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Electronics and Communications (De La Salle University)
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lOMoARcPSD|22671238
REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
AUGUST 2013
MATHEMATICS
1. Simplify 1/(csc x + 1) ÷ 1/(csc – 1)
A. 2 sec x tan x B. 2 csc x cot x
C. 2 sec x
D. 2 csc x
SOLUTION:
2. A bus leaves Manila at 12 NN for Baguio 250 km away, traveling an average
of 55 kph. At the same time, another bus leaves Baguio for Manila traveling
65kph. At what distance from Manila they will meet?
A. 135.42 km B. 114.56 km
C. 129.24 km
D. 181.35 km
SOLUTION:
12NN for Baguio 250kM
Bus1 = V1 = 55kph
Bus2 = V2 = 65kph
55(250 –X) = 65(X)
X = 114.56 km
3. Simplify (cos ß – 1)(cos ß + 1)
A. -1/ sin2 ß
B. -1/cos2 ß
C. -1/ csc2 ß
D. -1/sec2 ß
SOLUTION:
cos2 ß – 1
(1 / csc2 ß)2 – 1 = -1 / csc2 ß
4. Simplify 1/(csc x + cot x) + 1/(csc x – cot x)
A. 2 cos x
B. 2 sec x
C. 2 csc x
SOLUTION:
𝑐𝑠𝑐𝑥−𝑐𝑜𝑡𝑥+𝑐𝑠𝑐𝑥+𝑐𝑜𝑡𝑥
(𝑐𝑠𝑐𝑥+𝑐𝑜𝑡𝑥)(𝑐𝑠𝑐𝑥−𝑐𝑜𝑡𝑥)
=
2𝑐𝑠𝑐𝑥
𝑐𝑠𝑐 2 𝑥− 𝑐𝑜𝑡 2 𝑥
=
2𝑐𝑠𝑐𝑠
1
1
−
𝑠𝑖𝑛2 𝑥 𝑡𝑎𝑛2 𝑥
D. 2 sin x
= 2cscx
5. From past experience, it is known 90% of one-year-old children can distinguish
their mother’s voice from the voice of a similar sounding female. A random
sample of 20 one year’s old are given this voice recognize test. Find the
probability that all 20 children recognize their mother’s voice.
A. 0.122
B. 0.500
C. 1.200
D. 1.22
6. Find the differential equtions of the family of lines passing through the origin.
A. xdx – ydy = 0
C. xdx + ydy = 0
B. xdy – ydx = 0
D. ydx + xdy = 0
7. A chord passing through the foci’s of the parabola y^2 = 8x has ones end at the
point (8,8). Where is the other end of the chord?
A. (1/2, 2)
B. (-1/2, -2)
C. (-1/2, 2)
D. (1/2, -2)
8. Find the radius of the circle inscribed in the triangle determined by the line y =
2
x + 4, y = -x – 4, and y = 𝑥 + 2
A. 2.29
B. 0.24
7
C. 1.57
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D. 0.35
lOMoARcPSD|22671238
REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
AUGUST 2013
MATHEMATICS
9. What would happen to the volume of a sphere if the radius is tripled?
A. Multiplied by 3
B. Multiplied by 9
C. Multiplied by 27
D. Multiplied by 6
SOLUTION:
V1 / V2 = (r1 / r2 )^3 = (r1 / 3r1)^3
∴V2 = 27 V1
10. Six non-parallel lines are drawn in a plane. What is the maximum number of
point of intersection of these lines?
A. 20
B.12
C. 8
D. 15
11. In a triangle ABC where AC=4 and angle ACB=90 degrees, an altitude t is
drawn from C to the hypotenuse. If t = 1, what is the area of the triangle ABC?
A. 1.82
B. 1.78
C. 2.07
D. 2.28
12. In a 15 multiple choice test questions, with five possible choices if which only
on is correct, what is the standard deviation of getting a correct answer?
A. 1.55
B. 1.65
C. 1.42
D. 1.72
13. What is the area bounded by the curve y = tan2 x and the y = 0 and x = pi/2?
A. 0
B. infinity
C. 1
D. Ɵ
SOLUTION:
y = tan2x
𝜋
= ∫02 𝑡𝑎𝑛2 𝑥 𝑑𝑥 = ∞
𝑒𝑥
14. What is the power series of 1−𝑥 about x = 0?
A.
B.
1 − 2𝑥 +
𝟏 − 𝟐𝒙 +
𝟓
𝟐
5
2
8
𝑥2 − 𝑥3 + ⋯
𝟖
3
𝒙𝟐 + 𝒙𝟑 + ⋯
𝟑
C. 2𝑥 −
D. 2𝑥 +
5
2
5
2
8
𝑥2 + 𝑥3 + ⋯
3
8
𝑥2 − 𝑥3 + ⋯
3
15. What is the vector which is orthogonal both to 9i + 9j and 9l + 9k?
A. 81l + 81j – 81k
C.81l - 81j + 81k
B. 81l – 81j – 81k
D.81l+81j – 81k
16. 34 is 76 percent of what number?
A. 16
B. 40
C. 36
SOLUTION:
24 = 0.75X ; X = 24/0.75 ; X = 32
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D. 32
lOMoARcPSD|22671238
REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
AUGUST 2013
MATHEMATICS
17. Evaluate lim(𝑥 2 − 4)/(𝑥 − 4)
𝑥→4
A. 4
B. 2
C. 16
D. 8
SOUTION:
lim =
𝑥→4
𝑥 2 −4
𝑥−4
= 2𝑥 ; X = 8
4
18. If sin A = − and cot B = 4, both in Quadrant III, the value of sin ( A + B) is
5
A. -0.844
B. 0.844
C. -0.922
D. 0.922
SOLUTION:
sin( A + B ) = (-4/5) (4/√7) + ( 3/5 ) (1/√17) = 0.922
19. A force of 100 m perimeter such that its width is 6m less than thrice its length.
Find the width?
A. 28 m
B. 14 m
C. 36 m
D. 40 m
SOLUTION:
P = 2L + 2W
100 = 2L + 2 ( 3L – 6 )
L = 14
W = 3(14) – 6 = 36m
20. Evaluate log (2 – 5i)
A. 0.7 – 0.5i
B. -0.7 + 0.5i
C. 0.7 + 0.5i D. -0.5 – 0.7i
21. An air balloon flying vertically upward at constant speed is situated 150m
horizontally from an observer. After one minute, it is found that the angle of
elevation from the observer is 28 deg 50 min. what will be then the angle of
elevation after 3 minutes from its initial position?
A. 48 deg
B. 56 deg
C. 61 deg
D. 50 deg
SOLUTION:
28.98° ( 2 ) = 57.96 ≈ 58°
22. If m is jointly proportional to G and x, where a,b,c and d are constant. Therefore.
A. M = aG + bx
C. m = aG
B. m = aGz
D. m = bG
23. In how many ways can a student going to abroad accompanied by 3 teachers
selecting from 6 teachers?
A. 16
B. 24
C. 20
D. 12
SOLUTION:
6!
(6−3 )!(3!)
= 20
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
AUGUST 2013
MATHEMATICS
24. If a man travels 1 km north, 3 km west, 5 km south, and 7 km east, what is his
resultant displacement vector?
A. 5.667 km, 45 deg above + x-axis C. 5.667 km, 225 deg above + x-axis
B. 5.667 km, 45 deg above – x-axis D. 5.667 km, 225 deg above – x-axis
25. What is the general solution of (D4 – 1) y(t) = 0?
A. y = c1Ɵt + c2Ɵ-t +c3 cost + c4 sint
B. y = c1Ɵt + c2Ɵt +c3 Ɵ-t + c4t Ɵ-t
SOLUTION:
(m4 – 1) = 0
(m2 – 1) (m2 + 1) = 0
m–1=0
m+1=0
m1 = 1
m2 = -1
C. y = c1Ɵt + c2Ɵ-t
D. y = c1Ɵt + c2tƟt
y = C1em1t + C2em2t + eAt ( C3cosB + C4sinB)
y = C1et + C2e-t + ( C3cost + C4sint)
m2 + 1 = 0
m2 = -1
m = √−1 = ±1
A=0;B=1
26. Marsha is 10 years older than John, who is 16 years old. How old is Marsha?
A. 24 yrs.
B. 26 yrs.
C. 6 yrs.
D. 12 yrs.
SOLUTION:
M = 10 + X
J = X = 16
M = 10 + 16 = 26
27. Seven times a number x increased by 2 is expressed as
A. 7(x + 20
B. 2x + 7
C. 7x + 2
D. 2(x + 7)
28. The plane rectangular coordinate system is divided into four parts which are
known as:
A. octants
B. quadrants
C. axis
D. coordinates
29. A student already finished 70% of his homework in 42 minutes. How many
minutes does she still have to work?
A. 18
B. 15
C. 20
D. 24
SOLUTION:
0.70/42 mins = 1 / t
t = 60 mins to finish all
60 – 42 = 18 mins
30. In how many ways can 5 people be lined up to get on a bus, if a certain 2
persons refuse to follow each other?
A. 36
B. 48
C. 96
D. 72
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
AUGUST 2013
MATHEMATICS
31. Water is being pumped into a conical tank at the rate of 12 cu.ft/mins. The
height of the tank is 10 ft and its radius is _ ft. How fast is the water level rising
when the water height is _ ft?
A. 2/3 pi ft/min B. 3/2 pi ft/min
C. 3/4 pi ft/min
D. 4/3pi ft/min
32. Write the equation of a line with x intercept a = -1, and y intercept b = 5
A. 8x + y – 8 = 0
C. 8x + y + 8 = 0
B. 8x – y + 8 = 0
D. 8x – y – 8 = 0
SOLUTION:
a = -1 ; b = 8
x/a+y/b=1
(x / -1 + y / 8 = 1) -8
8x –y + 8 = 0
33. In a single throw of a pair of dice, find the probability that the sum is 11
A. 1/12
B. 1/16
C. 1/36
D. 1/18
34. Find the area bounded by one arch of the companion to the cycloid x = a theta,
y = a (1 – cos theta) and the y-axis
A. 2pi a^2
B. 4pi a ^2
C. pi a ^2
D. 3pi a^2
35. A rectangular plate 6m by 8m is submerged vertically in a water. Find the force
on one face if the shorter side is uppermost and lies in the surface of the liquid.
A. 941.76 kN
B. 1,883.52 kN
C. 3,767.04 kN
D. 470.88 kN
SOLUTION:
F = WAh
= (9.81 kg/m2)(6x8)(8)
= 3767.04kN ÷ 2 = 1883.52kN
36. Michael is four times as old as his son Carlos. If Michael was 18 years old when
Carlos was born, how old is Michael now?
A. 36 yrs.
B. 20 yrs.
C. 24 yrs
D. 32 yrs.
SOLUTION:
x = 4 x – 18
∴ 4 ( 6) = 24
-4x + x = -18
-3x = -18
x=6
37. In polar coordinate system, the distance from a point to the pole is known as:
A. polar angle
C. x-coordinate
B. radius vector
D. y-coordinate
38. A certain man sold his balot at Php1.13 per piece. If there 100 balot sold all in
all, how much is his total collection?
A. Php 113.00
B. Php 115.00
C. Php 112.00
D. Php 116.00
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
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MATHEMATICS
SOLUTION:
Php 1.13 x 100 pieces = Php 113.00
39. A certain population of bacteria grows such that its rate of change is always
proportional to the amount present. It doubles in 2 years, if in 3 years there are
20,000 of bacteria present, how much is present initially?
A. 9,071
B. 10,071
C. 7,071
D. 8,071
SOLUTION:
q = Q0ekt
(2Q0 = Q0ek(2))1/2
ek = 21/2
20,000 = Q0 ( 21/2)3
= 7071.07 ≈ 7071
40. In throwing a pair of dice, what is the probability of getting a total of 5?
A. 1/36
B. 1/9
C. 1/16
D. 1/8
41. What is the distance between at any point P(x ,y) on the ellipse b 2x2 + a2y2 =
a2b2 to its focus.
A. by ±ax
B. b ± ay
C. ay ± bx
D. a ± ex
42. Calculate the eccentricity of an ellipse whose major axis and latus rectum has
length of 10 and 32/5, respectively.
A. 0.4
B. 0.5
C. 0.8
D. 0.6
SOLUTION:
2a = 10 ; a = 5
LR = 32/5 ≅ 2b2/a
32/5 = 2b2/5
b=4
C = √𝑎2 − 𝑏 2
= √52 − 42
C=3
43. Evaluate (3 + j4)(3 – j4)
A. 9 – j16
B. 9 + j16
C. 25
∴𝑒=
𝑐
𝑎
=
3
5
= 0.6
D. 36
SOLUTION:
(3 + j4) (3-j4) = 25
44. What is the area bounded between y = 6x^2 and y = x^2 + 7?
A. 9
B. 10
C. 11
D. 12
45. Two vertical poles are 10 m apart. The poles are 5 m and 8 m, respectively.
They are to be stayed by guy wires fastened to a single stake on the ground
and attached to the tops of the poles. Where should the stake be placed to use
the least amount of wire?
A. 6.15 m from 5 m pole
C. 6.51 m from 5 m pole
B. 6.15 m from 8 m pole
D. 6.51 m from 8 m pole
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
AUGUST 2013
MATHEMATICS
SOLUTION:
x = ab / b + c = 10(5) / 5 + 8 ; x = 3.85
a – x = 10 – 3.85 = 6.15 from 8m pole
46. A and B are points on circle Q such that triangle AQB is equilateral. If AB = 12,
find the length of arc AB.
A. 15.71
B. 9.42
C. 12.57
D. 18.85
SOLUTION:
C = rƟ
= 12(60)(𝜋/ 180) = 12.57
47. The area under the portion of the curve y = cosx from x = 0 to x = pi/2 is revolved
about the x-axis. Find the volume of the solid generated.
A. 2.47
B. 2.74
C. 3.28
D. 3.82
48. Find the length of arc of r = 2/(1 +costheta) from theta = 0 to theta = pi/2.
A. 2.64
B. 3.22
C. 2.88
D. 3.49
SOLUTION:
r = 2 / 1 + cosƟ ; cosƟ = 0
r+x=2
((x2 + y2)1/2 = 2- x)2
x2 + y2 = 4 – 4x + x2
y2 = (-4)(x – 1) ; x = y2/ -4 + 1
2
A = ∫−2 (
𝑦 2 −4
4
) 𝑑𝑦 = 8/3
49. Find the equation of the straight line which passes through the point (6, -3) and
with an angle of inclination of 45 degrees.
A. x + y = 3
B. 4x – y =27
C. x- 2y = 12
D. x – y = 9
SOLUTION:
y – y1 = m ( x – x1 )
y+3=1(x–6)
y+3=x–6
x–y=9
50. The equation of the directrix of the y^2 = 6x is
A. 2x – 3 = 0
B. 2x + 3 = 0
C. 3x – 2 = 0
D. 3x + 2 = 0
51. Find the area bounded by r = 4(sq.rt. of cos 2 theta).
A. 16
B. 8
C. 4
D. 12
52. In an arithmetic progression whose first term is 5, the sum of 8 terms is 208.
Find the common difference.
A. 3
B. 4
C. 5
D. 6
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
AUGUST 2013
MATHEMATICS
SOLUTION:
𝑛
8
S = [2𝑎1 + (𝑛 − 1)𝑑] ; 208 = [2(5) + (8 − 1)𝑑];
2
2
d=6
53. If 3x = 7y, then 3x2/7y2 = ?
A. 1
B. 3/7
SOLUTION:
3𝑥 2
3x = 7y ; then 7𝑦 2 ;
3𝑥
7
=𝑦;
D. 49/9
C. 7/3
3𝑥 2
3𝑥 2
7( )
7
=
32
9𝑥2
7(
49
)
=
3𝑥 2
92
7
= 3𝑥 2 ∙
7
9𝑥 2
=
𝟕
𝟑
54. What is the area of the ellipse whose eccentricity is 0.60 and whose major axis
has a length of 6?
A. 40.21
B. 41.20
C. 42.10
D. 40.12
55. Tickets to the school play sold at $4 each for adults and $1.50 each for children.
If there were four times as many adult’s tickets sold as children’s tickets, and
the total were $3500. How many children’s tickets were sold?
A. 160
B. 180
C. 200
D. 240
SOLUTION:
Let x be the children
4X(4) + X(1.50) = 3500
16x + 1.5 X = 3500
17.5X = 350
X = 200
56. If the line kx + 3y + 8 = 0 has a slope of 2/3, determine k.
A. -3
B. -2
C. 3
D. 2
SOLUTION:
Kx + 3y + 8 = 0 ; m = 2/3 ; k = ?
Y = mx + b
(3y = -kx – 8) 1/3
Y = -kx/3 – 8/3
∴ k = -2
57. The Rotary Club and the Jaycees Club had a joint party. 120 members of the
Rotary Club attended and 100 members of the Jaycees Club also attended but
30 of those who attended are members of both parts. How many persons
attended the party?
A. 190
B. 220
C. 250
D. 150
SOLUTION:
Rotary Club = 120 members
Jaycee Club = 100 members
120 + 100 -30 = 190
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
AUGUST 2013
MATHEMATICS
But 30 are both member club
58. Find the value of k for which the graph of y = x^3 + kx^2 + 4 will have an
inflection point at x = -1.
A. 3
B. 4
C. 2
D. 1
59. Solve for x if log4x = 5.
A. 2048
B. 256
SOLUTION:
C. 625
D. 1024
5 = log(X) ÷ log(4)
X= 1024
60. An observer wishes to determine the height of a tower. He takes sights 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 degrees and at
point B is 40 degrees. What is the height of the tower?
A. 85.60 ft
B. 143.97 ft
C. 110.29 ft
D.92.54 ft
61. If four babies are born per minute, how many babies are born in one hour?
A. 230
B. 250
C. 240
D. 260
SOLUTION:
In 1 hr = 60 mins
4 babies/min x 60 mins/hr = 240 babies/hr
62. What was the marked price of a shirt that sells at P 225 after a discount of
25%?
A. P 280
B. P 300
C. P 320
D. P 340
SOLUTION:
100% - 25% = 75%
0.75X = 225
X = 225 ÷ 0.75
X = 300
63. Which number is divisible by both 3 and 5?
A. 275
B. 445
C. 870
D. 955
SOLUTION:
870 is the only number that is divisible by both 3 and 5.
64. If s = t^2 – t^3, find the velocity when the acceleration is zero
A. 1/4
B. 1/2
C. 1/3
D. 1/6
65. Find k so that A = (3, -2) and B = (1, k) are parallel
A. 3/2
B. -3/2
C. 2/3
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D. -2/3
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
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MATHEMATICS
SOLUTION:
∴ Bslope = -2/3
Aslope = -2/3
66. A lady gives a dinner party for six guest. In how many may they be selected
from among 10 friends?
A. 110
B. 220
C. 105
D. 210
SOLUTION:
10!
(10−6)!(6!)
= 210
67. A wheel 4 ft in diameter is rotating at 80 rpm. Find the distance (in ft) traveled
by a point on the rim in 1 s.
A. 9.8 ft
B. 19.6 ft
C. 16.8 ft
D. 18.6 ft
SOLUTION:
D = 𝜋𝑟 2 =
𝜋(𝑟)2 ×80
60
= 𝟏𝟔. 𝟖 𝒇𝒕
68. If f(x) = 6x – 2 and g(x) = 4x + 3, then f(g(2)) = ____?
A. 52
B. 53
C. 50
D. 56
69. From the top of lighthouse, 120 ft above the sea, the angle of depression of a
boat is 15 degrees. How far is the boat from the lighthouse?
A. 444 ft
B. 333 ft
C. 222 ft
D. 555 ft
70. If 8 men take 12 days to assemble 16 machines, how many days will it take 15
men to assemble 50 machines?
A. 16
B. 24
C. 16
D. 20
71. Find the coordinate of the highest point of the curve x = 90t, y = 96t – 16t^2.
A. (288, 144)
B. (144, 288)
C. (288, -144)
D.(-144, 288)
72. The vertex of parabola y = (x – 1)^2 + 2 is _____.
A. (-1, 2)
B. (1, 2)
C. (1, -2)
D. (-1, -2)
73. Two angles measuring p deg and q are complementary. If 3p – 2q = 40 deg,
then the smaller angle measures
A. 40 deg
B. 44 deg
C. 46 deg
D. 60 deg
74. In an ellipse, a chord which contains a focus and is in a line perpendicular to
the major axis is a:
A. latus rectum
C. focal width
B. minor axis
D. conjugate axis
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
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MATHEMATICS
75. Determine the rate of a woman rowing in still water and the rate of the river
current, if it takes her 2 hours to row 9 miles with the current and 6 hours to
return against the current.
A. 1 mph
B. 2 mph
C. 3 mph
D. 4 mph
76. If f(x) = sin x and f(pi) = 3, then f(x) =
A. 4 + cos x
B. 3 + cos x
C. 2 – cos x
D. 4 – cos x
77. What is the value of the circumference of a circle at the instant when the radius
is increasing at 1/6 the rate the area is increasing?
A. 3
B. 3/pi
C. 6
D. 6/pi
78. A ball is thrown from the top of a 1200-foot building. The position function
expressing the height h of the ball above the ground at any time t is given as
h(t) = -16t^2 – 10t + 1200. Find the average velocity for the first 6 seconds of
travel.
A. -202 ft/sec
B. -106 ft/sec
C. -96 ft/sec
D. -74 ft/sec
−1
79. ∫−2 |𝑥 3 |𝑑𝑥 =
A. -7/8
SOLUTION:
B. 7/8
C. -15/4
D. 16/4
−1
∫ 𝑥 3 𝑑𝑥 = −𝟏𝟓/𝟒
−2
80. The distance covered by an object falling freely rest varies directly as the
square of the time of falling. If an object falls 144 ft in 3 sec, how far will it fall
in 10 sec?
A. 1200 ft
B. 1600 ft
C. 1800 ft
D. 1400 ft
81. For what values(s) of x will the tangent lines to f(x0 + ln x and g(x) = 2x^2 be
parallel?
A. 0
B. 1/4
C. 1/2
D. ±1/2
82. What kind of graph has r =2 sec theta?
A. Straight line
B. parabola
C. ellipse
D. hyperbola
83. The probability of A’s winning a game chess against B is 1/3. What is the
probability that A will win at least 1 of a total 3 games?
A. 11/27
B. 6/27
C. 19/27
D. 16/27
84. If f(x) = 2^(x^3 + 1), then to the nearest thousandth f(1) =
A. 2.000
B. 2.773
C. 4.000
D. 8.318
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
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MATHEMATICS
𝑎
𝑎
85. If line function f is even and ∫0 𝑓(𝑥)𝑑𝑥 = 5𝑚 − 1, then ∫−𝑎 𝑓(𝑥)𝑑𝑥 =
A. 0
B. 10m – 2
C. 10m – 1
D. 10m
86. What is the slope of the line through (-1, 2) and (4, -3)?
A. 1
B. -1
C. 2
SOLUTION:
𝑚=
D. -2
(−3 − 2)
−5
=
= −𝟏
(4 + 1)
5
87. The axis of the hyperbola through its foci is known as:
A. Conjugate axis
B. major axis
C. transverse axis
D. minor axis
88. Determine a point of inflection for the graph of y = x^3 + 6x^2
A. (-2, 16)
B. (0, 0)
C. (-1, 5)
D. (2, 32)
89. Clarify the graph of the equation x^2 + xy + y^2 – 6 = 0.
A. circle
B. parabola
C. ellipse
D. hyperbola
90. What is the coefficient of the (x – 1)^3 term in the Taylor series expansion of
f(x) = ln x expanded about x = 1?
A. 1/6
B.1/4
C. 1/3
D. 1/2
91. If x varies directly as y and inversely as z, and x = 14, when y = 7 and z = 2,
find x when y = 16 and z = 4.
A. 4
B. 14
C. 8
D. 16
SOLUTION:
x=y
z = 1/y
92. Solve the differential equation
A. y = cx
∴ x = y ; 𝐱 = 𝟏𝟔
find x = ?
y = 16
z=4
1
B. y = + 𝑐
𝑥
𝑑𝑦
𝑑𝑥
𝑦
+ =2
𝑥
C. y = 3x + c
D. y = x +
𝒄
𝒙
93. In triangle ABC, AB = 40 m, BC = 60 m and AC = 80m. How far from a will the
other end of the bisector angle B located along the line AC?
A. 40
B. 32
C. 38
D. 35
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REGISTERED ELECTRICAL ENGINEERS PRE-BOARD EXAMINATION
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MATHEMATICS
SOLUTION:
40 + 60 + 80
𝑠=
= 90
2
2
√80(60)(90)(90 − 60) = 𝟒𝟎
ℎ𝑎 =
80 + 40
94. What amount should an employee receive a bonus so that she would net $500
after deducting 30% from taxes?
A. $ 714.29
B. $814.93
C. $ 624.89
D. $ 538.62
SOLUTION:
500 + 0.30X = X
500 = X – 0.30X
X = 714.29
95. A rectangular trough us 8ft long, 2ft across the top, and 4 ft deep. If water flows
in at a rate of 2 cu. Ft per min. how fast is the surface rising when the water is
1ft deep?
A. 1/4 ft/min
B. 1/6 ft/min
C. 1/3 ft/min
D. 1/5 ft/min
96. If the parabola y = x^2 + C is tangent to the line y = 4x + 3, find the value of C.
A. 4
B. 7
C. 6
D. 5
97. A parabola having its axis along the x-axis passes through (-3, 6). Compute the
length of latus rectum if the vertex is at the origin.
A. 12
B. 8
C. 6
D. 10
98. If the average value of the function f(x) = 2x^2 on the interval (0, c) is 6, then c
=
A. 2
B. 3
C. 4
D. 5
99. Find the volume of the tetrahedron bounded by the coordinate planes and the
plane z = 6 – 2x + 3y.
A. 4
B. 5
C. 6
D. 3
100. Compute the curvature of r = 2 + sin theta when theta = 90 degrees.
A. 4/9
B. 27/4
C. 5/9
D. 27/5
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