
b) 0.86xy
c) xy
d) 7.18xy
119. The log10 (8)(6) equal to:
a) log10 8 + log10 6
b) log10 8 - log10 6
c) log10 8 log10 6
d) log10 8 / log10 6
120. 38.5 to the x power = 6.5 to the x – 2 power, solve for x using logarithms.
a) 2.70
b) -2.10
c) 2.10
d) -2.02
121. Given the triangle ABC in which A = 30°30’, b = 100 m and c = 200 m. Find the length of
the side a.
a) 124.64 m
b) 142.24 m
c) 130.5 m
d) 103.00 m
122. An observer wishes to determine the height of the tower. He takes sight at the top of the
tower from A and B, which are 50 ft apart at the same elevation on a direct line with the tower.
The vertical angle at point A is 30 deg and at point B is 40 deg. What is the height of the tower?
a) 85.60 ft
b) 110.29
c) 143.97
d) 92.54 ft
123. What is the value of log to the base of 1000^3.3?
a) 9.9
b) 99.9
c) 10.9
d) 9.5
124. In a triangle, find the side c if angle C = 100 deg, side b = 20, and side a = 15.
a) 28
b) 29
c) 27
d) 26
125. Given a triangle with an angle C = 28.7 deg, side a = 132 units and side b = 224 units. Solve
for the side c.
a) 95 units
b) 110 units
c) 125.4 units
d) 90 units
126. A PLDT tower and a monument stand on a level plane. The angles of depression of the top
and bottom of the monument viewed from the top of the PLDT tower are 13 deg and 35 deg
respectively. The height of the tower is 50 m. Find the height of the monument.
a) 33.51 m
b) 47.3 m
c) 7.48 m
d) 30.57 m
127. Find the value of x if log12 x = 2.
a) 144
b) 414
c) 524
d) 425
128. If tan x = 1/2, tan y = 1/3. What is the value of tan (x + y)?
a) 1
b) 2
c) 3
d) 4
129. The logarithm of the quotient M/N and the logarithm of the product MN is equal to
1.55630251 and 0.352182518 respectively. Find the value of M.
a) 6
b) 7
c) 8
d) 9
130. The angle of elevation of the top tower B from the top of the tower A is 28 deg and the
angle of elevation of the top tower A from the base of the tower B is 46 deg. The two towers lie
in the same horizontal plane. If the height of the tower B is 120 m, find the height of tower A.
a) 87.2 m
b) 90.7 m
c) 79.3 m
d) 66.3 m
131. Evaluate the log6 845 = x.
a) 3.76
b) 5.84
c) 4.48
d) 2.98
132. Find the value of log8 48.
a) 1.86
b) 6.81
c) 8.61
d) 1.68
133. Find the value of sin 920 deg.
a) 0.243
b) -0.243
c) 0.342
d) -0.342
134. Log (x)^n =
a) log x
b) n log x
c) 1/n log x
d) n
135. Sin 2θ is equal to:
a) 2 sin θ cos θ
b) 1/2 sin θ
c) sin θ cos θ
d) 1 – sin^2 θ
136. What is the interior angle (in radian) of an octagon?
a) 2.26 rad
b) 2.36 rad
c) 2.8 rad
d) 2.75 rad
137. The trigonometric function (1 + tan^2 θ) is also equal to:
a) sec^2 θ
b) cos^2 θ
c) csc^2 θ
d) sin θ
138. Derive the formula of each interior angle (in degrees).
a) (no. of sides – 2)180
b) [(no. of sides – 2)180/no. of sides]
c) [(no. of sides – 1)180/no. of sides]
d) [no. of sides – 2]/180
139. What is the Cartesian logarithm of 402.9?
a) 2.605
b) 2.066
c) 3.05
d) 3.60
𝑥2− 9
140. What is the value of the following limit? lim [ 𝑥−3 ]
𝑥→3
a) 3
b) 6
c) 9
d) 0
141. Given the three sides of a triangle: 2, 3, 4. What is the angle in radians opposite the side
with length 3?
a) 0.11
b) 0.41
c) 0.55
d) 0.81
142. Find the area of the geometric figure whose vertices are at (3, 0, 0), (3, 3, 0), (0, 0, 4) and (0,
3, 4).
a) 12 sq. units
b) 14 sq. units
c) 15 sq. units
d) 24 sq. units
143. A central angle of 45 degrees subtends an arc of 12 cm. What is the radius of the circle?
a) 15.28 cm
b) 18.28 cm
c) 20.28 cm
d) 30.28 cm
144. It is a part of circle bounded by a chord and an arc.
a) slab
b) segment
c) section
d) sector
145. What is the area (in sq. inches) of a parabola with a base of 15 cm and a height of 20 cm?
a) 87
b) 55
c) 31
d) 11
146. Triangle ABC is a right triangle with right angle at C. CD is perpendicular to AB. BC = 4
and CD = 1. Find the area of the triangle ABC.
a) 2.95
b) 2.55
c) 2.07
d) 1.58
147. The tangent and a secant are drawn to a circle from the same external point. If the tangent is
6 inches and the external segment of the secant is 3 inches, the length of the secant is ________
inches.
a) 15
b) 14
c) 13
d) 12
148. If a regular polygon has 27 diagonals, then it is a,
a) nonagon
b) pentagon
c) hexagon
d) heptagon
149. A regular dodecagon is inscribed in a circle of radius 24. Find the perimeter of the
dodecagon.
a) 125
b) 135
c) 149
d) 169
150. An annulus is a plane figure, which is composed of two concentric circles. The area of the
annulus can be calculated by getting the difference between the area of the larger circle and the
area of the smaller circle. Also, it can be calculated by removing the hole. The method is called:
a) Law of Extremities
b) Law of Reduction
c) Law of Deduction
d) Sharp Theorem
151. The sides of a triangle are 195, 157, and 210 respectively. What is the area of the triangle?
a) 73250 sq. units
b) 14586 sq. units
c) 10250 sq. units
d) 11260 sq. units
152. Given a triangle of sides 10 cm and 15 cm an included angle of 60 degrees. Find the area of
the triangle.
a) 70
b) 80
c) 72
d) 65
153. The sides of a triangle are 8 cm, 10 cm, and 14 cm. Determine the radius of the inscribed
and circumscribed circle.
a) 3.45, 7.14
b) 2.45, 7.14
c) 2.45, 8.14
d) 3.45, 8.14
154. The sides of a cyclic quadrilateral are a = 3m, b = 3m, c = 4m and d = 4m. Find the radius
of the inscribed and circumscribed circle.
a) 1.71, 2.50
b) 1.91, 2.52
c) 2.63, 4.18
d) 2.63, 3.88
155. From the point inside a square the distance to three corners are 4, 5 and 6 m respectively.
Find the length of the sides of a square.
a) 7.53
b) 8.91
c) 6.45
d) 9.31
156. A regular pentagon has sides 20 cm. An inner pentagon with sides of 10 cm is inside and
concentric to the larger pentagon. Determine the area inside and concentric to the larger
pentagon but outside of the smaller pentagon.
a) 430.70 cm^2
b) 573.26 cm^2
c) 473.77 cm^2
d) 516.14 cm^2
157. A rhombus has diagonals of 32 and 20 inches. Determine its area.
a) 360 in^2
b) 280 in^2
c) 320 in^2
d) 400 in^2
158. In a circle with a diameter of 10 m, a regular five pointed star touching its circumference is
inscribed. What is the area of the part not covered by the star?
a) 60.2 m^2
b) 50.48 m^2
c) 45.24 m^2
d) 71.28^m
159. Find the area of a regular octagon inscribed in a circle of radius 10 cm.
a) 186.48 cm^2
b) 148.91 cm^2
c) 282.24 cm^2
d) 166.24 cm^2
160. Find the area of a regular pentagon whose side is 25 m and apothem is 17.2 m.
a) 846 m^2
b) 1090 m^2
c) 1075 m^2
d) 988 m^2
161. The area of a circle circumscribing a hexagon is 144π m^2. Find the area of the hexagon.
a) 374.12 m^2
b) 275.36 m^2
c) 415.26 m^2
d) 225.22 m^2
162. Determine the area of a regular 6-star polygon if the inner regular hexagon has 10 cm sides.
a) 441.66 cm^2
b) 467.64 cm^2
c) 519.60 cm^2
d) 493.62 cm^2
163. Find each interior angle of a hexagon.
a) 90 deg
b) 120 deg
c) 150 deg
d) 180 deg
164. Find the length of the side of pentagon if the line perpendicular to its side is 12 units from
the center.
a) 8.71
b) 17.44
c) 36.93
d) 18.47
165. How many sides are in a polygon if each interior angle is 165 degrees.
a) 12 sides
b) 24 sides
c) 20 sides
d) 48 sides
166. Find the area of triangle whose sides are: 25, 39 and 40.
a) 468
b) 684
c) 486
d) 864
167. Find the area of a regular hexagon inscribed in a circle of radius 1.
a) 2.698
b) 2.598
c) 3.698
d) 3.598
168. A goat is tied to a corner of a 30 ft by 35 ft building. If the rope is 40 ft long and the goat
can reach 1 ft farther than the rope length. What is the maximum area the goat can cover.
a) 4840
b) 4804
c) 8044
d) 4084
169. In triangle BCD, BC = 25 m, and CD = 10 m. The perimeter of the triangle maybe:
a) 79 m
b) 70 m
c) 71 m
d) 72 m
170. A quadrilateral have sides equal to 12 m, 20 m, 8 m and 16.97 m respectively. If the sum of
the two opposite angles is equal to 225, find the area of the quadrilateral.
a) 168
b) 100
c) 124
d) 158
171. The area of a circle inscribed in a hexagon is 144π m^2. Find the area of the hexagon.
a) 498.83 m^2
b) 489.83 m^2
c) 439.88 m^2
d) 349.88 m^2
172. Each angle of the regular dodecagon is equal to _________ degrees.
a) 135
b) 150
c) 125
d) 105
173. If an equilateral triangle is circumscribe about a circle of radius 10 cm, determine the side
of the triangle.
a) 34.64 cm
b) 64.12 cm
c) 36.44 cm
d) 32.10 cm
174. The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector.
a) 59.8 cm^2
b) 58.9 cm^2
c) 89.5 cm^2
d) 85.9 cm^2
175. The distance between the center of the three circles which are mutually tangent to each
other externally are 10, 12 and 14 units. Find the area of the largest circle.
a) 72π
b) 64π
c) 23 π
d) 16 π
176. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base and
the altitude of the other is 3 units less than its base. Find the altitude, if the areas of the triangles
differ by 21 square units.
a) 6 & 12
b) 5 &11
c) 3 & 9
d) 4 & 10
177. If the sides of a parallelogram and an included angle are 6, 10 and 100 degreess respectively,
find the length of the shorter diagonal.
a) 10.63
b) 10.73
c) 10.23
d) 10.37
178. In triangle ABC, angle C = 34 degrees, side a = 29 cm, b = 40 cm. Solve the area of the
triangle.
a) 324 cm^2
b) 342 cm^2
c) 448 cm^2
d) 484 cm^2
179. An oblique equilateral parallelogram.
a) square
b) rectangle
c) rhombus
d) recession
180. What is the interior angle (in radian) of an octagon
a) 2.26 rad
b) 2.36 rad
c) 2.8 rad
d) 2.75 rad
181. The circumference of a great circle of a sphere is 18π. Find the volume of the sphere.
a) 3053.6
b) 4053.6
c) 5053.6
d) 6053.6
182. A pyramid whose altitude is 5 ft weighs 800 lbs. At what distance from its vertex must it be
cut by a plane parallel to its base so that the two solids of equal weight will be formed?
a) 3.97 ft
b) 2.87 ft
c) 4.97 ft
d) 5.97 ft
183. Find the increase in volume of a spherical balloon when its radius is increased from 2 to 3
inches.
a) 75. 99 cu. in.
b) 74.59 cu. in.
c) 74.12 cu. in.
d) 79.59 cu. in.
184. If the lateral area of a right cylinder is 88 and its volume is 220, find its radius.
a) 2 cm
b) 3 cm
c) 4 cm
d) 5 cm
185. It is desired that the volume of the sphere be tripled. By how many times will the radius be
increased?
a) 2^1/2
b) 3^1/3
c) 3^1/2
d) 3^3
186. A cone and a cylinder have the same height and the same volume. Find the ratio of the
radius of the cone to the radius of the cylinder.
a) 0.577
b) 0.866
c) 1.732
d) 2.222
187. Compute the surface area of the cone having a slant height of 5 cm and a diameter of 6 cm.
a) 47.12 cm^2
b) 25.64 cm^2
c) 38.86 cm^2
d) 30.24 cm^2
188. The ratio of the volume of the lateral area of a right circular cone is 2:1. If the altitude is 15
cm, what is the ratio of the slant height to the radius?
a) 5:2
b) 5:3
c) 4:3
d) 4:2
189. A conical vessel has a height of 24 cm and a base diameter of 12 cm. It holds water to a
depth of 18 cm above its vertex. Find the volume of its contents in cubic centimeter.
a) 387.4
b) 381.7
c) 383.5
d) 385.2
190. A circular cylinder is circumscribed about a right prism having a square base one meter on
an edge. The volume of the cylinder is 6.283 m^3. Find its altitude in m.
a) 4.5
b) 5.5
c) 4
d) 5
191. The volume of water in a spherical tank having diameter of 4 m is 5.236 m^3. Determine
the depth of the water in the tank.
a) 1.6
b) 1.4
c) 1.2
d) 1.0
192. The corners of a cubical block touched the closest spherical shell that encloses it. The
volume of the box is 2744 cm^3. What volume in cm^3 inside the shell is not occupied by the
block?
a) 4713.56
b) 3360.14
c) 4133.25
d) 5346.42
193. A circular cone having an altitude of 9 m is divided into 2 segments having the same vertex.
If the smaller altitude is 6m, find the ratio of the volume of the small cone to the big cone.
a) 0.296
b) 0.396
c) 0.186
d) 0.486
194. A frustum of a regular pyramid has an upper base of 8 m x 80 m and a lower base of 10 m x
100 m and an altitude of 5 m. Find the volume of the pyramid.
a) 4066.67 m^3
b) 5066.67 m^3
c) 6066.67 m^3
d) 7066.67 m^3
195. The bases of a right prism is a hexagon with one each side equal to 6 cm. The bases are 12
cm apart. What is the volume of a right prism?
a) 1211.6 cm^3
b) 2211.7 cm^3
c) 1212.5 cm^3
d) 1122.4 cm^3
196. The volume of the water in hemisphere having a radius of 2 m is 2.05 m^3. Find the height
of the water.
a) 0.602
b) 0.498
c) 0.782
d) 0.865
197. Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and a
central angle of 150 deg.
a) 7711.82 cm^3
b) 6622.44 cm^3
c) 5533.32 cm^3
d) 8866.44 cm^3
198. A cubical container that measures 2 in on a side is tightly packed with marbles and is filled
with water. All the 8 marbles are in contact with the walls of the container and the adjacent
marbles are the same size. What is the volume of water in the container?
a) 0.38 in^3
b) 2.5 in^3
c) 3.8 in^3
d) 4.2 in^3
199. If one edge of a cube measures12 cm, calculate for the surface area of the cube and the
volume of the cube.
a) 864 cm^2; 1728 cm^3
b) 468 cm^2; 1728 cm^3
c) 863 cm^2; 8721 cm^3
d) 468 cm^2; 8721 cm^3
200. A pyramid with a square base has an altitude of 25 cm. If the edge of the base is 15 cm.
Calculate the volume of the pyramid.
a) 1785 cm^3
b) 1875 cm^3
c) 5178 cm^3
d) 5871 cm^3
201. If a right cone has a base radius of 35 cm and an altitude of 45 cm. Solve for the total
surface area and the volume of the cone.
a) 10,116.89 cm^2 and 57,726.76 cm^3
b) 9,116.89 cm^2 and 57,726.76 cm^3
c) 10,116.89 cm^2 and 67,726.76 cm^3
d) 9,116.89 cm^2 and 67,726.76 cm^3
202. If the volume of a sphere is 345 cm^3. Solve for its diameter.
a) 8.70 cm
b) 7.70 cm
c) 6.70 cm
d) 9.70 cm
203. A group of children playing with marbles placed 50 pieces of the marbles inside a
cylindrical container with water filled to a height of 20 cm. If the diameter of each marble is 1.5
cm and that of the cylindrical container 6 cm. What would be the new height of water inside the
cylindrical container after the marbles were placed inside?
a) 23.125 cm
b) 24.125 cm
c) 22.125 cm
d) 25.125 cm
204. A pipe lining material silicon carbide used in a conveyance of pulverized coal to fuel a
boiler, has a thickness of 2 cm and inside diameter of 10 cm. Find the volume of the material
with pipe length of 6 meters.
a) 45,239 cm^3
b) 42,539 cm^3
c) 49,532 cm^3
d) 43,932 cm^3
205. Given of diameter x and altitude h. What percent is the volume of the largest cylinder which
can be inscribed in the cone to the volume of the cone?
a) 44%
b) 56%
c) 46%
d) 65%
206. Each side of a cube is increased by 1%. By what percent is the volume of the cube
increased?
a) 23.4%
b) 30.3%
c) 34.56%
d) 3.03%
207. Two vertical conical tanks are joined at the vertices by a pipe. Initially the bigger tank is full
of water. The pipe valve is open to allow the water to flow to the smaller tank until it is full. At
this moment, how deep is the water in the bigger tank? The bigger tank has a diameter of 6 ft and
a height of 10 ft, the smaller tank has a diameter of 6 ft and a height of 8 ft. Neglect the volume
of water in the pipeline.
𝟑
a) √𝟐𝟎𝟎
3
b) √50
3
c) √25
4
d) √50
208. A pyramid has a square base of 8 m on a side and an altitude of 10 m. How many liters of
water will it hold when full and inverted?
a) 223,330
b) 203,330
c) 213,330
d) 233,330
209. What solid figure that has many faces?
a) octagon
b) decagon
c) polygon
d) polyhedron
210. If the length of the latus rectum of an ellipse is three-fourth of the length of its minor axis,
find its eccentricity.
a) 0.15
b) 0.33
c) 0.55
d) 0.66
211. Find the equation of a line where x-intercept is 2 and y-intercept is -2.
a) 2x + 2y +2 = 0
b) x – y – 2 = 0
c) -2x + 2y = -2
d) x – y – 1 = 0
212. A point (x, 2) is equidistant from the points (-2, 9) and (4, -7). The value of x is:
a) 11/3
b) 20/3
c) 19/3
d) 3
213. A parabola y = -x^2 – 6x – 9 opens ______________.
a) to the right
b) upward
c) to the left
d) downward
214. A line with a curve approaches indefinitely near as its tracing point passes off infinitely is
called the:
a) tangent
b) asymptote
c) directly
d) latus rectum
215. Find the eccentricity of an ellipse when the length of the latus rectum is 2/3 of the length of
the major axis.
a) 0.58
b) 0.68
c) 0.78
d) 0.98
216. The directrix of a parabola is the line y = 5 and its focus is at the point (4, -3).
a) 20
b) 18
c) 16
d) 12
217. The radius of a sphere is r inches at time t seconds. Find the radius when the rates of
increase of the surface area and the radius are numerically equal.
a) 1/(8π) in
b) 1/(4π) in
c) 2π in
d) π^2 in
218. In general quadratic equation, if the discriminant is zero, the curve is a figure that represents
________.
a) hyperbola
b) circle
c) parabola
d) ellipse
219. The equation of the tangent to the curve y = x + 5/x at point P(1, 3) is:
a) 4x – y + 7 = 0
b) x + 4y – 7 = 0
c) 4x + y -7 = 0
d) x – 4y + 7 = 0
220. A line 4x + 2y – 2 = 0 is coincident with the line:
a) 4x + 4y – 2 = 0
b) 4x + 3y + 33 = 0
c) 8x + 4y – 2 = 0
d) 8x + 4y – 4 = 0
221. A locus of a point which moves so that it is always equidistant from a fixed point (focus) to
a fixed line (directrix) is a _____________.
a) circle
b) ellipse
c) parabola
d) hyperbola
222. Find the equation of the line passing through (7, -3) and (-3, -5).
a) x + 5y + 22 = 0
b) x + 5y – 22 = 0
c) x – 5y + 22 = 0
d) x – 5y – 22 = 0
223. Find the vertex of the parabola, x^2 = 8y
a) (0, 0)
b) (0, 4)
c) (4, 0)
d) (0, 8)
224. What type of conics is x^2 – 4y + 3x + 5 = 0.
a) parabola
b) ellipse
c) hyperbola
d) circle
225. Determine the coordinates of the point which is three-fifths of the way from the point (2, -5)
to the point (-3, 5).
a) (-1, 1)
b) (-2, -1)
c) (-1, -2)
d) (1, 1)
226. A line passing through a point (2, 2). Find the equation of the line if the length of the
segment intercepted by the coordinate’s axes is equal to the square root of 5.
a) 2x – y – 2 = 0
b) 2x + y + 2 = 0
c) 2x – y + 2 = 0
d) 2x + y – 2 = 0
227. Point P(x, y) moves with a distance from point (0, 1) one half of its distance from line y = 4,
the equation of its locus is:
a) 2x^2 – 4y^2 = 5
b) 4x^2 + 3y^2 = 12
c) 2x^2 + 5y^2 = 3
d) x^2 + 2y^2 = 4
228. The major axis of the elliptical path in which the earth moves around the sun is
approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the
apogee of the earth.
a) 93,000,000 miles
b) 94,335,000 miles
c) 91, 450,000 miles
d) 94,550,000 miles
229. What is the equation of the asymptote of the hyperbola (x^2)/9 – (y^2)/4 = 1.
a) 2x – 3y = 0
b) 3x – 2y = 0
c) 2x – y = 0
d) 2x + y = 0
230. Compute the focal length and the length of the latus rectum of the parabola y^2 + 8x – 6y +
25 = 0.
a) 2, 8
b) 4, 16
c) 16, 64
d) 1, 4
231. Find the equation of the axis of symmetry of the function y = 2x^2 – 7x + 5.
a) 7x + 4 = 0
b) 4x + 7 = 0
c) 4x – 7 = 0
d) x – 2 = 0
232. Find the value of k for which the equation x^2 + y^2 + 4x – 2y – k = 0, represents a point
circle.
a) 5
b) 6
c) -6
d) -5
233. Find the equation of the circle whose center is at (3, -5) and whose radius is 4.
a) x^2 + y^2 – 6x + 10y + 18 = 0
b) x^2 + y^2 + 6x + 10y + 18 = 0
c) x^2 + y^2 – 6x – 10y + 18 = 0
d) x^2 + y^2 + 6x – 10y + 18 = 0
234. Determine B such that 3x + 2y – 7 = 0 is perpendicular to 2x – By + 2 = 0.
a) 5
b) 4
c) 3
d) 2
235. In a Cartesian coordinates, the coordinates of a square are (1, 1), (0, 8), (4, 5), and (-3, 4).
What is the area?
a) 25
b) 20
c) 18
d) 14
236. The segment from (-1, 4) to (2, -2) is extended three times its own length. Find the terminal
point.
a) (11, -24)
b) (-11, -20)
c) (11, -18)
d) (11, -20)
237. Find the distance between A(4,-3) and B(-2, 5).
a) 10
b) 8
c) 9
d) 11
238. Given three vertices of a triangle whose coordinates are A(1, 1), B(3, -3) and C(5, -3). Find
the area of the triangle.
a) 3
b) 4
c) 5
d) 6
239. The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3). Find the values
of x and y.
a) 33, 12
b) 5, 0
c) 6, 9
d) 14, 6
240. A line passes through (1, -3) and (-4, -2). Write the equation of the line in slope-intercept
form.
a) y – 4 = x
b) y = -x – 2
c) y = x – 4
d) y – 2 = x
241. What is the x-intercept of the line passing through (1, 4) and (4, 1).
a) 4.5
b) 5
c) 6
d) 4
242. Find the distance between the lines, 3x + y – 12 = 0 and 3x + y – 4 = 0.
a) 16/√10
b) 12/√10
c) 4/√10
d) 8/√𝟏𝟎
243. Find the area of the circle whose equation is x^2 + y^2 = 6x – 8y.
a) 25π
b) 5π
c) 15π
d) 20π
244. Find the major axis of the ellipse x^2 + 4y^2 – 2x – 8y + 1 = 0.
a) 2
b) 10
c) 4
d) 6
245. An arch 18 m high has the form of parabola with a vertical axis. The length of a horizontal
beam placed across the arch 8 m from the top is 64 m. Find the width of the arch at the bottom.
a) 86 m
b) 96 m
c) 106 m
d) 76 m
246. Find the equation of the hyperbola whose asymptotes are y = ± 2x and which passes
through (5/2, 3).
a) 4x^2 – y^2 – 16 = 0
b) 2x^2 – y^2 – 4 = 0
c) 3x^2 – y^2 – 9 = 0
d) 5x^2 – y^2 – 25 = 0
247. Find the eccentricity of the curve 9x^2 – 4y^2 – 36x + 8y = 4.
a) 1.80
b) 1.90
c) 1.70
d) 1.60
248. The equation of a line that intercepts the x-axis at x = 4 and the y-axis at y = - 6 is:
a) 3x + 2y = 12
b) 2x – 3y = 12
c) 3x – 2y = 12
d) 2x – 3y = -12
249. What is the radius of a circle defined by the equation x^2 – 6x + y^2 – 4y – 12 = 0.
a) 3.46
b) 7
c) 5
d) 6
250. Find the slope of the line defined by y – x = -5.
a) 1
b) 1/4
c) -1/2
d) 5 + x
251. What conic section is represented by 4x^2 – y^2 + 8x + 4y = 15.
a) parabola
b) ellipse
c) hyperbola
d) circle
252. What conic section is represented by x^2 + y^2 – 4x + 2y – 20 = 0
a) circle
b) parabola
c) ellipse
d) hyperbola
253. Find the equation of the straight line with a slope of 3 and a y-intercept of 1.
a) 3x – y + 1 = 0
b) 3x + y + 1 = 0
c) 3x – y – 1 = 0
d) 3x + y – 1 = 0
254. What is the equation of the line that passes through (4, 0) and is parallel to the line x – y – 2
= 0?
a) y + x + 4 = 0
b) y – x – 4 = 0
c) x – y – 4 = 0
d) x + y – 4 = 0
255. Find the distance from the line 4x – 3y + 5 = 0 to the point (2, 1).
a) 1
b) 2
c) 3
d) 4
256. What is the center of the curve x^2 + y^2 – 2x – 4y – 31 = 0.
a) (-1, -2)
b) (1, -2)
c) (-1, 2)
d) (1, 2)
257. Determine the equation of the curve such that the sum of the distances of any point on the
curve from two points whose coordinates are (-3, 0) and (3, 0) is always equal to 8.
a) 7x^2 + 16y^2 – 112 = 0
b) 16x^2 + 7y^2 – 112 = 0
c) 7x^2 + 16y^2 + 112 = 0
d) 16x^2 + 7y^2 + 112 = 0
258. The equation 9x^2 + 16y^2 + 54x - 64y = -1 describes:
a) a hyperbola
b) a sphere
c) a circle
d) an ellipse
259. The sum of the distances from the two foci to any point in a/an ______________ is a
constant.
a) a parabola
b) any conic
c) hyperbola
d) ellipse
260. Determine the curve: 9x^2 + 6y^2 + 2x + 3y + 9 = 0.
a) ellipse
b) hyperbola
c) parabola
d) circle
261. Locus of points on a side which rolls along a fixed line:
a) cardoid
b) epicycloid
c) cycloid
d) hypocycloid
262. What is the radius of a circle with the following equation? x^2 – 6x + y^2 – 12 = 0
a) 2
b) 5
c) 7
d) 25
253. Find the slope of the line passing to the point (-3, -4) and (2, 4).
a) 0
b) 5
c) 10
d) 1.6
254. What is the slope of the line perpendicular to y = (1/4)x + 6?
a) 4
b) 1
c) -4
d) -1
255. Given the polar coordinates (4, 20°). Find the rectangular coordinates.
a) -2, 3.46
b) -3.46, -2
c) 2, -3.46
d) -3.46, 4
256. Find the equation of the line which passes through the point (2, 1) and perpendicular to the
line whose equation is y = 4x + 3.
a) x – 4y + 6 = 0
b) y – 4x + 6 = 0
c) x + 4y – 6 = 0
d) y – 4x + 6 = 0
257.What is the second derivative of a function y = 5x^3 + 2x + 1?
a) 25x
b) 30x
c) 18
d) 30
258. Find the height of a circular cylinder of a maximum volume, which can be inscribed in a
sphere of radius 10 cm.
a) 11.55 cm
b) 12.55 cm
c) 14.55 cm
d) 15.55 cm
259. Find the maximum point of y = x + 1/x.
a) (2, 5/2)
b) (1, 2)
c) (-1, -2)
d) (2, 3)
260. Simplify the expression Lim(x^2 – 16)/(x – 4) as x approaches 2.
a) 8
b) 6
c) 4
d) 2
261. Evaluate the Lim (x^2 + 3x – 4) as x approaches 3.
a) 18
b) 12
c) 4
d) 2
262. The distance a body travels is a function of time t and is defined by: x(t) = 18t + 9t^2. What
is its velocity at t = 3?
a) 36
b) 45
c) 72
d) 92
263. Water running out a conical funnel at the rate of 1 cu. in per second. If the radius of the base
of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping
when it is 2 in from the top.
a) -1/9 π in/sec
b) -3/2 π in/sec
c) -8/9 π in/sec
d) -4/9 π in/sec
264. ________ is the concept of finding the derivative of composite functions.
a) Logarithmic differentiation
b) Chain rule
c) Trigonometric differentiation
d) Implicit differentiation
265. The volume of the sphere is increasing at the rate of 6 cm^3/hr. At what rate is its surface
area increasing (in cm^2/hr) when the radius is 50 cm?
a) 0.54
b) 0.44
c) 0.34
d) 0.24
266. A man on a wharf 3.6 m above sea level is pulling a rope tied to a raft at 0.60 m per second.
How fast is the raft approaching the wharf when there are 6 m of rope out?
a) -0.95 m/s
b) -0.85 m/s
c) -0.75 m/s
d) -0.65 m/s
267. If the distance x from the point of departure at time t is defined by the equation x = -16t^2 +
5000t + 5000, what is the initial velocity?
a) 2000
b) 0
c) 5000
d) 3000
268. Using two existing corner sides of an existing wall, what is the maximum rectangular area
that can be fenced by a fencing material 30 ft long?
a) 225 sq. ft
b) 240 sq. ft
c) 270 sq. ft
d) 335 sq. ft
269. The radius of a sphere is r inches at time t seconds. Find the radius when the rates of
increase of the surface area and the radius are numerically equal.
a) 1/(8π) in
b) 1/(4π) in
c) 2π in
d) π^2 in
270. Three sides of a trapezoid are each 8 cm long. How long is the fourth side when the area of
the trapezoid has the greatest value?
a) 8 cm
b) 12 cm
c) 16 cm
d) 20 cm
271. Find the change in y = 2x – 3 if x changes from 3.3 to 3.5.
a) 0.1
b) 0.2
c) 0.3
d) 0.4
272. If y = arctan(ln x), find dy/dx at x = 1/e.
a) e
b) e/2
c) e/3
d) e^2
273. Evaluate the limit (ln x)/x as x approaches positive infinity.
a) 1
b) 0
c) infinity
d) -1
274. lim[(x^3 – 27)/(x – 3)] as x approaches 3.
a) 0
b) infinity
c) 9
d) 27
275. A box is to be constructed from a piece of zinc 20 in square by cutting equal squares from
each corner and turning up zinc to form the side. What is the volume of the box that can so
constructed?
a) 599.95 in^3
b) 592.59 in^3
c) 579.50 in^3
d) 622.49 in^3
276. Given the function f(x) = x to the 3rd power – 6x + 2, find the value of the first derivative at
x = 2, f(2).
a) 6
b) 7
c) 3x^2 – 5
d) 8
277. Water is pouring into a swimming pool. After t hours there are t + √𝑡 gallons in the pool. At
what rate is the water pouring into the pool when t = 9 hours?
a) 7/6 gph
b) 1/6 gph
c) 2/3 gph
d) 1/2 gph
278. Evaluate Lim [(x^2 – 16)/(x – 4)] as x approaches 4.
a) 1
b) 8
c) 0
d) 16
279. Evaluate Lim [(x - 4)/(x^2 – x – 12)] as x approaches 4.
a) undefined
b) 0
c) infinity
d) 1/7
280. Evaluate Lim [(x^3 – 2x + 9)/(2x^3 – 8)] as x approaches infinity.
a) 0
b) 2
c) 1/2
d) 1/4
281. If y = 1/(t + 1) and x = t/(t + 1), find dy/dx or y’.
a) 1
b) -1
c) t
d) –t
282. Differentiate: y = [(sin x)/(1 – 2cos x)].
a) (cos x – 1)/(1 – 2cos x)^2
b) (cos x – 2)/(1 – 2cos x)^2
c) (cos x)/(1 – 2cos x)^2
d) (-2)/(1 – 2cos x)^2
283. Given the curve y = 12 – 12x + x^3, determine its maximum, minimum and inflection
points.
a) (-2, 28), (2, -4), & (0, 12)
b) (2, -28), (2, 4), & (0, 2)
c) (-2, -28), (-2 -4) & (2, 12)
d) (-2, 28), (-2, 4) & (1, 12)
284. Given the curve y^2 = 5x – 1 at point (1, -2), find the equation of tangent and normal to the
curve.
a) 5x + 4y + 3 = 0 & 4x – 5y – 14 = 0
b) 5x + 4y – 3 = 0 & 4x + 5y – 14 = 0
c) 5x – 4y + 3 = 0 & 4x + 5y + 14 = 0
d) 5x – 4y – 3 = 0 & 4x + 5y – 14 = 0
285. Find the radius of the curvature at any point on the curve, y + ln cos x = 0
a) cos x
b) 1.5707
c) sec x
d) 1
286. Find the minimum volume of a right circular cylinder that can be inscribed in a sphere
having a radius r.
a) 1/√𝟑 volume of sphere
b) √3 volume of sphere
c) 2/√3volume of sphere
d) √2/3 volume of sphere
287. Find the point in the parabola y^2 = 4x at which rate change of the ordinate and abscissa are
equal.
a) (1, 2)
b) (-1, 4)
c) (2, 1)
d) (4, 4)
288. What is the allowable error in measuring the edge of cube that is intended to hold 8 m^3, if
the error of the computed volume is not to exceed 0.03 m.
a) 0.002
b) 0.003
c) 0.0025
d) 0.001
289. Find the slope of x^2 y = 8 at point (2, 2)
a) 2
b) -1
c) -2
d) 1/2
290. Water is flowing into a conical vessel 15 cm deep and having a radius of 3.75 cm across the
top. If the rate at which the water rises is 2 cm/sec, how fast is the water flowing into the conical
vessel when the water is 4 cm deep?
a) 6.28 m^3/s
b) 2.37 m^3/s
c) 4.57 m^3/s
d) 5.73 m^3/s
291. Find the slope of the line having a parametric equation y = 4t + 6 and x = t + 1.
a) 1
b) 2
c) 3
d) 4
292. Determine the diameter of a closed cylindrical tank having a volume of 11.3 m^3 to obtain a
minimum surface area.
a) 1.44
b) 2.44
c) 3.44
d) 4.44
293. Determine the velocity of progress with the given equation, D = 20t + 5/(t + 1) when t = 4
sec.
a) 16.8 m/s
b) 17.8 m/s
c) 18.8 m/s
d) 19.8 m/s
294. Find the slope of the curve x^2 + y^2 – 6x + 10y + 5 = 0 at point (1, 0).
a) 1/3
b) 3/4
c) 2/5
d) 1/5
295. Two posts 10 m high and the other is 15 m high stands 30 m apart. They are to be stayed by
transmission wires attached to a single stake at ground level, the wires running to the top of the
posts. Where should the stake be placed to use the least amount of wire?
a) 12 m
b) 14 m
c) 18 m
d) 16 m
296. Find the slope of the line having the parametric equations x = t – 1 and y = 2t.
a) 1
b) 3
c) 2
d) 4
297. Find the second derivative of y with respect to x for: 4x^2 + 8y^2 = 36.
a) 9/4y^3
b) 4y^3
c) -9/4y^3
d) -4y^3
298. Find the derivative of h with respect to u; for h = π^2u.
a) π^2x
b) 2u ln π
c) 2π^2u ln π
d) 2π^2u
299. Find y’ if y = x ln x – x.
a) ln x
b) x ln x
c) (ln x)/x
d) x/ln x
300. Differentiate, y = sec x^2.
a) 2x sec x^2
b) 2sec x^2
c) 2xtan x^2
d) 2xsec x^2 tan x^2
301. What is the derivative of the function with respect to x of (x + 1)^3 – x^3?
a) 3x + 3
b) 3x – 3
c) 6x – 3
d) 6x + 3
302. Evaluate the Lim [(x^2 – 1)/(x^2 + 3x – 4)] as x approaches 1.
a) 3/5
b) 2/5
c) 4/5
d) 1/5
303. Evaluate: Lim [(1 – cos x)/x^2] as x approaches 0
a) 0
b) 1/2
c) 2
d) -1/2
304. Evaluate: Lim [(3x^4 – 2x^2 + 7)/(5x63 + x – 3)] as x approaches infinity.
a) undefined
b) 3/5
c) infinity
d) 0
305. Differentiate: (x^2 + 2)^1/2
a) [(x^2 + 1)^1/2]/2
b) x/(x^2 + 2)^1/2
c) 2x/(x + 2)^1/2
d) (x^2 + 2)^2
306. Differentiate y = e^x cos x^2
a) –e^x sin x^2
b) e^x (cos x^2 – 2xsin x^2)
c) e^x cos x^2 – 2xsin x^2
d) -2xe^x sin x
307. Differentiate: y = log (x^2 + 1)^ 2
a) log e (x)(x^2 + 1)^2
b) 4x(x^2 + 1)
c) (4xlog e)/(x^2 +1)
d) 2x(x + 1)
308. If y = 4cos x + sin 2x, what is the slope of the curve then x = 2.
a) -2.21
b) -4.94
c) -3.25
d) -2.22
309. Find y’ = arcsin cos x.
a) -1
b) -2
c) 1
d) 2
310. A poster is to contain 300 m^2 of printed matter with margins of 10 cm at the top and
bottom and 5 cm at each side. Find the overall dimensions, if the total area of the poster is a
minimum.
a) 27.76 cm, 47.8 cm
b) 20.45 cm, 35.6 cm
c) 22.24 cm, 44.5 cm
d) 25.55 cm, 46.7 cm
311. Water is flowing into a conical cistern at the rate of 8 m^3/min. If the height of the inverted
cone is 12 m and the radius of its circular opening is 6 m. How fast is the water level rising when
the water is 4 m deep?
a) 0.74 m/min
b) 0.64 m/min
c) 0.54 m/mid
d) 0.84 m/min
312. An isosceles triangle with equal sides of 20 cm has these sides at variable equal angles with
the base. Determine the maximum area attainable by the triangle.
a) 250 cm^2
b) 200 cm^2
c) 180 cm^2
d) 300 cm^2
313. A triangle has variable sides x, y, z subject to the constraint such that the perimeter P is
fixed to 18 cm. What is the maximum possible area for the triangle?
a) 15.59 cm^2
b) 18.71 cm^2
c) 14.03 cm^2
d) 17.15 cm^2
314. What is the limit value of y = (x^3 + x)/(x^2 + x) as x approaches zero?
a) 1
b) indeterminate
c) 0
d) 3
315. A fencing is limited to 20 ft high. What is the maximum rectangular area that can be fenced
in using two perpendicular corner sides of an existing wall?
a) 120
b) 100
c) 140
d) 190
316. Find the point on the curve x^2 = 2y which is nearest to the point (4, 1).
a) (2, 4)
b) (4, 2)
c) (2, 2)
d) (2, 3)
317. Find the largest area of a rectangle which can be inscribed in the ellipse, 4x^2 + 9y^2 = 36.
a) 12
b) 24
c) 6
d) 48
318. The derivative with respect ot v of the function f(y) = 3√𝑦 is:
a) (y^-2/3)/3
b) 3y^2/3
c) 3y^-2/3
d) (y^2/3)/3
319. If a is the simple constant, what is the derivative of y = x^a?
a) ax – x
b) ax
c) ax to the a - 1 power
d) x to the a – 1 power
320. The first derivative with respect to y of the function d(y) = 3√9 is _____.
a) 3(9/2)
b) 3(9) to the 1/2 power
c) 0
d) 9
321. Find the derivative of f(x) = [x to the 3rd power – (x – 1) to the 3rd power] to the 3rd
power?
a) 3x – 3 (x – 1)
b) 3[x to the 3rd power – x – 1] to the 3rd power
c) 9[x to the 3rd power – (x – 1) to the 3rd power]^2 [x –(x – 1)]^2
d) 9[x to the 3rd power – (x – 1) to the 3rd power]^2 [x^2 – (x – 1)^2]
322. Water from the filtering facility is pouring into a swimming pool. After n hours, there are n
+ √𝑛 gallons in the pool. At what rate is the water pouring into the pool when n = 16 hrs?
a) 1/2 gph
b) 9/8 gph
c) 1 gph
d) 7/6 gph
323. Find the slope of the equation y = x^2 when x = 2.
a) 2
b) 6
c) 4
d) 1
324. What is the value of the following limit? Lim (x^2 – 9)/(x – 3) as x approaches 3.
a) 3
b) 6
c) 9
d) 0
325. The position of an object as a function of time is describe by x = 4t^3 + 2t^2 – t + 3. What
is the distance traveled by an object at t = -2 and t = 2?
a) 44
b) 63
c) 78
d) 108
326. Lim (x^2 0 4)/(x – 2) as x approaches 2, compute the indicated limit.
a) 4
b) 8
c) 6
d) 10
327. Evaluate the integral of [(3^x) /(e^x)]dx from 0 to 1.
a) 1.510
b) 1.051
c) 1.105
d) 1.510
328. Evaluate the integral of tan^2 x dx.
a) tan x – x + c
b) sec^2 x + x + c
c) 2sec x – x + c
d) (tan^2 x)/s + x + c
329. Evaluate the integral of sqrt(3t – 1) dt.
a) (2/9)(3t – 1)^5/2 + c
b) (2/9)(3t – 1)^3/2 + c
c) (1/2)(3t – 1)^5/2 + c
d) (1/2)(3t – 1)^3/2 + c
330. Evaluate the integral of (3t – 1)^3 dt.
a) (1/12)(3t – 1)^4 + c
b) (1/4)(3t – 1)^4 + c
c) (1/3)(3t – 1)^4 + c
d) (1/12)(3t – 1)^3 + c
331. Integrate the square root of (1 – cos x) dx.
a) -2 sqrt(2) cos (x/2) + c
b) -2sqrt(2) cos x + c
c) 2sqrt(2) cos (x/2) + c
d) -2sqrt(2) cos x+ c
332. Find the area bounded by the parabolas x^2 – 2y = 0 and x^2 + 2y – 8 = 0.
a) 32/2
b) 20/3
c) 16/3
d) 64/3
333. Evaluate: integral of cos^8 3A dA from 0 to π/6.
a) 35π/768
b) 45π/768
c) 125π/768
d) 5π/768
334. Evaluate: integral of 1/(4 + x^2)^3/2 dx.
a) x/(4sqrt(x^2 + 4)) + c
b) -1/(4sqrt(x^2 + 4)) + c
c) - x/(4sqrt(x^2 + 4)) + c
d) 1/(4sqrt(x^2 + 4)) + c
335. Evaluate: integral of (e^x)/(e^x + 1) dx
a) ln(e^x + 1) + c
b) ln(e^-x + 1) + c
c) ln^2 (e^x + 1) + c
d) ln^2 (e^x + 1) + c
336. Evaluate: integral of (e^x – 1)/(e^x + 1)
a) ln (e^x -1)^2 + x + c
b) ln (e^x + 1) + x + c
c) ln (e^x + 1)^2 –x + c
d) ln (e^x + 1)^2 –x + c
337. Evaluate integral of ln x dx from 1 to 0.
a) infinity
b) 1
c) 0
d) e
338. Find the area bounded by the line x – 2y + 10 = 0, the x-axis, the y-axis and x = 10.
a) 75
b) 45
c) 18
d) 36
339. Find the area bounded by the curves x^2 + y^2 = 9 and 4x^2 + 9y^2 = 36, on the first
quadrant.
a) 2/3π
b) 3/4π
c) 1/2π
d) 3/2π
340. Determine the integral of z sin z with respect to z, then r from r = 0 to r = 1 and from z = 0
to z = π/2.
a) 1/2
b) 4/5
c) 1/4
d) 2/3
341. Integrate 1/(3x + 4) with respect to x and evaluate the result from x = 0 to x = 2.
a) 0.278
b) 0.336
c) 0.252
d) 0.305
342. An area in the xy plane is bounded by the following lines: x = 0 (y-axis), y = 0 (x-axis), x +
4y = 20, and 4x + y = 20. The linear function z = 5x + 5y attains its maximum value within the
bounded area only at one of the vertices (intersections of the above lines). Determine the
maximum value of z.
a) 40
b) 25
c) 50
d) 45
343. Find the area bounded by the parabola x^2 = 4y and y = 4.
a) 21.33
b) 33.21
c) 31.32
d) 13.23
344. Find the area in the first quadrant bounded by the parabola y^2 = 4x, x = 1 ad x = 3.
a) 9.555
b) 5.955
c) 5.595
d) 9.955
345. Evaluate integral of 12 sin^5 x cos^5 x dx from 0 to π/2.
a) 0.20
b) 0.50
c) 0.25
d) 0.35
346. Evaluate integral of x(x – 5)^12 dx from 5 to 6.
a) 0.456
b) 0.587
c) 0.708
d) 0.672
347. What is the area bounded by the curve y^2 = x and the line x – 4 = 0.
a) 32/3
b) 34/7
c) 64/3
d) 16/3
348. Find the area bounded by the curve r = 8 cos 2θ.
a) 16π
b) 32π
c) 12π
d) 8π
349. The area bounded by the curve y = 2x^1/2, the line y = 6 and the y-axis is to be resolved at
y = 6. Determine the centroid of the volume generated.
a) 0.56
b) 1.80
c) 1.0
d) 1.24
350. Find the area of the region bounded by the polar curve r^2 = a^2 cos 2θ.
a) 2a^2
b) 4a^2
c) 3a^2
d) a^2
351. The area bounded by the curve y^2 = 12x and the line x = 3 is resolved about the line x = 3.
What is the volume generated?
a) 185
b) 187
c) 181
d) 183
352. Find the moment of inertia with respect to the x-axis of the area bounded by the parabola
y^2 = 4x and the line x = 1.
a) 2.35
b) 2.68
c) 2.13
d) 2.56
353. Given the area in the first quadrant bounded by x^2 = 8y, the line y – 2 = 0 and the y-axis.
What is the volume generated when the area is resolved about the line y – 2 = 0?
a) 28.41
b) 27.32
c) 26.81
d) 25.83
354. Find the area of the horizontal differential rectangle xdy by the x-axis and the line y = 4.
The parabola y = 4x. Rectangle area = (4 – x)dy.
a) 64/2
b) 32/3
c) 32/4
d) 32/2
355. What is the approximate area bounded by the curves y = 8 – x^2 and y = -2 + x^2?
a) 22.4
b) 29.8
c) 44.7
d) 26.8
356. What retarding force is required to stop a 0.45 caliber bullet of mass 20 grams and speed of
200 m/s as it penetrates a wooden block to a depth of 2 inches?
a) 17,716 N
b) 19,645 N
c) 15,500 N
d) 12,500 N
357. A freely falling body is a body in rectilinear motion and with constant ________.
a) velocity
b) speed
c) deceleration
d) acceleration
358. A ball is thrown upward with an initial velocity of 50 ft/s. How high does it go?
a) 39 ft
b) 30 ft
c) 20 ft
d) 45
359. It takes an airplane one hour and forty-five minutes to travel 500 miles against the wind and
covers the same distance in one hour and fifteen minutes with the win. What is the speed of the
airplane?
a) 342 mph
b) 375 mph
c) 450 mph
d) 525 mph
360 When the total kinetic energy of a system is the same as before and after the collision of two
bodies, it is called:
a) static collision
b) elastic collision
c) inelastic collision
d) plastic collision
361. An airplane travels from points A to B with a distance of 1500 km and a wind along its
flight. If it takes the airplane 2 hours from A to B with the tailwind and 2.5 hours from B to A
with the headwind, what is the velocity?
a) 700 kph
b) 675 kph
c) 450 kph
d) 750 kph
362. The periodic oscillations either up or down or back and forth motion in a straight line is
known as ________.
a) transverse harmonic motion
b) resonance
c) rotational harmonic motion
d) translational harmonic motion
363. A flywheel of radius 14 inches is rotating at the rate of 1000 rpm. How fast does a poin on
the rim travel in ft/sec?
a) 122
b) 1456
c) 100
d) 39
364. Pedro started running at a speed of 10 kph. Five minutes later, Mario started running in the
same direction and catches up with Pedro in 20 minutes. What is the speed of Mario?
a) 12.5 kph
b) 15.0 kph
c) 17.5 jph
d) 20.0 kph
365. A flywheel accelerates uniformly from rest to a speed of 200 rpm in one-half second. It then
rotates at the same speed for 2 seconds before decelerating to rest in one-third second. Determine
the total number of revolutions of the flywheel during the entire time interval?
a) 8.06 rev
b) 9.12 rev
c) 6.90 rev
d) 3.05
366. A ball is thrown upward with an initial velocity of 60 ft/s. Determine the velocity at the
maximum height.
a) 6.12 ft/s
b) 2.61 ft/s
c) 2.12 ft/s
d) 0 ft/s
367. A bullet if fired vertically upward with a mass of 3 grams. If it reaches an altitude of 100 m,
what is its initial velocity?
a) 54.2 m/s
b) 47.4 m/s
c) 52.1 m/s
d) 44.2 m/s
368. What is the acceleration of a point on a rim of a flywheel 0.8 m in diameter turning at the
rate of 1400 rad/min?
a) 214.77 m/s
b) 217.77 m/s
c) 220.77 m/s
d) 227.77 m/s
369. Impulse causes ______________.
a) the object’s momentum to change
b) the object’s momentum to decrease
c) the object’s momentum to increase
d) the object’s momentum to remain constant or to be conserve
370. A DC-9 jet with a takeoff mass of 120 tons has two engines producing average force of
80,000 N during takeoff. Determine the plane’s acceleration down the runway if the takeoff time
is 10 seconds.
a) 1.52 m/s^2
b) 1.33 m/s^2
c) 3.52 m/s^2
d) 2.45 m/s^2
371. In a hydraulic press, the small cylinder has a diameter of 8 cm, while the larger piston has a
diameter of 2 cm. If the force of 600 N is applied to the small piston, what is the force of the
large piston, neglecting friction?
a) 3895 N
b) 4125 N
c) 4538 N
d) 5395 N
372. A car accelerates uniformly from standstill to 80 mi/hr in 5 seconds. What is its
acceleration?
a) 23.47 ft/sec^2
b) 33.47 ft/sec^2
c) 43.47 ft/sec^2
d) 53.47 ft/sec^2
373. A stone is thrown vertically upward at the rate of 20m/s. It will return to the ground after
how many seconds?
a) 3.67 sec
b) 5.02 sec
c) 4.08 sec
d) 2.04 sec
374. A plane is headed due east with airspeed of 240 mph. If a wind at 40 mph is blowing from
the north, find the ground speed of the plane.
a) 190 mph
b) 210 mph
c) 243 mph
d) 423 mph
375. The study of motion without reference to the force that causes the motion is known as
__________.
a) statics
b) dynamics
c) kinetics
d) kinematics
376. A car accelerates from rest and reached a speed of 90 kph in 2- seconds. What is the
acceleration in meter per second?
a) 0.667
b) 0.707
c) 0.833
d) 0.866
377. Momentum is a property related to the object’s __________.
a) motion and mass
b) mass and acceleration
c) motion and weight
d) weight and velocity
378. A gulf weighs 1.6 ounce. If its velocity immediately after being driven is 225 fps, what is
the impulse of the bow in slug-ft/sec?
a) 0.855
b) 0.812
c) 0.758
d) 0.699
379. A missile is fired with a speed of 100 fps in a direction 30 degrees above the horizontal.
Determine the maximum height to which it rises?
a) 60 ft
b) 52 ft
c) 45 ft
d) 39 ft
380. When the total kinetic energy of a system is the same as before and after collision of two
bodies, it is called:
a) plastic collision
b) inelastic collision
c) elastic collision
d) static collision
381. A man travels in a motorized banca at the rate of 15 kph from his barrio to the poblacion
and come back to his barrio at the rate of 12 kph. If his total time of travel back and forth is 3
hours, the distance from the barrio to the poblacion is:
a) 10 km
b) 15 km
c) 20 km
d) 25 km
382. A 50,000 N car travelling with a speed of 150 km/hr rounds a curve whose radius is 150 m.
Find the centripetal force.
a) 70 kN
b) 25 kN
c) 65 kN
d) 59 kN
383. A ball is dropped from a building 100 m high. If the mass of the ball is 10 grams, after what
time will the ball strikes the earth?
a) 5.61 s
b) 2.45 s
c) 4.52 s
d) 4.42 s
384. A 900 N weight hangs on a vertical plane. A man pushes this weight horizontally until the
rope makes an angle of 40° with the vertical. What is the tension in the rope?
a) 1286 N
b) 1175 N
c) 918 N
d) 825 N
385. A plane dropped a bomb at an elevation 1000 meters from the ground intended to hit a
target which is 200 m from the ground. If the plane was flying at a velocity of 300 kph, at what
distance from the target must the bomb be dropped to hit the target? Wind velocity and
atmospheric pressure to be disregarded.
a) 1864.71 m
b) 2053.20 m
c) 1574.37 m
d) 1064.20 m
386. What is the minimum distance can a truck slide on a horizontal asphalt road if it is
travelling at 25 m/s? The coefficient of sliding friction between the asphalt and rubber tire is at
0.60. The weight of the truck is 8500 kg.
a) 44.9
b) 58.5
c) 53.2
d) 63.8
387. A concrete highway curve with a radius of 500 ft is banked to give lateral pressure
equivalent to f = 0.15. For what coefficient of friction will skidding impend for a speed of 60
mph.
a) µ > 0.360
b) µ < 0.310
c) µ > 0.310
d) µ < 0.360
388. A circle has a diameter of 20 cm. Determine the moment of inertia if the circular area
relative to the axis perpendicular to the area through the center of the circle in cm^4.
a) 14,280
b) 15,708
c) 17,279
d) 19,007
389. An isosceles triangle has a 10 cm base and a 10 cm altitude. Determine the moment of
inertia of the triangle area relative to a line parallel to the base and through the upper vertex in
cm^4.
a) 2,750
b) 3,025
c) 2,500
d) 2,273
390. Two electrons have speeds of 0.7c and x respectively. If their relative velocity is 0.65c, find
x.
a) 0.02c
b) 0.12c
c) 0.09c
d) 0.25c
391. A baseball is thrown from a horizontal plane following a parabolic path with an initial
velocity of 100 m/s at an angle of 30° above the horizontal. How far from the throwing point will
the ball attain its original level?
a) 890 m
b) 883 m
c) 878 m
d) 875 m
392. What is the speed of a synchronous earth’s satellite situated 4.5 x 10^7 m from the earth?
a) 11,070 kph
b) 12,000 kph
c) 11,777.4 kph
d) 12,070.2 kph
393. What is the inertia of a bowling ball (mass 0.50 kg) of radius 15 cm rotating at an angular
speed of 10 rpm for 6 seconds.
a) 0.001 kg-m^2
b) 0.002 kg-m^2
c) 0.0045 kg-m^2
d) 0.005 kg-m^2
394. The angle or inclination of ascend of a road having 8.25% grade is ____________ degrees.
a) 4.72
b) 4.27
c) 5.12
d) 1.86
395. A highway curve has a super elevation of 7 degrees. What is the radius of the curve such
that there will be no lateral pressure between the tires and the roadway at a speed of 40 mph?
a) 265.71 m
b) 438.34 m
c) 345.34 m
d) 330.78 m
396. A shot is fired at an angle of 30 degrees with the horizontal and a velocity of 120 m/s.
Calculate the range of the projectile.
a) 12.71 km
b) 387.57 ft
c) 0.789 mile
d) 423.74 yd
397. A stone dropped from the top of a building 55 yd elevation will hit the ground with a
velocity of:
a) 37 ft/sec
b) 33 ft/sec
c) 105 ft/sec
d) 103 ft/sec
398. What is the kinetic energy of a 4000 lb automobile which is moving at 44 ft/sec?
a) 1.21 x 10^5 ft-lb
b) 2.10 x 10^5 ft-lb
c) 1.80 x 10^5 ft-lb
d) 1.12 x 10^5 ft-lb
399. Find the rate of increase of velocity if a body increases its velocity from 50 m/sec to 130
m/sec in 16 sec.
a) -4.0 m/sec^2
b) 80 m/sec^2
c) -80 m/sec^2
d) 5.0 m/sec^2
400. A 20 kg sack is raised vertically 5 meters in 0.50 sec. What is the change in Potential
Energy?
a) 98.1 J
b) 981 J
c) 200 J
d) 490.5 J
401. A 350 lbf acts on a block at an angle of 15 degrees with the horizontal. What is the work
done by this force if it is pushed 5 feet horizontally?
a) 1350.3 ft-lb
b) 1690 ft-lb
c) 1980 ft-lb
d) 2002 ft-lb
402. A 20 kg object moving at 10 m/sec strikes an unstretched spring to a vertical wall having a
spring constant of 40 kN/m. Find the deflection of the spring.
a) 111.8 mm
b) 223.6 mm
c) 70.7 mm
d) 50.0 mm
403. A 300 kg box impends to slide down a ramp inclined at an angle of 25 degrees with the
horizontal. What is the frictional resistance?
a) 1243.76 N
b) 9951.50 N
c) 1468.9 N
d) 3359.7 N
404. A marksman fires a rifle horizontally at a target. How much does the bullet drop in flight if
the target is 150 m away and the bullet has a muzzle velocity of 500 m/sec?
a) 0.34 m
b) 0.44 m
c) 0.64 m
d) 0.54 m
405. A ball is thrown from a building at an angle of 60 degrees with the horizontal at an initial
velocity of 30 m/sec. After hiting level ground at the base of the building, it has covered a total
distance of 150 m. How tall is the building?
a) 230.7 m
b) 756.7 m
c) 692.5 m
d) 1089 m
406. A highway curve with radius 800 ft is to be banked so that a car travelling 55 mph will not
skid sideways even in the absence of friction. At what angle should the curve be banked?
a) 0.159 deg
b) 75 deg
c) 6.411 deg
d) 14.2 deg
407. An airplane flying horizontally at a speed of 200 m/sec drops a bomb from an elevation of
2415 meters. Determine the time required for the bomb to reach the earth.
a) 11.09 sec
b) 22.18 sec
c) 44.37 sec
d) 8.20 sec
408. Find the banking angle of a highway curve of 100 m radius designed for cars travelling at
180 kph, if the coefficient of friction between the tires and the road is 0.58.
a) 19.23 deg
b) 38.5 deg
c) 76.9 deg
d) 45 deg
409. A pulley has a tangential speed of 14m/sec and an angular velocity of 6/5 rad/sec. What is
the normal acceleration of the pulley?
a) 91 m/sec^2
b) 99 m/sec^2
c) 105 m/sec^2
d) 265 m/sec^2
410. An elevator weighing 4000 kb attains an upward velocity of 4 m/sec in 3 sec with uniform
acceleration. Find the apparent weight of a 40 kg man standing inside the elevator during its
ascent.
a) 339 N
b) 245 N
c) 446 N
d) 795 N
411. A stone is dropped from a cliff and 2 sec later another stone is thrown downward with a
speed of 22 m/sec. How far below the top of the cliff will the second stone overtake the first?
a) 375 m
b) 507 m
c) 795 m
d) 994 m
412. How much horizontal force is needed to produce an acceleration of 8 m/sec^2 on a 75 kg
box?
a) 600 N
b) 500 N
c) 400 N
d) 200 N
413. An elevator with a mass of 1500 kg descends with a acceleration of 2.85 m/sec^2. What is
the tension in the supporting cable?
a) 10,440 N
b) 12,220 N
c) 15,550 N
d) 20,220 N
414. A dictionary is pulled to the right at a constant velocity by a 25 N force pulling upward at
60 degrees above the horizontal. What is the weight of the dictionary if the coefficient of kinetic
friction is 0.30?
a) 31 N
b) 21 N
c) 20 N
d) 63 N
415. The breaking strength of a string is 500 N. Find the maximum speed that it can attain if a
1.5 kg ball is attached at one end while the other end is held stationary and is whirled in a circle.
The string is 0.65 m long.
a) 15.4 m/sec
b) 55.2 m/sec
c) 24.4 m/sec
d) 14.7 m/sec
416. The position of a body weighing 72.6 kg is given by the expression S = 5t^2 + 3t + 4, where
S is in meters and t is in seconds. What force is required for this motion?
a) 625 N
b) 695 N
c) 726 N
d) 985 N
417. Assuming a shaft output of 3,000 kW and a fuel rate of (JP-4) 34.2 lbs/min. What is the
overall thermal efficiency of the machine? (HHV of JP-4 is 18,000 Btu/lb)
a) 24.2%
b) 28.3%
c) 27.7%
d) 29.1%
418. g = 32.2 ft/sec^2. How is it expressed in SI?
a) 9.81 m/sec^2
b) 9.86 m/sec^2
c) 9.08 m/sec^2
d) 9.91 m/sec^2
419. A winch lifted a mass of 1600 kg through a height of 25 m in 30 sec. If the efficiency of the
winch is 60%, calculate the energy consumed in kWh.
a) 0.1718 kWh
b) 0.1881 kWh
c) 0.1817 kWh
d) 0.218 kWh
420. Cast iron weighs 640 pounds per cubic foot. The weight of a cast iron block 14” x 12” x 18”
is:
a) 1120 lbs
b) 1000 lbs
c) 1200 lbs
d) 1088 lbs
421. A solid disk flywheel (l = 2—kg-,^2) is rotating with a speed of 900 rpm. What is its
rotational kinetic energy?
a) 730 x 10 to the 3rd power J
b) 680 x 10 to the 3rd power J
c) 1100 x 10 to the 3rd power J
d) 888 x 10 to the 3rd power J
422. The path of a projectile is a:
a) ellipse
b) parabola
c) part of a circle
d) hyperbola
423. What is the name for a vector that represent the sum of two vectors?
a) moment
b) torque
c) scalar
d) resultant
424. Determine the super elevation of the outer rail of a 4-ft wide railroad track on a 10 degrees
curve. (A 10 degrees curve is one which a chord 100 ft long subtends an angle of 10 degrees at
the center). Assumed velocity of 45 mph.
a) 0.90 ft
b) 2.80 ft
c) 2.50 ft
d) 1.15 ft
425. A 10” diameter helical gear carries a torque of 4000 in-lb. It has a 20 degree involute stub
teeth and a helix angle of 30 degree. Determine the axial component of the load on the teeth.
a) 451.4 lb
b) 218 lb
c) 471.5 lb
d) 461.6 lb
426. A winch lifted a mass of 1600 kg through a height of 25 m in 30 sec. Calculate the input
power in kW if the efficiency of the winch is 60%.
a) 18.1 kW
b) 21.8 kW
c) 28.1 kW
d) 13.08 kW
427. A diagram which shows only the forces acting on the body:
a) free body diagram
b) cash flow
c) forces flow diagram
d) motion diagram
428. One horse power is equivalent to:
a) 746 watts
b) 7460 watts
c) 74.6 watts
d) 7.46 watts
429. Which is a true statement about the vector? V1 = i + 2j + k and v2 = i + 3j – 7k
a) the vectors coincide
b) the angle between them is 17.4 degree
c) the vectors are parallel
d) the vectors are orthogonal
430. In a lifting machine, a load of 50 kN is moved by a distance of 10 cm using an effort of 10
kN which moves through a distance of 1 m, the efficiency of the machine is:
a) 20%
b) 50%
c) 10%
d) 40%
431. What is the angle between two vectors A and B? A = (3, 2, 1) and B = (2, 3, 2)
a) 24.8 deg
b) 36.7 deg
c) 42.5 deg
d) 77.5 deg
432. What is the equivalent of one horsepower?
a) 746 W
b) 3141 kW
c) 33,000 ft-lb/min
d) 2545 Btu/lb
433. Two people are driving towards each other between two towns 160 km apart. The first man
drives at the rate of 45 kph and the other drives at 35 kph. From their starting point how long
would it take that they will meet.
a) 3 hr
b) 4 hr
c) 2 hr
d) 1 hr
434. Resistance to motion, caused by one surface rubbing against another.
a) inertia
b) resistance
c) gravity
d) friction
435. What happens to the acceleration if the mass is tripled and the force remains the same?
a) it will be tripled
b) it will be 1/3 of the original
c) it will remain the same
d) it will be 3 times the original
436. Which number has five significant digits?
a)0.01410
b)0.00101
c)1.0140
d)0.01414
437. The prefix of a no. 10 raise ot the power minus 6 is:
a) tera
b)deci
c) centi
d) micro
438. The length of a bar is one million of a meter is called:
a) omicron
b) micron
c) one bar
d)one milli
439. 120 Giga Newton is how many Mega Newton?
a) 12,000
b) 120
c) 1,200
d) 120,000
440. Factor the expression ( 289x^3 - 204x^2 + 36x )
a)4x( 17/2 x – 3)( 17/2 x – 3 )
b) 4x(17x-3)(17x-3)
c) 4x(4x-3)(4x+3)
d)4x(17x-3)(17x+3)
441. Factor the expression as completely as possible: (2x^3 -7x^2 +6x)
a) x(x-2)(x-3)
b) x(x-2)(x+3)
c) x(x-2)(2x+3)
d) x(x-2)(2x-3)
442. ( (xyz)^(1/n) )^n is equal to:
a) (xyz)^(1/n)
b) (xyz)^n
c) xyz
d) (xyz)^(n-1)
443. If x raise to the one half of one equals 4, x equal to:
a) 24
b) 8
c) 12
d) 16
444. If the numbers one and above divided by zero the answer is:
a) zero
b) infinity
c) indeterminate
d) absurd
445. Solve for x and y: 4x + 3y = 11 and 8x^2 – 9y^2 = -7.
a) x = 5/3 and y = 3/2
b) x = 3/2 and y = 3/2
c) x = 3/5 and y = 5/3
d) x = 3/2 and y = 5/3
446. If A can do the work in a days and B in b days, how long will it take to do the job working
together?
a) ( a + b ) / ab days
b) ( a + b ) / 2 days
c) ab / ( a + b ) days
d) a + b days
447. Five hundred kg of steel containing 8% nickel to be made by mixing a steel containing 14%
nickel with another containing 6% nickel. How much of each is needed?
a) 125 kg and 375 kg
b) 150 kg and 350 kg
c) 200 kg and 300 kg
d) 250 kg and 250 kg
448. Logarithm of 10th root of, x raise to 10 equals to:
a) log x
b) ( log x^(1/10) ) / 10
c) 10 log x
d) log x^10
449. What is the natural logarithm of e to the a plus b power?
a) ab
b) log ab
c) a + b
d) 2.718 ( a + b)
450. What is the logarithm of negative one hundred?
a) No logarithm
b) Zero
c) Positive log
d) Negative log
451. The logarithm of 1 to base e is:
a) One
b) 2.718
c) Infinity
d) Zero
452. What is the value of (0.101)^(5/6)?
a) antilog [ log 0.101/(5/6) ]
b) antilog [ 6/5 log 0.101 ]
c) 6/5 antilog [ log 0.101 ]
d) antilog [ 5/6 log 0.101]
453. A box contains 8 black and 12 white balls. What is the probability of getting 1 black and 1
white ball in two consecutive draws from the box?
a) 0.53
b) 0.45
c) 0.50
d) 0.55
454. What is the sum of the following finite sequence of terms? 28, 35, 42, ..., 84.
a) 504
b) 525
c) 540
d) 580
455. Solve for x that satisfy the equation, x^2 + 36 = 9 – 2x^2
a) ±6i
b) +9i
c) ±3i
d) -9i
456. 35.2 to the x power = 7.5 to the x-2 power, solve for x using logarithms.
a) -2.06
b) -2.10
c) -2.60
d) +2.60
457. Solve algebraically: 4x^2 + 7y^2 = 32 and 11y^2 – 3x^2 = 41.
a) y = 4, x = ±1 and y = -4, x = ±1
b) y = +2, x = ±1 and y = -2 , x = ±1
c) x = 2, y = 3 and x = -2, y = -3
d) x = 2, y = -2 and x = 2, y = -2
458. Factor the expression 16 – 10x + x^2.
a) (x+8)(x-2)
b) (x-8)(x+2)
c) (x-8)(x-2)
d) (x+8)(x+2)
459. What is the value of e^-4 = _____________.
a) 0
b) 0.183156
c) 0.1381560
d) 0.0183156
460. A pump can pump out a tank in 15 hrs. Another pump can pump out the same tank in 20 hrs.
How long will it take both pumps together to pump out the tank?
a) 8.57 hrs
b) 7.85 hrs
c) 6.58 hrs
d) 5.50 hrs
461. A tank can be filled by one pipe in 9 hrs and another pipe in 12 hrs. Starting empty, how
long will it take to fill the tank if water is being taken out by a third pipe at a rate per hour equal
to one-sixth the capacity of the tank?
a) 36 hrs
b) 25 hrs
c) 30 hrs
d) 6 hrs
462. A rubber ball was dropped from a height of 42 m and each time it strikes the ground it
rebounds to a height of 2/3 of the distance from which it fell. Find the total distance travelled by
the ball before it comes to rest.
a) 180 m
b) 190 m
c) 210 m
d) 220 m
463. From a box containing 8 red balls, 8 white balls and 12 blue balls, one ball is drawn at
random. Determine the probability that it is red or white:
a) 0.571
b) 0.651
c) 0.751
d) 0.0571
464. If 1/x, 1/y, 1/z are in A.P., then y is equal to:
a) x-z
b) ½(x+2z)
c) (x+z)/2xz
d) 2xz/(x+z)
465. A class of 40 took examination in Algebra and Trigonometry. If 30 passed algebra, 36
passed Trigonmetry, and 2 failed in both subjects, the number of students who passed the two
subjects is:
a) 22
b) 28
c) 30
d) 60
466. Simplify: ( ab / (ab)^(1/3) )^(1/2)
a) (ab)^(1/3)
b) ab
c) (ab)^(1/2)
d) (ab)^(1/5)
467. Combine into a single fraction: (3x-1)/(x^2-1) – (x+3)/(x^2+3x+2) – 1/(x+2)
a) x-1
b) x+1
c) 1/(x+1)
d) 1/(x-1)
468. Two cars start at the same time from nearby towns 200 km apart and travel toward each
other. One travel at 60 kph and the other at 40 kph. After how many hours will they meet on the
road?
a) 1 hour
b) 2 hrs
c) 3 hrs
d) 2.5 hrs
469. A single engine airplane has an airspeed of 125 kph. A west wind of 25 kph is blowing. The
plane is to patrol due to east and then return toa is base. How far east can it go if the round trip is
to consume 4 hrs?
a) 240 km
b) 180 km
c) 200 km
d) 150 km
470. A car travels from A to B, a distance of 100 km, at an average speed of 30 kph. At what
average speed must it travel back from B to A in order to average 45 kph for the round trip of
200 km?
a) 70 kph
b) 110 kph
c) 90 kph
d) 50 kph
471. Two trains A and B having average speed of 75 mph and 90 kph respectively, leave the
same point and travel in opposite direstions. In how many minutes would they be 1600 miles
apart?
a) 533
b) 733
c) 633
d) 833
472. It takes Butch twice as long as it takes Dan to do a certain piece of work. Working together,
they can do the work in 6 days. How long would it take Dan to do it alone?
a) 12 days
b) 10 days
c) 11 days
d) 9 days
473. A man leaving his office one afternoon noticed the clock at past two o’clock. Between two
to three hours, he returned to his office noticing the hands of the clock interchanged. At what
time did he leave the office?
a) 2:26.01
b) 2:10.09
c) 2:30.01
d) 2:01.01
474. A company has a certain number of machines of equal capacity that produced a total of 180
pieces each working day. If two machines breakdown, the work load of the remaining machines
is increased by three pieces per day to maintain production. Find the number of machines.
a) 12
b) 18
c) 15
d) 10
475.A rectangular field is surrounded by a fence 548 meters long. The diagonal distance from
corner to corner is 194 meters. Determine the area of the rectangular field.
a) 18,270 m^2
b) 18,720 m^2
c) 18,027 m^2
d) 19,702 m^2
476. Solve for x: (x+2)^(1/2) + (3x-2)^(1/2) = 4
a) x = 1
b) x = 3
c) x = 2
d) x = 4
477. Solve for x: (1/x) + (2/x^2) = (3/x^3).
a) x=1,x=-3
b) x=3,x=1
c) x=-1,x=3
d) x=2,x=3
478. Solve for x: x^(2/3) + x^(-2/3) = 17/4
a) x=-4,x=-1/4
b) x=8,x=-1/4
c) x=4,x=1/8
d) x=8,x=1/8
479. A rectangular lot has a perimeter of 120 meters and an area of 800 square meters. Find the
length and width of the lot.
a) 10m and 30m
b) 30m and 20m
c) 40m and 20m
d) 50m and 10m
480. A 24-meter pole is held by three guy wires in its vertical position. Two of the guy wires are
of equal length. The third wire is 5 meters longer than the other two and is attached to the ground
11 meters farther from the foot of the pole than the other two equal wires. Find the length of the
wires.
a) 25m and 30m
b) 15m and 40m
c)20m and 35m
d) 50 and 10m
481. In a racing contest, there are 240 cars which will have fuel provisions that will last for 15
hours. Assuming a constant hourly consumption for each car, how long will the fuel provisions
last if 8 cars withdraw from race every hour after the first?
a) 20 hours
b)10 hours
c) 15 hours
d) 25 hours
482. A pile of boiler pipes contains 1275 pipes in layers so that the top layer contains one pipe
and each lower layer has one more pipe than the layer above. How many layers are there in the
pile?
a) 50
b) 45
c) 40
d) 55
483. A production supervisor submitted the following report on the average rate of production of
printed circuit boards(PCB) in an assembly line: “1.5 workers produce 12 PCB’s in 2 hours”.
How many workers are employed in the assembly line working 40 hours each per week with a
weekly production of 8000 PCB’s/
a) 50 workers
b) 60 workers
c) 55 workers
d) 70 workers
484. A man bought 20 calculators for P20,000.00. There are three types of calculators bought,
business type costs P3,000 each, scientific type costs P1,500 each and basic type costs P500 each.
How many calculators of each type were purchased?
a) 3, 6, 11
b) 2, 6, 12
c) 1, 4, 15
d) 2, 5, 13
486. A veterans organization in cebu city consists of men who fought in World War II and men
who fought in Korea. The secretary noted that 180 members had fought in Korea and that 70%
had taken part in World War II, while 10% of the members had fought in both World War II and
Korea. How many members are there together?
a) 400
b) 500
c) 450
d) 700
487. An angle greater than a straight angle and less than two straight angles is called:
a) Right angle
b) Obtuse angle
c) Reflex angle
d) Acute angle
488. A line segment joining two points on a circle is called:
a) Arc
b) Tangent
c) Sector
d) Chord
489. All circles having the same center but with unequal radii are called:
a) encircle
b) tangent circles
c) concyclic
d) concentric circles
490. A triangle having three sides equal is called:
a) equilateral triangles
b) scalene triangles
c) isosceles triangles
d) right triangles
491. In a regular polygon, the perpendicular line drawn from the center of the inscribed circle to
any one of the sides is called:
a) radius
b) altitude
c) median
d) rhombus
492. A quadrilateral with two and only two sides of which are parallel is called:
a) parallelogram
b) trapezoid
c) quadrilateral
d) rhombus
493. A polygon with fifteen sides is termed as:
a) dodecagon
b) decagon
c) pentedecagon
d) nonagon
494. A statement the truth of which is admitted without proof is called:
a) an axiom
b) a postulate
c) a theorem
d) a corollary
495. A rectangle with equal sides is termed as:
a) rhombus
b) trapezoid
c) square
d) parallelogram
496. The sum of the sides of a polygon is termed as:
a) circumference
b) altitude
c) apothem
d) perimeter
497. A line that meets a plane but not perpendicular to it, in relation to the plane, is:
a) parallel
b) collinear
c) coplanar
d) oblique
498. A quadrilateral whose opposite sides are equal is generally termed as:
a) a square
b) a rectangle
c) a rhombus
d) a parallelogram
499. A part of a line included between two points on the line is called:
a) a tangent
b) a secant
c) a sector
d) a segment
500. Lines which pass through a common point are called:
a) collinear
b) coplanar
c) concurrent
d) congruent
501. Points which lie on the same plane is called:
a) collinear
b) coplanar
c) concurrent
d) congruent
502. In two intersecting lines, the angles opposite to each other are termed as:
a) opposite angles
b) vertical angles
c) horizontal angles
d) inscribed angles
503. A normal to a given plane is:
a) perpendicular to the plane
b) lying on the plane
c) parallel to the plane
d) oblique to the plane
504. Which of the following statements is correct?
a) all equilateral triangles are similar
b) all right-angled triangles are similar
c) all isosceles triangles are similar
d) all rectangles are similar
505. A polygon is ________ when no side, when extended, will pass through the interior of the
polygon.
a) equilateral
b) isoperimetric
c) congruent
d) none of the above
506. The sum of the sides of a polygon:
a) perimeter
b) hexagon
c) square
d) circumference
507. What are the exact values of the cosine and tangent trigonometric functions of the acute
angle A, given sin A = 5/8?
a) cos A = 8 / 39^(1/2) and tan A = 39^(1/2) / 5
b) cos A = 39^(1/2) / 5 and tan A = 8 / 39^(1/2)
c) cos A = 39/8 and tan A = 5/ 39^(1/2)
d) cos A = 8/5 and tan A = 5/8
508. Given a triangle with angle C=290, side a =132 units and side b=233.32 units. Solve for
angle B.
a) B=1200
b) B=122.50
c) B=125.20
d) B=1300
509. Simplify: cos2 θ ( 1 + tan2 θ )
a) tan 2θ
b) 1
c) sin 2θ
d) cos θ
510. What is the cosine of 1200?
a) -0.500
b) -0.450
c) -0.866
d) 0.500
511. What is the sine of 8400?
a) -0.866
b) -0.500
c) 0.866
d) 0.500
512. If the sine of angle A is given as k, what would be then tangent of angle A? Symbol h for
hypotenuse, o for opposite and a for adjacent.
a) hk/o
b) hk/a
c) ha/k
d) ok/a
513. Which is true regarding the signs of the natural functions for angles between 900 and 1800?
a) The tangent is positive
b) The cotangent is positive
c) The cosine is negative
d) The sine is negative
514. What is the inverse natural function of the cosecant?
a) secant
b) sine
c) cosine
d) tangent
515. What is the sum of the squares of the sine and cosine of an angle?
a) 0
b) 1
c) 3^(1/2)
d) 2
516. What is an equivalent expression for sin 2x?
a) ½ sin x cos x
b) 2 sin x cos ½ x
c) -2 sin x cos x
d) 2 sin x/sec x
517. A transit set-up 112.1 feet from the base of a vertical chimney reads 32030’ with the
crosshairs set on top of the chimney. With the telescope level, the vertical rod at the base of the
chimney is 5.1 feet. How tall is the chimney?
a) 66.3 ft
b) 71.4 ft
c) 76.5 ft
d) 170.9 ft
518. If sin θ – cos θ = 1/3, what is the value of in 2θ?
a) 1/3
b) 1/9
c) 8/9
d) 4/9
519. If cos θ = 3^(1/2)/2, then find the value of x if x = 1 – tan2 θ:
a) -2
b) -1/3
c) 4/3
d) 2/3
520. Solve for x: x = 1-(sin θ-cos θ)^2
a) sin θcos θ
b) -2cos θ
c) cos 2 θ
d) sin 2 θ
521. A mobiline tower and a Nipa Hut stand on a level plane. The angles of depression of the top
and bottom of the Nipa Hut viewed from the top of the mobiline tower are 150 and 400,
respectively. The height of the tower is 100m. Find the height of the Nipa hut.
a) 78.08 m
b) 87.08 m
c) 68.07 m
d) 77.08 m
522. Ship A started sailing N40032’E at the rate of 3 mph. After 2 hours, ship B started from the
same port going S45018’E at the rate of 4 mph. After how many hours will the second ship be
exactly south of ship A?
a) 2.25 hrs
b) 2.97 hrs
c) 3.73 hrs
d) 4.37 hrs
523. Solve for the value of x in the equation: ln (2x+7) – ln (x-1) = ln 5
a) x=4
b) x=5
c) x=6
d) x=8
524. Two ships started sailing from the same point. One travelled N200E at 30 mph while the
other travelled S500E at 20 mph. After 3 hrs, how far apart are the ships?
a) 124 miles
b) 129 miles
c) 135 miles
d) 145 miles
525. A quadrilateral ABCD is inscribed in a semi-circle such that one of the sides coincides with
the diameter AD. AB = 10 meters, and BC = 20 meters. If the diameter AD of the semi-circle is
40 meters, find the area of the quadrilateral.
a) 350 m^2
b) 420 m^2
c) 470 m^2
d) 530 m^2
526. Solve for x: Arcsin 2x - Arcsin x = 150
a) 0.1482
b) 0.2428
c) 0.3548
d) 0.4282
527. Solve for x: 2^x + 4^x = 8 ^x
a) 0.694242
b) 0.692424
c) 0.964242
d) 0.742420
528. Given: Triangle ABC whose angle A is 320 and a = 75 m. The opposite side of angle B is
100m. Find angle C.
a) 1000
b) 1030
c) 1100
d) 1150
529. Given triangle ABC with sides AB=210 m, BC=205 m, and AC=110 m. Find the largest
angle.
a) 72.7510
b) 75.7210
c) 77.1570
d) 82.5170
530. A pole which leans 10015’ from the vertical towards the sun casts a shadow 9.43m long on
the ground when the angle of elevation of the sun is 54050’. Find the length of the pole.
a) 12.5m
b) 14.2m
c) 15.4m
d) 18.3m
531. Two points lie on a horizontal line directly south of a building 35 m high. The angles of
depression to the points are 29010’ and 43050’, respectively. Determine the distance between the
points.
a) 26.3 m
b) 28.7 m
c) 30.2 m
d) 36.4 m
532. Two points lie on a horizontal line directly south of a building 35 m high. The angles of
depression to the points are 29010’ and 43050’, respectively. Determine the distance between the
building and the farthest point.
a) 62.7 m
b) 36.5 m
c) 26.5 m
d) 72.6 m
533. Given triangle ABC with sides AB=210 m, BC=205 m, and AC=110 m. Find the largest
angle.
a) C = 1100
b) C = 85.20
c) C = 77.10
d) C = 43.50
534. Given triangle ABC whose angle A is 320 and opposite side of A is 75 meters. The opposite
side of angle B is 100 m. find the opposite side of angle C.
a) c = 137.8 m
b) c = 181.2 m
c) c = 117.7 m
d) c = 127.8 m
535. A point P within an equilateral triangle has a distance of 4m, 5m, and 6m respectively from
the vertices. Find the side of the triangle.
a) 8.53m
b) 6.78m
c) 9.45m
d) 17.8m
536. The diagonal of the floor of a rectangular room is 7.50 m. The shorter side of the room is
4.5 m. What is the area of the room?
a) 36 sq. m
b) 27 sq. m
c) 58 sq. m
d) 24 sq. m
537. A semi-circle of radius 14 cm is formed from a piece of wire. If it is bent into a rectangle
whose length is 1 cm more than its width, find the area of the rectangle.
a) 256.25 sq. cm
b) 323.57 sq. cm
c) 386.54 sq. cm
d) 452.24 sq. cm
538. The length of the side of’ a square is increased by 100%. Its perimeter is increased by:
a) 25%
b) 100%
c) 200%
d) 300%
539. A piece of wire of length 52 cm is cut into two parts. Each part is then bent to form a square.
It is found that total area of the two squares is 97 sq. cm. the dimension of the bigger square is:
a) 4
b) 9
c) 3
d) 6
540. A sector has a radius of 12 cm. If the length of its arc is 12 cm, its area is:
a) 66 sq. cm
b) 82 sq. cm
c) 144 sq. cm
d) 72 sq. cm
541. The perimeter of a sector is 9 cm and its radius is 3 cm. What is the area of the sector?
a) 4 sq. cm
b) 9/2 sq. cm
c) 11/2 sq. cm
d) 27/2 sq. cm
542. An iron bar 20 cm long is bent to form a closed plane area. What is the largest area
possible?
a) 21.56 sq. m
b) 25.68 sq. m
c) 28.56 sq. m
d) 31.83 sq. m
543. A swimming pool is to be constructed in the shape of partially-overlapping identical circles.
Each of the circles has a radius of 9 cm, and each passes through the center of the other. Find the
area of the swimming pool.
a) 302.33 sq. m
b) 362.55 sq. m
c) 398.99 sq. m
d) 409.44 sq. m
544. A circle of radius 5 cm has a chord which is 6 cm long. Find the area of the circle
concentric to this circle and tangent to the given chord.
a) 14 π
b) 16 π
c) 9 π
d) 4 π
545. The diagonals of a rhombus are 10 cm and 8 cm, respectively. Its area is:
a) 10 sq. cm
b) 50 sq. cm
c) 60 sq. cm
d) 40 sq. cm
546. The diagonals of a parallelogram are 10 cm and 16 cm, respectively, if one of its side
measures 6 cm, what is the area?
a) 59.92 sq. cm
b) 65.87 sq. cm
d) 69.56 sq. cm
d) 78.56 sq. cm
547. Given a cyclic quadrilateral whose sides are 4 cm, 5cm, 8cm and 11cm. its area is:
a) 40.25 sq. cm
b) 48.65 sq. cm
c) 50.25 sq. cm
d) 60.25 sq. cm
548 How many cubic meters is 100 gallons of liquid?
a) 1.638
b) 37.85
c) 3.7850
d) 0.37854
549. How many cubic meters is 100 cubic feet of liquid?
a) 3.785
b) 28.31
c) 37.85
d) 2.831
550. The volume of a sphere is 904.78 m^3. Find the volume of the spherical segment of height 4
m.
a) 234.57 m^3
b) 256.58 m^3
c) 145.69 m^3
d) 124.58 m^3
551. A sector of radius of 6 cm and central angle of 600 is bent to form a cross. Find the volume
of the cone.
a) (35)^(1/2) π / 3
b) π (35)^(1/2)
c) 35 π / 3^(1/2)
d) 35 π / 3
552. A spherical wedge of a sphere of radius 10 cm has an angle of 400. Its volume is:
a) 523.42 cm^3
b) 465.42 cm^3
c) 683.42 cm^3
d) 723.45 cm^3
553. If a solid steel ball is immersed in an eight cm diameter cylinder, if displaces water to a
depth of 2.25 cm. The radius of the ball is:
a) 3 cm
b) 6 cm
c) 9 cm
d) 12 cm
554. The volume of a cube is reduced by how much if all sides are halved?
a) 1/8
b) 5/8
c) 6/8
d) 7/8
555. If 23 cm^3 of water are poured into a conical vessel, it reaches a depth of 12 cm. How much
water must be added so that the depth reaches 18 cm?
a) 95 cm^3
b) 100 cm^3
c) 54.6 cm^3
d) 76.4 cm^3
556. A cylindrical tank, lying horizontally, 0.90 m in diameter and 3 m long is filled to a depth of
0.60 m. How many gallons of gasoline does it contain?
a) 250
b) 360
c) 300
d) 270
557. A closed cylindrical tank is 8 ft long and 3 ft in diameter. When lying in a horizontal
position, the water is 2 feet deep. If the tank is in the vertical position, the depth of the water tank
is:
a) 5.67 m
b) 5.82 m
c) 5.82 ft
d) 5.67 ft
558. The surface area of a sphere is 4πr^2. Find the percentage increase in its diameter when the
surface area increases by 21%.
a) 5%
b) 10%
c) 15%
d) 20%
559. Find the percentage increase in volume of a sphere if its surface area is increased by 21%.
a) 30.2%
b) 33.1%
c) 34.5%
d) 30.9%
560. Determine the estimated weight of steel plate size ¼ x 4 x 8.
a) 184.4 kg
b) 148.7 kg
c) 327 kg
d) 841 kg
561. The no. of board feet in a plank 2 in. thick, 6 in. wide and 20 ft long is:
a) 15
b) 30
c) 20
d) 25
562. Determine the volume of a right truncate triangle prism with the following dimensions: Let
the corners of the triangular base be defined by A, B ad C. The length AB=11ft, BC=10ft and
CA=13ft. The sides at A, B and C are perpendicular to the triangular base and have the height of
8.6ft, 7.1ft and 5.5ft, respectively.
a) 377 ft^3
b) 337 ft^3
c) 358 ft^3
d) 389 ft^3
563. A right circular conical vessel is constructed to have a volume of 100,000 liters. Find the
diameter if depth is to be 1.25 times the diameter.
a) 6.736 m
b) 7.632 m
c) 8.24 m
d) 9.45 m
564. A hollow sphere with an outer radius of 32 cm is made of a metal weighing 8 grams per
cubic cm. The weight of the sphere is 150 kg so that the volume of the metal is 24,000 cubic cm.
Find the inner radius.
a) 30 cm
b) 35 cm
c) 40 cm
d) 45 cm
565. A circular cylindrical tank, axis horizontal, diameter 1 meter, and length 2 meters, is filled
with water to a depth of 0.75 meters. How much water is in the tank?
a) 2.578 m^3
b) 2.125 m^3
c) 1.2638 m^3
d) 1.0136 m^3
566. A machine foundation has the shape of a frustrum of a pyramid with lower base 6m x 2m,
upper base 5.5m x 1.8m, and altitude of 1.5m. Find the volume of the foundation.
a) 12.5 m^3
b) 14.2 m^3
c) 15.6 m^3
d) 16.4 m^3
567. An elevated water tank is in the form a circular cylinder with diameter of 3 m and a
hemispherical bottom. The total height of the tank is 5 m. Water is pumped into the tank at a rate
of 30 gallons per minute. How long will it take to fully fill the tank starting empty?
a) 4.668 hrs
b) 5.468 hrs
c) 7.725 hrs
d) 9.245 hrs
568. The intercept form for algebraic straight equation:
a) a/x + y/b = 1
b) y = mx + b
c) Ax + By + C = 0
d) x/a + y/b = 1
569. Find the slope of the line y-x=5.
a) 1
b) 5+x
c) -1/2
d) ¼
570. Find the equation of the line that passes through the points (0,0) and (2,-2).
a) y=x
b) y=-2x+2
c) y=-2x
d) y=-x
571. Find the equation of the line with slope=2 and y-intercept=-3.
a) y=-3x+2
b) y=2x-3
c) y=2/3x+1
d) y=2x+3
572. The equation y=a1+a2x is an algebraic expression for which of the following:
a) A cosine expansion
b) projectile motion
c) a circle in polar form
d) a straight line
573. In finding the distance, d, between two point, which equation is the appropriate one to use?
a) d=((x1-x2)^2 + (y2-y1)^2)^(1/2)
b) d=((x1-y1)^2 + (x2-y2)^2)^(1/2)
c) d=((x1^2 – x2)^2 + (y1^2 - y2^2))^(1/2)
d) d=((x2-x1)^2 + (y2-y1)^2)^(1/2)
574. The slope of the line 3x + 2y + 5 = 0 is:
a) -2/3
b) -3/2
c) 3/2
d) 2/3
575. Find the area of the circle whose center is at (2,-5) and tangent to the lien 4x+3y-8=0.
a) 6π
b) 3 π
c) 9 π
d) 12 π
576. Given the equation of the parabola: y^2 – 8x -4y -20 =0. The length of its latus rectum is:
a) 2
b) 4
c) 6
d) 8
577. Find the equation of the tangent to the circle x^2 + y^2 – 34 = 0 through point (3,5).
a) 3x+5y-34=0
b) 3x-5y-34=0
c) 3x+5y+34=0
d) 3x-5y+34=0
578. If the distance between the points (8,7) and (3,y) is 13, what is the value of y?
a) 5
b) -19
c) 19 or -5
d) 5 or -19
579. Which of the following is perpendicular to the line x/3 + y/4 =1?
a) x-4y-8=0
b) 4x-3y-6=0
c) 3x-4y-5=0
d) 4x+3y-11=0
580. The two straight lines 4x-y+3=0 and 8x-2y+6=0
a) intersects at the origin
b) are coincident
c) are parallel
d) are perpendicular
581. A line which passes through (5,6) and (-3,-4) has an equation of:
a) 5x+4y+1=0
b) 5x-4y-1=0
c) 5x-4y+1=0
d) 5x+4y-1=0
582. The equation of the line through (1,2) parallel to the line 3x-2y+4=0.
a) 3x-2y+1=0
b) 3x-2y-1=0
c) 3x+2y+1=0
d) 3x+2y-1=0
583. Find the area of the polygon which is enclosed by the straight lines x-y=0, x+y=0, x-y=2a
and x+y=2a.
a) 2a^2
b) 4a^2
c) 2a
d) 3a^2
584. Find the equation of the circle with center at (2, -3) and radius of 4.
a) x^2 + y^2 -6x + 4y + 3 = 0
b) x^2 + y^2 -4x + 6y - 3 = 0
c) x^2 + y^2 -6x + 4y - 3 = 0
d) x^2 + y^2 -2x + 3y - 1 = 0
585. Find the area of the curve whose equation is : 2x^2 – 8x + 2y^2 + 12y = 1.
a) 35.4 sq. units
b) 39.2 sq. units
c) 42.4 sq. units
d) 44.2 sq. units
586. Find the area of the curve whose equation is : 9x^2 – 36x + 25y^2 = 189.
a) 41.7 sq. units
b) 43.4 sq. units
c) 46.2 sq. units
d) 47.1 sq. units
587. Given the curve Ax^2 + By^2 + F = 0. It passes through the points (4,0) and (0,3). Find the
value of A, B and F.
a) 9,16,144
b) 9,16,121
c) 3,4,112
d) 3,4,144
588. A straight line passes through (2,2) such that the length of the line segment intercepted
between the coordinate axis is equal to the square root of 5. Find the equation of the straight line.
a) 4x-y-2=0
b) x-4y-2=0
c) 2x-y-2=0
d) 2y-x-4=0
589. Find the area of the circle whose equation is : 2x^2 – 8x + 2y^2 + 12y = 1.
a) 24.4 sq. units
b) 34.2 sq. units
c) 42.4 sq. units
d) 54.2 sq. units
590. Find the area of the curve whose equation is : 9x^2 – 36x + 25y^2 = 189.
a) 27.2 sq. units
b) 32.8 sq. units
c) 47.1 sq. units
d) 75.4 sq. units
591. What is the first derivative with respect to x of the function G(x) = 4 * 9^(1/2) ?
a) 0
b) 4/9
c) 4
d) 4(9^(1/2))
592. If a is a simple constant, what is the derivative of y = x^a?
a) ax
b) x^(a-1)
c) a x^(a-1)
d) (a-1)x
593. Find the derivative of F(x) = [x^3 – (x-1)^3]^3.
a) 3x^2 – 3(x-1)^2
b) 3[x^3 – (x-1)^3]^2
c) 9[x^3 – (x-1)^3][x^2 – (x-1)^2]
d) 9[x^3 – (x-1)^3]^2 [x^2 – (x-1)^2]
594. Differentiate f(x) = [2x^2 +4x +1]^(1/2)
a) 2x+2
b) ½[2x^2 + 4x + 1]^(1/2)
c) (2x + 2)/ [2x^2 +4x +1]^(1/2)
d) (4x + 4)/ [2x^2 +4x +1]^(1/2)
595. Find the second derivative of y = (x^2 + x^-2)^(1/2)
a) 1 - 2x^-3
b) 1 - 6x^4
c) 3
d) 6 / x^4
596. If y=cos x, what is dy/dx?
a) sec x
b) – sec x
c) csc x
d) – sin x
597. What is the slope of the graph y = -x^2 at the point (2,3)?
a) -4
b) -2
c) 1
d) 3
598. Given the function f(x) = x^3 – 5x + 2, find the value of the first derivative at x=2.
a) 2
b) 3x^2 – 5
c) 7
d) 8
599. Find the slope of the tangent to a parabola y = x^2, at a point on the curve where x=1/2.
a) 0
b) 1/2
c) -1/2
d) 1
600. What is the slope of the curve y = x^2 -4x as it passes through the origin?
a) 0
b) -3
c) -4
d) 4
601. Find the slope of the line tangent to the curve y = x^3 – 2x + 1 at the point (1,2).
a) 1/4
b) 1/3
c) 1/2
d) 1
602. Determine the equation of the line tangent to the graph y = 2x^2 + 1, at the point (1,3).
a) y = 2x + 1
b) y = 4x - 1
c) y = 2x - 1
d) y = 4x + 1
603. Given Y1 = 4x + 3 and Y2 = x^2 + C, find C such that Y2 is tangent to Y1.
a) 2
b) 4
c) 5
d) 7
604. The distance of a body travels is a function of time and is given by x(t) = 18t + 9t^2. Find
its velocity at t=2.
a) 20
b) 24
c) 36
d) 54
605. If x increases uniformly at the rate of 0.001 feet per second, at what rate is the expression
(1+x)^3 increasing when x becomes 9 feet?
a) 0.001
b) 0.003
c) 0.3
d) 1.003
606. A spherical balloon is being filled with air at a rate of 1 cubic foot per second. Compute the
time rate of rate of the surface area of the balloon at the instant when its volume is 113.1 cubic
feet.
a) 0.67 ft^2 / s
b) 1.73 ft^2 / s
c) 3.0 ft^2 / s
d) 3.7 ft^2 / s
607. What is the maximum of the function y = -x^3 +3x for x=-1?
a) -2
b) -1
c) 0
d) 2
608. The cost C of a product is a function of the quantity x, of the product: C(x) = x^2 – 4000x +
50. Find the quantity for which the cost is minimum.
a) 1000
b) 1500
c) 2000
d) 3000
609. Compute the following limit Lim x+2
x →∞ x-2
a) 0
b) 1
c) 2
d) ∞
610. Find the equation of the tangent to the ellipse: 4x^2 + 9y^2 = 40 at point (1,-2).
a) 2x – 9y – 20 = 0
b) 9x + 5y + 2 = 0
c) 9x – 2y + 20 = 0
d) 2x + 9y +20 = 0
611. Find the equation of the tangents to the graph y = x^3 + 3x^2 – 15x – 20 at the points of the
graph where the tangents to the graph have a slope of 9.
a) 9x + y + 70 = 0
b) 9y + x + 60 = 0
c) 9x – y – 48 = 0
d) x - y - 9 = 0
612. A rectangular field to contain a given area is to be fenced off along a straight river. If no
fencing is needed along the river, show that the least amount of fencing will be required when
the length of the field is twice its width.
a) L = 3W
b) L = 4W
c) L = W
d) L = 2W
613. Find the shape of the largest rectangle that can be inscribed in a given circle.
a) Trapezoid
b) Rectangle
c) Parallelogram
d) Square
614. Divide the number 60 into two parts so that the product P of one part and the square of the
other is a maximum.
a) 30 and 30
b) 25 and 35
c) 50 and 10
d) 40 and 20
615. What is the maximum volume of a box that is constructed from a piece of cardboard 16
inches square by cutting equal squares out of the corners and turning up the sides.
a) 303.4 in^3
b) 404.5 in^3
c) 202.2 in^3
d) 101.1 in^3
616. A square sheet of galvanized iron, 100 cm x 100 cm will be used in making an open-top
container by cutting a small square from each corner and bending up the sides. Determine how
large the square should be cut from each corner in order to obtain the largest possible volume.
a) 16 2/3 cm x 16 2/3 cm
b) 11 ½ cm x 11 ½ cm
c) 12 1/3 cm x 12 1/3 cm
d) 14 ¼ cm x 14 ¼ cm
617. The sum of two positive numbers is 36. What are the numbers if their product is to be the
largest possible?
a) 10 and 10
b) 15 and 15
c) 12 and 12
d) 18 and 18
618. A bus company charges P85 per passenger from Manila to Baguio for 100 or less
passengers. For group tours, the company allows for P0.50 discount of the ticket price for every
passenger in excess of 100. How many passengers give the maximum income?
a) 110
b) 150
c) 120
d) 135
619. A tinsmith wishes to make a gutter of maximum cross-section (carrying capacity) whose
bottom and sides are each 6 inches wide and whose sides have the same slope. What will be the
width at the top?
a) 10 in
b) 12 in
c) 8 in
d) 14 in
620. A lot is in the shape of a quadrant of a circle of radius 100 meters. Find the area of the e
largest rectangular building that can be constructed inside the lot.
a) 2500 m^2
b) 7500 m^2
c) 5000 m^2
d) 9000 m^2
621. The cost of setting up a geothermal power plant is P10M for the first MW, P11M for the
second MW, P12M for the third MW, etc., the other expenses (land rights, desing fee, etc.)
amount to P50M. If the expected annual income per MW is 2M, find the plant capacity that will
yield a maximum rate of return of investment.
a) 8 MW
b) 10 MW
c) 9 MW
d) 14 MW
622. If the fuel cost to run a boat is proportional to the square of her speed and is P25 per hour
for a speed of 30 kph, find the most economical speed to run the boat, other expenses
independent from the speed amount to P100 per hour and the distance is 200 km.
a) 60 kph
b) 100 kph
c) 70 kph
d) 30 kph
623. The strength of a rectangular beam is proportional to the breadth and the square of the depth.
Find the dimensions of the strongest beam that can be cut from a log 30 cm in diameter.
a) b = 17.32 cm, h = 24.49 cm
b) b = 22.45 cm, h = 31.55 cm
c) b = 12.45 cm, h = 19.85 cm
d) b = 19.65 cm, h = 28.49 cm
624. Two posts, one 8 meters high and the other 12 meters high, stand 15 meters apart. They are
to be stayed by wires attached to a single stake at ground level, the wires running to the tops of
the posts. How far from the shortest post should the stake be placed, to use the least amount of
wire?
a) 6m
b) 4m
c) 8m
d) 12m
625. A cylindrical glass jar has a metal top. If the metal costs three times as much as the glass per
unit area, find the proportions of the least costly jar that holds a given amount.
a) H = D
b) H = ¼ D
c) H = ½ D
d) H = 2D
626. The parcel post regulations limit the size of a package to such a size that the length plus the
girth equals 6 feet. Determine the volume of the largest cylindrical package that can be sent by
the parcel post.
a) 2.546 cu. ft
b) 3.846 cu. ft
c) 4.234 cu. ft
d) 6.870 cu. ft
627. A cylindrical steam boiler is to be constructed having a capacity of 30 cu. meters. The
material for the sides costs P430 per sq. meter and for the ends P645 per sq. meter. Find the
radius when the cost is least.
a) 1m
b) 1.47m
c) 2.1m
d) 1.7m
628. A boat is being towed toward a pier which is 20 feet above the water. The rope is pulled in
at a rate of 6 ft/sec. How fast is the boat approaching the base of the pier when 25 feet of rope
remain to be pulled in?
a) 8 ft/sec
b) 12 ft/sec
c) 10 ft/sec
d) 15 ft/sec
629. A water tank is in the form of a right circular cone with vertex down, 12 feet deep and 6 feet
across the top. Water is being pumped into the tank at the rate of 10 cu. ft/min. How fast is the
surface of the water in the tank rising when the water is 5 feet deep?
a) 8 ft/min
b) 4 ft/min
c) 6 ft/min
d) 2 ft/min
630. Water is flowing out of a conical funnel at a rate of 1 cu. in/sec. If the radius of the funnel is
2 inches and the altitude is 6 inches, find the rate at which the water level is dropping when it is 2
inches from the top.
a) 0.179 in/sec
b) 1.245 in/sec
c) 0.889 in/sec
d) 2.225 in/sec
631. A helicopter is rising vertically from the ground at constant rate of 15 ft per second. When it
is 250 feet off the ground, a jeep passed beneath the helicopter travelling in a straight line at a
constant speed of 50 mph. Determine how fast is the distance between them is changing after one
second.
a) 34 ft/sec
b) 45 ft/sec
c) 38 ft/sec
d) 60 ft/sec
632. A plane flying north at 640 kph passes over a certain town at noon and a second plane going
east at 600 kph is directly over he same town 15 minutes later. If the planes are flying at the
same altitude, how fast will they be separating at 1:15 PM?
a) 872 kph
b) 287 kph
c) 782 kph
d) 728 kph
633. The height of a cylindrical cone is measured to be four meters which is equal to its radius
with a possible error of 0.04. Determine the percentage error in computing the volume.
a) 3%
b) 10%
c) 5%
d) 1%
634. Divide 94 into three parts such that one-half the product of one pair, plus one-third the
product of another pair, plus one-fourth the product of the third pair may seem to be a maximum
value.
a) 42,40,12
b) 35,40,19
c) 38,40,16
d) 30,50,14
635. Integrate (3x^4 + 2x^3 + x^2 + 1)dx
a) (3x^3)/5 + (2x^2)/4 + x + 1 + c
b) (3x^5)/5 + (x^4)/2 + (x^3)/3 + x + c
c) (5x^5)/3 + 4x^2 + x + c
d) 3x^3 + 2x^4 + x^3 + x^2 + c
636. The integral of cos x dx with respect to x:
a) –sin x +c
b) sin x +c
c) cos x +c
d) –cos x +c
637. Find the area under the curve y = 1/x between the limits y=2 and y=10.
a) 1.61
b) 2.39
c) 3.71
d) 3.97
638. Fill in the blank in the following statement: The integral of a function between certain limits
divided by the difference in abscissas between those limits gives the ___________ of the
function.
a) average
b) middle
c) intercept
d) limit
639. Find the area bounded between y = 6x-1 and y = x/4 + 3 by x=0 and the intersection point.
a) 32/529
b) 16/23
c) 32/23
d) 64/23
640. If it is known that y=1 when x=1, what is the constant of integration for the following
integral? Y(x) = (e^(2x) - 2x)dx
a) c = 2 – e^2
b) c = 3 – e^2
c) c = 4 – e^2
d) ½(4 – e^2)
641. Evaluate integral of Tan (ln x) dx
x
a) ln cos (ln x) + c
b) ln sec (ln x) + c
c) 1/2 Tan^2 (ln x) + c
d) Tan (ln x) + c
642. Evaluate integral of cos x ln sin x dx
a) sin x (1- ln sin x) + c
b) sin x (1+ ln sin x) + c
c) sin x (ln sin x - 1) + c
d) ln sin x + c
643. Evaluate ∫ _e^x_dx_
1 + e^(2x)
a) 1/2 ln (1 + e^2x) + c
b) ln (1 + e^2x) + c
c) 1/2 (1 + e^2x)^2 + c
d) Arctan (e^x) + c
644. Evaluate ∫ _______dx__________
ln x^x [(ln x)^2 -1]^(1/2)
a) Arc sec (ln x) + c
b) 2/3[(ln x)^2 -1]^(3/2) + c
c) ln (ln x)^2 – 1 + c
d) Arc sin (ln x) + c
1
645. Evaluate ∫0 (2𝑥 + 4𝑥 3 ) 𝑑𝑥
a) 2
b) -2
c) -3
d) 3
𝑑𝑥
646. Evaluate ∫ 10𝑥+1
a) ln (10x + 1) + c
b) 1/10 ln(10x + 1) + c
c) ln(10x) + c
d) 10x + 1 + c
647. Evaluate ∫ 8dx / x^5
a) 8x^4 + c
b) 2x^4 + c
c) -2x^-4 + c
d) 2x^-4 + c
648. Evaluate ∫ (x^2)[(8 - x^3)^(1/2)]dx
a) -2/9 (8 – x^3)^(3/2) + c
b) -8 (8 – x^3)^(3/2) + c
c) 2/9 (8 – x^3)^(3/2) + c
d) -2/3 (8 – x^3)^(3/2) + c
649. Evaluate ∫ x^2a dx
a)
𝒙^(𝟐𝒂+𝟏)
𝟐𝒂+𝟏
𝑥^(2𝑎+1)
+c
b) 2𝑎−1 + c
c) x^a / a + c
d) x / 2a + c
650. Find the area bounded by the parabola y = x^2, the x-axis and the lines x=1 and x=3.
a) 8 2/3 sq. units
b) 7 1/2 sq. units
c) 9 1/4 sq. units
d) 12 sq. units
651. An ellipsoidal tank measuring 6 ft by 12 ft has its axis vertical, the axis of rotation being the
major axis. It is filled with water to a depth of 7 feet. Find the amount of water in the tank.
a) 111 cu. ft
b) 121 cu. ft
c) 141 cu. ft
d) 161 cu. ft
652. Find the area enclosed by the curves: y^2 = 8x – 24 and 5y^2 = 16x.
a) 20 sq. units
b) 16 sq. units
c) 18 sq. units
d) 22 sq. units
653. An open cylindrical tank 3 feet in diameter and 4.5 feet high is full of water. It is then tilted
until one-half of its bottom is exposed. How many gallons of water was spilled out?
a) 187.4 gal
b) 148.7 gal
c) 178.4 gal
d) 147.8 gal
654. The parabolic reflector of an automobile headlight is 12 inches in diameter and 4 inches
depth. What is the surface area in square inches?
a) 135.9 sq. in
b) 195.3 sq. in
c) 153.9 sq. in
d) 159.3 sq. in
655. A cistern in the form of an inverted right circular cone is 20 meters deep and 12 meters
diameter at the top. If the water is 16 meters deep in the cistern, find the work in kJ in pumping
out the water to a height of 10 meters above the top of the cistern.
a) 61,817 kJ
b) 55,004 kJ
c) 64,890 kJ
d) 68,167 kJ
656. A flour bag originally weighing 60 kg is lifted through a vertical distance of 9 meters.
While the bag is being lifted, flour is leaking from the bag at such a rate that the weight lost is
proportional to the square root of the distance travelled. If the total loss is 12 kg, find the amount
of work in kJ done in lifting the bag?
a) 4.59 kJ
b) 9.54 kJ
c) 5.94 kJ
d) 4.95 kJ
657. What is the name for a vector that represents the sum of two vectors?
a) scalar
b) tensor
c) resultant
d) tangent
658. What is the acceleration of a body that increases its velocity from 60 m/s to 110 m/s?
a) 5 m/s
b) 3.0 m/s
c) 4.0 m/s
d) 5.0 m/s
659. A cyclists on a circular track of radius r = 250 m is travelling at 9 m/s. His speed in the
tangential direction increases at a rate of 1.5 m/s^2. What is the cyclist’s total acceleration?
a) -1.53 m/s^2
b) 1.53 m/s^2
c) 2.3 m/s^2
d) -2.3 m/s^2
660. A bus weighing 9000N is switched to a 2% upgrade with a velocity of 40 kph. If the train
resistance is 950 N, how far up the grade will it go?
a) 50 m on slope
b) 5 m on slope
c) 500 m on slope
d) 75 m on slope
661. Moment of inertia on SI is described as:
a) N-m
b) N/m
c) kg/m
d) Farad/m
662. A solid disks flywheel (I=200 kg-m^2) is rotating with a speed of 900 rpm. What is the
rotational KE?
a) 730 x 10^3 J
b) 680 x 10^3 J
c) 888 x 10^3 J
d) 1100 x 10^3 J
663. The weight of a mass 10 kg at a location where the acceleration of gravity is 9.7 m/s^2 is:
a) 79.7 N
b) 77.9 N
c) 97.7 N
d) 977 N
664. A standard acceleration due to gravity in SI unit:
a) 32.2 ft/s^2
b) 35.5 m/s^2
c) 9.81 ft/s^2
d) 9.81 m/s^2
665. A 50 kg sack is raised vertically 5 meters. What is the change in potential energy?
a) 2452.5 kJ
b) 2.4525 kJ
c) 2452.5 N
d) 2.4525 kN
666. A shot is fired at an angle of 300 with the horizontal and a velocity of 90 m/s. Calculate the
range of the projectile.
a) 715 km
b) 715 cm
c) 0.444 mi
d) 250 ft
667. A ball dropped from the top of a building 60 meters elevation will hit the ground with a
velocity of:
a) 34.31 m/s
b) 31.34 m/s
c) 43.31 m/s
d) 33.41 m/s
668. What horizontal force P can be applied to a 100 kg block in a level surface (µ = 0.20) that
will cause an acceleration of 2.50 m/s^2?
a) 343.5 N
b) 224.5 N
c) 53.8 N
d) 446.2 N
669. Which of the following is not a vector quantity?
a) mass
b) torque
c) displacement
d) velocity
670. The product of force and the time during which it acts is known as:
a) impulse
b) momentum
c) work
d) impact
671. The property of the body which measures its resistance to changes in motion:
a) acceleration
b) weight
c) mass
d) rigidity
672. The study of motion without reference to the forces which causes motion is known as:
a) kinetics
b) dynamics
c) statics
d) kinematics
673. The branch of physical science which deals with state of rest or motion of bodies under the
action of forces is known as:
a) mechanics
b) kinetics
c) kinematics
d) statics
674. In physics, work is defined in terms of the force acting through a distance. The rate at which
the work is done is called:
a) force
b) energy
c) power
d) momentum
675. The point through which the resultant of the distributed gravity force passes regardless of
the orientation of the body in space is known as:
a) center of inertia
b) center of gravity
c) center of attraction
d) moment of inertia
676. The momentum of a moving object is the product of its mass(m) and velocity(v). Newton’s
second law of motion says that the rate of change of momentum with respect to time is:
a) power
b) energy
c) momentum
d) force
677. A coin is tossed vertically upward from ground at a velocity of 12 m/s. How long will the
coin touch the ground?
a) 4.45 asec
b) 3.45 sec
c) 2.45 sec
d) 1.45 sec
678. A bullet is fired at an angle of 750 with the horizontal with an initial velocity of 420 m/s.
How high can it travel after 2 seconds?
a) 840 m
b) 792 m
c) 750 m
d) 732 m
679. A flywheel rotates at 150 rpm slowed down to 120 rpm during the punching portion of the
cycle. Compute the angular acceleration of the flywheel in rad/sec^2, if time is 1 sec.
a) 3.14 rad/sec/sec
b) -3.14 rad/sec/sec
c) 4.31 rad/sec/sec
d) -4.31 rad/sec/sec
680. A shot is fired at an angle of 300 with the horizontal and a velocity of 400 ft per sec. Find
the height of the projectile.
a) 600 ft
b) 622 ft
c) 700 ft
d) 680 ft
681. A projectile is fired with a velocity of 1600 fps and the target distance is 50,000 ft.
Determine the angle of elevation of the projectile.
a) 38057’
b)32017’
c) 24032’
d) 19028’
682. Given the component velocities Vsubx and Vsuby, what is the resultant velocity at t = 3.
a) 19
b) 23
c) 21
d) 24
683. A 500 lbf acts on a block at an angle of 300 with respect to the horizontal. The block is
pushed 5 feet horizontally. What is the work done by this force?
a) 2.936 kJ
b) 2,936 kJ
c) 3.396 kJ
d) 3,396 kJ
684. Traffic travels at 110 mph around a banked highway curve with a radius of 2000 ft and f =
0.3. What banking angle to resist the centrifugal force?
a) 5.330
b) 5.990
c) 6.660
d) 7.770
685. A plane dropped a bomb at an elevation of 1000m from the ground intending to hit a target
which elevation is 200 m from the ground. If the plane was flying at a velocity of 300 kph, at
what distance from the target must the bomb be dropped to hit the target?
a) 1064 m
b) 1046 m
c) 1275 m
d) 1146 m
686. A projectile is launched from a level plane at 300 from the horizontal with an initial velocity
of 1500 ft/sec. What is the maximum height and maximum range the projectile can reach?
a) 2772 m ; 18,500 m
b) 2727 m ; 18,885 m
c) 2266 m ; 18,994 m
d) 2663 m ; 18,449 m
687. A flywheel stops in 10 sec from a speed of 80 rpm. Compute the number of turns the
flywheel makes before it stops.
a) 6.56 rev
b) 6.96 rev
c) 5.56 rev
d) 6.65 rev
688. An elevator weighing 4000 lb attains an upward velocity of 20 fps in 5 sec with uniform
acceleration. What is the tension in the supporting cables?
a) 4947 lbs
b) 4974 lbs
c) 4749 lbs
d) 4497 lbs
689. A gun is fired horizontally at a 10 kg block of wood suspended at the end of a cord. The
block with the bullet embedded in it rises vertically by 10 cm. Mass of bullet is 40 grams. Find
the velocity of the bullet just before it hit the block.
a) 354.1 m/s
b) 351.4 m/s
c) 341.5 m/s
d) 315.4 m/s
690. A body weighing 100 kg is hanging at the end of a rope 5 m long. What horizontal force is
needed to move the body a horizontal distance of 1m.
a) F = 24.1 kg
b) F = 22.4 kg
c) F = 21.4 kg
d) F = 20.4 kg
691. A light rail transit travels between two terminals 1 km apart in a minimum time of 1 min. If
the LRT cart accelerates and decelerates at 3.4 m/s^2, starting from rest at the first terminal and
coming to stop at the second terminal, find the maximum speed in km per hr.
a) 63.9 kph
b) 64.9 kph
c) 65.9 kph
d) 66.9 kph
692. A body weighing 2000 kg is suspended by a cable 20 meters and pulled 5 meters to one side
by a horizontal force. Find the tension in the cable.
a) 2066 kg
b) 2660 kg
c) 5166 kg
d) 3020 kg
693. A body weighing 350 kg rests on a plane inclined 300 with the horizontal. The angle of
static friction between the body and the plane is 15 degrees. What horizontal force P is necessary
to hold the body from sliding down the plane?
a) 93.7 kg
b) 73.9 kg
c) 97.3 kg
d) 119 kg
694. A 200 kg crate is on a 300 ramp. The coefficient of friction between the crate and the ramp
is 0.35. If a force is applied to the crate horizontally, calculate the force F to start the crate
moving up the ramp.
a) 244 kg
b) 38 kg
c) 232 kg
d) 223 kg
695. A 600 N block rests on a 300 inclined plane. The coefficient of static friction is 0.30 and the
coefficient of kinetic friction is 0.20. If a force P is applied to the block horizontally, find the
value of P needed to keep the block moving up the plane.
a) 257 N
b) 750 N
c) 275 N
d) 527 N
696. A steam pipe weighing 200 kg per meter will cross a road by suspension on a cable
anchored between supports 6 meters apart. The maximum allowable sag of the cable is 50 cm,
calculate the length of the cable.
a) 2.5 m
b) 3.6 m
c) 6.1 m
d) 9.5 m
697. A parabolic cable has a span of 400 feet. The difference in elevation of the supports is 10
feet and the lowest point of the cable is 5 feet below the lower support. If the load supported by
the cable is 12 lbs per horizontal foot, find the maximum tension in the cable.
a) 25,902 lbs
b) 27,857 lbs
c) 29,345 lbs
d) 34,876 lbs
698. A tripod whose legs are each 4 meters long supports a load of 1000 kg. The feet of the
tripod are the vertices of a horizontal equilateral triangle whose side is 3.5 m. Determine the load
on each leg.
a) 256 kg
b) 386 kg
c) 296 kg
d) 458 kg
699. Two cars A and B accelerate from a stationary start. The acceleration of A is 4 ft/sec^2 and
that of B is 5 ft/sec^2. If B was originally 20 feet behind A , how long will it take B to overtake
A.
a) 18.6 sec
b) 10 sec
c) 12.5 sec
d) 6.32 sec
700. Two cars, A and B, are travelling at the same speed of 80 km/hr in the same direction on a
level road, with car A 100 meters ahead of car B. Car A slows down to make a turn decelerating
at 7 ft/sec^2. In how many seconds will B overtake A.
a) 6.96 sec
b) 5.55 sec
c) 7.85 sec
d) 9.69 sec
701. In a 25 storey office building, the elevator starting from rest at first floor, is accelerated at
0.8 m/sec^2 for 5 seconds then continues at constant velocity for 10 seconds more and is stopped
in 3 seconds with constant deceleration. If the floors are 4 meters apart, at what floor does the
elevator stop?
a) 12th floor
b) 14th floor
c) 10th floor
d) 15th floor
702. A stone is dropped from a cliff into the ocean. The sound of the impact of the stone on the
ocean surface is heard 5 seconds after it is dropped. The velocity of sound is 1100 fps. How high
is the cliff?
a) 352.5 ft
b) 255.5 ft
c) 325.5 ft
d) 335.5 ft
703. Water drips from a faucet at a rate of 8 drops per second. The faucet is 18 cm above the sink.
When one drop strikes the sink, how far is the next drop above the sink?
a) 15.8 cm
b) 12.5 cm
c) 18.5 cm
d) 25.6 cm
704. Bombs from a plane drop at a rate of one drop per second. Calculate the vertical distance
after two bombs after the first had dropped for 7 seconds. Assume freely falling body with g =
9.8 m/sec^2.
a) 37.6 m
b) 73.6 m
c) 63.7 m
d) 76.3 m
705. A weight is dropped from a helicopter that is rising vertically with a velocity of 6 m/sec. If
the weight reaches the ground in 15 seconds, how high above the ground was the helicopter
when the weight was dropped?
a) 1100 m
b) 1013 m
c) 1580 m
d) 1130 m
706. A bomber flying at a horizontal speed of 800 kph drops a bomb. If the bomb hits the ground
in 20 seconds, calculate the vertical velocity of the bomb as it hit the ground.
a) 169 m/sec
b) 196 m/sec
c) 175 m/sec
d) 260 m/sec
707. A flywheel starting from rest develops a speed of 400 rpm in 30 seconds. How many
revolutions did the flywheel make in 30 seconds it took to attain 400 rpm.
a) 100 rev
b) 150 rev
c) 120 rev
d) 360 rev
708. A 100 kg block of ice is released at the top of a 300 incline 10 meters above the ground. If
the slight melting of the ice renders the surface frictionless, calculate the velocity at the foot of
the incline.
a) 30 m/sec
b) 24 m/sec
c) 14 m/sec
d) 10 m/sec
709. What drawbar pull is required to change the speed of a 120,000 lb car from 15 mph to 30
mph on a half mile while the car is going up a 1.5% upgrade? Car resistance is 10 lb/ton.
a) 3425 lbs
b) 3542 lbs
c) 3245 lbs
d) 4325 lbs
710. A body weighing 200 kg is being dragged along a rough horizontal plane by a force of 45
kg. If the coefficient of friction is assumed to be 1/12 and the line pull makes an angle of 180
with the horizontal, what is the velocity acquired from rest in the first 3 meters.
a) 2.8 m/sec
b) 3.1 m/sec
c) 3.5 m/sec
d) 4.9 m/sec
711. A 50 kN Diesel Electric Locomotive (DEL) has its speed increased from 30 kph to 120 kph
in a distance of 1 km while ascending a 3% grade. What constant trust (drawbar pull) parallel to
the surface of the railway must be exerted by the wheel? The total frictional resistance is 30
N/kN of DEL weight.
a) 5.655 kN
b) 7.889 kN
c) 6.556 kN
d) 7.996 kN
712. Water is flowing through a cast iron pipe at the rate 3500 GPM. The inside diameter of pipe
is 6 in. Find the flow velocity?
a) 39.7 m/s
b) 32.5 m/s
c) 12.1 m/s
d) 17.84 m/s
713. Find the water pressure reading if manometer is 0.45 m Hg. Mercury is 13.6 times heavier
than water.
a) 60 kPa
b) 50 kPa
c) 70 kPa
d) 65 kPa
714. Determine the velocity of the fluid in a tank at the exit, given that surface h1 = 1m and h2 =
100 cm.
a) 3.9 m/s
b) 4.2 m/s
c) 4.8 m/s
d) 5.6 m/s
715. Water is flowing at a rate of 3500 GPM. The inside radius is 8cm and coefficient of friction
is 0.0181. What is the pressure drop over a length of 50 m?
a) 317 kPa
b) 301 kPa
c) 341 kPa
d) 386 kPa
716. The unit of kinematic viscosity in SI is described as:
a) Newton per meter
b) Watt per meter
c) Pascal second
d) Sq. m per sec
717. Which of the following is not a unit of viscosity?
a) Pa-sec
b) Poise
c) stoke
d) Dyne
718. Which of the following describes laminar flow?
a) NR = 2180
b) NR = 1989
c) NR = 4100
d) NR = 2100
719. Water is flowing in a pipe with radius of 30 cm at a velocity of 12 m/s. The density and
viscosity of water are: Density = 1000 kg/m^3 ; Viscosity = 1.12 Pa-s. What is the Reynold’s
number?
a) 6428
b) 6386
c) 4534
d) 2187
720. What is the density of a solid that weights 194 N (43.9 lbf) in air and 130 N (29.4 lbf) in
water?
a) 3534.50 kg/m^3
b) 3031.25 kg/m^3
c) 2989.34 kg/m^3
d) 3235.96 kg/m^3
721. What is the buoyant force of a body that weighs 100 kg in air and 70 kg in water?
a) 234.17 N
b) 329.68 N
c) 285.6 N
d) 294.3 N
722. A venturi meter with a 15 cm throat is installed in a 20 cm pipe which inclined upward at an
angle of 300 to the horizontal. If the distance between pressure tape along the pipe is 1 m, the
differential pressure is 65 kPA. What is the discharge of water in m^3/s? Assume coefficient of
0.995.
a) 0.109 m^3/s
b) b) 0.536 m^3/s
c) 0.233 m^3/s
d) 0.0123 m^3/s
723. What is the pressure of point A in the tank if h = 2 feet from the water level? (g = 32.2
ft/s^2 and ρ = 1.94 slug/ft^3).
a) 75 lbf/ft^2
b) 85 lbf/ft^2
c) 100 lbf/ft^2
d) 125 lbf/ft^2
724. Steam with an enthalpy of 700 kcal/kg enters a nozzle and leaves with an enthalpy of 650
kcal/kg. Find the initial velocity if steam leaves with a velocity of 700 m/s, assuming the nozzle
is horizontal and disregarding heat losses.
a) 276 m/s
b) 296 m/s
c) 376 m/s
d) 267 m/s
725. The flow of water through a cast iron pipe is 6000 GPM. The pipe is 1 ½ ft nominal
diameter. What is the velocity of water?
a) 8.56 ft/sec
b) 7.56 ft/sec
c) 6.56 ft/sec
d) 5.56 ft/sec
726. A perfect venturi with throat diameter of 2 in is placed horizontally in a pipe with a 2 inches
is placed horizontally in a pipe with a 6 inches inside diameter. What is the difference between
the pipe and venturi throat static pressure if the mass flow rate of water is 100 lb/sec.
a) 38.8 lb/in^2
b) 36.8 lb/in^2
c) 37.8 lb/in^2
d) 35.8 lb/in^2
727. A deposit of P1000 is made in a bank account that pays 8% interest compounded annually.
Approximately how much money will be in the account after 10 years?
a) P2160
b) P2345
c) P1860
d) P1925
728. You need P4000 per year for your college four year course. Your father invested P5000 in
7% account for your education when you were born. If you withdraw P4000 at the end of your
17th, 18th,19th, and 20th birthday, how much money will be left in the account at the end of the
21st year?
a) P2500
b) P3400
c) P1700
d) P4000
729. What is the acid test ratio?
a) The ratio of the owners equity to the total current liabilities
b) The ratio of all assets to total liabilities
c) The ratio of gross margin to operating sales and administrative expenses
d) The ratio of current assets (exclusive of inventory) to total current liabilities
730. An interest rate is quoted as being 7 1/2 % compounded quarterly. What is the effective
annual interest rate?
a) 21.8 %
b) 7.71%
c) 7.22%
d) 15.78%
731. Mr. Ayala borrows P100,000.00 at 10% effective annual interest. He must pay back the loan
over 30 years with uniform monthly payments due on the first day of each month. What does Mr.
Ayala pay each month?
a) P870
b) P846
c) P878
d) P839
732. A steel drum manufacturer incurs a yearly fixed operating cost of P200,000. Each drum
manufactured cost P160 to produce and sells for P200. What is the manufacturers break-even
sales volume in drums per year?
a) 1250
b) 2500
c) 1000
d) 5000
733. The length of time, usually in years, for the cumulative net annual profit to equal the initial
investments is called:
a) receivable turnover
b) return on investment
c) price earning ratio
d) pay back period
734. A local firm is establishing a sinking fund for the purpose of accumulating a sufficient
capital to retire its outstanding bonds at maturity. The bonds are redeemable in 10 years, and
their maturity value is P150,000. How much should be deposited each year if the fund pays
interest at the rate of 3%?
a) P12,547.14
b) P13,084.58
c) P14,094.85
d) P16,848.87
735. What is the formula for a straight line depreciation rate?
a) 100% - %net salvage value over estimated life
b) 100% net salvage value over estimated service life
c) 100% net salvage value over estimated service life
d) average net salvage value over estimated service life
736. A machine is under consideration for investment. The cost of the machine is P25,000. Each
year it operates, the machine will generate a savings of P15,000. Given an effective annual
interest rate of 18%, what is the discounted payback period, in years, on the investment of the
machine?
a) 1.75 years
b) 3.17 years
c) 1.67 years
d) 2.16 years
737. A businessman wishes to earn 7% on his capital after payment of taxes. If the income from
an available investment will be taxed at an average rate of 42%, what minimum rate of return,
before payment of taxes, must the investment offer to be justified?
a) 12.1 %
b) 10.7%
c) 11.1 %
d) 12.7 %
738. Liquid assets such as cash and other assets that can be converted quickly into cash such as
accounts receivable, and merchandise is called:
a) current assets
b) fixed assets
c) total assets
d) land and buildings
739. Instead of the profits being paid out to the stockholders or owners as dividends, they are
retained in the business and used to finance expansion. This is called:
a) retained earnings
b) flow back
c) bonds
d) deposits
740. A term used to describe payment of an employee for time spent on the property of the
employer though not actually working at the job, e.g. time spent changing clothes to get ready
for work or time spent travelling from the plant entrance to the place of work.
a) portal-to-portal pay
b) down-time pay
c) call-in pay
d) lost time pay
741. A machine has an initial cost of P50,000 and a salvage value of P10,000 after 10 years.
What is the straight-line method depreciation rate as a percentage of the initial cost?
a) 10%
b) 8%
c) 12%
d) 9%
742. Fifteen years ago, P1000 was deposited in a bank account, and today it is worth P2370. The
bank pays interest semi-annually. What was the interest rate paid on this account?
a) 4.9%
b) 5.8%
c) 5.0%
d) 3.8%
743. Company A purchases P200,000 of equipment in year zero. It decides to use straight-line
depreciation over the expected 20 year life of the equipment. The interest rate is 14%. If its
average tax rate is 40%, what is the present worth of the depreciation tax held?
a) P3,500
b) P26,500
c) P98,700
d) P4,000
744. A product has a current selling price of P325. If its selling price is expected to decline at the
rate of 10% per annum because of obsolescence, what will be its selling price four years hence?
a) P213.23
b) P202.75
c) P302.75
d) P156.00
745. You borrow P3500 for one year from a friend at an interest rate of 1.5% per month instead
of taking a loan from a bank at a rate of 18% per year. Compare how much money will you save
or lose on the transaction.
a) You will pay P155 more than if you borrowed from the bank
b) You will save P55 by borrowing from your friend
c) You will pay P85 more than if you borrowed from the bank
d) You will pay P55 less than if you borrowed from the bank
746. Instead of paying P100,000 in an annual rent for offices space at the beginning of each year
for the next 10 years, an engineering has decided to take out a 10 year P1,000,000 loan for a new
building at 6% interest. The firm will invest P100,000 of the rent save and earn 18% annual
interest on that amount. What will be the difference between the firm’s annual revenue and
expenses?
a) The firm will need P17,900 extra.
b) The firm will break even.
c) The firm will have P21,500 left over.
d) The firm will need P13,000 extra.
747. The peso amount as earned from an investment or project is called:
a) ROI
b) Interest
c) ROR
d) Surplus
748. Those funds that are required to make the enterprise or project a going concern:
a) Working capital
b) Accumulated amount
c) Banking
d) Principal or present worth
749. You borrowed the amount of P10,000 for 120 days at 30% per annum simple interest. How
much will be due at the end of 120 days?
a) P10,100
b) P11,000
c) P11,600
d) P12,000
750. You obtain a loan of P0.5 million at the rate of 12% compounded annually in order to build
a house. How much must you pay monthly to amortize a loan within a period of five years?
a) P10,968
b) P11,968
c) P12,968
d) P13,968
751. An asset is purchased for P25,000. Its estimated life is 10 years after which it will be sold
for P500. Find the depreciation for the first three years using the sum of the years digit.
a) P11,000.72
b) P13,007.72
c) P12,027.27
d) P13,027.72
752. If P10,000 is invested at the end of each year for 6 years, at an annual interest of 10%, what
is the total amount available upon the deposit of the sixth payment?
a) P77,651
b) P80,156
c) P78,156
d) P77,156
753. The original cost of an equipment is P50,000, the salvage value after 5 years is P8,000, and
the rate of interest on the investment is 10%. Determine the capital recovery per year.
a) P11,879.50
b) P12,897.50
c) P10,879.50
d) P11,379.50
754. A small shop in Leyte fabricates portable threshers for palay producers in the locality. The
shop can produce each thresher at a labor cost of P2000. The cost of materials for each unit is
P4500. The variable costs amount to 800 per unit, while fixed charges incurred per annum totals
to P90,000. If the portable threshers are sold at P14,000 per unit, how many units must be
produced and sold per annum to break even?
a) 14 units
b) 17 units
c) 19 units
d) 21 units
755. You want to save an amount of P100,000 at the end of 10 years. You are given 8% interest
compounded quarterly. How much would you have to save per month in order to accumulate the
sum of P100,000 ten years from now.
a) P864.50
b) P590.00
c) P648.50
d) P548.40
756. With an interest at 10% compounded annually, after how many years will a deposit now of
P1000 become P1331?
a) 3 years
b) 4 years
c) 5 years
d) 6 years
757. What rate (%) compounded quarterly is equivalent to 6% compounded semi-annually?
a) 5.93
b) 5.99
c) 5.96
d) 5.9
758. Determine the break-even point in terms of number of units produced per month using the
following data:
(the costs are in pesos per unit)
Selling price per unit
= 600
Total monthly overhead expenses
= 428,000
Labor cost
= 115
Cost of materials
= 76
Other variable cost
= 2.32
a) 1036
b) 1044
c) 1053
d) 1025
759. The present value of an annuity of “R” pesos payable annually for 8 years, with the first
payment at the end of 10 years, is P187,481.25. Find the value of R if money is worth 5%.
a) P45,000
b) P44,000
c) P42,000
d) P43,000
760. The amount of P50,000 is deposited in a bank. How much money are you going to
withdraw after 8 years at 8% compounded annually?
a) P83,546
b) P85,456
c) P92,546
d) P97.856
761. A machine has an initial cost of P300,000. Its salvage value after 5 years is P30,000. What
is the straight line depreciation rate of the machine?
a) 25%
b) 23%
c) 18%
d) 15%
762. An asset is purchased for P120,000 and it can be sold for P12,000. Its estimated life is 10
years. Find the depreciation for the second year using the sum-of-the-years digit method.
a) P17,672
b) P17,850
c) P18,276
d) P19,636
763. A bank offers 2% effective monthly interest. What is the effective annual rate?
a) 26.82%
b) 25.28%
c) 24.65%
d) 22.45%
764. How much must you invest today in order to accumulate P20,000 at 8% after 6 years?
a) P20,004.50
b) P18,450.80
c) P15,305.60
d) P12,603.40
765. A machine that cost P1000 will save P0.10 per unit produced. Maintenance cost will be
P100 annually. 2000 units are produced annually. What is the payback period at 12% interest?
a) 8 years
b) 9 years
c) 10 years
d) 12 years
766. An item is purchased for P100,000. Annual cost is P18,000. Using 10%, what is the
capitalized cost of the perpetual service?
a) P220,000
b) P250,000
c) P265,000
d) P280,000
767. A car was bought at P549,492.13 with 14% down payment and the remaining balance will
be paid on installment basis with a monthly payment of P12,000 for 60 months. Determine the
interest rate compounded annually.
a) 19.56%
b) 18.25%
c) 16.45%
d) 14.35%
768. A businessman wishes to earn 9% on his capital after payment of taxes. If the minimum rate
of return, before payment of taxes is 12.1 %. What is the available average taxed rate of the
income from a businessman’s investment?
a) 25.6 %
b) 24.6%
c) 22.4%
d) 20.5%
769. A debt of P1000 is to be paid in five equal yearly payments, each payment combining an
amortization installment an interest at 8% on the previously unpaid balance of the debt. What
should be the amount of each payment?
a) P365.50
b) P310.20
c) P290.60
d) P250.45
770. A father wishes to develop a fund for his new born son’s college education. The fund is to
pay P5000 on the 18th, 19th 20th and the 21st birthdays of his son. The fund will be built up by the
deposit of a fixed sum on the son’s first to seventeenth birthdays. If the fund earns 4%, what
should the yearly deposit into the fund be?
a) P985.44
b) P845.66
c) P795.65
d) P765.88
771. A man owns a building on which there is a P100,000 mortgage which earns 6% per annum.
The mortgage is being paid for in 20 equal year-end payments. After making 8 payments, the
man desires to reduce his payments by refinancing the balance of the debt with a 30-year
mortgage at 8%, and to be retired by equal annual payments. What would be the reduction in the
yearly payment?
a) P2,225.70
b) P2,550.80
c) P2,985.30
d) P3,120.90
772. An engineer borrows P150,000 at 12% effective annual interest. He must pay back the loan
over 25 years with uniform monthly payments due on the first day of each month. What is this
monthly payment?
a) P1126
b) P1265
c) P1398
d) P1498
773. Funds are deposited in a savings account at an interest rate of 8% per annum compounded
semi-annually. What is the initial amount that must be deposited to yield a total of P10,000 in 10
years?
a) P1458
b) P2550
c) P3875
d) P4564
774. A machinery has an initial cost of P40,000 and results in an increase in annual maintenance
costs of P2000. If the machinery saves the company P10,000 per year, in how many years will
the machine pay for itself if compounding is considered? (i = 7%)
a) 8 years
b) 9 years
c) 7 years
d) 11 years
775. How long will it take a sum of money to double at a 5% annual percentage rate?
a) 14.2 years
b) 15.9 years
c) 18.4 years
d) 19.3 years
776. A sum of P1000 is invested now and left for eight years, at which time the principal is
withdrawn. The interest that has accrued is left for another eight years. If the effective annual
interest rate is 5%, what will be the withdrawal amount at the end of the 16th year?
a) P980
b) P830
c) P780
d) P706
777. How many horsepower is 746 kW?
a) 1 HP
b) 100 HP
c) 74.6 HP
d) 1000 HP
778. What is the origin of the energy conservation equation used in flow system?
a) Newton’s First Law of Motion
b) Newton’s Second Law of Motion
c) First Law of Thermodynamics
d) Second Law of Thermodynamics
779. A volume of 560 cc of air is measured at a pressure of 10 mm Hg vacuum and a
temperature of 200C. What will be the volume at standard pressure and 00C?
a) 6.9 cc
b) 535.5 cc
c) 437.5 cc
d) 1071 cc
780. What is the specific weight of a liquid substance if it specific weight relative to water is
8.77 and the specific weight of water is 62.4 lb per cubic foot?
a) 86.03 kN/m^3
b) 82.20 kN/m^3
c) 102.56 kN/m^3
d) 89.90 kN/m^3
781. Steam at a pressure of 12.5 MPa has a specific volume of 1160 x 10^-6 m^3 per kg and a
specific enthalpy of 2560 kJ/kg. Find the internal energy per mass of steam.
a) 2574.5 kJ per kg
b) 2545.5 kJ per kg
c) 2634.17 kJ per kg
d) 2560.50 kJ per kg
782. A heat engine (Carnot cycle) has its intake and exhaust temperature of 2100C and 1200C
respectively. What is its efficiency?
a) 42.86%
b) 34.85%
c) 16.34%
d) 18.63%
783. One kilogram of water is heated by 2000 Btu energy. What is the change in temperature in
0
K?
a) 55.6 0K
b) 54.1 0K
c) 50.4 0K
d) 48.5 0K
784. A pressure reading of 35 psi in kPa abs is:
a) 427.3
b) 724
c) 273.4
d) 342.72
785. What conditions exists in a adiabatic throttling process?
a) Enthalpy is variable
b) Enthalpy is constant
c) Entropy is constant
d) Volume is constant
786. The specific gravity of a substance is the ratio of its density to the density of:
a) mercury
b) gas
c) air
d) water
787. What do you call the weight of the column of air above the earth’s surface?
a) air pressure
b) aerostatic pressure
c) wind pressure
d) atmospheric pressure
788. An air bubble rises from the bottom of a well where the temperature is 200C, to the surface
where the temperature is 320C. Find the percent increase int eh volume of the bubble if the depth
of the well is 8.5 m. Atmospheric pressure is 101,325 Pascals.
a) 45.5%
b) 72.5%
c) 89.76%
d) 91.34%
789. Gas being heated at constant volume is undergoing the process:
a) isentropic
b) adiabatic
c) isometric
d) isobaric
790. What is the required heating energy in raising the temperature of a given amount of water
when the energy applied is 1000 kw-hr with heat losses at 25%?
a) 1000
b) 1500
c) 1333
d) 1250
791. What is the process that has no heat transfer?
a) reversible
b) isothermal
c) polytropic
d) adiabatic
792. Heat normally flowing from a high temperature body to a low temperature body where in it
is impossible to convert heat without other effects is called the:
a) First Law of Thermodynamics
b) Second Law of Thermodynamics
c) Third Law of Thermodynamics
d) Zeroth Law of Thermodynamics
793. What equation applies in the first law of thermodynamics for an ideal gas in a reversible
open steady state system?
a) Q – W = U2 – U1
b) Q + VdP = H2 – H1
c) Q - VdP = H2 – H1
d) Q - PdV = H2 – H1
794. Form of energy associated with kinetic energy of the random motion of large number of
molecules:
a) internal energy
b) kinetic energy
c) heat of fusion
d) heat
795. Which of the following is a set of standard condition of atmospheric air?
a) 1 atm, 255 0K, 22 cu./kg mole
b) 101.325 kPa, 273 0K, 22.4 cu./kg mole
c) 101.325 kPa, 273 0K, 23.66 cu./kg mole
d) 1 atm, 10 0C, 22.41 cu./kg mole
796. Steam flows into a turbine at a rate of 20 kg/s and 21 kw of heat/ are lost from the turbine.
Ignoring elevation and other energy effects, calculate the power output from the turbine if the
energy input is 2850 kJ/kg and energy output is 2410 kJ/kg.
a) 8800 kw
b) 8821 kw
c) 8779 kw
d) 8634 kw
797. What pressure of water is a column of 100 cm high equivalent to:
a) 9807 dynes/cm^2
b) 9807 N/m^2
c) 0.1 bar
d) 100 kPa
798. An engine has an efficiency of 26%. It uses 2 gallons of gasoline per hour. Gasoline has
heating value of 20,500 Btu/lb and a specific gravity of 0.80. What is the power output of the
engine?
a) 41.7 kw
b) 0.33 kw
c) 26.0 kw
d) 20.8 kw
799. A thermodynamic system which undergoes a cyclic process during a positive amount of
work done by the system:
a) reversed Rankine cycle
b) heat pump
c) reversible-irreversible process
d) heat engine
800. In a constant temperature, closed system process, 100 Btu of heat is transferred to the
working fluid at 1000F. What is the change in entropy of the working fluid?
a) 0.18 kJ/0K
b) 0.57 kJ/0K
c) 0.25 kJ/0K
d) 0.34 kJ/0K
801. If an initial volume of an ideal gas is compressed to one-half of its original volume and to
twice its original temperature, the pressure:
a) doubles
b) quadruples
c) remains constant
d) halves
802. (u + pv) is a quantity called:
a) flow energy
b) shaft work
c) enthalpy
d) internal energy
803. What horsepower is required to isothermally compress 800 ft^3 per minute of air from 14.7
psia to 120 psia?
a) 13,800 HP
b) 28 HP
c) 256 HP
d) 108 HP
804. A pressure of one bar is equivalent to:
a) 110 kPa
b) 14 psi
c) 720 mm Hg
d) 1,000,000 dynes/cm^2
805. A pressure reading of 4.5 kg/cm^2 is equal to:
a) 441.40 kPaa
b) 451.60 kPaa
c) 542.72 kPaa
d) 582.92 kPaa
806. A water temperature rise of 380F in the condenser is equivalent to:
a) 3.33 0C
b) 33.3 0C
c) 21.1 0C
d) 38.1 0C
807. A boiler installed where the atmospheric pressure is 752 mm Hg has a pressure of 12
kg/cm^2. What is the absolute pressure in MPa?
a) 1.277 MPa
b) 1.772 MPa
c) 2.177 MPa
d) 3.771 MPa
808. An oil storage tank contains oil with specific gravity of 0.88 and depth of 20 meters. What
is the absolute pressure in kPa?
a) 274
b) 247
c) 724
d) 742
809. A pressure tank for a water pump system contains 2/3 water by volume when the pressure is
10 kg/cm^2 gauge. What is the absolute pressure at the bottom of the tank if the water is 2
meters depth?
a) 1012 kPa
b) 1201 kPa
c) 1102 kPa
d) 1080 kPa
810. Convert 360F to temperature difference to 0C.
a) 36
b) 40
c) 20
d) 25
811. At what temperature are the two temperatures scales 0C and 0F equal?
a) -20 0C
b) -40 0C
c) -30 0C
d) 40 0C
812. The temperature inside a furnace is 320 0C and the temperature of the outside/ is -100C.
What is the temperature difference in 0F?
a) 495 0F
b) 549 0F
c) 594 0F
d) 645 0F
813. Convert 60 lbs/ft^3 to kN/m^3:
a) 9.426
b) 7.356
c) 8.956
d) 5.479
814. A boiler feed pump delivers 200,000 kg of water per hour at 10 MPa and 2300C. What is the
volume flow rate in m^3/sec?
a) 0.0666
b) 0.0888
c) 0.0777
d) 0.0999
815. The radiator of a heating system was filled with dry and saturated steam at 0.15 MPa after
which the valves on the radiator were closed. As a result of heat transfer to the room, the
pressure drops to 0.10 MPa. What percentage of steam has condensed?
a) 31.6%
b) 25.4%
c) 36.1%
d) 45.7%
816. A throttling calorimeter receives a sample of steam from a steam main in which the pressure
is 1 MPa. After throttling, the steam is at 100 kPa and 120 0C. What is the quality of steam in the
steam main?
a) 96.9 %
b) 95.5%
c) 99.6%
d) 92.4%
817. Steam at 2.5 MPa and 320 0C expands through a nozzle to 1.5 MPa at the rate of 10,000
kg/hr. If the process occurs isentropically and the initial velocity is low, calculate the exit area of
the nozzle.
a) 853 x 10^-6 m^2
b) 358 x 10^-6 m^2
c) 835 x 10^-6 m^2
d) 583 x 10^-6 m^2
818. Water at a pressure of 10 MPa and the temperature of 2300C is throttled to a pressure of 1
MPa in an adiabatic process. What is the quality after throttling?
a) 11.3%
b) 12.5%
c) 14.5%
d) 19.3%
819. An air compressor delivers air to an air receiver having a volume of 2 m^3. At the start, the
air in the receiver is at atmospheric condition of 250C and 100 kPa. After 5 minutes, the pressure
of the air in the tank is 1500 kPa and the temperature is 600C. What is the capacity of the
compressor in m^3/min of free air?
a) 4.97
b) 5.55
c) 6.95
d) 8.45
820. At the suction of an air compressor, in which the conditions are 97.9 kPa and 270C, the air
flow rate is 10.3 m^3/min. What is the volume flow rate at the free air conditions of 100 kPa and
200C?
a) 7.635 m^3/min
b) 6.590 m^3/min
c) 9.848 m^3/min
d) 3.568 m^3/min
821. Steam at 5 MPa and 3500C enters a turbine and expands isentropically to 0.01 MPa. If the
steam flow rate is 100,000 kg/hr, determine the turbine power.
a) 28.5 kw
b) 22.5 kw
c) 25.8 kw
d) 33.8 kw