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