MAth

2.  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}

3.  A U B = distinct elements that are either in A
or in B, so given that
A = {-4,-2,0,2,4},
B= {-4-2,0,3,4}
A U B = { -4, -2, 0, 2, 3, 4}

4.  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}

5.  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

6.  Break-even point for a business is given by
the formula:
B = F/P –V
where B = units sold to break-even point,
F = fixed costs
P = price per unit
V = variable costs
Simply put, break even point means NO GAIN,
NO LOSS.

7.  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

8.  Simplify (a^2 – 5a)/(5 –a)

 A. a C. –a
 B. a-5 D. 5-a

9.  (a^2 – 5a)/(5 – a)
 a(a – 5)/ (5 – a) common factoring
 a(a – 5)/ -(-5 + a) distributive property
 a(a – 5)/ -(a – 5) commutative property
 -a

10.  Simplify (a^2 – 5a)/(5 –a)

 A. a C. –a
 B. a-5 D. 5-a

11.  Simplify the expression

13.  Simplify the expression

14.  Simplify the expression

15.  List of four smallest elements of the set
{ y|y=2x+1, x ԑ natural numbers}
A. 1,2,3,4 C. 3,5,7,9
B. 1,3,5,7 D. 3,4,5,6

16.  List of four smallest elements of the set
{ y|y=2x+1, x ԑ natural numbers}
 Natural numbers are the set of positive
integers = {1, 2, 3, 4, …}
 if x = 1, then y = 2(1) + 1 = 3
 if x = 2, then y = 2(2) + 1 = 5
 if x = 3, then y = 2(1) + 1 = 7
 if x = 4, then y = 2(1) + 1 = 9

17.  List of four smallest elements of the set
{ y|y=2x+1, x ԑ natural numbers}
A. 1,2,3,4 C. 3,5,7,9
B. 1,3,5,7 D. 3,4,5,6

18.  Factor over the integers by grouping:
3x3+x2+6x+2

19.  Factor over the integers by grouping:
3x3+x2+6x+2
 x2(3x + 1) + 2(3x+1)
 (x2+ 2)(3x+1)

20.  Factor over the integers by grouping:
3x3+x2+6x+2

21.  Solve the rational expression:
A. x=1/3 C. x=-1/3
B. x=-3 D. x=3

23.  Solve the rational expression:
A. x=1/3 C. x=-1/3
B. x=-3 D. x=3

24.  use absolute value notation to describe the
given situation:
 the distance between x and 3.
A. -|x-3| C. –|x+3|
B. |x+3| D. |x-3|

25.  use absolute value notation to describe the
given situation:
 the distance between x and 3.
A. -|x-3| C. –|x+3|
B. |x+3| D. |x-3|

26.  Simplify this complex fraction :

28.  Simplify this complex fraction :

29.  Find the acute angle between two lines have
the direction numbers [1,1,0] and [2,1,2]
A. 20° C. 45°
B. 50° D. 30°

31.  Find the acute angle between two lines have
the direction numbers [1,1,0] and [2,1,2]
A. 20° C. 45°
B. 50° D. 30°

32.  Simplify the given exponential expression:

33.  Simplify the given exponential expression:

34.  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.

35.  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.

36.  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
privateTeacher Education Institutions?
A. 72 C. 48
B. 18 D. 24

38.  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
privateTeacher Education Institutions?
A. 72 C. 48
B. 18 D. 24

39.  If (x)=2x-3 and g( x) =
 find (f o f) (x)

40. (f o f)(x) = f(f(x)) = f (2x -3)
= 2(2x -3) – 3
= 4x – 6 – 3
= 4x – 9

41.  If (x)=2x-3 and g( x) = , find (f o f) (x)

42.  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

43.  Let x be the amount deposited in 5% account.
 Then 75000 – x is the amount deposited in the 7% account.
 Let I be the combined interest gained from the two accounts.
 Using the formula I = PRT
 where I = interest gained
 P = principal amount
 R = interest rate
 T = time in years
 There are two interests here so I = I1 + I2, where I1 is the interest
from the 5% account and I2 is from the 7% account. Since we are
dealing with a 1 year term, we can ignore theT here.
 I = x(0.05) + (75000-x)(0.07)
 4050 = 0.05x + 5250 – 0.07x
 -0.02x = -1200
 x = 60000
 thus 60000 was invested at 5% while 15000 was at 7%

44.  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

45.  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]

46.  Let A(1, 3, 4) and B(-2, 3, 7) define directed
line segmentAB.Then its direction numbers
l, m, n are given by
l = -2 – 1 = -3
m = 3 – 3 = 0
n = 7 – 4 = 3
(-3, 0, 3) or any of its multiple such as (-1, 0, 1)

47.  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]

48.  Determine the percentage : Rate =200% ,
Base =30
A. 60
B. 2,400
C. 360
D. 120

49.  Determine the percentage : Rate =200% ,
Base =30
A. 60
B. 2,400
C. 360
D. 120

50.  The intersection of Sets A and B is defined by
A Ω B = {x/x ԑA and ԑB}
If A={a,b,c,d,e}, B={a,c,f,g}, find A Ω B
A. {b,c,g} C. {a,c}
B. {a,f,g} D. {a,b,c,g}

51.  The intersection of Sets A and B is defined by
A Ω B = {x/x ԑA and ԑB}
If A = {a,b,c,d,e}, B = {a,c,f,g}, findA Ω B
A. {b,c,g} C. {a,c}
B. {a,f,g} D. {a,b,c,g}

52.  If i(x)=2x-3 and g(x)=
find (g o g) (x)

54.  If i(x)=2x-3 and g(x)=
find (g o g) (x)

55.  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 C. 8 minutes
B. 28 minutes D. 10 minutes

57.  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 C. 8 minutes
B. 28 minutes D. 10 minutes

58.  Use absolute value notation to describe the
given situation:
The distance between x and -2 is 4.
A. |x+2|=-4 C. |x+2|=4
B. |x-2|=4 D. |x-2|=-4

59.  Use absolute value notation to describe the
given situation:
The distance between x and -2 is 4.
|x – (-2)| = 4
|x + 2| = 4

60.  Use absolute value notation to describe the
given situation:
The distance between x and -2 is 4.
A. |x+2|=-4 C. |x+2|=4
B. |x-2|=4 D. |x-2|=-4

61.  Lyn Santos is paid a salary of
Php5,000.00/week plus 10% commission on a
net sale over Php50,000.00. what is her gross
wage if her weekly net sales are
Php70,000.00?
A. Php4,700.00 C. Php5,000.00
B. Php7,000.00 D. Php2,000.00

63.  Lyn Santos is paid a salary of
Php5,000.00/week plus 10% commission on a
net sale over Php50,000.00. what is her gross
wage if her weekly net sales are
Php70,000.00?
A. Php4,700.00 C. Php5,000.00
B. Php7,000.00 D. Php2,000.00

64.  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 C.16
B. 20 D. 10

65.  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.
2ᶯ = 2^5
= 32

66.  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 C.16
B. 20 D. 10

67.  If f(x)=2x-3 and g(x)=
 Find(g o f) (x)
A. C. 4x-9
B. D.

69.  If f(x)=2x-3 and g(x)=
 Find(g o f) (x)
B.

70.  In three dimensions, where is the point
located if x=y=z=0?
A. xz plane C. yz plane
B. origin D. xy plane

71.  In three dimensions, where is the point
located if x=y=z=0?
A. xz plane C. yz plane
B. origin D. xy plane

72.  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 C. 250
B. 150 D. 200

73. 550 – 400 = profit per bag
= 150
150x = 60000, x is the number of bags needed
to be produced
x = 400

74.  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 C. 250
B. 150 D. 200

75.  Annual interest at 8% for 3 months on
P6,000.00
A. P480.00 C. P150.00
B. P120.00 D.P160.00

76.  Annual interest at 8% for 3 months on
P6,000.00
 I = PRT
 I = 6000(0.08)(3/12)
 I = 120

77.  Annual interest at 8% for 3 months on
P6,000.00
A. P480.00 C. P150.00
B. P120.00 D.P160.00

78.  Find the units in {1,2,3,4,5,6,7}
A. 2 C. 1
B. 4 D. 8

79.  Find the units in {1,2,3,4,5,6,7}
 The units in Zn are precisely those m in Zn,
such that gcd(m, n) = 1
 Thus, 1, 3, 5 and 7 are the units in Z8.

80.  Find the units in {1,2,3,4,5,6,7}
A. 2 C. 1
B. 4 D. 8

81.  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 C. 9,500
B. 2,000 D. 7,000

82. Let x be the number of cellphones.
(4/5)x = number of those who have cellphones
(4/5)x = 10000
x = 12500
That tells us that only 2500 do not have
cellphones.

83.  Four out of every five households have
cellphone. If 10,000 households in a certain
barangay have cellphone, how many do NOT
have cellphone? No correct answer.
A. 7,500 C. 9,500
B. 2,000 D. 7,000

84. 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. P22,700.00

87. 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. P22,700.00

88.  Perform the indicated operation and reduce
to lowest terms:
A. C.

B. D.

90.  Perform the indicated operation and reduce
to lowest terms:
A. C.

B. D.
 No correct answer but A is nearest.

91.  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 C. z= cxy
B. z=1/xy D. z= xy

92.  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 C. z= cxy
B. z=1/xy D. z= xy

93.  Evaluate dy / dx when x=2 for y = 8x -
A. 8 C. 4
B. -4 D. 0

95.  Evaluate dy / dx when x=2 for y = 8x -
A. 8 C. 4
B. -4 D. 0

96.  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

99.  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

100.  Find the area of the region bounded by the
curves: y = x2,,y = x.
A. 1/ 6 C. 1/3
B. 1/2 D. 3/4

104.  Find the area of the region bounded by the
curves: y = x2,,y = x.
A. 1/ 6 C. 1/3
B. 1/2 D. 3/4

105.  Perform the indicated operation and reduce
result to simplest form.
 A. C.
 B. D.

106.  Perform the indicated operation and reduce
result to simplest form.
 A. C.
 B. D.

108.  Perform the indicated operation and reduce
result to simplest form. No correct answer.
 A. C.
 B. D.

109.  Perform the indicated operation and reduce
result to simplest form.
 A. C.
 B. D.

111.  Perform the indicated operation and reduce
result to simplest form.
 A. C.
 B. D.

112.  Find the distance between the points(-3,2)
and (5,3).
 A. √45 C. √65
 B. √55 D. √56

114.  Find the distance between the points(-3,2)
and (5,3).
 A. √45 C. √65
 B. √55 D. √56

115.  Perform the indicated operation and reduce
to lowest terms:
 A. C.
 B. D.

117.  Perform the indicated operation and reduce
to lowest terms:
 A. C.
 B. D.

118.  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+18y-
96y+9=0.
 A. C.
 B. D.

120.  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+18y-
96y+9=0.
 A. C.
 B. D.

121.  Perform the indicated operation and reduce
result to simplest form.
 A. C.
 B. D.

123.  Perform the indicated operation and reduce
result to simplest form.
 A. C.
 B. D.

124. 
 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

125. 
 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

126.  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)

128.  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)

129.  What is the area of a triangle with vertices at
(5,3)(11,13) and (8,8)?
A. 30 C. 7
B. 15 D.24

130.  What is the area of a triangle with vertices at
(5,3)(11,13) and (8,8)? Not possible, there is
no triangle formed because the points are
collinear.
A. 30 C. 7
B. 15 D.24

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

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

134.  The approximate shape of the earth is
A. Sphere C. Cone
B. Circle D. Cube

135.  The approximate shape of the earth is
A. Sphere C. Cone
B. Circle D. Cube

136.  The motion of a particle is given by the
equation s=t3-3t-5. Find the velocity when
t=2.
A. 9 C. 3
B. 10 D. 5

138.  The motion of a particle is given by the
equation s=t3-3t-5. Find the velocity when
t=2.
A. 9 C. 3
B. 10 D. 5

139.  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 C. 167 square tiles
B. 168 square tiles D. 169 square tiles

140.  Check the pattern,
 1x1 --- 1
 2x2 --- 3
 3x3 --- 5
 4x4 --- 7
 …
 nxn ---25
 This follows the pattern in arithmetic
progression

141.  Hence, to find n:
 an = a1 + (n -1)d
 25 = 1 + (n – 1)2
 24 = (n – 1)2
 12 = n – 1
 n = 13
 Thus there are 13 x 13 tiles = 169

142.  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 C. 167 square tiles
B. 168 square tiles D. 169 square tiles

143.  Area of the Circle with equation: x2+ y2=4 is
A. 2π C. 4π
B. π D. 5π

144.  x2+ y2=4 is a circle with center at the origin
and r = 2.Thus,

145.  Area of the Circle with equation: x2+ y2=4 is
A. 2π C. 4π
B. π D. 5π

146.  The surface on the earth between the topic of
cancer and the Arctic Circle is called
A. Plane C. cone
B. Circle D. zone

147.  The surface on the earth between the topic of
cancer and the Arctic Circle is called
A. Plane C. cone
B. Circle D. zone

148.  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

149.  Volume = lwh

150.  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

151.  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.
B. 8 cm. x 8 cm. x 1 cm. D. 4 cm. x 4 cm. x 4 cm.

153.  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.
B. 8 cm. x 8 cm. x 1 cm. D. 4 cm. x 4 cm. x 4 cm.

154.  The sum of the sides of a polygon is the
of the polygon.
A. Perimeter C. area
B. Leg D. volume

155.  The sum of the sides of a polygon is the
of the polygon.
A. Perimeter C. area
B. Leg D. volume

156.  If the opposite sides of a quadrilateral are
equal, the figure is a
A. Rectangle C. parallelogram
B. Shambers D. square

157.  If the opposite sides of a quadrilateral are
equal, the figure is a
A. Rectangle C. parallelogram
B. Shambers D. square

158.  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 C. 86 meters
B. 85 meters D. 80 meters

160.  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 C. 86 meters
B. 85 meters D. 80 meters

161.  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 C. x=(2)(19)-19
B. x=(2)(19)+19 D. x=(2)(19)+17

162.  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 C. x=(2)(19)-19
B. x=(2)(19)+19 D. x=(2)(19)+17

163.  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 ?
 108 C.111
 110 D.109

164.  Sum of interior angles of quadrilateral = 360
 50 + 2(50) + 2(50) + x = 360
 250 + x = 360
 X = 110

165.  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 ?
 108 C.111
 110 D.109

166.  What is the value of x if x= log3 27?
A. 3 C. 9
B. 27 D. -3

168.  What is the value of x if x= log3 27?
A. 3 C. 9
B. 27 D. -3

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

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

173.  The statement of 3= log 10 (x+8)implies
A. 103=x+8
B. 33=x+8
C. (x+8)10=3
D. (x+8)3=10

174.  The statement of 3= log 10 (x+8)implies
A. 103=x+8
B. 33=x+8
C. (x+8)10=3
D. (x+8)3=10

175.  The given multiplication table represents a
cyclic group
 Find the order of the group
A. 2 C. 1
B. 3 D. 4
Find the order of the group
1.2 C. 1
2.3 D. 4

176.  The order of the group is the number of
elements in that group.
 There are four elements (a, b, c, d) in the
group.

177.  The given multiplication table represents a
cyclic group
 Find the order of the group
A. 2 C. 1
B. 3 D. 4
Find the order of the group
1.2 C. 1
2.3 D. 4

178.  log216 equals _____________

A. 3 C. 2
B. 4 D. 1

179.  log 2 16 = x  2^x = 16
 Thus, x = 4

180.  log216 equals _____________

A. 3 C. 2
B. 4 D. 1

181.  The given multiplication table represents a
cyclic group.
 Find d2
A. a C. b
B. d D. c

182.  The given multiplication table represents a
cyclic group.
 Find d2
A. a C. b
B. d D. c

183.  if sin ϴ =4/5 , and 0<ϴ<π/2, then cos 2Ɵ is
equal to
A. 24/25 C.-7/25
B. 7/25 D. 44/125

185.  if sin ϴ =4/5 , and 0<ϴ<π/2, then cos 2Ɵ is
equal to
 24/25 C.-7/25
 7/25 D. 44/125

186.  Tan π/10 is equal to
A.[2 tan[π/5)]/[1-tan2(π/5)] C. sin(π/5)/[1+cos(π/5)]
B.(sin π/3)/[1-cos(π/5)] D.[2tan(π/20)]/[1+tan2(π/5)]

187.  Tan π/10 is equal to
A.[2 tan[π/5)]/[1-tan2(π/5)] C. sin(π/5)/[1+cos(π/5)]
B.(sin π/3)/[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.

188.  When a logarithm is expressed as an integer
plus a decimal, the integer is called the
A. Mantissa C. base
B. Characteristic D. antilogarithm

189.  Characteristic is the integer part while
mantissa is the decimal or fractional part.

190.  When a logarithm is expressed as an integer
plus a decimal, the integer is called the
A. Mantissa C. base
B. Characteristic D. antilogarithm

191.  If log a 16=12, then a equals No
answer. Answer is
A. 2 C. 8
B. 4 D. 32

193.  If log a 16=12, then a equals No
correct answer.
A. 2 C. 8
B. 4 D. 32

194.  The logarithm of the product of two numbers
is equal to the of the logarithms of
the factors
A. Sum C. difference
B. Product D.antilogarithm

195.  The logarithm of the product of two numbers
is equal to the of the logarithms of
the factors
A. Sum C. difference
B. Product D.antilogarithm

196.  What is the simplest form of (sin1/2x-
cos1/2x)2?
A. 1+sin x C. 1-cos x
B. 1+cos x D. 1-sin x

198.  What is the simplest form of (sin1/2x-
cos1/2x)2?
A. 1+sin x C. 1-cos x
B. 1+cos x D. 1-sin x

199.  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

201.  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

202.  What is the exact value of sin [(2π/3)+(π/4)]?
A. (√6-√2)/4 C. √3
B. √2+1 D. (√6+√2)/4

204.  What is the exact value of sin [(2π/3)+(π/4)]?
A. (√6-√2)/4 C. √3
B. √2+1 D. (√6+√2)/4

205.  If tan Ɵ=1/3, then cot 2 Ɵ equals
A. 4/3 C.3/2
B. 2/3 D. 3/4

207.  If tan Ɵ=1/3, then cot 2 Ɵ equals
A. 4/3 C.3/2
B. 2/3 D. 3/4

208.  Which among the measures of central
tendency is not influenced by outliers?
A. Mean C. Mode
B.Weighted Mean D. Median

209.  Which among the measures of central
tendency is not influenced by outliers?
A. Mean C. Mode
B.Weighted Mean D. Median

 Note: Median is most reliable when there are
outliers in the given data set but mode is not
influenced by the outlier.

210.  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

211.  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

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

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

214.  A random sample of 200 adults are classified
by sex and their level of education attained.
If a person is picked at random from this group, find
the probability that the person is male.
A. 95/112 C. 11/25
B. 14/39 D.45/25

215.  A random sample of 200 adults are classified
by sex and their level of education attained.
If a person is picked at random from this group, find
the probability that the person is male.
A. 95/112 C. 11/25
B. 14/39 D.45/25

216.  The figure shows
A. Same negative correlation
B. Perfect positive correlation
C. Perfect negative correlation
D. Same positive correlation

217.  The figure shows
A. Same negative correlation
B. Perfect positive correlation
C. Perfect negative correlation
D. Same positive correlation

218.  To express that there is significant difference
between the income of family A and that of the
income of Family B.

219.  To express that there is significant difference
between the income of family A and that of the
income of Family B.

220.  A subset of the sample space is
A. Discrete variable
B. Event
C. Phenomenon
D. Continuous variable

221.  A subset of the sample space is
A. Discrete variable
B. Event
C. Phenomenon
D. Continuous variable

222.  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

223.  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

224.  If a die is rolled, what is the probability of
getting a number divisible by 2?
A. 1/6
B. 1/4
C. 1/2
D. 1/3

225.  If a die is rolled, what is the probability of
getting a number divisible by 2?
A. 1/6
B. 1/4
C. 1/2
D. 1/3

226.  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

227.  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

228.  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

229.  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

230.  For a sequence of eventsA,B, and C
 P(A U B U C )= P(A),+P(B/A), P(C/AU B)
A. Subtraction rule C. General rule
B. Addition rule D. Multiplicative rule

231.  For mutually exclusive eventsA and B,
 P(A U B)=P(A) +P(B)
A. Addition rule C. Subtraction rule
B. General rule D. Multiplicative rule

232.  For mutually exclusive eventsA and B,
 P(A U B)=P(A) +P(B)
A. Addition rule C. Subtraction rule
B. General rule D. Multiplicative rule

233.  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.

234.  Find the probability that the respondent
chosen at random is a female.
 12/25 C. 13/25
 6/25 D. 18/25
Find the probability that the respondent chosen at random is a female.
1.12/25 C. 13/25
2.6/25 D. 18/25

235.  Find the probability that the respondent
chosen at random is a female.
 12/25 C. 13/25
 6/25 D. 18/25
Find the probability that the respondent chosen at random is a female.
1.12/25 C. 13/25
2.6/25 D. 18/25

236.  To express that there is significant difference
between the food values of the nutrition
students and those of the nursing students:

237.  To express that there is significant difference
between the food values of the nutrition
students and those of the nursing students:

238.  Find the absolute maximum value of f(x)
=x(2/3) on the interval (-2,3)
A. 3√9 C. 0
B. 1 D. √9

240.  Find the absolute maximum value of f(x)
=x(2/3) on the interval (-2,3)
A. 3√9 C. 0
B. 1 D. √9

241.  Find the area of the triangle with vertices; (-
2,0)(2,3) and (5, 0)
A. 12 ½ C. 12
B. 11 D. 10 ½

243.  Find the area of the triangle with vertices; (-
2,0)(2,3) and (5,1)
A. 12 ½ C. 12
B. 11 D. 10 ½

244.  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

245.  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

246.  Find the equation of an ellipse in the general
form if the equation of the ellipse in the
standard
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
1.25x -4y -350x+16y +1141 = 0
2.25x2+4y2-350x-16y+1141=0
3.25x2-4y2-350x-16y+1141=0
4.25x2+4y2-350x-16y-1141=0

248.  Find the equation of an ellipse in the general
form if the equation of the ellipse in the
standard
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
 NO ANSWER!!!
1.25x -4y -350x+16y +1141 = 0
2.25x2+4y2-350x-16y+1141=0
3.25x2-4y2-350x-16y+1141=0
4.25x2+4y2-350x-16y-1141=0

249.  Find the absolute minimum value of f(x)=x2/3
on the interval (-2,3)
A. 0 C. 1
B. √9 D. 3√9

251.  Find the absolute minimum value of f(x)=x2/3
on the interval (-2,3)
A. 0 C. 1
B. √9 D. 3√9

252.  Evaluate:
A. 3 C. 2
B. 0 D. 1

254.  Evaluate:
A. 3 C. 2
B. 0 D. 1

255.  Find the derivative of f(x)=(x-3)(x+5)
A. 2x C. x+2
B. 2(x+1) D. x+1

256.  Find the derivative of f(x)=(x-3)(x+5)
f’(x) = (x – 3)(1) + (x+5)(1)
= (x – 3) + (x + 5)
= 2x – 2
= 2(x – 1)

257.  Find the derivative of f(x)=(x-3)(x+5)
A. 2x C. x+2
B. 2(x+1) D. x+1

258.  Find the distance between the points (-3,2)
and (5,3).
A. √55 C. √65
B. √56 D.√45

259.  Find the distance between the points (-3,2)
and (5,3).
A. √55 C. √65
B. √56 D.√45

260.  Find the area of the isosceles triangle that can
be inscribed in a circle with radius of 6 inches.
A. 27√3 C. 29
B. 27 D. 29√3
•Find the area of the isosceles triangle that can be inscribed in a circle with radius of 6 inches.
1.27√3 C. 29
2.27 D. 29√3

261.  Find the area of the isosceles triangle that can
be inscribed in a circle with radius of 6 inches.
 Question is a bit insufficient so we will just
assume we are solving for the largest area of
the isosceles triangle that can be inscribed.
 The area is maximum when the triangle is
equilateral. (Equilateral triangle are always
isosceles in nature but isosceles are not
always equilateral.)
•Find the area of the isosceles triangle that can be inscribed in a circle with radius of 6 inches.
1.27√3 C. 29
2.27 D. 29√3

262.  Side s of equilateral triangle inscribed in circle
is given by s = r √3
•Find the area of the isosceles triangle that can be inscribed in a circle with radius of 6 inches.
1.27√3 C. 29
2.27 D. 29√3

263.  Consider the right triangle in yellow shade.
Height H can easily be computed by inspection
(1,2 ,√3) or PythagoreanTheorem.
H = 9
So Area of
triangle =
½(9)(6 √3) =
27√3

264.  Find the area of the isosceles triangle that can
be inscribed in a circle with radius of 6 inches.
A. 27√3 C. 29
B. 27 D. 29√3
•Find the area of the isosceles triangle that can be inscribed in a circle with radius of 6 inches.
1.27√3 C. 29
2.27 D. 29√3

265.  Find the equation of the parabola in the
standard form if the equation of the parabola
is the general form is given by: y2-12x-23=0
A. (y+1)2=12(x+2) C. (y-1)2=-12(x+2)
B. (y-1)2=12(x+2) D. (y-1)2=-12(x-2)

266.  Find the equation of the parabola in the
standard form if the equation of the parabola
is the general form is given by: y2-12x-23=0
y2 – 12x – 23=0
y2 = 12x+23
y2 = 12(x + 23/12)

267.  Find the equation of the parabola in the
standard form if the equation of the parabola
is the general form is given by: y2-12x-23=0
No correct answer
A. (y+1)2=12(x+2) C. (y-1)2=-12(x+2)
B. (y-1)2=12(x+2) D. (y-1)2=-12(x-2)

268.  Find the derivative of f(x) = x2-2x+5
A. 3 C. 1
B. 0 D. 2

269. f(x) = x2-2x+5
f’(x) = 2x – 2

270.  Find the derivative of f(x) = x2-2x+5
A. 3 C. 1
B. 0 D. 2
 No correct answer due to insufficient
information.

271.  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) C. (x+1)2=-4(y+1)
B. (x+1)2=-4(y-1) D. (x+1)2=4(y+1)

272. x2+ 2x-4y-3=0
x2+ 2x + ___ = 4y+ 3 + ____
x2+ 2x + 1 = 4y+3 + 1
(x + 1)2 = 4(y + 1)

273.  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) C. (x+1)2=-4(y+1)
B. (x+1)2=-4(y-1) D. (x+1)2=4(y+1)

274.  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 C. 2/3 π
B. 1/3 π D. 2π

275.  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

276.  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

277.  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) C.(-14,10)
B. (14,10) D. (14,-10)

278.  Find the range of the function y=5-2x2
A. All real numbers
B. y≤0
C. y≠5
D. y≥5

279.  Find the range of the function y=5-2x2
y=5-2x2 is a parabola that opens downward
Given y= ax2 + bx + c, the range is the set of all y
such that
y ≤ (4ac – b2)/4a
Hence, y ≤ (4(-2)(5) – 02)/4(-2)
y ≤ 5

280.  Find the range of the function y=5-2x2
A. All real numbers
B. y≤0
C. y≠5
D. y≥5
 No correct answer

281.  evaluate the limit:
A. undefined C. 0
B. 2 D. 1


282.  evaluate the limit:
A. undefined C. 0
B. 2 D. 1


283.  If 22≡12 mod 5 and -1 ≡ 14 mode 5, find the
sum of the two congruences.
A. 21≡26 mod 5 C. 21≡26 mod 10
B. 23≡ 2 mod 5 D. 20≡26mod 5

284.  If 22≡12 mod 5 and -1 ≡ 14 mode 5, find the
sum of the two congruences.
A. 21≡26 mod 5 C. 21≡26 mod 10
B. 23≡ 2 mod 5 D. 20≡26mod 5

285.  If 22≡mod 5 and -1≡14 mode 5, find the
product of the two congruences.
A. -22≡168 mod 5 C. 21≡168 mod 25
B. -22≡ 168 mod 25 D. 22≡168mod 5

286.  If 22≡mod 5 and -1≡14 mode 5, find the
product of the two congruences.
A. -22≡168 mod 5 C. 21≡168 mod 25
B. -22≡ 168 mod 25 D. 22≡168mod 5

287.  Find the area of the region bounded by the
curves: y=x2, y=x
A. 3/4 C. 1/2
B. 1/6 D. 1/3

288.  Find the domain of the function y=5-2x2
 x≥2 C. x≥0
 x≥5 D. all real numbers

289.  Find the domain of the function y=5-2x2
 x≥2 C. x≥0
 x≥5 D. all real numbers

290.  evaluate:
A. 33 1/3 C. 39 3/5
B. 393/10 D. 39 ½

292.  evaluate:
A. 33 1/3 C. 39 3/5
B. 393/10 D. 39 ½

293.  Find the distance between the parallel lines
3x-4y-10 = 0 and 3x -4y-20=0
A. -2 C. 2
B. √2 D. -√2

295.  Find the distance between the parallel lines
3x-4y-10 = 0 and 3x -4y-20=0
A. -2 C. 2
B. √2 D. -√2

296.  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)

297.  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)

298.  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 C. a
B. e D. b


299.  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 C. a
B. e D. b
 Answer is based on the table, although the
topmost row should probably be e, a, b, c.

300. The trace of the square matrix A, to (A), is the
sum of its diagonal elements if
Find tr (A)+tr(B)
A. 19 C. 21
B. 26 D. 24

301. The trace of the square matrix A, to (A), is the sum
of its diagonal elements if
Find tr (A)+tr(B)
A. 19 C. 21
B. 26 D. 24
We just get the sum of the main diagonal if we want the
trace.

302.  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

303.  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

304. Find the x and y intercepts of the following: y=
2x2-3x-2
A. (0,-2),(2,0),(-1/2,0) C. (2,0),(2,0),(-1/2,0)
B.(0,2),(1,0),(-1/2,0) D.(0,-2),(2,0),(-2.0)

305.  y= 2x2-3x-2
 Let y = 0
 0 = 2x2-3x-2
 (2x + 1)(x – 2) = 0
 x = -1/2 and x = 2
 Let x = 0 in y= 2x2-3x-2
 y = -2
 Thus intercepts are (0, -2), (-1/2, 0) and (2, 0)


306. Find the x and y intercepts of the following: y=
2x2-3x-2
A. (0,-2),(2,0),(-1/2,0) C. (2,0),(2,0),(-1/2,0)
B.(0,2),(1,0),(-1/2,0) D.(0,-2),(2,0),(-2.0)

307.  Find the determinant of the co-factor of q33 of
 30 C. 13
 23 D. -13

308.  Determinants of q33
 = q11 x q22 – q21 x q12
 = 2(1) – 5(3)
 = 2 – 15
 = -13

309.  Find the determinant of the co-factor of q33 of
 30 C. 13
 23 D. -13

310.  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

311.  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

312.  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 C. Albert Gerard
B. John Napier D. Johann Herdde

313.  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 C. Albert Gerard
B. John Napier D. Johann Herdde

314.  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 C. George Dantzig
B. Bertrand Russel D. Richard Dedelind

315.  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 C. George Dantzig
B. Bertrand Russel D. Richard Dedelind

316.  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
•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 sam
1.Girolamo Cardano C. Jacob Bernouli
2.Bertrand Ruseel D. Stephen Baldwin

317.  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
•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 sam
1.Girolamo Cardano C. Jacob Bernouli
2.Bertrand Ruseel D. Stephen Baldwin