Republic of the Philippines
OPENSOURCE REE/RME REVIEW GROUP
facebook.com/groups/ree.opensource
OPENSOURCE ELECTRICAL ENGINEERING DIVISION
REGISTERED ELECTRICAL ENGINEERS Pre-Board Examination
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MATHEMATICS
INSTRUCTION: Select the correct answer for each of the following questions. Mark only
one answer for each item by shading the box corresponding to the letter of your
choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 2
only. Use only scratch paper(s) provided. Use also back page as scratch paper. Do not
detach the staple wire.
1.
The sum of the distances from the two foci to any point in what curve is
constant?
A. Hyperbola
2.
C. Parabola
B. a⁴b⁶
C. a²b⁶
B. 24.5 lbs
C. 40.2 lbs
D. 31.5 lbs
B. 0.09
C. 0.92
D. 1.92
What is 20% of 96?
A. 19.20
6.
C. Parallel to the plane
D. Oblique to the plane
If a person throws away 3.5 lbs of trash daily, how much trash will the person
throw away in one week?
A. 24.0 lbs
5.
What conic section is described by the equation 4x2 – y2 + 8x + 4y = 15?
A. Ellipse
B. Parabola
7.
B. 75%
C. 96%
D. 95%
When two lines are parallel, the slope of one is:
A.
B.
C.
D.
9.
C. Hyperbola
D. Circle
Sam scored 96% on his first Calculus quiz; 74% on his second and 85% on his
third. What is his quiz average?
A. 85%
8.
D. a²b⁵
A normal to a given plane is:
A. Perpendicular to the plane
B. Lying in the plane
4.
D. Any conic
Find the area of a square whose side is a²b³.
A. a4⁴b⁵
3.
B. Ellipse
The negative of the other
Equal to the other
The negative reciprocal of the other
The reciprocal of the other
If 1 cm = 0.39 in, about how many cm are there in 0.75 in?
A. 0.52
B. 1.75
C. 0.29
D. 1.92
10. Which of the following is not a multiple of 11?
A. 221
B. 759
C. 121
Page 1
D. 1111
11. What is the conic section whose eccentricity is less than 1?
A. Circle
B. Parabola
C. Ellipse
D. Hyperbola
12. Nicole had 75 stuffed animals. Her grandmother gave fifteen of them to her. What
percentage of the stuffed animals did her grandmother give her?
A. 15%
B. 20%
C. 10%
D. 25%
13. What type of conic section is x2 - 4y + 3x + 5 = 0?
A. Circle
B. Parabola
C. Ellipse
D. Hyperbola
14. The line passing through the focus and perpendicular to the directrix of a
parabola is called _______.
A. axis
B. secant line
C. latus rectum
D. tangent line
15. Sand is being poured into a conical pile in such a way that the height is always
1/3 of the radius. At what rate is sand being added to the pile when it is 4 ft
high and height increasing at 2 in/min?
A. 100,132.88 in/min
B. 30,288.13 in/min
C. 53,288.13 in/min
D. 130,288.13 in/min
16. Find the volume generated by revolving the circle x² + y² + 6x + 4y + 12 = 0
about the y-axis.
A. 22.58
B. 55.28
C. 65.55
D. 59.22
17. From a sample size of 100, the following description measures were calculated:
median = 23; mean = 20; standard deviation = 5; range = 35. Seventy five sample
values are between 5 and 35. If you know the sample mean, median, standard
deviation were correct, which of the following conclusions might you draw?
A. The number of sample values between 10 and 30 were miscounted.
B. The range must have been calculated incorrectly because it should not be seven
times the standard deviation’s value.
C. The number of sample values between 5 and 35 have been miscounted because all
100 values must be in this interval.
D. The distribution is skewed to the right because the median exceeds the mean.
18. A high school band teacher has a record of each student’s attendance. The result
is listed below in days each student has been absent.
3, 4, 7, 2, 2, 1, 0, 0, 1, 0, 3, 3, 2, 1, 6, 0, 1
0, 1, 1, 1, 5, 3, 1, 1, 0, 0, 2, 1, 2, 1, 0, 0, 4
What proportion of students have been absent less than 5 days?
A. 0.06
B. 0.60
C. 0.91
D. 0.09
19. Each of the questions on a quiz is a five-part multiple choice question with
exactly only one correct answer. A student totally unprepared for the quiz,
guesses on each of the 15 questions. How many questions should the student expect
to answer correctly?
A. 2
B. 13
C. 5
D. 3
20. Given the 2 functions, f(x) and g(x), table of values are shown below. What is
the value of g(f(3))?
x
°
f(x)
x
°
g(x)
---------------------------5
°
7
-2
°
3
-1
°
-5
1
°
-1
1
°
3
2
°
-3
3
°
2
3
°
-5
A. – 1
B. – 5
C. – 3
Page 2
D. 2
21. Find the volume generated when the area bounded by y = 2x + 3 and y = x 2 is
revolved about the x-axis.
A. 422
B. 300
C. 308
D. 228
22. Solve [y – square root of (x2 + y2)]dx - xdy = 0.
A. Square root of (x2 + y2 + y) = C
B. Square root of (x2 – y2) + y = C
C. Square root of (x2 + y2) + y = C
D. Square root of (x + y) + y = C
23. A man is running around a circular track 200 m in circumference. An observer uses
a stopwatch to time each lap, obtaining the data as follows:
Time (sec)
Distance (m)
30
200
68
400
114
600
168
800
230
1000
300
1200
378
1400
What is the man’s average between 68 sec and 168 sec?
A. 3 m/s
B. 8 m/s
C. 1.82 m/s
D. 4 m/s
24. A Statistics Department is contacting alumni by telephone asking for donations to
help fund a new computer laboratory. Past history shows that 80% of the alumni
contacted in this manner will make a contribution of at least P 50. A random
sample of 20 alumni is selected. What is the probability that less than 17 alumni
will make a contribution of at least P 50?
A. 0.589
B. 0.301
C. 0.200
D. 0.421
25. At exactly what time after 5 o’clock will the hour hand and the minute hand be
perpendicular for the first time?
A. 5:10 and 54 sec
B. 5:05 and 34 sec
C. 5:15 and 25 sec
D. 5:20 and 14 sec
26. Find the equation of the normal line to x2 + y2 = 1 at point (2, 1).
A. y = 2x
B. x – y = 0
C. x = 2y
D. x + y = 1
27. What is the smallest positive value for x where y = sin 2x reaches its maximum?
A. π/2
B. π/4
C. π
D. π/3
28. When the energy/hour required in driving a boat varies as the cube of the
velocity, find the most economical rate/hour when going against the current of 4
kph.
A. 5 kph
B. 12 kph
C. 8 kph
D. 6 kph
29. What is the maximum rectangular area that can be fenced in 20 ft using two
perpendicular corner sides of an existing wall?
A. 310 square feet
B. 100 square feet
C. 120 square feet
D. 250 square feet
30. Determine the correct equation for the line with a slope of 7 and y-intercept of
– 4.
A. y = - 1/7x – 4
B. y = 7x + 4
C. y = 7x – 4
D. y = - 7x + 4
31. Parcel charges of a courier company are as follows:
P 40 for the first 2 kilograms
P 15 for each of the succeeding kilogram weight of parcel
With these rates, what amount would be charged of a parcel weighing 30 kg?
A. P 660
B. P 450
C. P 460
Page 3
D. P 650
32. The dimension of a rectangular prism can be expressed as x + 1, x – 2 and x + 4.
In terms of x, what is the volume of the prism?
A. x3 + 5x2 - 2x + 8
B. x3 + 3x2 + 6x – 8
C. x3 + 3x2 - 6x – 8
D. x3 - 5x + 2x + 8
33. Larry finds the angle of elevation of the top of the 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. 73.61 m
B. 53.61 m
C. 83.61 m
D. 63.61 m
34. If log 2 = a, log 3 = b, log 5 = c, then log (7.5) = ________.
A. c/(a + b)
B. ab/c
C. c/ab
D. b + c – a
35. From the base of a building, the angle of elevation to the top of a 4.0 m
vertical pole a distance away is 18 deg 50 min. From the top of the building, the
angle of depression of the base of the pole 48 deg 10 min. Find the height the
building.
A. 9.1 m
B. 8.1 m
C. 11.2 m
D. 13.1 m
36. Michael walks to school. He leaves each morning at 7:32 A.M. and arrives at
school 15 minutes later. If he travels at a steady rate of 4.5 miles/hr, what is
the distance between his home and school?
A. 1.8 miles
B. 1.5 miles
C. 1.9 miles
D. 1.1 miles
C. 48
D. 32
37. Evaluate f(-3) if f(x) = x2 - 2x + 1.
A. 16
B. 8
38. Find the sum of the first five terms of the geometric progression if the third
term is 144 and the sixth term is 486.
A. 540
B. 748
C. 984
D. 844
39. From the top of a building 100 m high, the angle of depression of two cars due
east of the observer are 32 degrees 25’ and 58 degrees 33’, respectively. Find
the distance between the two cars.
A. 106.00 m
B. 96.30 m
C. 9.36 m
D. 63.91 m
40. The position vectors of points A and B are 2 + i and 3 – 2i, respectively. Find
an equation for line AB.
A. x – 3y = - 4
B. 3x – y = 2
C. x + 3y = 4
D. 3x + y = 7
41. A line segment is a side of a square and also the hypotenuse of an isosceles
right triangle. What is the ratio of the area of the square to the area of the
triangle?
A. 2 : 1
B. 4 : 1
C. 1 : 1
D. 3 : 2
42. The current I flowing in an RL circuit is given by I = (E/R)(1 – e^-Rt/L), where
E is the voltage applied to the current, R is the resistance and L is the
inductance. Express I in terms of E and R when t = L/R.
A. 0.632(E/R)
B. 0.584(E/R)
C. 0.435(E/R)
D. 0.388(E/R)
43. The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3
times the length. Find the width of the rectangle.
A. 14.5 inches
B. 12.5 inches
C. 37.5 inches
D. 15 inches
Page 4
44. The area of the square whose side measures 4 units is added to the difference of
11 and 9 divided by 2. What is the total value?
A. 5
B. 9
C. 16
D. 17
45. Two towns are located near the straight shore of a lake. Their nearest distance
to point in the shore are 1 km and 2 km, respectively, and these points on the
shore are 6 km apart. Where should the fishing port be located to minimize the
total amount of pavement necessary to build a straight road from each town to the
pier?
A.
B.
C.
D.
12 km from the point on the shore nearest the first town
12 km from the point on the shore nearest the second town
2 km from the point on the shore nearest the first town
2 km from the point on the shore nearest the second town
46. A movie is schedule for 2 hours. The theater advertisements are 3.8 min long.
There are two previous ones; 4.6 min and 2.9 min long. The rest of the time is
devoted to the feature. How long is the feature film?
A. 94.3 min
B. 97.5 min
C. 108.7 min
D. 118.9 min
47. Find the solution to the system of equations x – 2y = 5 and 2x + 5y = 1.
A. (3, - 1)
B. (-1, - 3)
C. (3, 1)
D. (1, 3)
C. (0, 4)
D. (-4, 0)
48. Find the vertex of the parabola x2 = 4y.
A. (4, 0)
B. (0, 0)
49. The difference between six times the quantity 6x + 1 and three times the quantity
x – 1 is 108. What is the value of x?
A. 35/11
B. 3
C. 12
D. 12/11
50. Daniel has one more Algebra exam to take before computing the average of his
grades. His Algebra scores so far are 93, 94, 94, 95, 96, 98. What must be his
score on this last exam so that he can maintain his present average?
A. 94
B. 95
C. 92
D. 97
51. Find the area of the region enclosed by the triangle with vertices (1, 1), (3, 2)
and (2, 4).
A. 7/2
B. 5/2
C. 1/2
D. 3/2
52. Find the area of the polygon whose vertices are 2 + 3i, 3 + i, -2 – 4i, -4, - i,
-1 + 2i.
A. 47
B. 25/2
C. 25
D. 47/2
53. Find the area bounded by y2 = 4x and x2 = 4y.
A. 5.33
B. 0.33
C. 8.33
D. 2.33
54. It is estimated that the annual cost of driving a certain new car is given by the
formula: C = 0.25 m + 1,600, where m represents the number of miles driven per
year and C is the cost in dollars. Jane purchased such a car and determines
between $5,350 and $5,600 for the next year’s driving cost. What is the
corresponding range of miles that she can drive her new car?
A. Between 13,000 miles and 18,000 miles C. More than 16,000 miles
B. Between 15,000 miles and 16,000 miles D. Between 13,000 miles and 16,000 miles
55. Find the equation of the line passing through the intersection of x – y = 0 and
3x – 2y = 2 cutting from the first quadrant a triangle whose area is 9.
A. x + y + 1 = 0
B. 3x + y – 3 = 0
C. 2x + y – 2 = 0
D. x + 2y – 6 = 0
Page 5
56. A ball bounces 2/3 of the altitude from which it falls. Suppose the ball is
dropped from the height of 18 feet, how far will it travel before coming to rest?
A. 99 feet
B. 90 feet
C. 19 feet
D. 9 feet
57. A chord of a circle of a diameter 10 ft is decrease in length 1 ft/min. Find the
rate of change of the smaller arc subtended by the chord when the chord is 8 ft
long.
A. 3/5 ft/min
B. 2 ft/min
C. 5/3 ft/min
D. 5 ft/min
58. Hotels, like airlines, often overbook, counting on the fact that some people with
reservation will cancel at the last minute. A certain hotel chain finds 20% of
the reservations will not be used if four reservations are made. What is the
chance fewer than two will cancel?
A. 0.3825
B. 0.7241
C. 0.5211
D. 0.8192
59. A periodic function has zero average value over a cycle and its Fourier series
consist of only odd cosine terms. What is the symmetry possessed by this
function?
A. Even quarter-wave
B. Even
C. Odd
D. Odd quarter-wave
60. Evaluate the integral of ln x dx from 1 to e.
A. 0
B. 1
C. 2
D. 3
61. What is the differential equation of the family of parabolas having their
vertices at the origin and their foci on the x-axis?
A. 2ydx – xdy = 0
B. 2xdx – ydy = 0
C. 2xdy – ydx = 0
D. dy/dx – x = 0
62. Which of the following equations is an exact differential equation?
A. xdx + (3x – 2y)dy = 0
B. y²dx + (2x – 3y)dy = 0
C. (2xy + x)dx + (x² + y)dy = 0
D. (x² + 1)dx – xydy = 0
63. Compute log (3 – 2i).
A. 0.5570 – 0.2554i
B. 0.2575 – 0.3545i
C. 1.6575 + 0.8544i
D. 0.7580 – 0.7580i
64. Find the maximum value of 3 sin x.
A. 1/3
B. 1
C. 3
D. infinity
65. What is the ratio of the sides of a triangle if the product of the sides is a
maximum?
A. 1:2:2
B. 1:1:2
C. 1:1:1
D. 1:3:3
66. Evaluate the limit of x/sqrt (1 + x2) as x approaches infinity.
A. 0
B. Infinity
C. 1
D. None of the choices
67. When a metallic ball bearing is placed inside a cylindrical container of radius 2
cm, the height of water inside the cylinder increases by 0.6 cm. What is the
radius of the ball bearing?
A. 2.2 cm
B. 0.6 cm
C. 1.8 cm
D. 1.2 cm
68. If the coefficient ao of a Fourier series of a periodic function is zero, it
means that the function has:
A. Odd quarter-wave symmetry
B. Odd symmetry
C. Even quarter-wave symmetry
D. All of the choices
Page 6
69. Solve the equation 5z2 + 2z + 10 = 0.
A. 1 – i, 1 – 2i
B. 1 + i, 1 – 2i
C. 1 + i, 1 – 2i
D. (-1 + 7i)/5, (-1 + 7i)/5
70. Solve the differential equation y” – 4y’ + 3y = sin x.
A.
B.
C.
D.
y(x)
y(x)
y(x)
y(x)
=
=
=
=
C₁e3x + C₂ex + 1/5 cos x + 1/10 sin x
C₁e3x + C₂ex sin x
C₁sin 3x + C₂x + cos 3x
C₁sin 3x + C₂x + 1/10 sin x
71. The Fourier series of waveform processing even quarter-wave symmetry contains
only ______.
A.
B.
C.
D.
even harmonics
odd cosine terms
odd sine terms
both odd cosine terms and odd sine terms
72. A periodic waveform possessing half-wave symmetry has no _____.
A. even harmonics
B. sine terms
C. odd harmonics
D. cosine terms
73. Which of the following periodic function possesses even symmetry?
A. cos 3t
B. t cos 50t
C. sin t
D. (t + t2 + t⁵)
74. The symbol j represents counterclockwise rotation of a vector through ____
degrees.
A. 180
B. 90
C. 360
D. 270
C. (-a – jb)
D. (jb – a)
75. The conjugate of (- a + jb) is ______.
A. (a – jb)
B. (a – jab)
76. When the negative half-cycle of a complex waveform is reversed, it becomes
identical to its positive half-cycle. This feature indicates that the complex
waveform is composed of:
A. Fundamental
B. Even harmonics
C. Odd harmonics
D. Both fundamental and odd harmonics
77. All opposite rays:
A. Are also straight angles
B. Extend in the same direction
C. Have different end points
D. Do not form straight lines
78. Angles that share a common vertex point cannot:
A.
B.
C.
D.
Share a common angle side
Be right angle
Use the vertex letter name as an angle name
Share interior points
79. If angle EDF and angle HIJ are supplementary angles, and angle SUV and angle EDF
are also supplementary angles, then angle HIJ and angle SUV are:
A. Acute angles
B. Right angles
C. Obtuse angles
D. Congruent angles
80. Tori was asked to give an example of the commutative property of addition. Which
of the following choices would be correct?
A. 3 + (4 + 6) = (3 + 4) + 6
B. 3 + 4 = 4 + 3
C. 3(4 + 6) = 3(4) + 3(6)
D. 3 + 0 = 3
Page 7
81. Evaluate sin [arccos (-2/3)].
A. Square root of 3
B. (1/3) square root of 5
C. Square root of 5
D. (1/5) square root of 3
82. Four is added to the quantity two minus the sum of negative seven and six. This
answer is then multiplied by three. What is the result?
A. 57
B. – 21
C. 15
D. 21
83. The value of a computer is depreciated over 5 years for tax purpose, that is, at
the end of 5 years, the computer is worth 0. If a business paid P 21,000 for a
computer, how much will it have depreciated after 2 years?
A. P 4,200
B. P 8,400
C. P 10,500
D. P 8,200
84. Evaluate lim (2 – x)^tan πx/2 as x approaches 1.
A. Infinity
B. e2/π
C. e^(2/π)
D. e
85. Find the centroid of a semi-circular region of radius a.
A. a/2π
B. 4a/3π
C. 3a/4π
D. a/π
C. π/2
D. π/3
86. If y = 2x + sin 2x, find x when y’ = 0.
A. 3π/2
B. 2π/3
87. The time a student spends learning a computer software package is normally
distributed with a mean of 8 hours and standard deviation of 1.5 hours. A student
is selected at random. What is the probability that the student spends less than
6 hours learning a software package?
A. 1
B. 0.15
C. 0.21
D. 0.09
88. Mon and Mila can restock an aisle of the supermarket in 1 hour working together.
Working alone, Mon can restock an aisle in 1.5 hours and Mila in 2 hours. If they
work together for 2 hours and then work separately for another two hours, how
many aisles will they have completed?
A. 5.11
B. 4.33
C. 4.50
D. 3.50
89. Liza thought she had the exact money to buy 10 chocolate bars. However, the price
per bar had increased by 50 centavos. Consequently, she was able to buy only 8
bars and had P 2 left. How much money did Liza have?
A. 80
B. 40
C. 60
D. 30
90. After the price of gasoline went up by 10%, a consumer reduced his consumption by
the same percent. By what percent would his gasoline bill be changed?
A. 1 %
B. 10%
C. 11 %
D. 0.1%
91. Evaluate the limit of [(z2 – 1 – i)/(z2 - 2z + 2)]2 as z approaches 1 + i.
A. – 1/4
B. – 4/3 – 4i
C. – 12 + 6i
D. Square root of 2(1 + i)/2
92. sin θ/2 + sin 2θ/22 + sin 3θ/2³ + … =
A. 2 sin θ / (5 – 4 cos θ)
B. 2 cos θ / (5 – 4 sin θ)
C. 2 sin θ / (5 + 4 cos θ)
D. 2 cos θ / (5 + 4 sin θ)
93. Find the volume (in cubic cm) of a right heptagonal prism with base sides that
measure 13 cm, an apothem that measures 6 cm, and a height that measures 2 cm.
A. 546
B. 564
C. 528
Page 8
D. 582
94. Find the measure of a triangular pyramid’s base side if its volume measures 72
sqrt 3 cubic meters and its height measures 6 meters. The base of the pyramid
forms an equilateral triangle.
A. 12
B. 10
C. 11
D. 13
95. What is the area of a circle inscribed in a dodecagon with an apothem 13 meters
long?
A. 26π meters
B. 156π meters
C. 42.2π meters
D. 169π meters
96. Marci filled her car’s gas tank on Monday, and the odometer read 32,461.3 miles.
On Friday when the car’s odometer read 32,659.7 miles, she filled the car’s tank
again. It took 12.4 gallons to fill the tank. How many miles to the gallon does
Marci’s car get?
A. 16 miles per gallon
B. 21.3 miles per gallon
C. 18.4 miles per gallon
D. 14 miles per gallon
97. Kelly plans to fence in her yard. The OS Company charges $3.25 per foot
of fencing and $15.75 an hour for labor. If Kelly needs 350 feet of fencing and
the installers work a total of 6 hours installing the fence, how much will she
owe the OS Fence Company?
A. $1,153.25
B. $1,232.00
C. $1,069.00
D. $1,005.50
98. If the areas of two sections of a garden are 6a + 2 and 5a, what is the
difference between the areas of the two sections in terms of a?
A. a – 2
B. 3a + 2
C. a + 2
D. 11a – 2
99. The measures of two complementary angles are in the ratio of 7:8. Find the
measure of the smallest angle.
A. 84°
B. 42°
C. 48°
D. 96°
100. The sum of three times a greater integer and 5 times a lesser integer is 9. Three
less than the greater equals the lesser. What is the value of the lesser integer?
A. 0
B. 1
C. 2
END
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