CONTROLLED COPY: 2022 Rev.

01

LET MAJORSHIP – MATHEMATICS

GENERAL INSTRUCTIONS:
1. The test questionnaire contains 200 test questions. Examinees shall manage to use three (3) hours.
2. Read INSTRUCTIONS printed on your answer sheet.
3. Shade only one (1) box for each question on your answer sheets. Two or more boxes shaded will invalidate your answer.
4. AVOID ERASURES.
5. WARNING: This material is protected by Copyright Laws. Unauthorized used shall be prosecuted in the full extent of
the Philippine Laws. For exclusive use of CBRC reviewees only.

1. Dana spends 15% of her monthly income for house rental, 10 % for the electric bill and 25% for food and other
miscellaneous expenses. After paying all these expenses, she still has P6,000 left. How much does she earn every
month?
A. P 8,000.00 C. P 12,000.00
B. P 9,000.00 D. P 15,000.00

2. How much would Php 180, 000. 00 amount to in 20 years if it earns 9% per annum?
A. Php 404, 000 C. Php 704, 000
B. Php 604, 000 D. Php 504, 000

3. In a survey to determine the reaction of people about having a new GSIS card, 80% of the 2,400 people voted in
favor of the new card. How many of the voters did not vote for the new card?
A. 480 B.1600 C. 800 D. 1920

4. Find the amount and compound interest converted quarterly in 5 years on P20,000.00 at 8%
A. P19,600.95 C. P25,600.00
B. P29,718.95 D. P22,700.0

5. Skyway Company manufactures tables. In its catalog, a round table is priced P4,000.00 less a discount at 20%.
What will Frankie Department Store have to pay for the round table?
A. P3,200.00 C. P2,600.00
B. P3,400.00 D. P3,500.00
6. Mrs. Perez bought a DVD player at 15% discount and paid P12,500. What is the list price of the DVD player?
A. P15,000 C. P1,875
B. P14,705.88 D. P83,333.33
7. The proceeds of a P20, 000 rate discounted for 2 years were P15,000. What was the discount rate?
A. 25% B. 12.5% C .33% D. 16.7
8. One fourth of the width and one-fifth of the length of a sheet of cartolina are cut off. What percent of the original
sheet is the remaining area?
A. 9% B. 60% C. 40% D. 5%
9. What is the unit digit of 7218 + 4?
A. 3 B. 4 C. 5 D. 6

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 10. Perform the indicated operation and reduce to lowest terms: ÷

A.

B.

C.

D.
Answer: A
11. If m<0 and n>0 , which of the following is true?
A. M/n = 0 C. Mn > 0
B. 1/m < 1/n D. 1/m > 1/n
12. Find the equation of a line passing through the points (-5, 4) and (3, 1).
A. 3x -8y + 17 = 0 C. 3x +8y + 17 = 0
B. 3x -8y - 17 = 0 D. 3x +8y -17 = 0
13. Find the equation of the line with slope two and passing through the points (3, -1).
A. 2x + y + 7 = 0 C. 2x + y -7 = 0
B. 2x – y + 7 = 0 D. 2x – y - 7 = 0
14. Find the general equation of the line which passes through the points (2, -1) and (3 , 5).
A. 6x + 6y – 5 = 0 C. 5x – 6y – 7 =0
B. 6x + 5y – 7 = 0 D. 6x + 7y – 5 = 0

15. Which is true for subgroups of a group?

A. Subgroups for a partition of a group
B. The intersection of two subgroups is empty
C. The union of two subgroups is also a group
D. The intersection of two subgroups is also a group
16. Mrs. Santiago weighed 60 kg. She lost 4 kg on her first week of exercise, gained 2 kg on her second week, lost
6kg on the 3rd week and remained her weight during the fourth week. What was her weight on the 4th week?
A. 72 kg B. 68 kg C. 58 kg D. 52 kg
17. Three fourths of the participants in a regional training program are from private universities. Two thirds of these
are from Teacher Education Institutions. If there are 96 participants, how many of them represent private Teacher
Education Institutions?
A. 72 B. 18 C. 48 D. 24
18. A meter stick break into two pieces at the 36 cm mark. What is the ratio of the smaller piece to the larger piece?
A. 9:25 B. 9:16 C. 13:15 D. 2:3
19. The unit digit of a two-digit number exceeds the ten digit by 2. Find the number if four times the sum of its digits.
A. 24 B. 42 C. 82 D.84
20. Cramny car travelling at a rate of 70 km/h leaves the station two hours after a Vios car has left and overtakes it in
five hours. At what rate was the Vios Car traveling?
A. 50 km/h B. 20 km/h C. 30 km/h D.40 km/h
21. Samantha laid tiles on the floor. She began with 1 square tile at the corner of the room. She added three tiles to
form 2 x 2 tile square and then 5 tiles to form 3 x 3 tiles square. She continues in this way until the whole floor is
covered. Last, she adds 25 tiles. What is the size of the floor?
A. 166 square tiles B. 168 square tiles C. 167 square tiles D. 169 square tiles

22. The seventh term of the geometric sequence is 192 and its common ratio is r=2. Find the second term.
A. 8 B. 6 C. 12 D.15
23. The logarithm of the product of two numbers is equal to the of the logarithms of the factors
A. Sum B. Product C. Difference D. Antilogarithm

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 24. Express + as a single fraction in simplest form.

A.

B.

C.

D.
Answer: B
25. Simplify (3x-9)/(x2-9):
A. 3/(x-3) B. 3/(x+3) C. 3/(x+1) D. 3/(x-1)

26. The simplest form of

A.

B.

C.

D.
Answer: B

27. What are the factors of the polynomial P(x) = x3 + 3x2 – 10x -24?
A. (x+4)(x+2)(x-3) C. 4,2,-3
B. (x-4)(x-2)(x+3) D. -4,-2,3

28. How many roots does the function f(x) = x2-3x+4.

A. No real roots B. 1 C. 2 D. 3

29. The tens digit of a certain two-digit number is 4 more than the unit’s digit; the sum of the squares of two digits
is 26. Find the number.

A. 51 B. 54 C. 15 D. 45
30. The sum of two consecutive numbers is 75. What is the smaller number?

A. 35 B. 40 C. 38 D. 37
31. What type of regular polygon is one whose each interior angle measures 108 degrees?

A. octagon
B. pentagon
C. heptagon
D. hexagon
32. A rectangular farm has dimensions 500 meters by 40 meters. Find its area in hectares.

A. 2
B. 3.5

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 C. 2.5
D. 3
33. Which of the following measures is not equal to the other measures?

A. Third quartile
B. median
C. fiftieth percentile
D. fifth deciles

34. How many kilograms of force must a man exert on one end of a 2.75 m lever to lift a 125 kg rock on the other end, if
the fulcrum is 0.75 m from the rock?

A. 28.5
B. 30.625
C. 42.35
D. 46.875

35. The average of two numbers is x + y, If one number is equal to x, find the other number.

A. y
B. x + 2y
C. 2x – y
D. x – 2y

36. Find the number of roots in the given function: f(x) = 2x2-11x+5.
A. No real roots B. 1 C. 2 D. 3

37. The solution set for the equation x2-4x-5=0

A. x=5, 9 B. x=5, 1 C. x=-5,1 D. x=5,-1
5 3
38. What is the solution of the equation: = x+2
2(x+1)
A. 4 B. 5 C. 12 D. 6

39. The roots of an equation are 4 and 5. Determine the equation.

A. x2+9x+20=0 C. x2+7x+6=0
B. x2+2x+15=0 D. x2-9x+20=0

40. Find the larger root in the given equation: x2- x- =0

A. B. C. D.
Answer: D.2/3
41. Find the equation of the line passing through (2,6) and parallel to the line 4x-3y+6=0
A. 4x-3y+8=0 C. 4x-3y+10=0
B. 3x+4y-30=0 D. 3x-4y+18=0

42. What is the equation of the line through (5, 1) perpendicular to 3x+4y-5=0?
A. 3x-4y+17=0 C. 4x-3y-17=0
B. 4x-3y+17=0 D. 3x+4y+17=0

43. What is the equation of the line which has a slope ½ and passing through the point (0,-2)?
A. y= 2x+1
B. y= 2x-1

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 LET PREBOARD MAJORSHIP MATH
C.

D.
Answer: D
44. A line has an equation y=4x-5. Which of the following points lie on the line?
A. (-5,7) B. (-3,7) C. (5,25) D. (6,19)
45. Find the equation of the line through (2,3) and the point common to x+y=1 and 2x+y=5
A. 3x+y-9=0 C. x+y-1=0
B. 3x+y+9=0 D. x-y+1

46. Find the equation of the line with slope 2 that passes through the midpoint of the line segment connecting (3, -2)
and (4, 7).
A. 4x + 2y +9 =0 C. 4x - 2y -9 =0
B. 4x - 2y +9 =0 D. 4x + 2y -9 =0
47. How many grams of salt must a chemist add to 50 grams of 25% solution to obtain it 40% salt solution?
A. 10 B. 15.75 C. 12.5 D. 16
48. A water tank is 2/3 full. After drawing out 15 liters of water from it, it became one-half full, what is the full
capacity of the tank in liters?
A. 10 C. 45
B. 90 D. 80

49. Peter can do a whole job in half the time it takes Henry to do it. Together they can finish the job in 10 days. How
many days will it take Peter to do the job alone?
A. 15 days B. 14 days C. 13 days D. 10 days
50. If and , what is x+y?
A. -5
B. 12

C.

D.

Aswer: C. 17/72
51. Solve for a: =2
A. a=3 B. a=20/3 C. a=4 D. a=20

52. What is the 30th term of the sequence 5, 8, 11, 14…?

A. 92 B. 95 C. 87 D. 4

53. At the end of 1998, the population of a certain bacteria grown in a biology laboratory was 10 000. If it kept on
doubling every year since then, what would its population be at the end of 2006?
A. 320 000 B. 160 000 C. 640 000 D. 1 280 000
54. The sum of the first “n” terms of a series is 3(n+2)-6. Find the 5th term.
A. 1723 B. 1724 C. 1458 D.145

55. The measure of an angle is 25 more than its supplement. What is the measure of the larger angle?
A. 110 degrees B. 90 degrees C. 77.5 degrees D. 102.5 degrees
56. One of the legs of a right triangle is 5 cm long and its hypotenuse is 15 cm, how long is the other leg?
A. 10 cm
B.
C.

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 LET PREBOARD MAJORSHIP MATH
D.
Answer: B
57. One right triangle has legs measuring 12 and 9. A second triangle has legs measuring 12 and 16. What is the
difference of their perimeters?
A. 12 B. 42 C. 54 D. 7
58. The sides of a triangle are 5 cm, 6 cm and 8 cm, find the length of the altitude to the shortest side.
A. 6.12 B. 5.46 C. 5.99 D. 4.99
59. What is the area of a triangle with vertices at (5, 3), (11, 13) and (8, 8)?
A. 30 B. 15 C. 7 D. 24
60. Find the area of the triangle with vertices; (-2,0), (2,3) and (5, 0)
A. 12 ½ B. 11 C. 12 D.10 ½
61. An isosceles triangle has a perimeter equal to 42 inches, the two equal sides are each 3 times as long as the third
side. How long is the third side?
A. 18 B. 21 C. 6 D. 8
62. Find the area of the isosceles triangle that can be inscribed in a circle with radius of 6 inches.
A. 27√3 B. 27 C. 29 D. 29√3

63. The area of a rectangle whose width is x – 7 is – 2x – 35. What is the length?
A. x-5 B. x+5 C. x+7 D. x-28
64. What do you calls the angles that share a common side and vertex?
A. Complementary B. Supplementary C. Opposite D. Adjacent

65. Three or more points that lie on a single straight line.

A. Collinear points B. Coplanar points C. Skew points D. Concurrent points

66. Two angles that have a common vertex and a common side.
A. Vertical angles B. Adjacent angles C. Supplementary angles D. Complementary angles
67. One of the angles of a parallelogram is 50. What are the measures of the remaining angles of the parallelogram?
A. 50,50,50,50 B. 50,40,50,40 C. 50,60,50,60 D. 50,130,50,130
68. A quadrilateral has its first angle measures 50 degrees. The second angle is twice the first while the third angle is
same as the second angle. Find the fourth angle
A. 110 degrees B. 95 degrees C. 102 degrees D. 77 degrees

69. In the triangle ABC with vertices A(2,3), B(4,-1) and C(1,2), find the equation and length of altitude from the
vertex A.
A. Equation=x−y=-1and length is √ 2units
B. Equation=x+y=1and length is 2 units
C. Equation=−x+y+1=0and length is √22 units
D. Equation=x−y=−1 and length is √12 units

70. if sin ϴ =4/5 , and 0<ϴ<π/2, then cos 2Ɵ is equal to

A. 24/25 B. 7/25 C. -7/25 D. 44/125

71. What is the simplest form of (sin1/2x-cos1/2x)2?

A. 1+sin x B. 1+cos x C. 1-cos x D. 1-sin x
b
72. Tan π/10 is equal to
A. [2 tan[π/5)]/[1-tan2(π/5)]
B. (sin π/3)/[1-cos(π/5)]
C. sin(π/5)/[1+cos(π/5)]
D. [2tan(π/20)]/[1+tan2(π/5)]
Too time consuming to solve using identities so just evaluate each of the options. Use π = 180.

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 LET PREBOARD MAJORSHIP MATH
73. Find the acute angle between two lines have the direction numbers [1,1,0] and [2,1,2]
A. 20° B. 50° C. 45° D. 30°

74. The figure shows

A. Same positive correlation
B. Same negative correlation
C. perfect positive correlation
D. perfect negative correlation
75. The figure shows
A. Same positive correlation
B. Same negative correlation
C. positive correlation
D. negative correlation

76. What principle of counting should be applied when an ordered arrangement of distinct elements in a set is
desired?
A. Probability B. Permutation C. Combination D. Cumulative Distribution
77. A ball is drawn at random from a box containing 6 red balls, 4 white balls and 5 blue balls. Find the probability
that it is white.
A. 1/3 B. 4/5 C. 4/15 D. 4/13
78. If a die is rolled, what is the probability of getting a number divisible by 2?
A. 1/3 B. 1/6 C. ¼ D. ½
79. If the outcome of one event does not affect the probability of another event, the two events are:
A. Dependent B. Complements C. Mutually Exclusive D. Independent
80. The probability that a man will be alive in 25 years is 3/5 and that his wife is 2/3. What is the probability that both
will be alive?
A. 1/5 B. 2/5 C. 50% D. 100%
81. For a sequence of events A,B, and C , P(A U B U C )= P(A)+P(B/A), P(C/A U B)
A. Subtraction rule
B. Addition rule
C. General rule
D. Multiplicative rule

82. A class is composed of 18 boys and 12 girls. In a quiz, the average score of the boys was 85 while the girl was 88.
Find the average score for the entire class.
A. 86.2 B. 85.4 C. 87.8 D. 88.2
83. The average of five different numbers is ten. What is the highest possible value that one of the numbers can be?
A. 20 B. 30 C. 33 D. 40
84. How many different signals can be made from four different flags if each signal consists of three flags hang in a
horizontal row?
A. 76 signals B. 24 signals C. 36 signals D. 72 signals
85. A conditional probability is the probability of
A. One event and another event
B. One event occurring give that another event has occurred
C. One event or another event
D. An event that is certain to happen
86. Find the distance between the points (-3, 2) and (5, 3).
A. √55 B. √56 C. √65 D. √45

87. What is the midpoint of the segment joining (3, 8) and (-5, 4)?

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 LET PREBOARD MAJORSHIP MATH
A. (8,4) B. (2,4) C. (2,12) D. (-1,6)
88. Area of the Circle with equation: x2+ y2=4 is
A. 2π B. π C. 4π D. 5π
89. Find the equation of the parabola in the standard form if the equation of the parabola in the general form is given
by; x2+ 2x-4y-3=0
A. (x-1)2=4(y+1)
B. (x+1)2=-4(y-1)
C. (x+1)2=-4(y+1)
D. (x+1)2=4(y+1)

90. Find the distance between the points of intersection of the line x-2y + 2=0 and the circle x2 + y2 + 6x + 6y + 8 = 0.
A. 4.47 B. 3.86 C. 4.12 D. 3.92
91. Determine the equation of the circle whose diameter is the segment joining (-2,3) and (4,-5)?
A. (x+1)2+(y-1)2=5
B. (x-1)2+(y+1)2=10
C. (x+1)2+(y-1)2=10
D. (x-1)2+(y+1)2=25
92. Find the midpoint of the segments that has endpoints (-1, 3) and (-2, -7).
A. (-3/2,2) B. (3/2,2) C. (3/2,-2) D. (-3/2,-2)

93. What is the midpoint of the line segment joining the points (5, -3) and (-2,-7)?
A. (1/2,-10) B. (7,4) C. (3/2,-5) D. (3,-10)

94. Form of linear equation in one variable

A. ax+b =0 C. ax2+bx+c=0
B. ax2-by2+dx+ey=f=0 D. ax+by+c=0
95. If the center of the circle is at the origin and its radius is 4, then its equation is ______.
A. x2+ y2=4
B. x2+ y2+16=0
C. x2+ y2+4=0
D. x2+ y2=16

96. Find the center of the circle whose equation is x2+2x-4y-6=0

A. (-3,2) B. (1,-2) C. (2,3) D. (-1,2)

97. Which of the following points is the center of the circle whose equation is 2x2+2y2+20x-8y+65=0?
A. (-5,2)
B. (5,2)
C. (5,-2)
D. (-5,-2)

98. What is the equation of a parabola whose vertex and focus are (-1, 2) and (-4, 2), respectively?
A. (x+1)=-3(y-2)2
B. (x+1)=-12(y-2)2
C. (y-2)2=-12(x+1)
D. (y+1)2=-12(x-2)
99. Find the derivative of f(x)=(x-3)(x+5)
A. 2x B. 2(x+1) C. x+2 D. x+1

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 LET PREBOARD MAJORSHIP MATH

100. Evaluate:
A. 3 B. 0 C. 2 D. 1

101. Evaluate the following limit: .

A. 1
B. -1
C. 0
D. The limit is not defined.
102. What is the equation of the normal line to the curve y= 6x2 – 3x + 1 at point (-1, 1)?
A. 15y = x +14
B. 15y = x + 16
C. 9y = -x + 8
D. 9y = -x – 10
103. Find the absolute minimum value of f(x)=x2/3 on the interval (-2,3)
A. 0
B. √9
C. 1
D. 3√9
104. Find the area of the region bounded by the curves: y=x2, y=x
A. 3/4
B. 1/6
C. ½
D. 1/3

105. Find the

A. -1
B. -1/2
C. ½
D. +∞
106. Given f(x) = ln , what is f’(x)?

A.
B. 2) ln (x2+ 2x)

C.
D. 2x + 2

107. Find the units in Z8{1, 2, 3, 4, 5, 6, 7}

A. 2 B. 4 C. 5 D. 6
108. In how many minutes after 2 o’clock will the hands of the clock extend in opposite direction for the first time?
A. 43.64 minutes B. 42.64 minutes C. 41.64 minutes D. 40.64 minutes
109. He invented a method of determining the optimal values of a linear function subject to certain constraints. This
method is known as linear programming. Who is he?
A. George Cantor B. Richard Dedekind C. Bertrand Russell D.George Dantzig
110. He has been described as the greatest “might-have-been” in the history of mathematics.
A. Blaise Pascal C. Bonaventura Cavalier
B. Gaspard Monge D. Gregorio de Saint

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 LET PREBOARD MAJORSHIP MATH
111. An 18th century Swiss Mathematician, he introduced the “Law of Large numbers” in his (The art of
Conjecture). In statistics, this implies that the larger the sample, the more likely will the sample become
representative of the population. Who was he?
A. Girolamo Cardano C. Jacob Bernouli
B. Bertrand Ruseel D. Stephen Baldwin
112. His greatest contributions include such groundbreaking texts in invention of dividing rods used as multiplication
table.
A. Francois Viete
B. Marin Mersenne
C. Johannes Kepler
D. John Napier
113. A rich mathematician in France who invented a new, non-Greek way of doing geometry, now called
“projective” or “modern geometry”.
A. Leonhard Euler
B. Francois Viete
C. Girard Desarques
D. John Napier
114. A “grand” Russian Mathematician who gave the basis for applying the theory of probability to a statistical data,
worked a number of prime numbers not exceeding a given number, and proved Bertrand’s conjecture in 1850.
A. Augutin Cauchy
B. Pafnuty Chebyshev
C. Francois Viete
D. Nikolai Lobachevsky
115. 19th century mathematician who added the integers from 1 to 100 within seconds by a flash of mathematical
insights.
A. Evariste Galois
B. Johann Dirichlet
C. Johann Gauss
D. Augutin Cauch
116. He published his greatest mathematical work Ars Magna(methods of solution of the cubic and quartic equation).
A. Evariste Galois
B. Augutin Cauchy
C. Girolamo Cardano
D. John Napier
117. Modern physics owes its beginning to him, who was the first astronomer to use a telescope.
A. Galileo Galelei
B. Copernicus
C. Ptolemy
D. Columbus
118. The decibel is 1/10 of this original unit. It was defined as a ratio of power levels of 10 to 1 (ten times the power
or one-tenth the power). Who originally invented the decibel unit?
A. Bernoulli Graham
B. Alexander Graham Bell
C. Alexander the Great
D. Decilde Bernoulli
119. The quote “logarithmic plots are a device of the devil” is attributed to him who is the most famous as the
creator of the magnitude scale, which, until the development of the moment magnitude scale in 1979, quantified
the size of earthquakes.
A. Beno Gutenrberg
B. Charles Francis Richter
C. Fred W. Kinsinger
D. Bertrand Ruseel

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 LET PREBOARD MAJORSHIP MATH
120. He was a Renaissance- and Reformation-era mathematician and astronomer who formulated a model of the
universe that placed the Sun rather than the Earth at the center of the universe.
A. Aristarchus of Samos
B. Columbus
C. Copernicus
D. Ptolemy
121. Which pair is relatively prime?
A. (18,4)
B. (14,7)
C. (24,18)
D. (6,45)
No answer: Relatively primes are numbers that have gcd of 1.
122. Simplify 8x+[(3x-2y)+(6x-9)-(x+y)]
A. 16x-3y+9
B. 16x+3y+9
C. 16x- 3y -9
D. 16x+3y-9
123. Ms. Santiago weighed 62kg. She lost 3kg on her first week of exercise, gained 4kg on her second week, lost 5kg
on the 3rd week and remained her weight during fourth week. What was her weight on the fourth week?
A. 56 B. 57 C. 58 D. 59
124. How much water containing 6% boric acid should be added to a 2 quartz containing 15% boric acid in order to
obtain a solution with 12% boric acid?
A. 4 quartz B. 1 quartz C. 2 quartz D. 3 quartz
125. What is the total amount after adding annual 8% interest for 3 months on 6000?
A. 11,050 B. 6,120 C. 11,500 D.10,500
126. Mr. Santos purchased a merchandise at 15000.00, the invoice showed 12,750.00. Find the discount rate.
A. 12% B. 15% C. 22% D. 25%
127. Simplify 3y-[2y+3x-(2x-3y)]+4x
A. x+2y B. 3x-2y C. x-2y D. 2x+y
128. Simplify 8x +(3x + 2y) + (6x - 9) -(x + y)
A. 16x - 3y + 9
B. 16x + 3y - 9
C. 16x + 3 y + 9
D. 16x - 3y – 9
129. How many roots does the equation 3𝑥 2 + 4𝑥 − 3 = 0 have ?
A. 3 B. 1 C. 0 D. 2
130. A triangle has a base of 12 feet long and an altitude 8 feet high. Find the area of the largest rectangle that can be
inscribed in the triangle so that the base of the rectangle falls on the base of triangle.
A. 24 ft²
B. 5 ft²
C. 10 ft²
D. 12 ft²
131. The cubic equation with the roots 3, 2, -1
A. x3-4x2+x+6
B. x3+4x2-x-6
C. x3-4x2+x-6
D. x3-4x2-x-6
132. How many zeros are there in the function (𝑥) = 𝑥 2 + 2𝑥 + 6 ?
A. 1 real root B. 0 real root C. 3 real roots D. 2 real roots
133. A ladder of 50 feet long is placed on the wall. The lower end forms an angle of 30 degrees with the ground.
Find the distance of the upper end from the ground.
A. 100 feet B. 40 feet C. 25 feet D. 20 feet
134. What is sin (π-2θ)?
A. 2cosθ B. cos2θ C. cos2θ D. 2sinθcosθ
135. When a logarithm is expressed as an integer plus a decimal, the integer is called the _____.
A. Base
B. Mantissa
C. Antilogarithm
D. Characteristic
136. Cos(-π/12) is equal to
A. (√3+1)/2√2 C. (√2+√3)/4
B. (-1√3)/2√2 D.(√3-1)/2√2

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137. There are 8 blue balls 3 green balls 9 white balls. Three balls are picked randomly without replacement. What
is the probability that the 3 balls picked are of the 3 colors?
A. 18/95
B. 7/95
C. 3/95
D. 20/95
138. To express that there is a significant difference between the food values of the nutrition students(1) and those
of the nursing students(2). 𝑥1 𝑚𝑒𝑎𝑛 𝑜𝑓 (1), 𝑥2 𝑚𝑒𝑎𝑛 𝑜𝑓 (2)
A. Ho: 𝑥1 = 𝑥2
B. Ha: 𝑥1 ≠ 𝑥2
C. Ho: 𝑥1 ≠ 𝑥2
D. Ha: 𝑥1 = 𝑥2

139. If a die is rolled, what is the probability of getting a number greater than 5?
A. 1/6 B. 1/3 C. ¼ D. 1/5
140. It is the probability of an event that is influenced by another event that has occurred.
A. Exhaustive probability
B. Total probability
C. Conditional Probability
D. Involving as many as possible
141. A ball is drawn on a box containing 6 red, 4 white and 5 blue. Find the probability that it is blue.
A. 4/15
B. 2/5
C. 1/3
D. 4/5

142. A set of all possible outcomes of a random experiment are called

A. Event
B. sample space
C. phenomenon
D. random variable

143. What is the equation of the parabola with V (0,2) and F (0,1)?
A. 𝑥 2 + 4𝑦 − 8 = 0
B. 𝑥 2 − 4𝑦 + 8 = 0
C. 𝑦 2 + 4𝑥 − 8 = 0
D. 𝑦 2 − 4𝑦 + 8 = 0
144. The grades of senior high school students are as follows 75,80,60,95,100. What is the range?
A. 25
B. 40
C. -40
D. -25
145. Find the midpoint of the line segment joining the points (2,-3) and (6,7)
A. (2, 2)
B. (4, 4)
C. (2, 4)
D. (4, 2)
146. Evaluate lim (𝑥 2 − 5𝑥 + 5)
𝑥→−2
A. -2
B. 19
C. -1
D. 20
147. Identify the conic section represented by 4x2 + 4y2- 8y + 16x – 5 = 0.
A. Circle
B. Parabola
C. Hyperbola
D. Ellipse
148. A 16th century Mathematician , who was first to define the probability of an event as the quotient of all
favourable outcome over the total number of outcomes
A. Gaspard Monge
B. Blaise Pascal

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C. Girolano Cardano
D. Francois Viete

1 2 3 4 5
149. What is the inverse permutation of 𝐴 = ( )?
3 5 2 1 4
1 2 3 4 5 1 2 3 4 5
− −
A. 𝐴 = ( ) C. 𝐴 =( )
2 4 5 3 1 4 1 2 5 3
1 2 3 4 5 1 2 3 4 5
B.𝐴− = ( ) D. 𝐴− = ( )
3 5 1 2 4 1 4 2 3 5
1 2 3 4 5 1 2 3 4 5
150. Given 𝐴 = ( ) and 𝐵 = ( ), what is AxB?
3 5 21 4 3 4 5 2 1
1 2 3 4 5 1 2 3 4 5
A.𝐴𝑥𝐵 = ( ) C. 𝐴𝑥𝐵 = ( )
2 4 5 3 1 4 1 2 5 3
1 2 3 4 5 1 2 3 4 5
B.𝐴𝐱𝐁 = ( ) D. 𝐴𝑥𝐵 = ( )
2 1 4 5 3 1 4 2 3 5
151. Which among the following is a possible value of x in 𝑥 ≡ 3(𝑚𝑜𝑑 10)?
A, 7 C. 30
B, 13 D. 10/3
152. Given that 25 ≡ 𝑥(𝑚𝑜𝑑12), find x.
A. 1 C. 24
B. 13 D. 3
153. What is x in 324 ≡ 𝑥(𝑚𝑜𝑑25)?
A,1 C. 3
B.2 D. 4
154. Which among the following is a possible value of x in 257 ≡ 𝑥(𝑚𝑜𝑑57)?
A,1 C. 3
B,2 D. 4
155. Anna is making bead necklaces. She has 90 green beads and 108 blue beads. What is the greatest number of
identical necklaces she can make if she wants to use all of the beads?
A. 12 B. 15 C. 16 D. 18
156. If 16 men or 20 women can finish the job in 25 days, how many days can 28 men and 15 women finish?
A. 15 B. 20 C. 10 D.25
157. If a-2, b-1, and c-3. What is the value of 1+2b-c?
A. 5 B. 0 C. 7 D. 11
158. Of the following discount, what is equal to the series discount of 30%, 20%, 10%?
A. 40 B. 46.9 C. 48 D. 49.6
159. A circle has its center at (3,-2) and one end of the diameter at (7,2). Find the other end of the diameter.
A. (-1,-6) B. (-1,6) C. (1,-6) D. (1,6)
2 3 1
160. Find the determinant of the co-factor of q33 of (5 1 6).
7 8 2
A. 30 B. 23 C. 13 D. -13

161. Evaluate lim (−1)𝑛 2𝑛

𝑛→∞
A. undefined B. 2 C. 0 D. 1
5 2 1
162. Evaluate ∫2 (𝑥 + 𝑥 2 ) 𝑑𝑥
A. 33 1/3 B. 39 3/10 C. 39 3/5 D. 39 ½

163. If a line is extended from A(2,3) through B(-2,0) to a point C so that AC=4AB, find the coordinates of C.
A. (-14,-9) B. (14,10) C. (-14,10) D. (14,-10)
164. Find the volume of the cone generated by revolving about y-axis the area bounded by the line 2x+y=2 and the
coordinates axes.
A. π B. 1/3 π C. 2/3 π D. 2 π

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165. What is the third side of the triangle if b=47, c=58, = 63° ?
A. 8048.2 B. 5573 C. 3090 D. √3097.8

166. What are the roots of 6x2-13x-5?

A. 5 and 3 B. -5/2 and 1/3 C. 5/2 and -1/3 D. -5/2 and -1/3
167. What type of conic section is 9x2-4y2+36x+24y-36=0?
A. Circle B. Parabola C. Ellipse D. Hyperbola
168. The average of the ages of two friends is 19. If one of them is 17, which equation will solve the age of the other
one?
A. x = 2(19) – 17
B. x = 2(19) – 19
C. x = 2(19) + 17
D. x = 2(19) + 19

169. Find the equation of the x-axis

A. x=0
B. x+y=0
C. y=0
D. x-y=0
170. What is the measurement of the sides of a trapezoid if its upper and lower base are 2 and 4, respectively, and altitude
is 3?
A. √10 B. √2 C. √8 D. √6

171. Find the equation of the circle with center (-2,3) and a diameter of 6.
A. (𝑥 + 2)2 + (𝑦 − 3)2 = 62
B. (𝑥 + 2)2 + (𝑦 − 3)2 = 32
C. (𝑥 + 2)2 + (𝑦 + 3)2 = 62
D. (𝑥 − 2)2 + (𝑦 + 3)2 = 32
172. Find the equation of the y-axis
A. x=0
B. x+y=0
C. y=0
D. x-y=0
173. A sample of 500 respondents was selected in large metropolitan area in order to determine various information
concerning behaviour. Among these questions asked was, “Do you enjoy shopping for clothing?” of 240 males, 136
answered yes, of 260 females, 224 answered yes.

Yes No Totals
Male 136 104 240
Female 224 36 260
Totals 360 140 500
Find the probability that the respondent chosen at random is a female.
A. 12/25
B. 6/25
C. 13/25
D. 18/25
174. Two events that cannot occur at the same time is called:
A. Mutually exclusive
B. Impossible events
C. Non-Mutually exclusive
D. Sure events
175. What is the absolute maximum value of f(x)=x2/3 on the interval (-2,3)?
A. 0
B. √9
C. 1
D. 3√9

176. Express z as a function of x and y if z is directly proportional to the product of x and y.

A. z = c/xy
B. z = 1/xy
C. z = cxy

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D. z = xy
177. What is the exact value of sin(2π/3+π/4)?
√6−√2 √2
A. 4
C. 4
√6+√2 √6
B. D.
4 4

178. What is the 4th term when (a+4)5 is expanded?

A. 64a C. 256a3
2
B. 640a D. 1024a4
179. A total of PHP 75,000.00 is deposited into two simple interest accounts. In one account the annual simple interest
rate is 5% and in the second account the annual simple interest rate is 7%. The amount of interest earned for 1 year was
Php 4,050.00 . how much was invested in each?
A. At 5 %= Php 60,000.00; at 7%= Php 15,000.00
B. At 5 %= Php 50,000.00; at 7%= Php 25,000.00
C. At 5 %= Php 55,000.00; at 7%= Php 20,000.00
D. At 5 %= Php 15,000.00; at 7%= Php 60,000.00

180. Find the direction numbers for the line that joins the points (1,3,4) and (-2,3,7).
A. [1,-1,0]
B. [1,0,-1]
C. [1,-1,2]
D. [-1,0,1]
181. Evaluate dy / dx when x=2 for y = 8x – x3
A. 8 C. 4
B. -4 D. 0
182. Point P(-3,-4) is on the terminal side of angle Ɵ in the standard position. Find tan Ɵ.
A. 4/3 C. 3/4
B. -3/5 D. -4/5
183. Find the equation of an ellipse in the standard form if the equation of the ellipse in the general form is given by:
9x2+16y2+18x-96y+9=0.
(𝑥+1)2 (𝑦−3)2 (𝑥−1)2 (𝑦−3)2
A. 16
− 9
=1 C. 16
− 9
=1

(𝑥+1)2 (𝑦−3)2 (𝑥−1)2 (𝑦−3)2

B. 16
+ 9
=1 D. 16
+ 9
=1

184. Area of an isosceles triangle with base of 2 meters and perimeter of 12 meters.
A. 2√(6cm2) C. 2m2
B. 4 m2 D. 6√(2m)

185. Find the distance between the line 3x-y=0 and the point(2,-4)
A. 10 C. -10
B. √10 D.-√10

186. The surface on the earth between the topic of cancer and the Arctic Circle is called
A. Plane C. cone
B. Circle D. zone
187. Nica received an aquarium as a graduation gift from her mother. It has length, width and height of 9 centimeters, 7
centimeters and 5 centimeters, respectively. Find its volume.
A. 315 cubic cm C. 314 cubic cm
B. 316 cubic cm D. 318 cubic cm
188. A cube has a volume of 64 cubic meters. What are its dimensions?
A. 16cm x 2 cm. x 2 cm. C. 3 cm. x 3 cm. x 7 cm.

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B. 8 cm. x 8 cm. x 1 cm. D. 4 cm. x 4 cm. x 4 cm.

189. The given multiplication table represents a cyclic group

Find the order of the group

A. 2 C. 1
B. 3 D. 4
190. The given multiplication table represents a cyclic group.

Find d2
A. a C. b
B. d D. c
191. The approximate shape of the earth is
A. Sphere C. Cone
B. Circle D. Cube
192. If tan Ɵ=1/3, then cot 2 Ɵ equals
A. 4/3 C.3/2
B. 2/3 D. 3/4

193. To express that there is significant difference between the income of family A and that of the income of Family B.
A. Ho: 𝑥1 = 𝑥2
B. Ha: 𝑥1 ≠ 𝑥2
C. Ho: 𝑥1 ≠ 𝑥2
D. Ha: 𝑥1 = 𝑥2
194. The motion of a particle is given by the equation s=t3-3t-5. Find the velocity when t=2.

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A. 9 C. 3
B. 10 D. 5
195. Find the range of the function y=5-2x2
A. All real numbers
B. y≤0
C. y≤5
D. y≥5
196. Find the pairs of lines that are perpendicular.
A. 2x-y+3=0,2x-y-5=0 C. x-y-=0, 2x+3y-5=0
B. x=1, y=5 D. 3x-y-5=0, x-3y+21=0
197. Find two positive numbers whose product is 64 and whose sum is minimum.
A. 8 and 8 C.1 and 64
B. 32 and 2 D. 63 and 1
198. A subset of the sample space is
A. Discrete variable
B. Event
C. Phenomenon
D. Continuous variable
199. Which among the measures of central tendency is not influenced by outliers?
A. Mean C. Mode
B. Weighted Mean D. Median
200. The statement of 3= log (x+8)implies
A. 103=x+8
B. 33=x+8
C. (x+8)10=3
D. (x+8)3=10

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