1. Global Experts Review Institute
Mathematics
Prepared by: John Paul L. Hablado, LPT, MAT Mathematics
GENERAL INSTRUCTIONS:
1. This test booklet contains 200-item test questions. Examinees shall manage to use 4 hours.
2. Shade only one box (1) box for each question on your answer sheet. Two or more boxes shaded
will invalidate your answer.
3. If none of the options/choices is correct, shade box “E” on the answer sheet.
4. AVOID ERASURES.
MULTIPLE-CHOICE
1. If f(x)= 2x2
and g(x) = 3x+2 , find (f+g)(x) .
a. 5x2
+2 b. 2x2
+3x+2 c. 2x2
-3x-2 d. 5x2
-2
2. Given two points A and B with the coordinates (3,2) and (6,4) respectively, the slope of the line
AB is
a.
−2
3
b.
4
6
c.
2
3
d.
1
2
3. It is the set of ordered pairs (x,y) where no two distinct pair have the same first element.
a. Solution set b. domain c. function d. ordinate
4. If the coordinate of the point are both negative, where is the point located?
a. Quadrant 1 b. Quadrant II c. Quadrant III d. Quadrant IV
5. Which of the following equations defines a function?
a. y2
= x2
-1 b. y= 2x+3 c. x= 7 d. x= ӀyӀ
6. Determine the trend of the line given the equation y= -3x-2.
a. rising to the right b. falling to the right c. horizontal d. vertical
7. What is the slope of the line whose graph is perpendicular to the graph of 3x+5y = 4?
a.
3
5
b.
5
3
c.
−3
5
d.
−5
3
8. What is the y-intercept of the line passing through point (4,1) and (3,-5) ?
a. 23 b. -23 c. 6 d. -6
9. What is the x-intercept of the linear function 3x+y = 9?
a. 1 b. 3 c. 0 d. 9
10. What is the zero of the function in f(x) = 3x+6?
a. 0 b. 3 c. 2 d. -2
11. The graph of the quadratic function is
a. line b. circle c. parabola d. hyperbola
12. All of the sentences except one describes a quadratic function . Which one does not?
a. y= x(x+1) b. y= x2
+1 c. y= 2x d. y= (x+1)2
13. Which of the following is the axis of symmetry of the equation y= 3x2
-12x+3 ?
a. 𝑥 =
2
3
b. 𝑥 =
1
3
c. 𝑥 =
−3
4
d. 𝑥 =
−3
2
14. What is the turning point of the parabola described by the equation y = 3x2
-12x+3 ?
a. (9,-3) b. (2,9) c. (3,-12) d. (1,4)
15. What is the equation of the parabola described by the graph of 𝑦 =
3
4
𝑥² shifted 5 units to the
left and 2 units upward?
a. 𝑦 =
3
4
(𝑥 + 5)2
+2 b. 𝑦 =
3
4
(𝑥 − 5)2
+2 c. 𝑦 =
3
4
(𝑥 + 5)2
-2 d. 𝑦 =
3
4
(𝑥 − 5)2
-2
16. Which of the following quadratic functions which has the vertex at (-2,3) and contains (4,12) ?
a. y= x2
+x+12 b. y= 4x2
+4x+2 c. 𝑦 =
1
4
𝑥² + 𝑥 +
1
4
d. 𝑦 =
1
4
𝑥² + 𝑥 + 4
17. Which of the following quadratic equations whose sum and product of its solutions are -3 and 6,
respectively?
a. y= x2
-3x+6 b. y= x2
-3x-6 c. y= x2
+3x+6 d. y= x2
-6x+3
2. Global Experts Review Institute
Mathematics
18. The roots of a polynomial function is also referred to as
a. factor of polynomial b. zero of a polynomial c. value of a polynomial d. remainder of a polynomial
19. What is the degree of the polynomial 8x3
-2x+6x2
+7x5
-6?
a. 3 b. 1 c. 5 d. 2
20. Which binomial is a factor of x3
+5x2
+2x+10?
a. x+5 b. x+2 c. x-2 d. x-5
21. In the polynomial f(x) = 3x3
-4x2
+5x-6 , what is f(-1)?
a. 12 b. -18 c. -7 d. 3
22. If x= 2, y= -1 and z= 0 , then 3x2
-y+3z is
a. 10 b. 13 c. 15 d. 18
23. Find the value of k so that x-1 is a factor of 2x3
-3x2
+kx-5.
a. 6 b. 12 c. 15 d. 18
24. The value of the constant is P(x) = x2
-7+2x is
a. 2 b. -7 c. 1 d. 0
25. What is x in log3 (x+1) = 2 ?
a. 9 b. 8 c. 6 d. 7
26. The range of the exponential function is consists of
a. Positive and real numbers c. All real numbers
b. Negative and real numbers d. Complex numbers
27. Which of the following statements is false?
a. The graph of y=loga x will all intersect at (1,0).
b. The graph of the function loga x= y will cross the y-axis.
c. The graph of y=loga x ,where a> 1, is increasing.
d. In loga x= y, y can be a negative ,zero or positive number.
28. Which equation describes an exponential function?
a. y=3x b. y=x3
c. y = 3x d. y= 𝑥
1
3
29. Which of the following could not be equal to 2?
a. (4)
1
2 b. 8
1
3 c. 32
1
5 d. (
8
4
)2
30. Transform 63
= 216 into logarithmic form.
a. log3 216 = 6 b. log6 216 = 3 c. log216 3 = 6 d. log6 6 = 216
31. Transform log3 h =
4
5
into exponential form.
a. ℎ = (
4
5
)3
b. ℎ = (
1
3
)4
c. ℎ = (
4
5
)5
d. ℎ = 3
4
5
32. What is the equivalent of 45˚ in radians?
a.
𝜋
4
b.
4
𝜋
c.
3𝜋
4
d. 4𝜋
33. The circumference of a unit circle is
a. 2𝜋 b. 𝜋 c.
3𝜋
4
d.
𝜋
2
34. What is the value of m in log3 243 = m?
a. 2 b. 3 c. 4 d. 5
35. Which among the graphs, used to show relationships among parts as well as the relationship of
a part to a whole?
a. line graph b. bar graph c. circle graph d. pictograph
36. What is
3
4
of a revolution equal to?
a. 90 degrees b. 120 degrees c. 180 degrees d. 270 degrees
3. Global Experts Review Institute
Mathematics
37.
𝜋
3
radians is equal to
a. 30 degrees b. 45 degrees c. 60 degrees d. 90 degrees
38. What is the base of the common logarithm?
a. 2 b. 3 c. 10 d. 1
39. Which of the following is the co-function of sin 72˚ ?
a. sin 28˚ b. cos 18˚ c. csc 18˚ d. tan 18˚
40. A 12-meter pole leans against the wall. The angle of elevation formed by the pole with the
ground is 50 degrees. Find the distance of the top of the pole from the ground. Round-off your
answer to the nearest one’s place.
a. 7 m b. 8 m c. 9 m d. 10 m
41. The amplitude of the tangent function is
a. 1 b. -1 c. 0 d. infinite
42. What is the mode in the distribution: 12, 11,10,12,12,13,14?
a. 12 b. 10 c. 11 d. 14
43. It is considered as the most popular and most widely used measure of central tendency.
a. standard deviation b. median c. mode d. mean
44. Which of the following is the example of a quantitative variable?
a. religion b. sex c. civil status d. weight
45. If the range of the data is 80, which are the possible highest and lowest values in the set of data
respectively?
a. 70, 10 b. 80 , 80 c. 98, 18 d. 100, 60
46. Which of the following data has no mode?
a. 1,2,3,4,5,6,7,8 b. 1,1,1,2,2,2,2,2 c. 1,2,3,4,4,5 d. 1,1,2,2,2,3,3
47. What is the mean of the data: 6,7,7,9,10,11,20?
a. 9 b. 10 c. 11.66 d. 12.6
48. Mr. Santos, 50 years of age has a 20-year- old son , Joel. In how many years will Mr. Santos be
twice as old as Joel?
a. 4 years b. 6 years c. 8 years d. 10 years
49. Driver A can travel a distance of 315 kilometers in 5 hours. Calculate his speed.
a. 163 kph b. 63 kph c. 53 kph d. 43 kph
50. Which indicates the relative position of an examinee in a certain group?
a. raw score b. percentile rank c. age equivalence d. grade equivalence
51. Which of the following is represented by the intersection of two adjacent walls and the ceiling of
the room?
a. line b. plane c. point d. ray
52. X,Y and Z are 3 non-collinear points. How many lines can be drawn that can contain all the three
points?
a. 0 b. 1 c. 2 d. 3
53. Which of the following is always true?
a. Chord is a diameter. c. Diameter is a radius.
b. Diameter is a chord. d. Radius is a diameter.
54. The area of a square is 144 cm2
, what is its perimeter?
a. 24 cm. b. 48 cm. c. 36 cm d. 40 cm.
55. Points on the same line are called
a. coincident b. collinear c. segment d. co-terminal
56. What is the dimension of a square garden whose perimeter is 24 m?
a. 4 m b. 5 m c. 6 m d. 8 m
4. Global Experts Review Institute
Mathematics
57. If each side of a triangle doubled in length , what happens to the angle of a triangle?
a. Their measures are also doubled.
b. Each angle is reduced to half of its original size.
c. The angles remain the same.
d. Cannot be determined unless we measure the angles.
58. The radii of two circles are 10 cm and 11 cm . How many square centimeters is the area of the
larger circle greater than the area of smaller circle?
a. 65.94 cm b. 75.94 cm c. 55.74 cm d. 60.94 cm
59. It is an angle pair which has a common side and a common vertex but no interior points in
common.
a. Vertical angles b. linear pair c. adjacent angle d. complementary angle
60. Line M and N intersect as shown in the figure below. What is the measure of angle 2 if measure
of angle 1 = 68˚?
a. 121 ˚ b. 112 ˚ c. 132˚ d. 142˚
1 2
M N
61. Two non-opposite angles of a parallelogram are
a. congruent b. complementary c. right d. supplementary
62. The measure of a semi-circle is
a. 360˚ b. 90˚ c. 180˚ d. 45˚
63. Which of the following is the area of a rectangle given the figure? x+3
x
a. 2x+2x+6 b. 4x+6 c. 4x2
+12 d. x2
+3x
64. Which of the following is false about triangle XYZ?
Y
X Z
a. 𝑋𝑌̅̅̅̅̅ ≅ 𝑌𝑍̅̅̅̅̅ c. 𝑋𝑌̅̅̅̅̅ ≅ 𝑋𝑍̅̅̅̅̅
b. ∆ XYZ is an isosceles. d. 𝑋𝑌̅̅̅̅̅, 𝑌𝑍̅̅̅̅̅ and 𝑋𝑍̅̅̅̅̅ are the sides of ∆ XYZ.
65. The measure of one of the angles in a supplementary pair is three times that of the other,the
measure of each angle is
a. 40˚ and 140˚ b. 60˚ and 120˚ c. 25˚ and 165˚ d. 45˚ and 135˚
66. The longest side of the right triangle is
a. hypotenuse b. side c. legs d. angle
5. Global Experts Review Institute
Mathematics
67. From the given angle measures, which of these form a triangle?
a. 125˚,25˚,30˚ b. 90˚,60˚,90˚ c. 90˚,90˚,50˚ d. 90˚, 45˚,35˚
68. When Joseph sorts his collection of marbles into groups of 2 ,3,4 or 8,there is always one
marble left. What is the smallest number of marbles Joseph can have?
a. 35 b. 28 c. 25 d. 21
69. Two brothers and their young sister are to divide an inheritance worth ₱ 300,000.00 in the ratio
of 5:6:4 , with the girl getting the least share. How much is the share of the sister?
a. ₱20,000.00 b. ₱ 80,000.00 c. ₱ 100,000.00 d. ₱ 40,000.00
70. Which of the following statements is false?
a. If a number is a multiple of 9, then it is also a multiple of 3.
b. If a number is divided by 9, then it is divisible by 3.
c. If 9 is a divisor of a number, then 3 is also a divisor of the number.
d. If the number is divisible by 3 , then it is divided by 9.
71. What is the perimeter of a square whose area is 256 m2
?
a. 1,024 m b. 64 m c. 32 m d. 16 m
72. A clock is 4 minutes ahead every 8 hours. If the clock is set correctly at 8:00 a.m. Monday, what
time will be shown in this clock at 8:00 a.m. Friday?
a. 8:48 a.m. b. 8:54 a.m. c. 9:08 a.m. d. 8:56 a.m.
73. Linda paid ₱360.00 for 12 notebooks, but she was given 3 additional notebooks for free. In
effect , what rate of discount did she enjoy?
a. 50% b. 40% c. 30% d. 20%
74. A tank that holds 400 gallons of water can be filled by one pipe in 15 minutes and emptied by
another in 40 minutes. How long would it take to fill the tank if both pipes are functioning?
a. 28 min b. 21 min c. 24 min d. 23 min
75. The initial temperature of the object was 27˚C. After exposing the object to different
surrounding media,its temperature decreased by 7˚C,the increased by 10˚C and then finally
decreased by 25˚C. What was the final temperature of the object?
a. 15˚C b. 20˚C c. -5˚C d. 5˚C
76. What number is exactly divisible by 8?
a. 7304 b. 5000 c. 3584 d. 5218
77. 40% of 35 is what percent of 140?
a. 29% b. 28% c. 10% d. 14%
78. An angle 7𝜋 radians is equal to _____________.
a. 115˚ b. 225˚ c. 105˚ d. 89˚
79. The roots of the equation (x-5)(x-3)=0 are ______________.
a. 3 or -5 b. 3 or 5 c. -3 or 5 d. -3 or -5
80. Three out of every 24 flashlights turned out by a particular factory are found to be defective. If
the factory turns out 1,248 flashlights in a week, how many are defective?
a. 18 b. 72 c. 156 d. 416
81. What must be the value of x in the arithmetic progression x-7, x-2, x+3,… so that its 10th
term
will be 40?
a. 2 b. 3 c. 1 d. 4
82. If ab+cd=12ad ,then
𝑏
𝑑
+
𝑐
𝑎
= _______________.
a. ab+cd b. 12 c. 12a+12d d. 12ac
83. What is √256
4
?
a. 5.4 b. 4 c. 16 d. 6
84. The same number is subtracted from the numerator and denominator of the fraction
8
11
. If the
resulting fraction is equivalent to
2
3
, what is the number subtracted?
a. 5 b. 2 c. 3 d. 4
6. Global Experts Review Institute
Mathematics
85. A falling body strikes to the ground with a velocity V, which varies directly as the square root of
the distance d it falls. If the body that falls 100 feet strikes the ground with a velocity of 80
ft./second, with what velocity will a ball dropped from a height of 550 ft. strike the ground?
a. 150 ft./sec. b. 190 ft./sec. c. 170 ft./sec. d. 188 ft./sec.
86. Which of the following is a true identity?
a. sin2
𝜃 = 𝑐𝑜𝑠2
𝜃 b. 𝑐𝑜𝑠2
𝜃 + 1 = sin2
𝜃 c. tan2
𝜃 = 𝑠𝑒𝑐2
𝜃 − 1 d. 𝑐𝑜𝑠2
𝜃 -1 = sin2
𝜃
87. Which statement is true?
I. 1 m is longer than 1km.
II. 1 mm is longer than 1 in.
III. 1 gallon is heavier than 1 lb.
IV. 1 gallon is more than 1 liter.
a. I only b. I and IV c. I and III d. III and IV
88. Two buses leave the same station at 9:00 p.m. One bus travels North at the rate of 30 kph and
thee other travels East at 40 kph. How many kilometers apart are the buses at 10 p.m.?
a. 100 km b. 70 km c. 50 km d. 140 km
89. Which of these is not factorable?
a. 6x2
-5x-6 b. 6x2
-13x+6 c. 6x2
+7x-6 d. 6x2
-35x-6
90. What is the value of x in this equation?
1
2
+
2
3
−
1
𝑥
=
1
6
a. 4 b. 2 c. 1 d. 3
91. If 16 is 4 more than 3x, then what is the value of 2x-5?
a. 2 b. 4 c. 5 d. 3
92. If 3x
= 81 and 4y
= 64, then what is (x-y)?
a. 17 b. 1 c. 0 d. -1
93. Which of the following is a factor of x4
-4x3
-6x2
+3x+10?
a. (x-2) b. (x+5) c. (x+1) d. (x-5)
94. Which of these could be the measures of the angles of an isosceles triangle?
a. 60˚,60˚, 80˚ b. 32˚, 32˚,116˚ c. 51˚,98˚, 51˚ d. 45˚,45˚,100˚
95. A box is 12” in width , 16” in length ,and 6” in height . How many square inches of paper would
be required to cover it on all sides?
a. 900 b. 192 c. 720 d. 360
96. The vertices of a triangle are (2,1) ,(2,5), and (5,1) . What is the area of a triangle?
a. 10 sq. units b. 8 sq. units c. 5 sq. units d. 6 sq. units
97. Four small squares are put together to form a bigger square . If the perimeter of the big square is
256, then what is the length of each side of smaller square?
a. 24 b. 16 c. 32 d. 8
98. What is the total length of fencing needed to enclose a rectangular area 46 ft. by 34 ft.?
a. 48 yd. b. 26 yd. and 1 ft. c. 53
1
3
yd. d. 52 yd. and 2 ft.
99. Three segments have lengths a, b, and c with a<b<c. Under what conditions could these
segments be used to form a triangle?
a. a+b> b b. b+c >a c. a+c<b d. a+b>c
100. Which of the following equations is parallel to 3x-2y=4 and has a y-intercept of -3?
a. y= 2x-3 b. 2x-3y=6 c. 2x-3y= 4 d. 3x-2y= 6
101. Given the equation of the circle x2
+y2
+4x-6y-12=0 , which of the following is its center?
a. (2,3) b. (-3,-2) c. (-3,2) d. (-2,3)
102. The longest line segment with endpoints on the circle is
a. chord b. radius c. circumference d. diameter
103. From the following choices, which represents the greatest possible distance between two points
on a circular table top with a circumference of approximately 12. 6 ft.?
a. 2 ft. b. 3.14 ft. c. 3.9 ft. d. 4 ft.
104. What is the midpoint of a line segment joined by P1(2,4) and P2(3,10)?
a. (2,3) b. (5/2,7) c. (4,10) d. (2,10)
7. Global Experts Review Institute
Mathematics
105. What is the equation of the line passing thru each pair of points (0,1) and (5,7)?
a. 𝑦 =
6𝑥+5
5
b. 𝑦 =
7𝑥+7
4
c. 𝑦 =
5𝑥+1
6
d. 𝑦 =
4𝑥+1
7
106. Which is a solution for equations x+y=2 and 2x-y=4?
a. (0,2) b. (2,0) c. (2,2) d. (1,2)
107. Find the other endpoint of a line segment having the midpoint (4,5) with one endpoint (-1,6).
a. (3,1) b. (9,4) c. (5,6) d. (4,-1)
108. What is the equation of the line with slope= 2 and passes at point (1,-3)?
a. y=x-1 b. y=x+2 c. y= 2x-1 d. y=2x-5
109. What is the equation of the line with a slope of -5 and a y-intercept of -3?
a. 5x-y-3=0 b. -5x-y+3=0 c. 5x +y+3=0 d. -5x-y-3=0
110. Find the slope of the line that passes through the origin and (-2,3)?
a. -3/2 b. -2/3 c. 2/3 d. 3/2
111. A quadrilateral with four equal sides is a
a. rectangle b. rhombus c. square d. trapezoid
112. Given that ABCD is a rectangle. If AC = 9x-35 and BD = 4x+70, then x is
A B
D C
a. 21 b. 154 c. 42 d. 144
113. The perimeter of a triangle is 35. The side has the ratio of 1:2:4. What is the length of the
shortest side?
a. 5 b. 10 c. 20 d. 7
114. Which of the following kinds of triangle inequalities exist?
a. isosceles b. scalene c. equilateral d. isosceles right
115. In which of the following quadrilaterals are the opposite sides NOT PARALLEL?
a. parallelogram b. rectangle c. squares d. kites
116. The angles of a quadrilateral are 70˚,90˚,2x˚ and 3x˚. The value of x must be:
a. 30˚ b. 40˚ c. 50˚ d. 60˚
117. What is the total surface area of the figure below?
5 m
4m
10 m
a. 220 m2
b. 200 m2
c. 225 m2
d. 240 m2
118. Given circle O, and m BAC = 20˚, what is the measure of arc BC?
A
D
O
a. 20˚ b. 140˚ c. 90˚ d. 100˚
C B
119. What is the equation of a circle with radius r= 8 and center C at (-3,4)?
a. (x+3)2
+(y-4)2
= 64 c. (x+3)2
+(y+4)2
= 64
b. (x-3)2
+(y-4)2
= 64 d. (x-3)2
+(y+4)2
= 64
120. In the proportion 2 : 3 = 6 : (2+x) ,what is the value of x?
a. 7 b. 8 c. 9 d. 12
8. Global Experts Review Institute
Mathematics
121. Two hexagons ,A and B,are similar and the ratio of corresponding sides of A:B is 4:3. If the
sides of hexagon A are each halved while the sides of hexagon B are doubled,what will be
the new ratio of the corresponding perimeters of the larger hexagon to the smaller
hexagon?
a. 1:3 b. 2:3 c. 3:2 d. 3:1
122. Three triangles are similar , and their sides are in the ratio of 2:5:6. If each side of the
smallest is tripled while each side of the largest triangle is divided by 3, what is the ratio
of the perimeters of the three triangles after these changes are made?
a. 6:5:3 b. 36:25:4 c. 216:125:8 d. 18:15:6
123. The measure of each interior angle of a regular polygon is 165 degrees. How many sides
does it have?
a. 12 b. 15 c. 24 d. 29
124. What happens to the circumference of a circle if the length of the radius is doubled?
a. It becomes 3 times longer. c. It is doubled.
b. It becomes 4 times longer. d. It is halved.
125. Which of the following equations is parallel to 3x-2y=4 and has y-intercept of -3?
a. y=2x-3 b. 2x-3y=6 c. 2x-3y=4 d. 3x-2y=6
126. Which line in the figure has an undefined slope?
1 2 3 4
a. 3 b. 4 c. 2 d. 1
127. All of the quadrilaterals have two pairs of opposite sides parallel, EXCEPT:
a. rectangle b. trapezoid c. square d. rhombus
128. The area of a circle is 49𝜋. What is its circumference, in terms of 𝜋 ?
a. 49𝜋 b. 14𝜋 c. 28𝜋 d. 98𝜋
129. What is the slope of a line that passes through he points (-1,2) and (3, -4)?
a.
3
2
b. 3 c. 2. d. −
3
2
130. A rectangular bin 4 ft long, 3 ft wide, and 2 ft high is solidly packed with bricks whose
dimensions are 8 inches,4 inches and 2 inches. How many bricks are there in the bin?
a. 54 b. 848 c. 648 d. 320
131. P is 7 less than the square of the sum of the quotient of x and y ,and the product of x
and y. Which equation expresses this relationship?
a. P = (7−
𝑥
𝑦
+ 𝑥𝑦)2
b. P= (
𝑥
𝑦
+ 𝑥𝑦 − 7)2
c. P= 7-(
𝑥
𝑦
+ 𝑥𝑦)2
d. (
𝑥
𝑦
+ 𝑥𝑦)2
-7
132. If the first derivative of f(x) is 3x2
+2x, what is f(x) ?
a. 3x3
+2x b. x3
+x2
c. 6x3
+2x2
d. 3x3
+x
133. What are the endpoints of the major axis of 9(x-3)2
+25(y-2)2
=225?
a. (1,-2) and (-7,-2) c. (-1,2) and (7, 2)
b. (0,2) and (6,2) d. (-2, 2) and (8, 2)
134. What is the equation of a straight line with a gradient -1 and y-intercept 4?
a. 2y= x+4 b. 4y=x+1 c. y= 2x+5 d. y= -x+4
135. If f(x) = 5x3
-x2
+3 , find the second derivative of f(x).
a. 45x2
-2x b. 30x-2 c. 3x3
-2x d. 15x3
-2xy
136. Evaluate: lim
𝑥→2
( √3𝑥2 + 4 ) is ________________.
a. -4 b. 4 c. 2 d. √10
137. What is the second derivative of y= (x3
+ 2)2
?
a. 2x2
(x3
-2) b. 6x (x3
+2) c. 6(x5
+3x2
) d. 6x2
(5x2
+8)
138. The cost C(m) in the thousand of pesos of producing m thousand Math books is given
C(m) = 30+20m-0.5m2
. What is the marginal cost of producing 12,000 Math books?
a. ₱ 12,000.00 b. ₱ 16,000.00 c. ₱10,000.00 d. ₱8,000.00
139. Determine the equation of the line parallel to 3x-8y+11= 0 , and passing thru (8,10).
a. 8x-3y-34=0 b. 3x-8y+56=0 c. 3x-8y-104=0 d. 3x+8y+56=0
9. Global Experts Review Institute
Mathematics
140. What is the equation of the line through (4,1) and parallel to the line through (7,3)
and (5,-1)?
a. x-4y=0 b. 3x+y= 13 c. 2x-y=7 d. 5x-6y= 14
141. One end of a line segment is P1(1,-2) . If the midpoint of the line segment is (4,3), find
the coordinates of the other endpoint of the line segment.
a. (6,9) b. (6,7) c. (5,8) d. (7,8)
142. What is the equation of the line with an x-intercept of 5 and a y-intercept of 2?
a. 5y+2x= 4 b. 2y+5x= 25 c. 2y+5x=10 d. 5x+2y= 10
143. What is the equation of a circle with center (-5,7) and a diameter that is 20 cm.?
a. (x+5)2
+(y-7)2
= 10 c. (x-5)2
+(y-7)2
= 100
b. (x+5)2
+(y-7)2
= 100 d. (x+5)2
+(y-7)2
= 100
144. Find the first derivative of (x2
+2x)(x3
).
a. x4
+6x3
b. 2x4
+2x3
c. 5x4
+8x3
d. 3x4
+6x3
145. What is the equation of the line with slope
−6
11
and passing through (4,9)?
a. 6x+11y-123= 0 b. 11x+6y+1= 0 c. 6x-11y+123= 0 d. 6x+11y-75=0
146. How long is the diameter of x2
+y2
-10x+14y= -10?
a. 128 units b. 16 units c. 8 units d. 64 units
147. In the graph of y= 2-2x2
-4x, what is the highest point?
a. (1,-4) b. (4,-1) c. (-4,1) d. (-1,4)
148. The derivative of y= 2x3
-5x2
+3x+2 is _________________.
a. y’= 6x2
-10x-3 b. y’= 6x2
-6x+3 c. y’= -6x2
+10x-3 d. y’= 6x2
-10x+3
149. Which of the following quadratic functions will have a graph which opens downward?
a. y = 1-(3x-x2
) b. y= 5x(x-1)+3 c. y= 7x-(5x2
+1) d. y=-4(2-x2
)+5x
150. What is he median of the following set of numbers: {11,8,3,2,3.2,14,13,8,7.8,6}?
a. 8.5 b. 7 c. 7.9 d. 5
151. The scores of eight boys in an IQ Test are as follows: 100,120,101,107,110,112,117,and
118. What is the percentile 75?
a. 120 b. 118 c. 116 d. 117
152. A pair of dice is thrown. If the sum of the dots on the two dice is 6,what is the
probability that one of the dice is 2?
a. 1/18 b. 2/5 c. 1/6 d. 11/36
153. If majority of the students in Statistics class was able to answer most of the questions
given during the examination, the score is expected to be ______________.
a. positively skewed b. normally distributed c. negatively skewed d. bimodal
154. Thirty people were asked a question answerable of yes, no or may be ,their responses
were recorded. Which measure of central tendency is MOST appropriate for the
recorded data?
a. range b. mode c. mean d. median
155. Determine the length of the latus rectum of the parabola: 5y2
+20y-6x+20=0.
a. 6 b. 3/5 c. 3/10 d. 6/5
156. Francisco received the following scores on tests in Calculus : 73,89,81,95, and 87.
What is his mean score?
a. 84 b. 85 c. 89 d. 87
157. How many ways can 3 books be selected from a group of 7 books?
a. 42 b. 35 c. 210 d. 21
158. How many different signals ,each consisting of 7 flags hung in a vertical line, can be
formed from 4 identical red flags and 3 identical green flags?
a.
7!
4!3!
b. (7-4)! c. 7! d. 4!3!
159. How many distinct permutations can be made from the letters of the word INFINITY if
all letters are to be taken?
a. 3,540 b. 4,512 c. 3,360 d. 3,124
160. Four married couples have reserved eight seats in a row for a basketball game. In how
many ways can they be seated if each couple is to sit together?
a. 350 b. 384 c. 320 d. 300
10. Global Experts Review Institute
Mathematics
161. A family has three children. What is the probability that all children are boys?
a. 3/8 b. ½ c. 1/8 d. 1/6
162. A card is selected at random from a box of 20 cards numbered 1 to 20 . What is the
probability that the number is a multiple of 3?
a. 7/20 b. 3/20 c. 5/20 d. 3/10
163. How much interest would be collected on a loan of ₱ 25,000.00 borrowed for 7
months at 5% per year?
a. ₱ 1,485.33 b. ₱ 1,585.33 c. ₱ 1,458.33 d. ₱ 1,785.33
164. A store is giving a 15% discount off on the marked price of every electrical item, what
is the discounted price of a water dispenser marked at ₱ 3,000.00?
a. ₱3,150.00 b. ₱2,550.00 c. ₱4,150.00 d. ₱3,450.00
165. If sin A=
1
2
, then what is tan2A?
a.
√3
4
b. √3 c.
√3
2
d.
1
3
166. In a sale, Janice paid ₱ 270.00 for a skirt originally marked ₱ 450.00. What was the
discount rate given?
a. 20% b. 60% c. 50% d. 40%
167. What is the area of the square lot whose diagonal is 6√2 m. ?
a. 28 sq. m. b. 72 sq. m. c. 12 sq. m. d. 36 sq. m.
168. Which of these is equal to 1 + tan2
x?
a. sec2
x b. cos2
x c. cot2
x d. sin2
x
169. What is the second derivative of y= (x3
+2)2
?
a. 6 (x5
+3x2
) b. 2x2
(x3
+2) c. 6x2
(x3
+2) d. 6x(x3
+2)
170. If sin𝐴 =
√2
2
, then what is sin 2A?
a. ½ b. 2 c. 2√2 d. 1
171. The formula for covering Farenheit thermometer reading to centigrade reading is
˚C =
5
9
(˚𝐹 − 32). What is the equivalent of 95 ˚𝐹?
a. 35 b. 40 c. 45 d. 50
172. The showing of the movie started at 6: 18 p.m. and lasted at 8:05 p.m. How many
minutes did the movie show?
a. 103 b. 123 c. 107 d. 143
173. The length of rectangular lot is one less than twice its width. If the perimeter is
16 cm., what is the width of the lot in centimeters?
a. 1 b. 2 c. 3 d. 4
174. A wood is divided into four pieces with a ratio of 2:3:4:6 .If the longest portion is 14
inches , what is the total length of the wood ?
a. 30” b. 35” c. 40” d. 45”
175. Find the square of the number in the set which appears most of the time.
{7, 3, 4, 5 6, 1 , 7 ,2, 3, 7}
a. 3 b. 9 c. 25 d. 49
176. The present population is 20% less than the previous population. If the present
population is 4,000 ,then what is the previous population?
a. 5,000 b. 4,500 c. 3,500 d. 5,200
177. The length of the rectangle is more than 8 meters more than twice its width . The
perimeter is 112 meters. Find its area.
a. 320 m2
b. 400 m2
c. 600 m2
d. 640 m2
178. For what value of x will x be the average of 2 , 4x , 6, 8, and 10?
a. 20 b. 24 c. 26 d. 28
179. Eighteen less than seven times the number of sandwiches is 269. How many
sandwiches are there?
a. 41 b. 82 c. 251 d. 287
180. Ann is 6 years older than John. Six years ago, she was twice as old as he. How old is
Ann now?
a. 12 years old b. 14 years old c. 16 years old d. 18 years old
11. Global Experts Review Institute
Mathematics
181. A reservoir can be filled by an inlet pipe in 24 hours and emptied by an outlet pipe
in 28 hours. The foreman starts to fill the reservoir, but he forgot to close the outlet
pipe. Six hours later, he remembers and closes the outlet. How long does it take
altogether to fill the reservoir?
a. 6 1/7 hours b. 26 1/7 hours c. 29 1/7 hours d. 36 1/3 hours
182. John can clean the house in 2 hours and Paul can clean the same house in 3 hours.
How long will it take them to clean the house together?
a. 1. 2 hr. b. 1.5 hr. c. 3.5 hr. d. 6 hr.
183. What is the period of the function y= cos
1
2
x?
a. 2𝜋 b. 4𝜋 c.
𝜋
4
d.
𝜋
2
184. Find the value of x if 9x
= 272
.
a. 3 b. 4 c. 5 d. 6
185. Solve for x: log x= 2.
a. 10 b. 20 c. 60 d. 100
186. Solve for x: √𝑥2 − 9 + 3 = x
a. 2 b. 3 c. 4 d. -3
187. If sin x=
3
5
, find sin 2x in QI .
a.
4
5
b.
12
25
c.
24
25
d.
20
25
188. Simplify:
tan 𝑥
sec 𝑥
a. cos x b. sin x c. csc x d. cot x
189. A 30-cm long plastic pipe costs ₱ 249.00 . At this rate, what is the price of the pipe
per meter?
a. ₱800 b. ₱ 830 c. ₱ 860 d. ₱ 900
190. Suppose the time now is 9:30 a.m. What will be the time 16 hours from now?
a. 12:30 a.m. b. 1:30 a.m. c. 2:30 a.m. d. 11:30 p.m.
191. John uses ten 100-Watt bulbs in his house. He uses these bulbs at an average of 5
hours each day. How many KWH do these bulbs use each day?
a. 5 b. 10 c. 20 d. 50
192. How many meters of fencing are needed to enclose an 84-meter by 84-meter
rectangular garden?
a. 168 m b. 200 m c. 336 m d. 400 m
193. The conjugate of 5 − 2𝑖 is ______________________.
a. 5+2i b. -5+2i c. -5-2i d. 3i
194. The Food Technology students support the feeding program. The students’
population to be fed is P=2,356e0.01t
where t=0 represents the students’ population
in AY: 2014-2015. Use e≈ 2.718. Approximately
a. 2,100 students b. 2,200 students c. 2,300 students d. 2,400 students
195. Which of the following is an odd function?
a. y= 3x+5 b. y=x2
c. y=-x4
+x2
d. y= x3
-5x
196. Find the degree measure of the angle for ½ rotation, clockwise.
a. 180˚ b. 360˚ c. -180˚ d. -360˚
197. If a string for a tree is 14 ft. long, making a 30-degree angle with the ground, then how
far is the base of the tree from the peg anchoring the wire? Approximately
a. 12 ft. b. 13 ft. c. 14 ft. d. 15 ft.
198. Find the area of the triangle: angle C= 60˚, side a= 30 cm, and side b= 45 cm.
a. 584.57 sq.cm. b. 675 sq. cm. c. 675 √3 sq. cm. d. 584 √3 sq. cm.
199. Two planes travel from opposite direction. Plane A travels 70 kph from one
direction, and plane B travels from opposite direction at the rate of 90 kph. If the
distance is 640 km, in how many hours the two planes intersect?
a. 1 hr b. 2 hr c. 3 hr d. 4 hr
200. Find the value of 𝐴𝑟𝑐𝑐𝑜𝑠 (𝑆𝑖𝑛
3𝜋
4
) .
a.
3𝜋
4
b.
𝜋
4
c.
5𝜋
6
d.
𝜋
6
***END OF EXAMINATION***
