1.Perform the operation given that:
A={-4,-2,0,2,4}, B= {-4-2,0,3,4}
A U B =?
A.{4,2,0,3}
B.{-4,-2,0,2,3,4}
C.{-4-2,0-3}
D.{-4,-2,0,2,3,4,5}
2. The cost of all items sold by Guzmart office
supply during the month of June is Php
95,000,00. What is the breakeven point?
A.Php 105,000.00
B.Php 85,000.00
C.Php 45, 000.00
D.Php 145,000.00
3. Simplify.
A. a
B.a-5
C.–a
D.5-a
4. simplify the expression:
A.
C.
A.
D.
5. List of four smallest elements of the set, {
y|y=2x+1, x ԑ natural numbers}
A.1,2,3,4
B.1,3,5,7
C.3,5,7,9
D.3,4,5,6
6. Factor over the integers by grouping:
3x3+x2+6x+2
A.
B.
C.
D.
7. Solve the rational expression:
A.x=1/3
B.x=-3
C.x=-1/3
D.x=3
8. use absolute value notation to describe the
given situation: the distance between x and 3.
A.-|x-3|
B.|x+3|
C.–|x+3|
D.|x-3|
9. Simplify this complex fraction :
A.
B.
C.
D.
10. 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°
11. Simplify the given exponential expression:
A.
B.
C.
D.
12. By inspection, determine whether each
percentage is greater than, equal to, less than,
or less than and equal to the base ; 100% of
0.12.
A.Percentage is less than the base.
B.Percentage is equal to the base.
C.Percentage is less than and equal to the base.
D.Percentage is greater than the base.
13. 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
14. If (x)=2x-3 and g( x) = , find (f o f) (x)
A.
B.
C. 4x-9
D.
15. 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
16. Fined 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]
17. Determine the percentage : Rate =200% ,
Base =30
A.60
B.2,400
C.360
D.120
18. The intersection of Sets A and B is defined by
A B = { x/xԑ A and ԑB}
If A={a,b,c,d,e}, B={a,c,f,g}, find A B
A.{b,c,g}
B.{a,f,g}
C.{a,c}
D. {a,b,c,g}
19. If i(x)=2x-3 and g(x)= , find (g o g) (x)
A.4x-9
B.
C.
D.
20. The sun is approximately
meters from
the Earth. If the light travels meters per
second, how many minutes does it take light
from the sun to reach Earth?
A.20 minutes
B.28 minutes
C.8 minutes
D.10 minutes
21. Use absolute value notation to describe the
given situation:
The distance between x and -2 is 4.
A.|x+2|=-4
B.|x-2|=4
C.|x+2|=4
D.|x-2|=-4
22. Lyn Santos is paid a salary of Php
5,000.00/week plus 10% commission on a net
sale over Php 50,000.00. what is her gross wag
if her weekly net sales are Php 70,000.00?
A.Php 4,700.00
B.Php 7,000.00
C.Php 5,000.00
D.Php 2,000.00
23. The number of subsets of a Set A with n
element is defined by 2ᶯ. If A= {1,2,3,4,5) find
the number of subsets of A.
A.32
B.20
C.16
D.10
24. If (x)=2x-3 and g(x)= , Find(g o f) (x)
A.
B.
C. 4x-9
D.
25. In three dimensions, where is the point
located if x=y=z=0?
A.xz plane
B.origin
C.yz plane
D.xy plane
26. it cost a lady’s bag manufacturer Php 400.00
to produce a lady’s bag that sells for Php
550.00. How many lady’s bags must be
manufacturer sell to make a profit of Php
60,000.00?
A.400
B.150
C.250
D.200
27. Annual interest at 8%
P6,000.00
A.P480.00
B.P120.00
C.P150.00
D.P160.00
for 3 months on
28. Find the units in {1,2,3,4,5,6,7}
A.2
B.4
C.1
D.8
29. Four out of every five households have
cellphone. If 10,000 households in a certain
barangay have cellphone, how many do NOT
have cellphone?
A.7,500
B.2,000
C.9,500
D.7,000
30. Find the amount and compound interest
converted quarterly in 5 years on P20,000.00
at 8%
A.P19,600.95
B.P29,718.95
C.P25,600.00
D.P22,700.00
31. Perform the indicated operation and reduce
to lowest terms:
A.
B.
C.
D.
32. 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
D.z= xy
33. Evaluate dy / dx when x=2 for y = 8x –
A.8
B.-4
C.4
D.0
34. Point P(-3,-4) is on the terminal side of angle
Ɵ in the standard position. Find tan Ɵ
A.4/3
B.-3/5
C.3/ 4
D.-4/5
35. Find the area of the region bounded by the
curves: y =x2,,y=x
A.1/ 6
B.1/2
C.1/3
D.3/4
36. Perform the indicated operation and reduce
result to simplest form
A.
B.
C.
D.
37. Perform the indicated operation and reduce
result to simplest form.
A.
B.
C.
D.
38. Find the distance between the points(-3,2)
and (5,3).
A.
B.
C.
D.
√45
√55
√65
√56
39. Perform the indicated operation and reduce
to lowest terms:
A.
B.
C.
D.
40. 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+18y96y+9=0
A.
B.
C.
D.
41. Perform the indicated operation and reduce
result to simplest form.
A.
B.
C.
D.
42. Form of linear equation in one variable
A.ax+b =0
B.ax2-by2+dx+ey=f=0
C.ax2+bx+c=0
D.ax+by+c=0
43. Area of an isosceles triangle with base of 2
meters and perimeter of 12 meters.
A.2√(6cm2)
B.4 m2
C.2m2
D.6√(2m)
44. 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
45. Find the distance between the line 3x-y=0
and the point(2,-4).
A.10
B.√10
C. -10
D.-√10
46. The approximate shape of the earth is
A.Sphere
B.Circle
C.Cone
D.Cube
47. The motion of a particle is given by the
equation s=t3-3t-5. Find the velocity when t=2.
A.9
B.10
C.3
D.5
48. 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 while 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
49. Area of the Circle with equation: x2+ y2=4 is
.
A.2π
B.π
C.4π
D.5π
50. The surface on the earth between the topic
of cancer and the Arctic Circle is called
A.Plane
B.Circle
C.cone
D.zone
51. Nica received an aquarium as a graduation
gift from her mother. It was length, width and
height of 9 centimeters, 7 centimeters and 5
centimeters, respectively. Find its volume
A.315 cubic meters
B.316 cubic meters
C.314 cubic meters
D.318 cubic meters
52. A cube has a volume of 64 cubic meters.
What are its dimensions?
A.16cm x 2 cm. x 2 cm.
B.8 cm. x 8 cm. x 1 cm.
C.3 cm. x 3 cm. x 7 cm.
D.4 cm. x 4 cm. x 4 cm.
53. The sum of the sides of a polygon is the
of the polygon.
A.Perimeter
B.Leg
C.area
D.volume
54. If the opposite sides of a quadrilateral are
equal, the figure is a
.
A.Rectangle
B.Shambers
C.parallelogram
D.square
55. The ULTRA football field is 100 meters from
goal line to goal line. If it is 360 meters around
a football field, how wide is the field?
A.70 meters
B.85 meters
C.86 meters
D.80 meters
56. The average of the ages of two friends is 19.
If one of them is 17, how old is the other
which equation will approximately solve this
problem?
A.x=(2)(19)-17
B.x=(2)(19)+19
C.x=(2)(19)-19
D.x=(2)(19)+17
57. the first angle of a quadrilateral is 50, the
second is twice the first and the third is equal
to the second. What is the fourth angle of the
quadrilateral?
A.108
B.110
C.111
D.109
58. What is the value of x if x= 27?
A.3
B.27
C.9
D.-3
59. What is the third side of the triangle if b=47,
c=58 and Ɵ=63°?
A.8048.2
B.5573
C.3090
D.√3097.8
60. The statement of 3= (x+8)implies
.
A.103=x+8
B.33=x+8
C.(x+8)10=3
D.(x+8)3=10
61. The give multiplication table represents a
cyclic group
Find the order of the group
A.2
B.3
C. 1
D.4
62.
A.3
B.4
C.2
D.1
16 equals _____________
63. The given multiplication table represents a
cyclic group.
Find d2
A.a
B.d
C.b
D.c
64. if sin ϴ =4/5 , and 0<ϴπ/2, then cos 2Ɵ is
equal to
.
A.24/25
B.7/25
C.-7-25
D.44/125
65. 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.[2 tan(π/20)]/[1+tan2(π/5)]
.
66. When a logarithm us expressed as an integer
plus a decimal, the integer is called the
.
A.Mantissa
B.Characteristic
C.Base
D.antilogarithm
67. If
A.2
B.4
C.8
D.32
16=12, then a equals
.
68. 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
69. What is the simplest form of (sin1/2xcos1/2x)2?
A.1+sin x
B.1+cos x
C.1-cos x
D.1-sin x
70. Cos(-π/12) is equal to
A.(√3+1)/2√2
B.(-1√3)/2√2
C.(√2+√3)/4
D.(√3-1)/2√2
.
71. What is the exact value of sin [(2π/3)+(π/4)]?
A.(√6-√2)/4
B.√2+1
C.√3
D. (√6+√2)/4
72. If tan Ɵ=1/3, then cot 2 Ɵ equals
A.4/3
B.2/3
C.3/2
D.3/4
.
73. Which among the measures of central
tendency is not influenced by outliers?
A.Mean
B.Weighted Mean
C.Mode
D.Median
74. 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 Canter
B.Richard Dedekind
C.Bertrand Russel
D.George Dantzig
75. The figure shows
A.A. Same positive correlation
B.Same negative correlation
C.perfect positive correlation
D.perfect negative correlation
76. A random sample of 200 adults are classified
by sex and their level of education attained.
Education
• Elementary
• Secondary
• College
Male
Female
38
28
22
45
50
17
If a person is picked at random from this
group, find the probability that the person is
male.
A.95/112
B.14/39
C.11/25
D.45/25
77. The figure shows
A.
B.
C.
D.
Same negative correlation
Perfect positive correlation
Perfect negative correlation
Same positive correlation
78. To express that there is significant difference
between the income of family A and that of
the income of Family B.
A. Ho: ≠
B.Ho: =
C.Ha: ≠
D.Ha:
79. A subset of the sample space is
.
A.Discrete variable
B.Event
C.Phenomenon
D.Continous variable
80. 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
81. If a die is rolied, what is the probability of
getting a number divisible by 2?
A.1/6
B.1/4
C.1/2
D.1/3
82. He was a 16th century mathematician, who
was the first to define that the probability of
an event to happen is the quotient of the
number of the favorable outcomes and the
number of all outcomes. Who was he?
A.Stephen Baldwin
B.Blaise Pascal
C.Girolamo Cardano
D.Richard Dedekind
83. There are 5 types of correlation between
paired data: perfect positive correlation,
perfect negative correlation, same positive
correlation, same negative correlation and no
correlation
The figure shows
A. Same negative
B.Same positive correlation
C.Perfect positive correlation
D.No correlation
84. 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
85. For mutually exclusive events A and B,
P(A U B)=P(A) +P(B)
A.Addition rule
B.General rule
C.Subtraction rule
D.Multiplicative rule
86. A sample of 500 respondents was selected in
a large metropolitan are in order to determine
various information concerning behavior.
Among the question asked was. “ Do you
enjoy shopping for clothing ?” of 240 males,
136 males answered yes of 260 females, 224
answered yes.
87. To express that there is significant difference
between the food values of the nutrition
students and those of the nursing students:
A.Ho:
B.Ha:
C.Ho:
D.Ha:
88. Find the absolute maximum value of f(x)
=x(2/3) on the interval (-2,3)
A.3√9
B.1
C.0
D.√9
89. Fine the area of the triangle with vertices; (2,0)(2,3) and (5,1)
A.12 ½
B.11
C.12
D.10 ½
90. Find two positive numbers whose product is
64 and whose sum is minimum.
A.8 and 8
B.32 and 2
C.1 and 64
D.63 and 1
91. Find the equation of an ellipse in the general
form if the equation of the ellipse in the
standard form is given by:
A.25x2-4y2-350x+16y +1141 = 0
B.25x2+4y2-350x-16y+1141=0
C.25x2-4y2-350x-16y+1141=0
D.25x2+4y2-350x-16y-1141=0
92. Find the absolute minimum value of f(x)=x2/3
on the interval (-2,3)
A.0
B.√9
C.1
D.3√9
93. Evaluate:
A.3
B.0
C.2
D.1
94. Find the derivative of f(x)=(x-3)(x+5)
A.2x
B.2(x+1)
C. x+2
D.x+1
95. Find the distance between the points (-3,2)
and (5,3).
A.√55
B.√56
C.√65
D.√45
96. 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
97. Find the equation of the parabola in the
standard form if the equation of the hyperbola
is the general form is given by: y2-12x-23=0
A.(y+1)2=12(x+2)
B.(y-1)2=12(x+2)
C.(y-1)2=-12(x+2)
D.(y-1)2=-12(x-2)
98. Find the derivative of f(x) = x2-2x+5
A.3
B.0
C.1
D.2
99. 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)
100. Find the volume of the cone generated by
revolving about y-axis the area bounded by
the line 2x+y=2 and the coordinate axes.
A.π
B.1/3 π
C.2/3 π
D. 2π
101. Find the
perpendicular.
pairs
A.2x-y+3=0,2x-y-5=0
B.x=1, y=5
C.x-y-=0, 2x+3y-5=0
D.3x-y-5=0, x-3y+21=0
of
lines
that
are
102. 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,-10)
B.(14,10)
C.(-14,10)
D.(14,-10)
103. Find the range of the function y=5-2x2
A.All real numbers
B.y≤0
C.y≠5
D.y≥5
104. evaluate the limit:
A.undefined
B.2
C.0
D.1
105. If 22≡12 mod 5 and -1 ≡ 14 mode 5, find
the sum of the two congruencies.
A.21≡26 mod 5
B.23≡ 2 mod 5
C.21≡26 mod 10
D.20≡26mod 5
106. If 22≡mod 5 and -1≡14 mode 5, find the
product of the two congruencies.
A.-22≡168 mod 5
B.-22≡ 168 mod 25
C.21≡168 mod 25
D.22≡168mod 5
107. Find the area of the region bounded by the
curves: y=x2, y=x
A.3/4
B.1/6
C.1/2
D.1/3
108. Find the domain of the function y=5-2x2
A.x≥2
B.x≥5
C.x≥0
D.all real numbers
109. evaluate:
A.33 1/3
B.39 3/10
C.39 3/5
D.39 ½
110. Find the distance between the parallel lines
3x-4y-10 = 0 and 3x -4y-20=0
A.-2
B.√2
C.2
D.-√2
111. The trace of the square matrix A, to (A), is
the sum of its diagonal elements. If
Find the relationship between tr (A+B) and tr
(A)+ tr(B)
A.tr(A+B)< tr(A)+tr(B)
B.tr(A+B)>tr(A)+tr(B)
C.tr(A+B) not equal tr(A)+tr(B)
D.tr(A+B)=tr(A)+tr(B)
112. the set G= {a,e,b,c} forms a group with the
operator O. The group table is given by:
Find the inverse of c
A.c
B.e
C.a
D.b
113. the trace of the square matrix A, to (A), is
the sum of its diagonal elements if
Find tr (A)+tr(B)
A. 19
B.26
C. 21
D.24
114. Which is true for subgroups of a group?
A.Subgroups for a partition of a group
B.The intersection of two subgroups is emty
C.The union of two subgroups is also a group
D.The intersection of two subgroups is also a group
115. Find the x and y intercepts of the following:
y= 2x2-3x-2
A.(0,-2),(2,0),(-1/2,0)
B.(0,2),(1,0),(-1/2,0)
C.(2,0),(2,0),(-1/2,0)
D.(0,-2),(2,0),(-2.0)
116. Find the determinant of the co-factor of
A.30
B.23
C.13
D.-13
117. He has been described as the greatest“
might-have-been” in the history of
mathematics.
A.Blaise Pascal
B.Gaspard Monge
C.Bonaventura Cavalier
D.Gregorio de Saint
118. Who published a treatise on trigonometry
which contains the earliest use of our
abbreviation : sin, tan, sec, for sine, tangent
and secant?
A.Gregorio de Saint
B.John Napier
C.Albert Gerard
D.Johann Herdde
119. He invented a method of determining the
optical values of a linear function subject to a
certain constraints. This method is known as
linear programming. Who is he?
A.George Canter
B.Bertrand Russel
C.George Dantzig
D.Richard Dedelind
120. 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
B.Bertrand Ruseel
C.Jacob Bernouli
D.Stephen Baldwin