1000 MMR Author: Victor A. Tondo Jr.

, LPT
1. How many line segments can be made from 30 8. What are the missing terms in the series
non-collinear points? 5, 20, 80, ___,1280, ___, 20480?
A. 900 B. 870 A. 50; 210 B. 40; 160
C. 450 D. 435 C. 35; 135 D. 320; 5120

2. Calculate the mean absolute deviation of the 9. At what rate per annum should P2400 be
following numbers: 60, 80, 100, 75 and 95 invested so that it will earn an interest of P800 in
A. 12.4 B. 14.2 8 years?
C. 16.1 D. 18.9 A. 6 ½ % B. 5 ½ %
C. 4.17 % D. 6 %

3. Which of the following is the factorization of

the binomial x2 - 42? 10. The area of a rectangle is (x2 + 2x - 8). If its
A. (x + 4)(x + 2) length is x + 4, what is its width?
B. (x – 4)2 A. x + 2 B. x - 2
C. x(x + 2x + 2) C. x + 1 D. x + 6
D. (x – 4)(x + 4)

11. What is the value of 12⅙ - 3 ⅜ - 5 ⅔ + 20 ¾?

1 7
4. What value of x will satisfy the equation: A. 21 8 B. 22 C. 23 8 D. 21
0.4(5x – 1470) = x?
A. 490 B. 2,130
C. 1470 D. 588
12. The vertex angle of an isosceles triangle is
20°. What is the measure of one of the base
angles?
5. Which of the following is ALWAYS true?
A. 150° B. 60° C. 75° D. 80°
A. Vertical pairs of angles are supplementary.
B. Vertical pairs of angles are complementary.
C. Linear pairs of angles are congruent.
13. Ana and Beth do a job together in three
D. Linear pairs of angles are supplementary.
hours. Working alone, Ana does the job in 5
hours. How long will it take Beth to do the job
alone?
6. The average of 5 different counting numbers is
A. 3 and 1/3 hours B. 2 and 1/3 hours
20. What is the highest possible value that one of
C. 3 hours D. 7 and 1/2 hours
the numbers can have?
A. 20 B. 40 C. 30 D. 90
14. How much greater is the sum of the first 100
counting numbers than the sum of the first 50
7. Three brothers inherited a cash amount of
counting numbers?
P62,000 and they divided it among themselves in
A. 110 B. 3,775
the ratio of 5:4:1. How much more is the largest
C. 3,155 D. 1200
share than the smallest share?
A. P75,000 B. P30,000
C. P24,800 D. P37,200
15. Which of the following has the largest value?
A. 85 B. 39 C. 65 D. 94

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1000 MMR Author: Victor A. Tondo Jr., LPT
16. A water tank contains 18 liters when it is 23. One side of a 45° - 45° - 90° triangle
20% full. How many liters does it contain when measures x cm. What is the length of its
50% full? hypotenuse?
A. 60 B. 30 C. 58 D. 45 A. x √3 cm B. x cm
C. (x √3)/2 cm D. x √2 cm

17. The edges of a rectangular solid have these

measures: 1.5 feet by 1½ feet by 3 inches. What 24. The legs of one right triangle are 9 and 12,
is its volume in cubic inches? while those of another right triangle are 12 and
A. 324 B. 225 C. 972 D. 27 16. How much longer is the perimeter of the
larger triangle than the perimeter of the smaller
triangle?
18. In a certain school, the ratio of boys to girls is A. 84 B. 7 C. 12 D. 14
5 is to 7. If there are 180 boys and girls in the
school, how many boys are there?
A. 105 B. 90 25. An online shop sells a certain calculator for
C. 45 D. 75 P950 and charges P150 for shipping within
Manila, regardless of the number of calculators
ordered. Which of the following equations shows
19. Ruben’s grades in 6 subjects are 88, 90, 97, the total cost (y) of an order as a function of the
90, 91 and 86. What is the grade that he should number of calculators ordered (x)?
aim for in the 7th subject if he has to have an A. y = (950 + 150)x B. y = 150x +950
average of 91? C. x = 950y + 150 D. y = 950x + 150
A. 97 B. 95 C. 92 D. 89

26. Which of these has the longest perimeter?

20. On a certain day, three computer technicians A. A square 21 cm on a side
took turns in manning a 24-hour internet shop. B. A rectangle 19 cm long and 24 cm wide
The number of hours Cesar, Bert, and Danny C. An equilateral triangle whose side is 28 cm
were on duty was in the ratio 3:4:5, respectively. D. A right triangle whose two legs are 24 and 32
The shop owner pays them P50 per hour. How cm
much would Danny receive for that day?
A. P 230 B. P500
C. P160 D. P480 27. How many square inches are in 2 square
yards?
A. 900 B. 144
21. A retailer buys candies for P90.25. The pack C. 1296 D. 2,592
has 35 pieces of candies. If she sells each candy
for P3.25, how much profit does she make?
A. P11.50 B. P23.50 28. In a playground for Kindergarten kids, 18
C. P37.50 D. P18.75 children are riding tricycles or bicycles. If there
are 43 wheels in all, how many tricycles are
there?
22. Determine the midpoint of the line segment A. 8 B. 9 C. 7 D. 11
joining the points (7, -3) and (-1, 6).
A. (2, 3/2) B. (2, -3/2)
C. (3, 3/2) D. (1, 5/2)

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1000 MMR Author: Victor A. Tondo Jr., LPT
29. Aira takes ¾ hour to dress and get ready for 𝑥 2 −4
36. Find the domain of f(x) = 𝑥+1 .
school. It takes 4/5 hour to reach the school. If
her class starts promptly at 8:00 am; what is the A. x ∈ ℝ B. x = 1
latest time she can jump out of bed in order not C. x = -1 D. x ∈ ℝ, x ≠ -1
to be late for school?
A. 6:42 am B. 6:27 am
C. 6:57 am D. 7:02 am 37. A car travels D km in H hours. Which of the
following expressions shows the distance
travelled by the car after M minutes?
30. Which common fraction is equivalent to A. MD/H B. 60MD/H
C. MD/60H D. 60HD/M
0.215?
A. 43/200 B. 27/125
C. 21/50 D. 108/375
38. Find the surface area of a rectangular box
whose dimensions are 30 cm x 40 cm x 50 cm.
31. What are the next three terms in the A. 4700 cm2 B. 7050 cm2
progression 1, 4, 16 …? C. 9400 cm2 D. 11750 cm2
A. 64, 256, 1024 B. 67, 259, 1027
C. 48, 198, 1026 D. 65, 257, 1025
39. If x – y = 3, then (y-x)-3 = ___.
A. 9 B. -9
32. A man is 3 times as old as his son now. Four C. 1/27 D. -1/27
years ago, the sum of their ages was 36. Find the
man’s age now.
A. 33 B. 11 40. Factorize (x4 – 81) completely.
C. 29 D. 36 A. (x-3)4
B. (x – 3)2 (x + 3)2
C. (x+3) (x-3) (x2+9)
33. What is the least common multiple of 12, 24 D. (x+3)3 (x-3)
and 72?
A. 12 B. 72 C. 144 D. 36
41. √8 + √18 − √2 = ____
A. 4√2 B. 5√2 C. √24 D. 2√6
34. The hypotenuse of a right triangle is 25 feet.
If one leg is 24 feet, what is the length of the
other leg? 42. By which property can we state the
A. 6 ft. B. 5 ft. C. 20 ft. D. 7 ft. following:
“If ax + b = c, then ax + b - b = c – b.”
A. transposition B. transitive
35. If two variables X and Y are directly related, C. additive inverse D. addition property
which of these is NOT true?
A. When X is low, Y is also low.
B. As X increases, Y also increases. 43. The midpoint of P and (-7, 4) is (-3, 1). What
C. When X increases, Y decreases. are the coordinates of P?
D. A high Y is associated with a high X. A. (-5, 5/2) B. (-11, 7)
C. (1, -2) D. (-2, 3/2)

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1000 MMR Author: Victor A. Tondo Jr., LPT
44. What is the slope of the line 3x – y = 11? 52. There are 33 red bags, 25 green bags, and 17
A. -1/3 B. 1/3 C. -3 D. 3 blue bags in a store. What percent of the bags is
red?
A. 33% B. 44%
45. What is the minimum value of C. 66% D. 67%
f(x) = 3x2 + 6x + 7?
A. 1 B. -1 C. 4 D. -4
53. Given sin θ = 0.28, which of the following
could possibly be cos θ?
46. If xy = 23 and x2 + y2 = 75, find x + y. A. 0.72 B. -0.86
A. 10.7845 B. 11 C. 0.96 D. 1.14
C. 11.2155 D. 11.7845

54. If the sum of the supplement and the

47. How much water must be evaporated from complement of an angle is 130 degrees, what is
90 ml of a 50% salt solution to increase its the angle?
concentration to 75%? A. 65o B. 70o
A. 40 ml B. 38 ml C. 50o D. 25o
C. 35 ml D. 30 ml

55. If today is a Saturday, what day is 125 days

48. ∠A and ∠B form a vertical pair. If m∠A = 3x from now?
and m∠B = 5x – 44, what is the value of x? A. Thursday B. Friday
A. 50.5 B. 28 C. 22 D. 16.75 C. Sunday D. Monday

49. The angle of elevation from an observer to 56. Car A is traveling towards the east at a speed
the top of a building is 30o. If the building is 50 of 35 kph, while car B is traveling towards the
meters high, how far is the observer from the west at 45 kph. If they left the same point at 1:00
building? PM, how far apart are they at 3:45 PM?
A. 25 B. 25√3 C. 50√3 D. 100 A. 240 km B. 220 km
C. 200 km D. 180 km

50. ∠1 and ∠3 are opposite angles in a

parallelogram. If m∠1 = 40o, what is m∠3? 57. Mr. Santos left the house at 1:00 PM and
A. 40o B. 50o C. 70o D. 140o traveled east at an average speed of 40 kph. His
wife Mrs. Santos left the at 2:00 PM and traveled
west at an average speed of 30 kph. How far
51. Two parallel lines are cut by a transversal, apart are they at 4:00 PM?
forming ∠H and ∠K. If the two angles are A. 180 km B. 140 km
exterior angles on the same side of the C. 100 km D. 60 km
transversal, what is the measure of ∠H if the
measure of ∠K is 50o?
A. 25o B. 50o 58. Five consecutive even numbers have a sum of
C. 100 o D. 130o 120. What is the sum of the 2nd and 5th even
numbers?
A. 46 B. 48 C. 50 D. 52

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1000 MMR Author: Victor A. Tondo Jr., LPT
59. If x = 3, which of the following is equal to 13? 68. If A and B are the roots of x2 + 7x + 15, what
A. 5x + 2 B. x2 + 2x + 1 is AB?
C. x – 4x – 2
3 D. x2 + x + 2 A. 7√3 + 2 B. 2√3 + 7
C. 3√2 + 2√3 D. 15

60. If f(x) = x2 + 4x + 3, which of the following is

equal to 99? 69. 1 + 2 + 4 + 8 + … + 2048 = ____
A. f(11) B. f(-12) A. 4095 B. 4096
C. f(12) D. f(-8) C. 4097 D. 4098

2 +2𝑥
61. Given f(x) = ln 𝑒 𝑥 , what is f ‘(x)? 70. 24 + 12 + 6 + 3 + 1.5 + … = ____
2𝑥+2 𝑥 2 +2𝑥 A. 48 B. 50 C. 54 D. 60
A. 𝑥 2 +2𝑥 B. 2𝑥+2
C. (2x+2) ln (x2+2x) D. 2x + 2
71. How many terms are there in the sequence
5, 13, 21, 29, …, 357?
62. Which of the following could be the value of x
A. 40 B. 44
if x ≅ 3(mod 11)?
C. 45 D. 70
A. 33 B. 47 C. 52 D. 2

𝑑𝑢 72. How many ways can a group of 5 be selected

63. If 𝑑𝑥 = 6x2 + 8x – 7, which could be u? from 5 boys and 5 girls if the group must contain
A. 12x + 8 B. 3x3 + 4x2 – 7x + 11 3 boys and 2 girls?
C. 2x + 4x -7x +1 D. 12x2 + 8x - 10
3 2 A. 151,200 B. 1200
C. 252 D. 100

64. What is the center of x2 + y2 – 8x + 6y = 0?

A. (-8.6) B. (8, -6) 73. What is the probability of getting a sum of 9
C. (-4, 3) D. (4, -3) when rolling 2 dice?
A. 1/9 B. 5/36
C. 1/6 D. 7/36
65. Which of the following is a parabola that
opens to the right?
A. 6y = (x+9)2 - 8 B. -4y = (x-6)2 + 3 ̅̅̅̅ where A is at (-3,4)
74. C is the midpoint of AB
C. -5x + 3 = (y-2)2 D. 2x + 6 = (y+3)2 and B is at (7,-10). Find the coordinates of C.
A. (5,-7) B. (-5,7) C. (2,-3) D. (-2,3)

66. Factorize: 12x2 – 7x – 10.

A. (6x + 5) (2x – 2) B. (6x – 2) (2x + 5) 75. It is a line segment formed by connecting two
C. (3x + 2) (4x – 5) D. (3x – 2) (4x + 5) non-consecutive vertices of a polygon.
A. side B. apothem
C. altitude D. diagonal
67. For which value of k does 4x2 + kx + 49 have
only one root?
A. -28 B. -14 C. 7/2 D. -7/4

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1000 MMR Author: Victor A. Tondo Jr., LPT
76. Find the equation of the line perpendicular to 84. Given ̅̅̅̅
BT bisects ∠ABC and m∠ABT = 40o,
2x – 3y = 7, passing through (1,2). find m∠ABC.
A. 2x + 3y = 8 B. 3x + 2y = 7 A. 20o B. 40o C. 60o D. 80o
C. 2x – 3y = -4 D. 3x – 2y = -1

85. A cone has a radius of 9 cm and a slant height

77. Two parallel lines are cut by a transversal to of 15 cm. Find its volume.
form ∠X, ∠Y, and ∠Z. Given that ∠X and ∠Y are A. 243 π cm3 B. 324 π cm3
alternate interior angles while ∠Y and ∠Z are C. 405 π cm 3 D. 486 π cm3
interior angles on the same side of the
transversal, find m∠Z if m∠X = 40o.
A. 40o B. 50o 86. If f(x) = x2 + 4x + 4 and g(x) = x-2, find
C. 130 o D. 140o f(g(x)).
A. x2 B. x3 – 6x2 + 6x – 9
C. x + 8x + 16
2 D. x2 – 8x + 16
78. The measure of each interior angle of a
regular polygon is 144o. How many vertices does
it have? 87. A 10 ft ladder leans against a wall, forming a
A. 36 B. 24 C. 12 D. 10 30o angle with it. How high on the wall does it
reach?
A. 5 ft B. 5 √3 ft
79. Solve: (x + 9) (x – 3) < 0 C. 10 √3 ft D. 10 √6 ft
A. -9 < x < 3 B. x < -3 ∪ x > 9
C. x < -9 ∪ x > 3 D. x ∈ ℝ; x ≠ -9, 3
88. How many ways can a committee of 5 be
selected from 9 people?
80. The product of two consecutive even A. 126 B. 120
counting numbers is 3248. Find the smaller C. 3024 D. 15120
number.
A. 42 B. 46 C. 52 D. 56
89. What is 60% of 80% of 500?
A. 480 B. 240
81. Solve for x: 2log2 3 – log2 18 = x C. 120 D. 60
A. ½ B. -1 C. -2 D. 1

90. If 3x = 7 and 2y = 5, what is 6(x-y)?

82. Twinkle Bucks has four serving sizes for their A. -1 B. 1-√35
milk tea: Small, Medium, Large, and Extra Large. 47
C. √7 - √5 D. 5
What level of data are they using for their
serving sizes?
A. nominal B. ordinal
C. interval D. ratio 91. If two numbers have a product of 71 and the
sum of their squares is 147, what is their sum?
A. -17 B. 5
83. After receiving a 20% markup, a bag was sold C. 12√3 + √5 D. 12 + √3
for P960. How much was it originally?
A. P1152 B. P4800
C. P800 D. P1200

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1000 MMR Author: Victor A. Tondo Jr., LPT
92. Find the median: 7, 9, 11, 10, 9, 13, 17, 14 99. Which of the following has two diagonals that
A. 10 and 11 B. 9 and 10 are perpendicular bisectors of each other?
C. 10.5 D. 9.5 A. kite B. rectangle
C. rhombus D. isosceles trapezoid

93. How many 3-digit numbers can be formed

using the digits 0, 1, 2, 3, 4 and 5 if repetition is 100. A pipe can fill a pool in 6 hours while
not allowed? another pipe can drain empty the pool in 15
A. 60 B. 80 C. 100 D. 120 hours. How long will it take to fill the pool if both
pipes are open?
A. 9 hours B. 9.125 hours
94. How many ml of 20% acid must be added to C. 9.45 hours D. 10 hours
400 ml of 50% acid to make a 30% acid solution?
A. 1000 ml B. 900 ml
C. 800 ml D. 750 ml 101. If log n – 1 = 2, find n.
A. 3 B. 1000 C. e3 D. 3e

95. How many ml each of 10% and 50% solution

should be mixed to make 500 ml of 18% 102. log2 3 + 2 log2 7 – log2 5 = ______.
42 9
solution? A. log2 5 B. log2 5
A. 400 ml of 10% and 100 ml of 50% 147 142
B. 350 ml of 10% and 150 ml of 50% C. log2 D. log2
5 5
C. 300 ml of 10% and 200 ml of 50%
D. 200 ml of 10% and 300 ml of 50%
103. The surface areas of two spheres are 12 π
cm2 and 108 π cm2. What is the ratio of their
96. It takes 28 men a total of 24 days to build a volumes?
house. How long would it take 32 men to build a A. 1:3√3 B. 1:9
similar house? C. 1:27 D. 2:3√3
3
A. 28 days B. 27 7 days
2
C. 21 days D. 19 7 days
104. The volume of a regular hexahedron is 64
in3. How long is each side?
A. 2 in B. 4 in C. 6 in D. 8 in
𝑥 2 −16
97. Evaluate: lim
𝑥→4 𝑥−4
A. undefined B. limit does not exist
C. 8 D. +∞ 105. Which of the following statements is
ALWAYS true?
A. The square of a prime number is odd.
98. A box contains 7 red, 8 blue, and 9 white B. The sum of two consecutive even numbers is
balls. When taking two balls in succession, what divisible by 4.
C. Any even number is composite.
is the probability that both balls are white?
A. 9/64 B. 9/69 D. The product of two consecutive even numbers
C. 7/64 D. 7/69 is divisible by 8.

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1000 MMR Author: Victor A. Tondo Jr., LPT
106. Find the volume of a steel cylinder of radius 114. Find the area of the triangle whose vertices
5 cm and height 12 cm. are (1,4), (2,3), and (3,0).
A. 300 π cm3 B. 250 π cm3 A. 0 B. 1 C. 5/3 D. 3/4
C. 200 π cm3 D. 100 π cm3

115. Find the tenth term: 3, 10, 17, 24, …

107. A cube sits perfectly inside a sphere of A. 66 B. 67 C. 68 D. 69
volume 108 √3 π cm3. Find the volume of the
cube.
A. 27 cm3 B. 54 cm3 116. Find the remainder when
C. 108 cm3 D. 216 cm3 x4 – 5x3 + 6x2 + 2x + 1 is divided by (x – 2).
A. 17 B. 13 C. 9 D. 5

108. Find the distance in cm of an 80 cm chord

from the center of a circle whose radius is 41 cm. 117. The sum of Fe’s age and Sita’s age is 60.
A. 41 - 2√10 B. 41 - 4√10 Twelve years ago, Fe was twice as old as Sita.
C. 9√2 D. 9 How old is Sita now?
A. 18 B. 24 C. 30 D. 36

109. Which quadrilateral has two congruent

diagonals that bisect each other? 118. If the length of a rectangle is increased by
A. kite B. isosceles trapezoid 20% while the width is decreased by 10%, what
C. rectangle D. rhombus will happen to its area?
A. decreased by 10%
B. increased by 10%
110. What is the longest side of ∆MTC if m∠M = C. increased by 8%
40o and m∠C = 60o? D. decreased by 2%
̅̅̅̅
A. MC ̅̅̅̅
B. TC ̅̅̅̅
C. MT ̅̅̅̅
D. CT
119. The 19th term of an arithmetic sequence is
111. Find the altitude to the hypotenuse of a 85 and the 12th term is 43. Find the common
right triangle whose legs measure 10 cm and 24 difference.
cm. A. 5 B. 6 C. 7 D. 8
120
A. 120 cm B. 13 cm
C. 120√2 cm D. 24√5 cm 120. If 2x = 3y and 4y = 5z, what is z in terms of
x?
6 15
A. z = 5 x B. z = 8 x
112. Find the inverse of y = x2 + 10x. 5 8
C. z = 6 x D. z = 15 x
A. y-1 = √𝑥 − 25 + 5
B. y-1 = √𝑥 − 25 – 5
C. y-1 = √𝑥 + 25 + 5
121. Victor had an average of 94 on his first four
D. y-1 = √𝑥 + 25 – 5
Math tests. After taking the next test, his average
dropped to 93. Find his most recent grade.
113. Find the intersection of y = 2x + 3 and
A. 88 B. 89 C. 90 D. 91
y = 4x – 11.
A. (-4/3, 0) B. (4/3, 0)
C. (7, 17) D. (-7,-17)

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1000 MMR Author: Victor A. Tondo Jr., LPT
3 5 𝑥+𝑦 5
122. X is 4 of Y and Y is 6 of Z. What part of Z is X? 129. Evaluate 𝑥−𝑦 when x = ¾ and y = 6.
5 3
A. X = 8 Z B. X = 5 Z A. -38 B. -19 C. 19 D. 38
8 5
C. X = 5 Z D. X = 3 Z
130. Today, Vic is 11 years old while his father is
37. How many years from now will his father be
123. Two buses leave the same station at 8:00 twice as old as he?
pm. One bus travels north at the rate of 30 kph A. 15 B. 13 C. 11 D. 10
and the other travels east at 40 kph. How many
kilometers apart are the buses at 10 pm?
A. 140 km B. 100 km 131. Carla and Diana are on a seesaw. Carla
C. 70 km D. 50 km weighs 50 kg and sits 168 cm to the left of the
fulcrum. If Diana weighs 60 kg, how far to the
right of the fulcrum must she sit to balance the
124. A bus drove for 6 hours at 75 kph and 4 seesaw?
hours at 80 kph. What was its average speed? A. 140 cm B. 170.8 cm
A. 76 kph B. 77 kph C. 201.6 cm D. 210 cm
C. 77.5 kph D. 78 kph

132. Twenty guests shake hands with each other.

125. 18 students failed a quiz. They represent If each guest is to shake hands with all the other
30% of the class. How many students passed the guests, how many handshakes will be made?
quiz? A. 400 B. 380 C. 200 D. 190
A. 60 B. 42 C. 36 D. 24

133. How many line segments can be made from

2
126. Rationalize: 30 non-collinear points?
√5+2
2√5 A. 900 B. 870 C. 450 D. 435
A. +1 B. 2√5 – 4
5
2√5+4 2√5
C. D.
9 3 134. The longest chord of a circle is 80 cm. How
long is its radius?
A. 20 cm B. 30 cm
127. RNHS has 130 quizzers. 67 of them are
C. 20√2 cm D. 40 cm
Math, 60 are Science, and 20 are quizzers for
both Math and Science. How many quizzers are
neither Math nor Science?
A. 0 B. 13 C. 17 D. 23 135. Find k such that 34k67 is divisible by 9.
A. 5 B. 6 C. 7 D. 8

128. Mr. Tondo has P100,000 to invest, from

which he wants to earn P5600 per year. Bank A 136. Find the largest area of a rectangle whose
offers 5% per annum while Bank B offers 6%. perimeter is 100 cm.
How much should he invest at Bank B? A. 2500 cm2 B. 2499 cm2
A. P45,000 B. P50,000 C. 625 cm 2 D. 624 cm2
C. P55,000 D. P60,000

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1000 MMR Author: Victor A. Tondo Jr., LPT
137. What time is 200 minutes past 10:30 PM? 146. Insert one term between 18 and 32 to make
A. 12:30 AM B. 12:30 PM a geometric sequence.
C. 1:50 AM D. 1:50 PM A. 20 B. 24 C. 25 D. 27

138. Find the product of two numbers whose 147. There are 100 pigs and chickens in a farm,
GCF is 24 and LCM is 120. all of which are healthy. If there are 340 legs in
A. 2880 B. 1440 C. 720 D. 360 total, how many pigs are there?
A. 70 B. 65
C. 60 D. 55
139. The salary of 4 men for 5 days is P9,000.
How much is the salary of 5 men for 6 days?
A. P12,000 B. P12,600 148. Adam can do a job alone in 8 hours, while
C. P13,500 D. P14,400 Bam can do the same job in 12 hours. One day,
they worked together for 1 hour before Bam left
Adam to finish the job. How long will it take
140. The average grade of eleven students is 83. Adam to finish the remaining job?
If the average of six of these students is 88, what A. 6 hrs 50 mins B. 6 hrs 40 mins
is the average of the other 5 students? C. 6 hrs 30 mins D. 6 hrs 20 mins
A. 77 B. 78 C. 79 D. 80

149. Find x if 2748 = 9x.

141. If x is 80% of y, what percent of y is x? A. 144 B. 81 C. 72 D. 60
A. 120% B. 125%
C. 130% D. 135%
150. Solve for x: 49x = 343
A. 1.142857 B. 7
142. Bus X left the terminal at 1 PM and traveled C. 1.5 D. √7
at a speed of 60 kph. Bus Y left the same terminal
2 hours later and traveled 80 kph on the same
route. What time will Bus B catch up with Bus A? 151. What is the highest possible product of two
A. 6 PM B. 9 PM numbers if their sum is 45?
C. 11 PM D. 1 AM A. 506 B. 506.25
C. 506.5 D. 506.725

143. What is the degree of the polynomial

-3 x2y3 + 21 x3y4 – 7 x5y6 – 15? 152. Which statistical test is used for comparing
A. 4 B. 5 C. 11 D. 21 observed frequencies to expected frequencies?
A. ANOVA B. t-test
C. Pearson R D. Chi Square
144. The average of x+5, 2x-4, and x+7 is 20.
Find x.
A. 18 B. 13 C. 9 D. 8 153. The product of two consecutive odd
counting numbers is 1443. What is their sum?
A. 76 B. 78 C. 80 D. 82
145. Mia is 16 years younger than Kia. 13 years
ago, Kia was thrice as old as Mia. What is Kia’s
present age?
A. 43 B. 40 C. 37 D. 34
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1000 MMR Author: Victor A. Tondo Jr., LPT
2𝑥 + 1; 𝑥 < 4 162. Which of the following angles in standard
154. Given 𝑓(𝑥) = { 4; 𝑥 = 4, position is coterminal with 40o?
2
𝑥 − 7; 𝑥 > 4 A. 2200o B. 1760o
find lim 𝑓(𝑥). C. 1520o D. 1360o
𝑥→4
A. 4 B. 9
C. 0 D. limit does not exist
163. Find the equation of the line passing
through (2,7) and (-3,-3).
155. If today is a Saturday, what day is 125 days A. y = 4x -1 B. y = 3x + 1
from now? C. y = 3x + 6 D. y = 2x + 3
A. Friday B. Sunday
C. Monday D. Tuesday
164. In which quadrant can we find θ if tan θ < 0
and sin θ > 0?
156. If the sum of the supplement and the A. First Quadrant
complement of an angle is 124, what is the B. Second Quadrant
angle? C. Third Quadrant
A. 71 B. 72 C. 73 D. 74 D. Fourth Quadrant

1 1
157. Find 𝑥 + 𝑦 given x + y = 20 and xy = 81. 165. Find the equation of the line passing
through the point of origin and (3,4).
81 40 81 20 4 3
A. 40 B. 81 C. 20 D. 81 A. y = 3 x B. y= 4 x
3 7
C. y = 4 x + 4 D. y = x + 1
158. What is the remainder when
534,214,557,989,215 is divided by 4?
A. 0 B. 1 C. 2 D. 3 166. Find the range of f(x) = -2x2 + 4x.
A. y ≤ 2 B. y ≥ 2
C. y ≤ -2 D. y ≥ -2
159. Dividing by 0.125 is the same as multiplying
by which number?
A. 5 B. 8 C. 10 D. 16 167. If a3/2 – 1 = 7, what is a?
A. 4 B. 8 C. 9 D. 18

160. Find the surface area of a sphere whose

radius is 6 cm. 168. Which of the following is true?
A. 72 π cm2 B. 108 π cm2 A. A rectangle is a square.
C. 144 π cm2 D. 192 π cm2 B. A rhombus is a rectangle.
C. A trapezoid is a rhombus.
D. A square is a rhombus.
161. Which of the following is the reference
angle of 216o?
A. 84o B. 66o C. 54o D. 36o 169. What is the measure of each exterior angle
of a pentagon?
A. 108o B. 72o
C. 60o D. 36o

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1000 MMR Author: Victor A. Tondo Jr., LPT
170. How many diagonals does a nonagon have? 178. Which of the following has its incenter,
A. 27 B. 36 C. 45 D. 54 circumcenter, centroid, and orthocenter in just
one point?
A. Right Triangles B. Equilateral Triangles
171. What is the fractional equivalent of C. Isosceles Triangles D. Scalene Triangles
0.123123123123…?
123 123 41 41
A. 1001 B. 1000 C. 333 D. 321
179. Dexter is twice as heavy as Pablo. Ming is
4kg heavier than Pablo. The sum of their masses
is 164kg. How heavy is Dexter?
172. Mrs. Pasay saved P250 after buying a phone
A. 40 kg B. 44 kg
with a 10% discount. How much did she pay for
C. 80 kg D. 88 kg
the phone?
A. P2500 B. P2250
C. P2000 D. P1750
180. A circle is drawn inside a triangle such that
it is tangent to the sides of the triangle. Its center
will be the triangle’s ___________________.
173. A book was sold for P270 after a 10% A. Incenter B. Circumcenter
discount was given. How much was the book C. Centroid D. Orthocenter
originally?
A. P330 B. P300
C. P297 D. P280 181. Rayon can do a job in 3 hours, while Carlyn
can do the same job in 7 hours. How long will it
take them to finish the job by working together?
174. Find the area of an equilateral triangle A. 2.1 hours B. 2.5 hours
whose sides measure 12 cm each. C. 5 hours D. 10 hours
A. 36√3 cm2 B. 48√3 cm2
C. 60√3 cm2 D. 72√3 cm2
182. This line is perpendicular to one side of the
triangle passing through the opposite vertex.
175. This is located at the intersection of the A. Longitude B. Median
angle bisectors of a triangle. C. Altitude D. Bisector
A. Incenter B. Circumcenter
C. Centroid D. Orthocenter
183. How many ways can Lola Leonor arrange
her six meals on the Lazy Susan (the rotating
̅̅̅̅ is 9 cm long
176. ∆ABC is similar to ∆DEF. AB circular wooden server on top of the table)?
̅̅̅̅
while DE is 12 cm long. If the area of ∆ABC is A. 720 B. 120 C. 36 D. 30
27 cm2, what is the area of ∆DEF?
A. 36 cm2 B. 48 cm2
C. 60 cm2 D. 72 cm2 184. In parallelogram
MATH, m∠M = 7x – 12 and
m∠T = 5x + 32. Find m∠A.
177. Find the remainder when x4 – 3x3 + 2x2 + A. 22 B. 38
3x – 9 is divided by (x-3). C. 44 D. 142
A. -18 B. -9 C. 9 D. 18

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1000 MMR Author: Victor A. Tondo Jr., LPT
185. Find the equation of the line perpendicular 193. Which of the following is false?
to 2x + 5y = 7, passing through (1, 2). A. sin2 θ + cos2 θ = 1
A. 2x + 5y = 12 B. 2x – 5y = -8 B. sin θ (csc θ) = 1
C. 5x + 2y = 9 D. 5x – 2y = 1 C. sin θ ÷ cos θ = tan θ
D. sin θ (tan θ) = cos θ

186. How many ways can the letters of the word

BANANA be rearranged? 194. If three-fourths of a number is 33 more than
A. 720 B. 240 C. 120 D. 60 its one-fifth, what is that number?
A. 240 B. 120
C.90 D. 60
187. “The temperature in Baguio City is 20o
while the temperature in Tuguegarao City is
40o”. What level of data is temperature in 195. Which of the following has the greatest
degrees Celsius? value:
A. Nominal B. Ordinal A. 3 + 32 + (3 + 3)2 B. 33
C. Interval D. Ratio C. [(3 + 3) ]
2 2 D. (3 + 3 + 3)2

188. What is formed by the intersection of two 196. Which of the following has an undefined
planes? slope?
A. a point B. a line A. a vertical line
C. a plane D. space B. a horizontal line
C. a line parallel to the x-axis
D. a diagonal line
189. What is formed when a plane intersects a
cone parallel to its circular base?
A. ellipse B. hyperbola 197. In solid geometry, what do you call a solid
C. circle D. parabola bound by polygons?
A. multigon B. tessellation
C. porygon D. polyhedron
190. In which non-Euclidean model for geometry
can we have any given line ℓ and a point A which
is not on ℓ, wherein all lines through A will 198. Tchr. Victor needs to randomly get 10 out of
intersect ℓ? his 50 students for drug testing. He proceeds by
A. hyperbolic B. elliptic making the students count off from 1 to 5. He
C. Saccheri D. Pythagorean then randomly picks a number from 1 to 5.
Which sampling method did he use?
A. stratified B. cluster
191. Which numerical system is sexagesimal C. systematic D. convenience
(base-60)?
A. Mayan B. Roman
C. Babylonian D. Hindu-Arabic 199. Which statistical test must be used in
testing the significance of group differences
between 2 or more groups?
192. Which numerical system makes use of dots A. Chi Square B. t-test
and horizontal lines, and shell shapes for zero? C. ANOVA D. Pearson R
A. Egyptian B. Roman
C. Greek D. Mayan
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1000 MMR Author: Victor A. Tondo Jr., LPT
200. Which Mathematician is famous for the 207. Victor deposited an amount of P200,000 in
Fibonacci sequence? a bank that offers 5% interest compounded per
A. Ptolemy annum. How much will he have in his account
B. Leonardo Pisano Bigollo after 3 years?
C. Pierre de Fermat A. P230,000 B. P231,525
D. Luca Pacioli C. P233,050 D. P234,575

201. Which Mathematician is famous for his last 208. Find the remainder when the polynomial
theorem? x4 – 3x3 + 2x2 – 5x + 8 is divided by (x – 3).
A. Pythagoras B. Isaac Newton A. 5 B. 8 C. 11 D. 14
C. Daniel Bernoulli D. Pierre de Fermat

209. What is 60% of 120?

202. Which of the following is a square? A. 50 B. 72 C. 180 D. 200
A. Polygon ABCD which has 4 congruent sides.
B. Polygon MATH which has 4 perpendicular
sides. 210. What percent of 80 is 55?
C. Quadrilateral HEAD which has one pair of A. 145.45% B. 135%
congruent perpendicular bisecting diagonals. C. 68.75% D. 44%
D. Quadrilateral FROG which has 4 right angles.

211. The hypotenuse of a right triangle measures

203. Which of the following is the set of points 40 cm. Find its area if one angle measures 30o.
whose sum of distance to two fixed points is A. 100√3 cm2 B. 200√2 cm2
constant? C. 200√3 cm2 D. 400√2 cm2
A. parabola B. circle
C. ellipse D. hyperbola
212. Nine cans of soda and four hamburgers cost
a total of P257. Five cans of soda and seven
204. Which of the following is not a triangle hamburgers cost a total of P224. How much is a
congruence postulate? can of soda?
A. SAS B. ASA C. SAA D. AAA A. P17 B. P19 C. P21 D. P23

205. If A is at (-8,5) and B is at (4,-11), find C if C 213. The product of two consecutive even
is three-fourths the way from A to B. numbers is 728. What is the smaller number?
A. (1, -7) B. (-4, 1) A. 22 B. 24 C. 26 D. 28
C. (1, 1) D. (-4, -7)

214. What time is 219 minutes past 6:40 AM?

206. CPCTC stands for “____________ parts of A. 8:59 AM B. 9:19 AM
congruent triangles are congruent”. C. 9:49 AM D. 10:19 AM
A. collinear B. complementary
C. corresponding D. conjugate

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1000 MMR Author: Victor A. Tondo Jr., LPT
215. Find the vertex of y = 3x2 – 2x + 11. 223. Which of the following is not a function?
1 32 1 −32 A. y = x2 + 2017x – 2017
A. (3 , 3 ) B. (3 , 3 )
−1 32 −1 −32 B. y = |2017x| - 2017
C. ( 3 , 3 ) D. ( 3 , ) C. y = √2017𝑥 + 2017
3
D. y2 = x + 2017

216. After getting a 20% discount, Mr. Lopez

paid P4,000 for a gadget. How much was its 224. 12 + 17 + 22 + 27 + … + 117 = _____
original price? A. 1409 B. 1414
A. P4,800 B. P5,000 C. 1419 D. 1424
C. P8,000 D. P20,000

225. Mr. G sold 80% of his apples and still had

217. When a number is increased by 3, its square 213 apples left. How many apples did he have
increases by 111. By what does its square originally?
increase when the number is increased by 6? A. 1704 B. 1065
A. 222 B. 240 C. 444 D. 480 C. 852 D. 293

218. How many prime numbers are there from 1 226. When a number is increased by 4, its square
to 100? also increases by 168. What is this number?
A. 23 B. 24 C. 25 D. 26 A. 15 B. 19 C. 23 D. 27

219. Find the range of f(x) = 2x2 – 8x + 9. 227. Solve for k to make a perfect square
A. y ≥ 0 B. y ≥ 1 trinomial: 9x2 + kx + 25
C. y ≥ 9 D. y ∈ ℝ A. 10 B. 15 C. 20 D. 30

𝑥 2 −100 228. Find the y-intercept of 2x + 3y = 4.

220. Find the domain of y = 𝑥 2 −49 4 3 1
A. 3 B. 4 C. 2 D. 2
A. x ≠ ±7, ±10 B. x ≠ ±7
C. x ≠ ±10 D. x ≠ 1

229. Which of the following points is on the line

221. Solve for x: (x+3)2 = (x-4)2. y = 2x + 5?
A. x = 0 B. x = ½ A. (1, 3) B. (2, 9)
C. x = 1 D. no solution C. (0, 10) D. (3, 10)

222. The diagonal of a rectangular prism is 13 230. Find the intersection of y = -2x + 1 and
cm long. If it is 3 cm thick and 12 cm long, how y = 3x + 16.
wide is it? A. (-3, 7) B. (-4, 9)
A. 3 cm B. 4 cm C. (3, -7) D. (4, -9)
C.4√3 cm D. 5 cm

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1000 MMR Author: Victor A. Tondo Jr., LPT
231. Find the slope of 3x + 5y = 7. 239. Find the slope of the line tangent to
−5 5 y = x3 – 6x2 + 2x + 7 at x = 4.
A. B.
3 3
−3 3 A. -8 B. -2 C. 2 D. 8
C. D. 5
5

240. Find the average rate of change of

232. Which of the following is a polynomial? y = x3 – 2x + 3 from x = 0 to x = 3.
A. √3𝑥 2 + 4𝑥 + 2 B. 2x + 3√𝑥 A. 5 B. 6 C. 7 D. 8
1
C. 2𝑥+5 + 3 D. √3 x + 7

241. Find the radius of x2 + y2 + 2x – 4y = 44.

233. What is the degree of the polynomial A. √39 B. 2√11 C. 7 D. 3√6
9x4 + 5x3 – 2x2 + 3x – 17?
A. 4 B. 5 C. 9 D. 10
242. Gian has 8 more P5 coins than P1 coins. If
he has a total of P106, how many P5 coins does
he have?
234. log2 32√2 = __________.
A. 13 B. 15 C. 17 D. 19
A. 2.5 B. 3.5 C. 4.5 D. 5.5

243. After using half of her budget on bills, one-

235. If y = √3𝑥 2 + 6𝑥, what is x in terms of y? third on groceries, and P270 on a shirt, Mrs. D
𝑦 2 +3 𝑦 2 −6𝑦 still had P130 left. How much was her budget?
A. x = √ –1 B. x = √ +1
3 3 A. P2400 B. P2700
𝑦 2 +6𝑦−3 𝑦 2 −6𝑦+3 C. P3000 D. P3300
C. x = √ +1 D. x = √ –1
3 2

244. x varies directly as y and inversely as z. If

236. Which of the following is a pair of parallel x = 24 when y = 32 and z = 4, what is x when
lines? y = 21 and z = 7?
A. y = 2 and x = 2 A. 3 B. 5 C. 7 D. 9
B. 12x + 13y = 14 and 13x + 14y = 15
C. y = 3x + 8 and 3y = x + 9
D. 4x + 5y = 6 and 8x + 10y = 21 245. Find the mode of the following scores:
78 78 78 78 79 79 79
79 80 80 80 80
237. Which of the following is a pair of A. 79 B. 78, 79, and 80
perpendicular lines? C. 80 D. no mode
A. x = 5 and y = 7
B. y = x and 2y = 4x + 5
C. x = 2y + 3 and 2x + 3y = 4 246. The average grade of 23 students in Section
D. y = 5x + 6 and y = 0.2x – 8 A is 86, while the average grade of 27 students in
Section B is 91. What is the average grade of all
50 students in both sections?
238. Find the altitude to the hypotenuse of a A. 88.5 B. 88.6 C. 88.7 D. 88.8
right triangle whose sides measure 5 cm, 12 cm,
and 13 cm.
60 156 65
A. 13 B. 5 C. 12 D. 26

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1000 MMR Author: Victor A. Tondo Jr., LPT
247. Find the axis of symmetry of y = 3x2 – 5x. 254. Find the equation of the circle with center at
5 −5 (2, 3), passing through (5, -1).
A. x = B. x =
3 3
5 −5 A. x2 + y2 + 4x + 6y = 0
C. x = 6 D. x = B. x2 + y2 + 4x + 6y = 12
6
C. x2 + y2 – 4x – 6y = 0
D. x2 + y2 – 4x – 6y = 12
248. Find the range of the following scores:
19 25 24 31 23 29 33
A. 12 B. 13 C. 14 D. 15 255. Find the equation of the vertical line passing
through (-3, 4).
A. x = -3 B. x = 4
249. Mr. C travels for 2 hours at a speed of 38 C. y = -3 D. y = 4
kph and then north for 3 hours at a speed of 53
kph. What is his average speed?
A. 44 kph B. 45.5 kph 256. Find the equation of the horizontal line
C. 47 kph D. 48.5 kph passing through (-3, 4).
A. x = -3 B. x = 4
C. y = -3 D. y = 4
250. Victor, Chris, and Aira volunteered to teach
at a nearby daycare. Chris worked for 2 hours
less than Aira. Victor worked twice as many 257. Which of the following lines passes through
hours as Chris. Altogether, they worked for 58 the point (3, -2)?
hours. How many hours did Victor work? A. y = x + 5 B. y = 2x – 8
A. 14 B. 16 C. 28 D. 32 C. y = 5 – x D. y = 5 – 2x

251. What conic figure does the equation 258. Given that I(2, -3) is the midpoint of V(-4, 5)
x2 + y2 + 4x = -4 form? and C, find the coordinates of C.
A. Real circle B. Degenerate circle A. (-1, 1) B. (1, -1)
C. Imaginary circle D. Ellipse C. (8, -11) D. (-10, 16)

252. What conic figure does the equation 259. The endpoints of the diameter of a circle are
x2 + y2 + 8x – 6y = -100 form? A(9, -5) and B(-3, 11). What is the equation of
A. Real circle B. Degenerate circle the circle?
C. Imaginary circle D. Ellipse A. (x – 3)2 + (y – 3)2 = 100
B. (x – 3)2 + (y – 3)2 = 400
C. (x + 3)2 + (y + 3)2 = 100
253. Find the center of x2 + y2 + 6x – 10y = 2. D. (x + 3)2 + (y + 3)2 = 400
A. (6, -10) B. (-6, 10)
C. (-3, 5) D. (3, -5)
260. Find the distance between the line
3x + 4y – 5 = 0 and the point (8, -1).
A. 2 B. 3 C. 4 D. 5

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1000 MMR Author: Victor A. Tondo Jr., LPT
261. B is one-fourth of the way from A(-13,9) to 267. Which of the following equations pertain to
C(7,-7). Find the coordinates of B. a parabola that opens to the right?
A. (2, -3) B. (-8, 5) A. 4(y + 3) = (x – 2)2
C. (2.5, -3.5) D. (-7.5, 5.5) B. -3(y – 4) = (x + 5)2
C. (y – 6)2 = 5(x + 1)
D. (y + 8)2 = -2(x – 3)
261. Find the area of the triangle whose vertices
are X(-9, -3), Y(-2, 8), and Z(5, 1).
A. 61 B. 62 C. 63 D. 64 268. Which of the following equations pertain to
a parabola that opens downward?
A. 4(y + 3) = (x – 2)2
262. Which of the following is outside the circle B. -3(y – 4) = (x + 5)2
defined by the equation (x – 3)2 + y2 = 40? C. (y – 6)2 = 5(x + 1)
A. (5, 6) B. (7, 5) D. (y + 8)2 = -2(x – 3)
C. (0, -5) D. (-1, 4)

269. How long is the latus rectum of the parabola

263. Which of the following is parallel to the line defined by 12(y – 4) = (x + 3)2?
defined by the equation y = 3x – 4? A. 12 B. 6 C. 4 D. 3
A. y + 3x = 5
B. x + 3y = 6
−1
C. y = 3 x + 7 270. How far is the vertex from the directrix of
the parabola defined by 16y = x2?
D. y = 3x + 8
A. 16 B. 8 C. 4 D. 2

264. Which of the following is perpendicular to

271. Find the equation of the directrix of the
the line defined by the equation y = 3x – 4?
parabola defined by (y – 2)2 = -4(x + 3).
A. y + 3x = 9 B. -x + 3y = 10
−1 A. x = -2 B. x = 2
C. y = 3 x + 11 D. y = 3x – 12 C. y = -4 D. y = -2

265. Which of the following is coincidental to the 272. Find the coordinates of the focus of the
line defined by the equation y = 2x + 13? parabola defined by -12(y – 4) = (x + 5)2.
A. y + 2x = 13 B. 2x – y + 13 = 0 A. (-5, 7) B. (-5, 1)
−1 C. (-8, 4) D. (-2, 4)
C. y = 2 x + 13 D. 2y = 2x + 13

273. In which quadrant would G(3,-4) fall?

266. Which of the following equations pertain to
A. First quadrant B. Second quadrant
a parabola?
C. Third quadrant D. Fourth quadrant
A. y2 + 5y = x
B. x2 + y2 + 3x – 4y = 0
(𝑥−2)2 (𝑦+3)2
C. + =1 274. Find the distance between the parallel lines
64 25
(𝑥+4)2 (𝑦−5)2 y = 3x + 9 and y = 3x – 12.
D. − =1
16 49 21√10 12√10
A. 7 B. 21 C. D.
10 5

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1000 MMR Author: Victor A. Tondo Jr., LPT
275. Find the intersection of the lines y = 2x + 5 282. Which of the following is NOT a cofunction
and y = -4x + 23. identity?
A. (3, 10) B. (3, 11) A. cos θ = sin (90 – θ)
C. (4, 10) D. (4, 11) B. cot (90 – θ) = tan θ
C. sec θ = csc (90 – θ)
D. csc θ = sin (90 – θ)
276. Which of the following pertains to a circle
that is concentric with (x – 3)2 + y2 = 24?
A. x2 + y2 – 6x + 3 = 0 283. The hypotenuse of a 30-60-90 triangle is 48
B. x2 + y2 + 6y –15 = 0 cm long. How long is its shortest side?
C. x2 + y2 + 6x – 25 = 0 A. 24 cm B. 24 √2 cm
D. x2 + y2 + 6x + 6y – 24= 0 C. 24 √3 cm D. 16√3 cm

277. Which of the following is the equation of the 284. In a right triangle, the side opposite an
parabola that opens upward, whose latus rectum angle measuring 50o is 100 cm long. How long is
is 12 units long, directrix is y = -3, and line of the side adjacent to the 50o angle?
symmetry is x = 7? A. 93.45 cm B. 83.91 cm
A. 12y2 = x – 7 C. 149.14 cm D. 200 cm
B. 12y = (x – 7)2
C. 12(y + 3) = (x – 7)2
D. 12(y – 3) = (x – 7)2 285. A hundred cards are numbered 1 to 100.
What is the probability of drawing a card whose
number is divisible by seven?
5𝜋 7 1 7 98
278. Convert rad to degrees. A. 100 B. 7 C. 50 D. 100
12
A. 1.309o B. 75o
C. 150o D. 216o
286. What is the probability of rolling a sum of
10 when rolling two dice?
1 1 1 1
279. Which of the following angles is coterminal A. 10 B. 11 C. 12 D. 13
with 143o?
A. 217o B. -37o
C. 323o D. 503o 287. Factorize 3x2 + 5x – 2.
A. (3x – 1) (x + 2) B. (3x + 1) (x – 2)
C. (3x – 2) (x + 1) D. (3x + 2) (x – 1)
280. Which of the following is NOT a
trigonometric identity?
A. sin2 θ + cos2 θ = 1 288. Six-sevenths of a number is 6 less than nine-
sin θ
B. tan θ = cos θ tenths of the same number. What is the number?
C. 1 + tan2 θ = sec2 θ A. 130 B. 140 C. 200 D. 210
D. 1 – cot2 θ = csc2 θ

281. Which of the following is false?

1 1
A. tan θ = cot θ B. csc θ = sin θ
1 1
C. cos θ = sec θ D. sec θ = sin θ

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1000 MMR Author: Victor A. Tondo Jr., LPT
289. A certain University has a dormitory. If 10 295. Determine the relation that matches the
students stay in a room, 24 students will not table of values.
have a room. If 12 students stay in a room, there x 1 2 3 4 5
will be 6 vacant beds. How many rooms are there y 13 11 9 7 5
in the dormitory? How many students are A. y = 21 – x B. y = 15 – 2x
staying in the dormitory? C. y = 3x + 7 D. y = 2x + 11
A. 116 B. 115 C. 114 D. 113

296. Determine which polynomial expression

−2
290. Which of the following is not between matches the algebra tile model.
5
−3
and ?
4
−4 −13 −1 −3
A. B. C. D. A. 2x2 + x + 4 B. 3x2 + x + 4
5 20 2 5
C. 3x2 – x + 4 D. 3x2 + x – 5

291. Which value describes the position of C?

297. Subtract: (–2x2 + 5x – 9) – (2x – 7)
A. 2x2 + 3x + 16 B. -2x2 + 3x + 2
A. -0.75 B. -0.6 C. -1.25 D. -1.4 C. -2x2 + 3x – 2 D. -2x2 + 7x + 2

292. Choose the correct value of (x + y)(x – y) 298. Evaluate the polynomial 4x2 – 6x – 3 if x = 2.
when x = 3.5 and y = –8.7 A. -1 B. 1 C. 3 D. 5
A. -63.44 B. 63.44
C. -148.84 D. 10.4
299. Determine the measure of ∠Y and ∠Z.

293. Which two triangles are similar?

A. 45o, 55o B. 40o, 50o

C. 48o, 48o D. 50o, 50o
A. A and B B. A and C
C. B and D D. B and C
300. Which of the following is equal to x?

294. Determine which equation is equivalent to

4x – 1 = 11.
A. 4x = 10 B. 3x = 11
C. 4 – 1x = 11x D. 4x = 12 A. 15 sin 72o B. 15 sin 18o
C. 72 sin 72o D. 72 sin 18o

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1000 MMR Author: Victor A. Tondo Jr., LPT
301. Find the points of intersection of the graphs
of y = x2 and y = 3x – 2.
A. (1, 1) and (1, 4) B. (1, 1) and (2, 4)
C. (1, -1) and (2, 4) D. (-2, 4) and (1, 1)
C. D.
302. An approximate value for
302476.984302145𝑥0.0403289925
is: 308. Which expression is equivalent to (9-2)8?
5962.47558321
1 1
A. 2 B. 20 A. -8132 B. -818 C. 916 D. 910
C. 200 D. 2000

309. What is 5 × 10–4 written in standard

303. The graph below represents the motion of a notation?
car. The graph shows us that the car is: A. 0.00005 B. 0.0005
C. 5,000 D. 50,000

310. What is the value of 54 × 5-6?

−1 1
A. accelerating A. -25 B. 25 C. 25 D. 25
B. standing still
C. travelling north-east
D. travelling at a constant speed 311. . Which comparison is true?
A. 4 < 180.5 < 4.5 B. 4.5 < 180.5 < 5
C. 8.5 < 18 < 9.5
0.5 D. 17 < 180.5 < 19
304. The units digit of the number 543444 is:
A. 3 B. 9 C. 7 D. 1
312. A weather station recorded the amount of
rain that fell during an 8-hour time frame using a
305. 4n+1 (4n+2) equals rain gauge. The findings are recorded in the
A. 42n + 3 B. 82n + 3 graph below.
C. 162n + 3 D. 4n + 3

306. The greatest number of Fridays that can

occur in a 75 day period is:
A. 10 B. 11 C. 12 D. 13

307. Which model is not a function?

Between which hours was the rate at which the

rain fell greater than the rate at which the rain
fell between hours 0 and 1?
A. B. A. between hours 3 and 4
B. between hours 4 and 5
C. between hours 5 and 6
D. between hours 7 and 8

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1000 MMR Author: Victor A. Tondo Jr., LPT
312. Each day of the month, Carl earns an 316. Praetor jogged on a path that was 2 miles
allowance, in cents, equal to the square of that long, took a break, and then jogged back along
date of the month. Which is a number of cents the same path to where he started. He jogged at
Carl could earn in a single day? different speeds for different distances along the
A. 21 B. 31 C. 64 D. 111 path as shown in the graph.

313. Which set of ordered pairs models a

function?
A. {(2, 9), (7, 5), (3, 14), (2, 6)}
B. {(5, 10), (5, 15), (5, 20), (5, 25)}
C. {(3, 10), (4, 15), (5, 20), (3, 25)}
D. {(–10, 20), (–20, 30), (–30, 40), (–40, 10)}

314. Rayon has a piece of rectangular paper that Between which times did Praetor jog the fastest?
is 12 inches wide by 16 inches long. He drew a A. 0 minutes and 10 minutes
straight line along the diagonal of the paper. B. 10 minutes and 25 minutes
What is the length of the line Rayon drew? C. 25 minutes and 30 minutes
A. √28 inches B. √192 inches D. 30 minutes and 60 minutes
C. 20 inches D. 28 inches

317. Which expression has a value of -2?

315. Which equation has infinitely many A. |2| + |-4| B. |-2| – |4|
solutions? C. |4| – |-2| D. |-4| + |2|
A. 2x + 4 = 7x + 9
B. 3(2x + 5) = 6x + 15
C. 4x + 13 = 5x + (20 – x) 318. Reion is tossing a six-sided number cube
D. x + 3 = 5x – 21 labeled 1, 2, 3, 4, 5, and 6. What is the probability
of tossing 6 twice in a row?
1 1 1 1
A. 12 B. 3 C. 36 D. 2

319. Which represents the value of x in

6 – 4x ≥26?
A. x ≤ -8 B. x ≥ -8
C. x ≤ -5 D. x ≥ -5

320. The table below shows the resting heart

rates in beats per minutes of six students. The
rate, 40 beats per minute, seems to be an outlier.
Which measure of central tendency changes the
least by dropping 40 from the data?
Heart
Rate
78 71 79 80 40 71
A. mean B. median
C. mode D. range

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1000 MMR Author: Victor A. Tondo Jr., LPT
321. The sum of a number, n, and 5 is subtracted 328. Which of the following is closest to the
from 8. Which expression represents this value of the expression below?
statement? (20.0143642359)2 x 8π
A. 8 – (n + 5) B. (n + 5) + 8 A. 1,000 B. 10,000
C. (n + 5) – 8 D. 8 + (n + 5) C. 100,000 D. 1,000,000

322. How is 0.5600 written in scientific notation? 329. Which of the following expressions has a
A. 5.6 × 10 B. 5.6 × 10-1 value of 0?
C. 5.6 × 10-2 D. 5.6 × 10-3 A. (2 – 3) – (2 – 3) B. (2 – 3) – |2 – 3|
C. (2 – 3) + (-3 + 2) D. |2 – 3| – (2 – 3)

323. What is the value of x in 3(x – 4) = –21?

A. x = –11 B. x = –3 330. What is the factorization of 10x2 – x – 21?
C. x = 3 D. x = 11 A. (5x – 7) (2x + 3) B. (5x + 7) (2x – 3)
C. (5x + 3) (2x – 7) D. (5x – 3) (2x – 7)

324. In the spinner, what is the probability of the

arrow NOT landing on the space with the ∆? 331. Evaluate: (√343)2
A. 7√7 B. 49 C. 49√7 D. 343

332. Find the length of the latus rectum of the

(𝑥−3)2 (𝑦+5)2
1 1 2 3 ellipse defined by + = 1.
25 16
A. 4 B. 2 C. 3 D. 4 32 25 16 25
A. B. C. D.
5 2 5 4

325. Which values of x and y make the system of

equations below true? 333. Let A be a set such that A = {v, w, x, y, z}.
2x - y = -1 How many subsets does set A have?
3x - y = -3 A. 5 B. 10 C. 25 D. 32

A. x = -4; y = -7 B. x =-2; y = -3
C. x = 2; y = 5 D. x = 4; y = 15 334. Solve for x:
2 (5x – 11) + 7 = 3 (x – 7) – 15
A. x = 3 B. x = 1
326. The lengths of two sides of a triangle are 8 C. x = -1 D. x = -3
inches and 13 inches. Which of the following
represents x, the possible length in inches of the
remaining side of the triangle? 335. What is the 4th term in the expansion of
A. 5 < x < 21 B. 5 ≤ x ≤ 21 (2x + 3y)7?
C. x < 5 or x > 21 D. x ≤ 5 or x ≥ 21 A. 15120 x4y3 B. 7560 x4y3
C. 3780 x3y4 D. 1890 x3y4

327. What is the value of the expression

below?
80 ÷ ( 6 + (3 – 5) x 2)
A. -8 B. 8 C. 10 D. 40

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1000 MMR Author: Victor A. Tondo Jr., LPT
336. The shell shape , as used in the Mayan 343. A ride in a Feak Taxi costs P25.00 for the
numeral system, is the symbol for which first km and P10.00 for each additional km.
number? Which of the following could be used to calculate
A. 100 B. 10 C. 1 D. 0 the total cost, y, of a ride that was x km?
A. y = 25x + 10
B. y = 10x + 25
337. Which of the following is irrational? C. y = 25(x − 1) + 10
̅̅̅̅̅
A. 0.125 B. 43.29% D. y = 10(x − 1) + 25
3
C. √200 D. √343

344. Which of the following points is in the

338. Aira is six years older than Zayne. Six years fourth quadrant?
ago, she was twice as old as he. How old is Aira A. (3, 4) B. (-3, 4)
now? C. (3, -4) D. (-3, -4)
A. 21 B. 18 C. 15 D. 12

345. The distance from the sun to the earth is

339. The two parallel sides of a trapezoidal lot approximately 9.3 × 107 miles. What is this
measure 100m and 70m. If these sides are 80m distance expressed in standard notation?
apart, what is the area of the lot? A. 9,300,000,000 B. 930,000,000
A. 13600 m2 B. 6800 m2 C. 93,000,000 D. 651
C. 3400 m2 D. 2400 m2

346. The square of a number added to 25 equals

340. If y = x and y = 2x + 2, find the value of x. 10 times the number. What is the number?
A. x = -2 B. x = -1 A. -10 B. -5 C. 5 D. 10
C. x = 0 D. x = 1

347. The sum of the square of a number and 12

341. If the difference between the squares of two times the number is −27. What is the smaller
consecutive counting numbers is 49, what is the possible value of this number?
larger number? A. -9 B. -3 C. 3 D. 9
A. 99 B. 49 C. 25 D. 7

348. Let x = 1. Find the corresponding y given

342. Rayon needed to find the perimeter of an that 2x − 3y = 5.
equilateral triangle whose sides measure x + 4 A. y = -1 B. y = 1
cm each. Jake realized that he could multiply C. y = 3 D. y = -3
3 (x + 4) = 3x + 12 to find the total perimeter in
terms of x. Which property did he use to
multiply? 349. The sum of two consecutive even integers is
A. Associative Property of Addition 126. What is the smaller integer?
B. Distributive Property of Multiplication over A. 63 B. 62 B. 61 D. 60
Addition
C. Commutative Property of Multiplication
D. Inverse Property of Addition

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1000 MMR Author: Victor A. Tondo Jr., LPT
350. Factorize: a2 – a – 90 358. The cost of renting a bike at the local bike
shop can be represented by the equation
A. (a – 10) (a + 9)
y = 2x + 2, where y is the total cost and x is the
B. (a + 10) (a + 9)
number of hours the bike is rented. Which of the
C. (a + 10) (a – 9)
following ordered pairs would be possible
D. (a – 10) (a – 9)
number of hours rented and the corresponding
total cost?
A. (0, −2) B. (2, 6)
351. Evaluate 10P5.
C. (6, 2) D. (−2, −6)
A. 2 B. 100,000
C. 1,024 D. 30,240
359. The distance from the earth to the moon is
approximately 240,000 miles.
352. Jay bought twenty-five P4.57 stamps. How
What is this distance expressed in scientific
much did he spend?
notation?
A. P 104.25 B. P 114.25
A. 24 × 104 B. 2.4 × 104
C. P 119.75 D. P124.25
C. 2.4 × 105 D. 2.4 × 10−5

353. Given f(x) = x3 + kx2 – 7, find k if f(2) = 41. 𝑥−1 𝑥 2 −4

A. 5 B. 10 C. 15 D. 20 360. 𝑥+2 ∙ 𝑥 2 −1 =
𝑥−1 𝑥+1 𝑥−2 𝑥+2
A. 𝑥+2 B. 𝑥−2 C. 𝑥+1 D. 𝑥−1
354. If y = x and y = 2x + 2, find x + y.
A. -8 B. -4 C. 0 D. 4
361. The sum of two angles is 180°. The measure
of one angle is 34° greater than the measure of
355. Mulan and Lilo are competing to see who the other angle. What is the measure of the
can sell the most candy bars for a fundraiser. smaller angle?
Mulan sold 4 candy bars on the first day and 2
A. 74° B. 73° C. 72° D. 71°
each day after that. Lilo sold 7 on the first day
and 1 each day after that. On what day will they
have the same number of candy bars sold?
362. Solve the following system of linear
A. 7th B. 6th C. 4th D. 3rd
equations:
3x + y = -9
−3x − 2y = 12
356. Which of the following is not a polynomial?
2 A. (−2, −3) B. (2, 3)
A. -3x2 + 3x – 9 B. √2x + π C. (3, 2) D. (−3, −2)
2
𝑥 3 −√5𝑥2 +2𝑥−9
C. D. 7𝑥 3 + 9
7

363. Find the x-intercept of 3x + 2y = 24

A. x = 8 B. x = -8
357. Factorize: 3p2 – 2p – 5 C. y = 12 D. y = -12
A. (3p – 5) (p + 1) B. (3p + 5) (p – 1)
C. (3p + 1) (p – 5) D. (3p – 1) (p + 5)

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1000 MMR Author: Victor A. Tondo Jr., LPT
364. A circle is drawn such that ̅̅̅̅
𝐴𝐵 is a diameter 370. Ten factorial is equal to _____.
and its midpoint is O. Given that C is a point on A. 100
the circle, what is the measure of ∠ACB? B. e10
A. 180o B. 90o C. 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
C. 60o D. not enough info D. 10e

365. Samantha owns a rectangular field that has 371. How many 3-digit numbers can be made
an area of 3,280 square meters. The length of the using the digits 5, 6, 7, 8, 9, and 0 if repetition is
field is 2 more than twice the width. What is the not allowed?
width of the field? A. 80 B. 100 C. 120 D. 140
A. 40 m B. 41 m
C. 82 m D. 84 m
372. A researcher is curious about the IQ of
students at the Utrecht University. The entire
366. Rayon used the following mathematical group of students is an example of a:
statement to show he could change an A. parameter B. statistic
expression and still get the same answer on both C. population D. sample
sides:
10 × (6 × 5) = (10 × 6) × 5
Which mathematical property did Rayon use? 373. Jordan filled a bottle with grains until it was
1/4 full and weighed 8 kg. He added more grains
A. Identity Property of Multiplication
into the bottle until it was 7/8 full. It now
B. Commutative Property of Multiplication
weighed 18 kg. What is the mass of the empty
C. Distributive Property of Multiplication over
bottle?
Addition
A. 16 B. 8 C. 4 D. 2
D. Associative Property of Multiplication

374. If 37 – 4x < 17, then

367. Factorize x3 – 27y3.
A. x < 5 B. x > 5
A. (x – 3y) (x2 – 3x + 9y2)
C. x < -5 D. x > -5
B. (x – 3y) (x2 + 3x + 9y2)
C. (x + 3y) (x2 + 3x – 9 y2)
D. (x + 3y) (x2 – 3x + 9 y2)
375. How many solutions are there for the
following system of linear equations?
-3x + 5y = 6
368. What is the intersection of the lines
6x −10y = 0
x + 3y = 5 and -2x + 4y = 0?
A. (2, 4) B. (-2, 1) A. only one solution
C. (2, 1) D. (-2, 4) B. two solutions
C. infinitely many solutions
D. no solution
369. Given f(x) = 7x3 – 3x2 + 2x – 9, f(2) =
A. 56 B. 48 C. 44 D. 39

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1000 MMR Author: Victor A. Tondo Jr., LPT
376. Find a and b so that the system below has 382. A teacher asks students to identity their
the unique solution (-2, 3). favorite reality television show. What type of
ax + by = 17 measurement scale do the different television
2ax − by = −11 shows make up?
A. Nominal B. Ordinal
A. a = −3, b = -1 B. a = −1, b = 5
C. Interval D. Ratio
C. a = 1, b = 3 D. a = 1, b = 5

383. What is the center of the circle defined by

377. What is the probability choosing only one
x2 + y2 – 8x + 6y – 10 = 0?
vowel when three letters are randomly selected
A. (-8, 6) B. (8, -6)
from the word NUMBERS?
3 4 5 67 C. (-4, 3) D. (4, -3)
A. 7 B. 7 C. 7 D. 140

384. Find the equation of the line passing (1, 4)

378. If A > B, which is always true? with slope equal to 5.
1 1
A. 𝐴 > 𝐵 B. A2 > B2 A. y = 5x + 3 B. y = 5x + 1
C. A < B + 2 D. A – B > 0 C. y = 5x – 1 D. y = 5x – 3

379. Statistical techniques that summarize and 385. The seminar rooms in the library are
organize the data are classified as what? identified by the letters A to H. A researcher
A. Population statistics records the number of classes held in each room
B. Sample statistics during the first semester. What kind of graph
C. Descriptive statistics would be appropriate to present the frequency
D. Inferential statistics distributions of these data?
A. Histogram B. Scatterplot
C. Bar chart D. Box plot
380. Five-point Likert scales (strongly disagree,
disagree, neutral, agree, strongly agree) are
frequently used to measure motivations and 386. Find the slope of the line passing the points
attitudes. A Likert scale is a: A(2, 3) and B(-7, -15).
A. Discrete variable. A. 1 B. -1 C. ½ D. 2
B. Ordinal variable.
C. Categorical variable.
D. All of the above 387. Factorize: 3n2 – 8n + 4
A. (3n – 2) (n – 2)
B. (3n – 2) (n + 2)
381. What is the radius of the circle defined by C. (3n + 2) (n + 2)
(x + 2)2 + (y – 3)2 = 16? D. (3n + 2) (n – 2)
A. 256 B. 16 C. 8 D. 4

388. In now many ways can the letters

AAABBCDEEE be arranged in a straight line?
A. 50,400 B. 25,200
C. 12,600 D. 6,300

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1000 MMR Author: Victor A. Tondo Jr., LPT
389. Find the smaller angle formed by the x-axis 395. Find the number of subsets having 4
and the line y = 5x. elements of the set {1,2,3,4,5,6,7,8,9,10,11}.
A. 78.69o B. 63.48o A. 165 B. 330
C. 54.15o D. 41.32o C. 660 D. 1320

390. Convert 48o to radians. 396. There are ten true - false questions in an
8 7
A. 15 π rad B. 15 π rad exam. How many responses are possible?
4 2 A. 1024 B. 256 C. 20 D. 10
C. 15 π rad D. 15 π rad

397. In a 500m speed skating race, time results

391. The median is always: would be considered an example of which level
A. The most frequently occurring score in set of of measurement?
data A. Nominal B. Ordinal
B. The middle score when results are ranked in C. Interval D. Ratio
order of magnitude
C. The same as the average
D. The difference between the maximum and 398. In how many ways can 4 girls and 5 boys be
minimum scores. arranged in a row so that all the four girls are
together?
A. 4,320 B. 8,640
392. A teacher gave a statistics test to a class of C. 17,280 D. 34,560
Geography students and computed the measures
of central tendency for the test scores. Which of
the following statements cannot be an accurate 399. A box contains 8 batteries, 5 of which are
description of the scores? good and the other 3 are defective. Two batteries
A. The majority of students had scores above the are selected at random and inserted into a toy. If
mean. the toy only functions with two good batteries,
B. The majority of students had scores above the what is the probability that the toy will function?
median. 5 5 5 15
A. 8 B. 14 C. 28 D. 56
C. The majority of students had scores above the
mode.
D. All of the above options (A, B and C) are false
400. IQ tests are standardized so that the mean
statements.
score is 100 for the entire group of people who
take the test. However, if you select a group of 50
who took the test, you probably would not get
393. Find the area of a semicircle whose radius
100. What statistical concept explains the
measures 28 cm.
difference between the two means?
A. 784 π cm2 B. 392 π cm2
A. Statistical error B. Inferential error
C. 28 π cm 2 D. 14 π cm2
C. Residual error D. Sampling error

394. Find the length of each side of an equilateral

401. Which Mathematician pioneered the study
triangle whose perimeter is 90 cm.
A. 45 cm B. 30 cm of conic sections?
A. Euclid B. Apollonius
C. 22.5 cm D. 10 cm
C. Archimedes D. Hipparchus

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1000 MMR Author: Victor A. Tondo Jr., LPT
402. A researcher studies the factors that 408. Which of the following sets of scores has the
determine the number of children future couples greatest variability or range?
decide to have. The variable ‘number of children’ A. 2, 5, 8, 11 B. 13, 13, 13, 13
is a: C. 20, 25, 26 ,27 D. 42, 43, 44, 45
A. Discrete variable
B. Continuous variable
C. Categorical variable 409. This Mathematician was the first to describe
D. Ordinal variable a pinwheel calculator in 1685 and invented the
wheel named in his honor, which was used in the
arithmometer, the first mass-produced
403. Surface area and volume, center of gravity, mechanical calculator. He also refined the binary
and hydrostatics are some of the studies of number system, which is the foundation of all
which Mathematician? digital computers. Which Mathematician is this,
A. Apollonius B. Euclid who is also crucial to the development of
C. Archimedes D. Hipparchus computers?
A. Gottfried Wilhelm Leibniz
B. Charles Babbage
404. The book Philosophiæ Naturalis Principia C. Ada Lovelace
Mathematica, more fondly known simply as D. Alexander Graham Bell
Principia, is the work of which Mathematician?
A. Euclid B. Newton
C. Einstein D. Archimedes 410. Solve for x, given 9x – 10 = 11x + 30
A. x = 40 B. x = 20
C. x = -20 D. x = -40
405. A researcher is interested in the travel time
of Rayon’s University students to college. A
group of 50 students is interviewed. Their mean
411. Using Calculus, this Mathematician
travel time is 16.7 minutes. For this study, the
explained why tides occur, why the shapes of
mean of 16.7 minutes is an example of a
planetary orbits are conic sections, and how to
A. parameter B. statistic
get the shape of a rotating body of fluid, among
C. population D. sample
many other things. Which Mathematician is this?
A. Kepler B. Euclid
C. Apollonius D. Newton
406. Who is considered by many Mathematicians
as “The Last Universalist”?
A. Jules Henri Poincare
412. Which of the following terms does NOT
B. Hendrik Lorentz
describe the number 9?
C. Georg Cantor
A. rational number B. integer
D. Gottfried Wilhelm Leibniz
C. real number D. prime number

407. In the theory he developed, there are

infinite sets of different sizes (called 413. Which expression below is equal to 5?
cardinalities). Which Mathematician formalized A. (1 + 2)2 B. 9 – 22
many ideas related to infinity and infinite sets C. 11 − 10 × 5 D. 45 ÷ 3 × 3
during the late 19th and early 20th centuries?
A. Jules Henri Poincare
B. Hendrik Lorentz
C. Georg Cantor
D. Gottfried Wilhelm Leibniz
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1000 MMR Author: Victor A. Tondo Jr., LPT
414. A bus picks up a group of tourists at a hotel. 421. Of the following Z-score values, which one
The sightseeing bus travels 2 blocks north, 2 represents the location closest to the mean?
blocks east, 1 block south, 2 blocks east, and 1 A. Z = +0.5 B. Z = +1.0
block south. Where is the bus in relation to the C. Z = -1.5 D. Z = -0.3
hotel?
A. 2 blocks north B. 1 block west
C. 3 blocks south D. 4 blocks east 422. The sum of five consecutive integers is 215.
What is the largest of these integers?
A. 43 B. 44 C. 45 D. 46
415. When five is added to three more than a
certain number, the result is 29. What is the
number? 423. You go to the cafeteria for lunch and have a
A. 24 B. 21 C. 8 D. 4 choice of 4 entrees, 5 sides, 5 drinks, and 4
desserts. Assuming you have one of each
category, how many different lunches could be
416. The math club is electing new officers. made?
There are 3 candidates for president, 4 A. 18 B. 81 C. 40 D. 400
candidates for vice-president, 4 candidates for
secretary, and 2 candidates for treasurer. How
many different combinations of officers are 424. What can be said about the following
possible? statements?
A. 13 B. 96 i. Any quadrilateral with four congruent sides is
C. 480 D. 17,160 a square.
ii. Any square has four congruent sides.
A. Only the first statement is true.
417. Twelve points lie on a circle. How many B. Only the second statement is true.
cyclic quadrilaterals can be drawn by using these C. Both statements are true.
points? [Note: Cyclic quadrilaterals are D. Both statements are fall.
quadrilaterals whose vertices are on a circle.]
A. 48 B. 495
C. 11,880 D. 1,663,200 425. Out of 6 boys and 4 girls, a committee of 5
has to be formed. In how many ways can this be
done if we take 2 girls and 3 boys?
418. What is the variance for the following set of A. 120 B. 186 C. 240 D. 256
scores? 143 143 143 143 143 143
A. 0 B. 2 C. 4 D. 25
426. In the figure, which of the following will
yield the value of the hypotenuse x?
419. When 18 is subtracted from six times a
certain number, the result is −42. What is the
number?
A. 10 B. 4 C. -4 D. -10
10 10
A. x = sin 35° B. x = cos 35°
10
420. Find the equation of the line passing (2, 3) C. x = tan 35° D. x = 10 tan 35o
and (-7, -15)
A. y = 2x + 1 B. y = 2x – 1
C. y = x + 2 D. y = x – 2

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1000 MMR Author: Victor A. Tondo Jr., LPT
427. The shortest side of a 30-60-90 triangle is 434. Which triangle has the centroid, incenter,
20.19 cm long. How long is the hypotenuse? circumcenter, orthocenter, and nine-point-center
A. 40.38 cm B. 30.29 cm at the same location?
C. 34.97 cm D. 17.48 cm A. isosceles right triangle
B. 30-60-90 triangle
C. equilateral triangle
428. The hypotenuse of a 30-60-90 triangle is D. hyperbolic triangle
34.96 cm long. How long is the shortest side?
A. 40.38 cm B. 30.29 cm
C. 34.97 cm D. 17.48 cm 5
435. Given cos θ = 13 and θ ∈ QIV, find tan θ.
12 −12 5 −5
A. B. C. 12 D. 12
5 5
429. The second angle of a triangle is three times
as large as the first. The measure of the third
angle is 40 degrees greater than that of the first 436. Find the measure of ∠T:
angle. How large is the first angle?
A. 28o B. 30o C. 35o D. 38o

430. Normally distributed data are normally

referred to as:
A. Bell-shaped B. Asymmetrical A. 59o B. 69o C. 79o D. 89o
C. Skewed D. Peaked
437. If the scores on a test have a mean of 26 and
431. A population has a mean of μ=35 and a a standard deviation of 4, what is the z-score for
standard deviation of σ=5. After 3 points are a score of 18?
added to every score of the population, what are A. -1.41 B. 11 C. -2 D. 2
the new values for the mean and standard
deviation?
A. μ=35 and σ=5 438. If a researcher sets a level of significance at
B. μ=35 and σ=8 0.05 (i.e. 5%), what does this mean?
C. μ=38 and σ=5 A. Five times out of 100, a significant result will
D. μ=38 and σ=8 be found that is due to chance alone and not to
true relationship.
B. Ninety-five times out of 100, a significant
7 result will be found that is due to chance alone
432. Given sin θ = 25, find cos θ.
and not to true relationship.
24 21 18 16
A. 25 B. 25 C. 25 D. 25 C. Five times out of 100, a significant result will
be found that is not due to chance, but to true
relationship.
433. In a triangle, what is located 2/3 of the D. None of the above
distance from each vertex to the midpoint of the
opposite side?
A. centroid B. incenter 439. When does a researcher risk a Type I error?
C. circumcenter D. orthocenter A. Anytime the decision is ‘fail to reject’.
B. Anytime H0 is rejected.
C. Anytime Ha is rejected.
D. All of the above options
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1000 MMR Author: Victor A. Tondo Jr., LPT
440. Solve for x: 446. How much water must be evaporated from
2000 mL of 30% acid solution to make a 50%
acid solution?
A. 800 mL B. 850 mL
C. 900 mL D. 950 mL

447. Which of the following is the intersection of

A. 4 B. 5 C. 6 D. 7 angle bisectors of a triangle?
A. circumcenter B. incenter
C. centroid D. orthocenter
441. Which of the following is equidistant from
the vertices of the triangle?
A. circumcenter B. orthocenter 448. In terms of a conditional statement, what is
C. incenter D. centroid the statement formed by exchanging and
negating the antecedent and the consequent?
A. inverse B. converse
442. Which of the following is equidistant from C. adverse D. contrapositive
the sides of the triangle?
A. circumcenter B. centroid
C. orthocenter D. incenter 449. What is formed when the hypothesis and
the conclusion of the conditional statement are
interchanged?
443. Although rarely used in proving, what is the A. converse B. inverse
extra line or line segment drawn in a figure to C. adverse D. contrapositive
help in a proof?
A. base line B. auxiliary line
C. converse line D. Euler’s line 450. What is formed when both the hypothesis
and the conclusion of the conditional statement
are negated?
444. What is the measure of ∠V in the following A. converse B. inverse
figure? C. adverse D. contrapositive

451. Which of the following is the converse of the

following statement?
“If two angles are congruent,
then they have the same measure.”
A. If two angles are not congruent, then they do
A. 60o B. 65o C. 70o D. 75o not have the same measure.
B. If two angles have the same measure, then
they are congruent.
445. What is the intersection of all three C. If two angles do not have the same measure,
altitudes of a triangle? then they are not congruent.
A. incenter B. centroid D. If two angles are not congruent, then they
C. orthocenter D. circumcenter have the same measure.”

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1000 MMR Author: Victor A. Tondo Jr., LPT
452. In which geometry are there no parallel 458. Which lines are not in the same plane and
lines? do not intersect but are not parallel?
A. elliptic geometry A. asymptotes B. tangent lines
B. hyperbolic geometry C. skew lines D. directrices
C. spatial geometry
D. solid geometry
459. Two adjacent angles whose distinct sides lie
on the same line are called what?
453. What do we call the ratio of two numbers A. linear pair B. vertical pair
(larger number: smaller number) whose ratio to C. alternate D. corresponding
each other is equal to the ratio of their sum to
the larger number? [Note: This is applied in
Fibonacci sequences] 460. The point of concurrency of a triangle’s
A. pi B. golden ratio three altitudes is called _____.
C. 1.618 D. Euler’s ratio A. circumcenter B. incenter
C. orthocenter D. centroid

454. Which of the following pertains to the law of

cosines? 461. What do we call three positive integers with
A. c2 = a2 + b2 – 2 ab cos C the property that the sum of the squares of two
B. c2 = a2 + b2 + 2 ab cos C of the integers equals the square of the third?
C. c2 = a2 + b2 – ab cos C A. Euclid’s triple
D. c2 = a2 + b2 + ab cos C B. Pythagorean triple
C. Newton’s triple
D. Cartesian triple
455. Solve for x:

462. Which of the following expressions will give

the value of x?

A. x = 8 B. x = 9
C. x = 10 D. x = 11
A. 50 tan 37o B. 50 cos 37o
C. 50 sin 37o D. 50 cot 37o
456. What do we call an angle formed by two
chords of the circle with a common endpoint
(the vertex of the angle)? 463. Solve for x:
A. inscribed angle B. tangential angle
C. circumscribed angle D. interior angle

2018𝑥+2019
457. Find the inverse of y = .
2020
2020𝑥−2019 2020𝑥−2018
A. y-1 = B. y-1 =
2018 2019
2019𝑥−2020 2019𝑥−2018
C. y-1 = D. y-1 =
2018 2020 A. 6 B. 7 C. 7.5 D. 8

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1000 MMR Author: Victor A. Tondo Jr., LPT
464. A bus travels 600 km in 7 hrs and another 470. Find the equation of the circle whose center
300 km in 5 hrs. What is its average speed? is at (7, -24) given that it passes the point of
A. 72.86 kph B. 75 kph origin.
C. 77.86 kph D. 80 kph A. (x + 7)2 – (y – 24)2 = 961
B. (x – 7)2 + (y + 24)2 = 961
C. (x + 7)2 + (y – 24)2 = 625
465. A sniper on a cliff observes that the angle of D. (x – 7)2 + (y + 24)2 = 625
depression to his target is 30o. If the cliff is 10
meters high, how far must the bullet travel to hit
the sniper’s target? 471. Ana left their house and jogged at a speed of
A. 20 meters B. 10√3 meters 60 meters per minute. Bea followed her two
C. 10√2 meters D. 10 meters minutes later and jogged at a speed of 70 meters
per minute. How many minutes after Bea left
would she catch up with Ana?
466. Rowena received a total of 25 bills. These A. 14 B. 13.5 C. 13 D. 12
bills are either P20 or P50 bills. If Rowena
received an amount of P800, how many P20 bills
did she receive? 472. How many mL of 40% acid must be added
A. 10 B. 13 C. 15 D. 17 to 1000 mL of 10% acid solution to make a 20%
acid solution?
A. 250 B. 500 C. 600 D. 750
467. How many ways can the word PILIPINAS be
rearranged?
A. 302 473. The hypotenuse of a 30-60-90 triangle is
B. 3,024 432 cm long. How long is the leg opposite the 30o
C. 30,240 angle?
D. 302,400 A. 216 cm B. 216 √2 cm
C. 216 √3 cm D. 432 cm

468. A coin is tossed 60 times. Head appeared 27

times. Find the experimental probability of 474. The shortest leg of a 30-60-90 triangle is
getting heads. 123 cm long. How long is the leg adjacent to the
9 1 11 43
A. 20 B. 2 C. 20 D. 60 30o angle?
A. 123 cm B. 123√2 cm
C. 123√3 cm D. 246 cm
469. A parabola is defined by the equation
5x = -3y2 – 4y + 2. Which of the following is true
about the parabola? 475. How many odd 4digit numbers can be
A. It opens to the left. formed using the digits 7, 6, 5, 4, 3, 2, and 1 if
B. It opens to the right. repetition is not allowed?
C. It opens upward. A. 720 B. 480 C. 240 D. 120
D. It opens downward.

476. There are 70 dogs and geese in a farm. If

there are a total of 200 legs, how many dogs are
there?
A. 25 B. 30 C. 35 D. 40

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1000 MMR Author: Victor A. Tondo Jr., LPT
477. Find the maximum area of a rectangle if the 485. What is the remainder when 3x6+ 4x5 – 5x4
perimeter is set at 350 cm. + 6x3 + 7x2 – 8x + 3 is divided by (x – 1)?
A. 8656.25 cm2 B. 7656.25 cm2 A. 8 B. 9 C. 10 D. 11
C. 6656.25 cm2 D. 5656.25 cm2

486. Seven people have an average weight of 49

478. A rectangle is 60 cm long and 45 cm wide. kg. A child was added to the group and the
How long is its diagonal? average became 45 kg. How heavy is the child?
A. 75 cm B. 85 cm A. 15 kg B. 16 kg
C. 95 cm D. 105 cm C. 17 kg D. 18 kg

479. Find the length of the diagonal of a cube 487. Six numbers have an average of 71. If 85 is
given each side measures 17 cm. added to the group, what is the new average?
A. √290 cm B. 17√2 cm A. 72 B. 73 C. 74 D. 75
C. 17√3 cm D. 34 cm

488. In an arithmetic sequence, the 7th term is 25

480. Find the measure of each exterior angle of a and the 10th term is 67. What is the common
regular 20-sided polygon. difference?
A. 162o B. 150o A. 42 B. 21 C. 14 D. 7
C. 144o D. 126o

489. Triangle ABC has sides measuring 20 cm, 20

481. How many diagonals does a regular 14- cm, and 29 cm. What kind of triangle is ABC?
sided polygon have? A. acute B. right
A. 81 B. 91 C. 96 D. 101 C. obtuse D. reflex

482. How many ways can 14 people be seated in 490. Find the surface area of a sphere given that
a Ferris wheel given that each cart can only the sphere sits perfectly inside a cube whose
contain one person? sides measure 20 cm each.
A. 15! B. 14! C. 13! D. 12! A. 400𝜋 cm2 B. 800𝜋 cm2
C. 1200𝜋 cm 2 D. 2400𝜋 cm2

483. There are 24 mangoes in a basket, of which

7 are rotten. What is the probability that when 491. Given f(x) = (25 x20 – 24x10)(x2 – 9x + 3),
randomly getting two mangoes at the same time, find f ’(x).
both are rotten? A. f ‘(x) = 550 x21 – 4725 x20 + 1500 x19 – 288 x11
7 49 36 49 + 2376 x10 – 720 x9
A. 92 B. 576 C. 529 D. 529
B. f ‘(x) = 450 x21 – 4725 x20 + 150 x19 + 288 x11
+ 2376 x10 – 720 x9
C. f ‘(x) = 550 x21 – 4725 x20 + 150 x19 – 288 x11
484. In a gathering of gamers and admins, there + 2376 x10 – 720 x9
are 24 gamers of which 6 are females, and 3 D. f ‘(x) = 450 x21 – 4725 x20 + 1500 x19 – 288 x11
admins of which one is female. If a female is + 2376 x10 – 720 x9
randomly called, what is the probability that she
is an admin?
1 1 7 1
A. 7 B. 4 C. 27 D. 9
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1000 MMR Author: Victor A. Tondo Jr., LPT
492. Simplify: eln 2019 x 499. Mocha can finish a job in 24 hours, while
A. 2019x B. 2019 x her sister Tiramisu can do the same job in only
1 1
C. 2019 x D. 2019 𝑥 20 hours. How long will it take them to finish the
job by working together?
119 120
A. 11 hrs B. 11 hrs
122
493. If the roots of a quadratic equation are C. 11 hrs D. hrs
−7 3 11
and , which of the following could be the
9 7
quadratic equation?
A. 63x2 + 22x – 21 = 0 500. What conic figure does the equation
B. 63x2 – 22x – 21 = 0 x2 + y2 + 10x – 16y = -100 form?
C. 63x2 + 22x + 21 = 0 A. Real circle B. Degenerate circle
D. 63x2 – 22x + 21 = 0 C. Imaginary circle D. Ellipse

494. If three more than twice a number is ⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯

seventeen less than seven times the number,
what is the number?
A. 2 B. 3 C. 4 D. 5 End of first 500 items.

495. A team is to be made from a group of seven

teachers and six scientists. If the team is to be Please, take a break.
composed two teachers and two scientists, how
many different ways can they form a team?
A. 325 B. 315 C. 300 D. 285
Remember:
Nasa Diyos ang awa,
496. Find the measure of the smaller angle Nasa tao ang gawa.
formed by the hands of the clock at 11:20.
A. 130o B. 135o
C. 140o D. 145o

497. How many even 3-digit even numbers can

be formed using the digits 7, 6, 5, 4, 3, 2, 1, and 0
if repetition is not allowed?
A. 150 B. 160 C. 170 D. 180

498. There are 50 students in a class. Twenty of

them have a laptop. Thirty-two of them have a
smartphone. Seven of them have both a laptop
and a smartphone. How many of them have
neither a laptop nor a smartphone?
A. 4 B. 5 C. 6 D. 7

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1000 MMR Author: Victor A. Tondo Jr., LPT
501. Victor, Praetor, and Rowena volunteered to 507. What is the sum of the first 2019 counting
teach at a nearby daycare. Praetor worked for numbers?
twice as long as Rowena did. Victor worked A. 2,021,019 B. 2,027,190
twice as many hours as Praetor. Altogether, they C. 2,039,190 D. 2,043,190
worked for 56 hours. For how many hours did
Victor work?
A. 14 B. 16 C. 28 D. 32 508. In a certain school, the ratio of boys to girls
is 4 is to 9. If there are 260 boys and girls in the
school, how many boys are there?
502. Which of the following is the factorization of A. 100 B. 90
the binomial x4 – 20194? C. 85 D. 80
A. (x + 2019)2 (x – 2019)2
B. (x – 2019)4
C. (x2 + 20192) (x + 2019) (x – 2019) 509. Solve for x: 8x + 9y = 17
D. (x – 4)(x + 4) 9x + 10y = 18
A. x = 9 B. x = 8
C. x = -9 D. x = -8
503. The average of 5 different counting
numbers is 143. What is the highest possible
value that one of the numbers can have?
510. Mr. Park is 20 years older than his son now.
A. 706 B. 705
Five years from now, the Mr. Park’s age will be 5
C. 704 D. 703
less than twice his son’s age. Find the son’s
present age.
A. 18 B. 20
504. What value of x will satisfy the equation:
C. 38 D. 40
0.25(20x – 2020) = x?
A. 125.25 B. 125.75
C. 126.25 D. 126.5
510. What is the minimum value of
f(x) = 3x2 + 6x + 11?
A. 1 B. 2 C. 4 D. 8
505. Three brothers inherited a cash amount of
P5,670,000 and they divided it among
themselves in the ratio of 2:3:4. How much more
511. What is the sum of the roots of
is the largest share than the smallest share?
5x2 + 10x – 17?
A. P1,260,000 B. P1,270,000 17 −17
C. P630,000 D. P635,000 A. 5 B. 5 C. 2 D. -2

506. Rayon and Wena can do a job together in 512. If xy = 17 and x2 + y2 = 135, find x + y.
four hours. Working alone, Rayon does the job in A. 13 B. 12.8749
six hours. How long will it take Wena to do the C. 12.5249 D. 12.5
job alone?
A. 12 hours B. 11 hours
C. 10 hours D. 9 hours 513. How many mL of 50% acid solution must be
added to 200mL of 10% acid solution to make a
40% acid solution?
A. 400 mL B. 500 mL
C. 600 mL D. 700 mL

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1000 MMR Author: Victor A. Tondo Jr., LPT
514. Nine consecutive even numbers have a sum 523. If two numbers have a product of 267 and
of 180. What is the smallest of these even the sum of their squares is 250, what is their
numbers? sum?
A. 18 B. 16 A. -30√3 B. 28
C. 14 D. 12 C. 7√3 + 2√5 D. 30

515. If x = 13, which of the following is equal to 524. How many ml of 10% acid must be added to
200? 500 ml of 40% acid to make a 30% acid solution?
A. 15x + 2 B. x2 + 2x + 5 A. 1000 ml B. 750 ml
C. x – 4x – 2
3 D. x2 + x + 2 C. 500 ml D. 250 ml

516. For which value of k does 9x2 – kx + 25 525. 3log2 3 + 2 log2 5 – log2 7 = ______.
have only one root? 1125 675
A. log2 7 B. log2 7
A. 3.75 B. 7.5 C. 15 D. 30 225 216
C. log2 D. log2
7 7

517. If A and B are the roots of x2 + 19x + 20,

what is AB? 526. Find the intersection of y = 3x + 4 and
A. 20 B. 2√5 + 5 y = 5x – 8.
C. 3√2 + 2√3 D. -19 A. (8/5, 0) B. (-4/3, 0)
C. (1, 7) D. (-2, -2)

518. 0.25 + 0.5 + 1 + 2 + 4 + … + 1024 = ____

A. 2046.75 B. 2047.75 527. Find the remainder when
C. 2048.75 D. 2049.75 x5 – 3x3 + 5x2 – 7x + 9 is divided by (x – 1).
A. 11 B. 9 C. 7 D. 5

519. How many terms are there in the sequence

2, 9, 16, 23, …, 345? 528. Multiply: (3x – 7) (5x + 9)
A. 40 B. 44 A. 15x2 – 8x – 63 B. 15x2 – 8x + 63
C. 45 D. 70 C. 15x + 8x – 63
2 D. 15x2 + 8x + 63

520. If 2x + 3 = 25, then what is (2x + 3)2 – 25? 529. Multiply: (2x2 – 5x + 3) (3x + 4)
A. 650 B. 625 C. 600 D. 575 A. 6x3 – 7x – 11x + 12
B. 6x3 + 7x + 11x + 12
C. 6x3 – 7x + 11x + 12
521. What is 50% of 200% of 2019? D. 6x3 + 7x – 11x + 12
A. 1009.5 B. 2019
C. 4038 D. 8076
530. x varies directly as y and inversely as z. If
x = 40 when y = 8 and z = 2, what is x when
522. If 3x = 5 and 2y = 11, what is 12(x – y)? y = 24 and z = 4?
A. -46 B. -45 C. 45 D. 46 A. 120 B. 90 C. 60 D. 30

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1000 MMR Author: Victor A. Tondo Jr., LPT
531. Pedro has 7 more P10 coins than P5 coins. If 540. Rowena can do a job in 15 hours, while
he has a total of P475, how many P5 coins does Victor can do the same job in 25 hours. How long
he have? will it take them to finish the job by working
A. 13 B. 15 C. 17 D. 19 together?
A. 9.375 hours B. 9.25 hours
C. 9.125 hours D. 8.875 hours
532. When a number is increased by 5, its square
also increases by 255. What is this number?
A. 22 B. 23 C. 24 D. 25 541. Armel is twice as heavy as Kuku. Gabbi is
17kg heavier than Kuku. The sum of their masses
is 217kg. How heavy is Kuku in kg?
533. Find k such that 16x2 + kx + 81 is a perfect A. 40 B. 45 C. 50 D. 55
square trinomial.
A. 144 B. 72 C. 36 D. 18
1 1
542. Find 𝑥 + 𝑦 given x + y = 30 and xy = 219.
53 63 73 10
534. Solve for x: (x + 4)2 = (x – 6)2. A. 73 B. 83 C. 10 D. 73
A. x = 0 B. x = ½
C. x = 1 D. no solution
543. The product of two consecutive odd
counting numbers is 1023. What is their sum?
535. When a number is increased by 3, its square A. 60 B. 64 C. 68 D. 72
increases by 135. By what does its square
increase when the number is increased by 5?
A. 222 B. 240 C. 444 D. 480 544. There are 250 pigs and chickens in a farm,
all of which are healthy. If there are 720 legs in
total, how many pigs are there?
536. Ten cans of soda and six hamburgers cost a A. 110 B. 100 C. 90 D. 80
total of P440. Five cans of soda and seven
hamburgers cost a total of P360. How much is a
hamburger? 545. Solve for x given 13x + 17 = 15x – 21.
A. P17 B. P19 C. P21 D. P23 A. x = 17 B. x = 18
C. x = 19 D. x = 20

537. The product of two consecutive odd

numbers is 1683. What is the smaller number? 546. Factorize: x3 + 3x2 – 4x – 12
A. 31 B. 37 C. 41 D. 47 A. (x + 2) (x + 3) (x – 2)
B. (x + 4) (x + 3) (x – 1)
C. (x + 2) (x – 3) (x + 2)
538. Find the remainder when the polynomial D. (x + 4) (x – 3) (x + 1)
x4 – 5x3 + 7x2 – 11x + 19 is divided by (x – 2).
A. 5 B. 3 C. 1 D. -1
547. Factorize (x4 – 16) completely.
A. (x – 2)4
539. If three-fourths of a number is 44 more than B. (x – 2)2 (x + 2)2
its one-fifth, what is that number? C. (x + 2)2 (x – 2)2
A. 120 B. 100 C.80 D. 60 D. (x + 2) (x – 2) (x2 + 4)

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1000 MMR Author: Victor A. Tondo Jr., LPT
548. √125 + √45 − √245 = ____ 556. Find the remainder when x4 – 4x3 + 3x2 +
A. 6√5 B. 4√5 5x – 6 is divided by (x – 2).
C. 2√5 D. √5 A. 3 B. 2 C. 1 D. 0

549. The product of two consecutive even 557. 2 + 9 + 16 + 23 + … + 135 = ____

counting numbers is 3968. Find the smaller A. 1353 B. 1360
number. C. 1370 D. 1377
A. 42 B. 46 C. 52 D. 56
558. Factorize: (2x + y) (2x + y + 3) + 2.
550. A pipe can fill a pool in 5 hours while A. (2x + y + 1) (2x + y + 2)
another pipe can drain empty the pool in 10 B. (2x + y + 1) (2x + y + 6)
hours. How long will it take to fill the pool if both C. (2x + y + 2) (2x + y + 3)
pipes are open? D. (2x + y + 3) (2x + y + 4)
A. 8 hours B. 9.25 hours
C. 9.5 hours D. 10 hours
559. The area of a rectangle is (x2 – x – 30). If its
length is x + 5, what is its width?
551. Today, Rayon is 13 years old while his A. x + 4 B. x – 3
father is thrice his age. How many years from C. x + 2 D. x – 6
now will his father be twice as old as he?
A. 15 B. 13 C. 11 D. 10
560. Factorize 81x2 – 225y2 completely.
A. (9x + 15y)(9x – 15y)
552. Roy and Wena are on a seesaw. Roy weighs B. 9(9x2 – 25y2)
48 kg and sits 160 cm to the left of the fulcrum. If C. 9(3x – 5y)2
Wena weighs 60 kg, how far to the right of the D. 9(3x + 5y)(3x – 5y)
fulcrum must she sit to balance the seesaw?
A. 115 cm B. 123 cm
C. 128 cm D. 135 cm 561. What are the missing terms in the series
3, 6, 12, 24, ___, 96, ____?
A. 48; 192 B. 36, 120
553. Insert one term between 81 and 169 to C. 46, 196 D. 46, 192
make a geometric sequence.
A. 113 B. 117 C. 121 D. 125
562. In a parking lot, there are 65 tricycles and
motorcycles. If there are 150 wheels in all, how
554. Find the common difference of an many tricycles are there?
arithmetic sequence whose 21st term is 1987 and A. 18 B. 19 C. 20 D. 21
29th term is 2019.
A. 2.5 B. 3 C. 3.5 D. 4
563. Which fraction is equivalent to 0.425?
A. 21/50 B. 27/50
555. Find the general term An of the sequence C. 27/40 D. 17/40
7, 16, 25, 34, 43, 52, 61, …
A. An = 9n – 2 B. An = 8n – 1
C. An = 9n + 2 D. An = 8n + 1

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1000 MMR Author: Victor A. Tondo Jr., LPT
564. What are the zeroes of 6x2 – x – 35? 571. Factorize 27x3 + 125.
−7 5 −5 7 A. (3x + 5)(9x2 + 15x + 25)
A. and B. and
3 2 3 2
7 −5 5 −7 B. (3x + 5)(9x2 – 15x + 25)
C. 3 and D. 3 and C. (3x – 5)(9x2 + 15x + 25)
2 2
D. (3x – 5)(9x2 – 15x + 25)

565. Seven more than four times a number is 79.

What is five less than three times the number? 572. What is the 5th term of (2x + 3)7?
A. 59 B. 49 C. 39 D. 29 A. 22680x3 B. 11340x3
C. 21600x3 D. 10800x3

566. Mr. Park is five times as old as his son. Eight

years from now, he will only be thrice as old as 573. In the equation 2x + 5y = 50, what is x
his son. How old is Mr. Park now? when y is 8?
A. 30 B. 35 C. 40 D. 45 A. 2 B. 3 C. 4 D. 5

567. Mr. Yu is four times as old as his daughter. 574. X varies directly as Y and inversely as Z. If X
Ten years from now, he will only be thrice as old is 24 when Y is 30 and Z is 5, find X when Y is 36
as her. How old is his daughter now? and Z is 4.
A. 10 B. 15 C. 20 D. 25 A. 36 B. 32 C. 24 D. 16

568. The speed of the current of a river is 9 kph. 575. What is the 4th term of (3x – 2)5?
Rayon rows his boat upstream for 8 hours, and A. 360x2 B. 240x2
then travels back to his original position by C. -240x2 D. -360x2
rowing downstream for 4 hours. What is Rayon’s
speed on calm water?
A. 9 kph B. 18 kph 576. Factorize 64x6 – y6.
C. 27 kph D. 36 kph A. (2x – y) (4x2 + 2xy + y2) (2x + y) (4x2 – 2xy + y2)
B. (2x – y) (4x2 + 2xy + y2) (2x + y) (4x2 + 2xy + y2)
C. (2x + y) (4x2 – 2xy – y2) (2x + y) (4x2 – 2xy + y2)
569. Thrice Rayon’s age 16 years ago is equal to D. (2x + y) (4x2 – 2xy – y2) (2x + y) (4x2 – 2xy + y2)
his age 16 years from now. How old is Rayon
now?
A. 16 B. 24 C. 32 D. 40 577. Factorize x2 + 6x – y2 + 2y +8.
A. (x + y + 2) (x + y + 4)
B. (x + y + 2) (x – y + 4)
570. Divide 8x5 – 4x3 + 2x2 – 3x + 4 by x + 2. C. (x + y + 2) (x + y – 4)
A. 8x4 – 16x3 + 28x2 – 54x + 105 r. -206 D. (x + y + 2) (x – y – 4)
B. 8x4 + 16x3 + 28x2 – 54x + 105 r. -206
C. 8x4 – 16x3 + 28x2 – 54x – 105 r. 206
D. 8x4 + 16x3 + 28x2 – 54x – 105 r. 206 578. What value of x will satisfy the equation:
2.5(4x – 504) = x?
A. 150 B. 145 C. 140 D. 135

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1000 MMR Author: Victor A. Tondo Jr., LPT
579. Factorize (2x + y) (2x + y + 6) + 5 588. Solve for x: 2x + 3y = -8, and 5x – 7y = 67
A. (2x + y + 5) (2x + y + 1) A. 5 B. 6 C. -5 D. -6
B. (2x + y – 5) (2x + y – 1)
C. (2x + y + 5) (2x – y + 1)
D. (2x – y + 5) (2x – y + 1) 589. A farmer has 15 goats, 23 pigs, and a few
chickens in his farm. If he counted a total of 200
legs in his farm (excluding his, of course), how
580. Simplify: (2x3y4z2)5 many chickens does he have?
A. 10x15y20z10 B. 25x15y20z10 A. 96 B. 72 C. 48 D. 24
C. 32x15y20z10 D. 100x15y20z10

2+√3
590. Rationalize 4−√5
581. Find k such that 5x2+ 30x + k has two
8+4√3+2√5+√15 8+4√3−2√5−√15
unequal real roots. A. B.
11 21
A. k > 6 B. k < 6 8+4√3−2√5−√15 8+4√3+2√5+√15
C. k > 45 D. k < 45 C. D.
11 21

582. Which of the following is not a polynomial? 591. If 3x + 2 = 4y and 5y – 3 = z, express z in

3 4
A. π r2 + 2 π r B. 4 m – 5 n terms of x.
C. √2 x + √3 y – √5 z D. ab √3 − cd A. 15x + 9 B. 15x + 7
15𝑥−2 15𝑥−7
C. 4 D. 9

583. Which of the following is irrational?

2489
A. 0.193193193193… B. 592. If 72x + 3 = B, what is B ÷ 49x?
1323
C. √1023 D. √2401 A. 343 B. 21 C. 7 D. 3

584. If x + y = 17 and x2 + y2 = 135, find xy. 593. Multiply: (7x + 4) (2x – 1) (3x + 5)
A. 78 B. 77 C. 76 D. 75 A. 42x3 + 73x2 + 7x – 20
B. 42x3 – 73x2 + 7x – 20
C. 42x3 + 73x2 – 7x – 20
585. If H and K are the roots of 5x2 – 8x + 9, find D. 42x3 – 73x2 – 7x – 20
H + K – HK.
A. -2/5 B. -1/5 C. 0 D. 1/5
594. Rayon invested P1,600,000.00 in a bank
that offers 2.5% interest per annum. How much
586. If H and K are the roots of 3x2 + 4x + 5, find will his account hold after 4 years?
H2 + K2. A. P160,000 B. P1,160,000
A. -5/9 B. -1 C. -14/9 D. -2 C. P1,460,000 D. P1,760,000

587. Factorize 9x2 + 24xy + 16y2 – 81z2. 595. Solve for x: 45x+3 = 82x+6
A. (3x + 4y + 9z) (3x + 4y – 9z) A. 2 B. 3 C. 4 D. 5
B. (3x – 4y + 9z) (3x + 4y – 9z)
C. (3x + 4y + 9z) (3x – 4y – 9z)
D. (3x – 4y + 9z) (3x – 4y – 9z)

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1000 MMR Author: Victor A. Tondo Jr., LPT
2𝑥𝑦 3𝑎𝑏 605. Which of these has the longest perimeter?
596. Given 𝑧 = 𝑐 , which of the following
A. A regular pentagon with sides 21 cm long
expressions is equal to x?
2𝑎𝑏𝑧 3𝑎𝑧 3𝑎𝑏𝑧 2𝑎𝑐𝑧 B. A rectangle 29 cm long and 24 cm wide
A. 3𝑐𝑦 B. 2𝑏𝑐𝑦 C. 2𝑐𝑦 D. 3𝑏𝑦 C. An equilateral triangle with sides 36 cm long
D. A square whose area is 1024 cm2

597. Add: (2x2 + 4x + 5) + (5 – 6x – x2)

A. x2 + 2x + 10 B. 3x2 + 2x + 10 606. The hypotenuse of a right triangle is 82 feet.
C. x – 2x + 10
2 D. 3x2 + 2x + 10 If one leg is 80 feet, what is the length of the
other leg in feet?
A. 15 B. 16 C. 17 D. 18
598. Solve for x: 272x–8 = 9x+10
A. 9 B. 10 C. 11 D. 12
607. Find the surface area of a rectangular box
whose dimensions are 25 cm x 35 cm x 45 cm.
599. If 25x – 49y = 2019, what is 49y – 25x? A. 7000 cm2 B. 7045 cm2
A. 2018 B. -2019 C. 7150 cm 2 D. 7745 cm2
1
C. 2019 D. cannot be determined

608. ∠A and ∠B form a linear pair. If m∠A = 3x

and m∠B = 5x + 40, what is the value of x?
600. If x + y = 90 and x2 + y2 = 2020, find xy.
A. 17.5 B. 18 C. 19 D. 19.75
A. 3025 B. 3030
C. 3035 D. 3040
609. ∠1 and ∠3 are opposite angles in a
parallelogram. If m∠1 = 50o, what is m∠3?
601. Which of the following is ALWAYS true?
A. 40o B. 50o C. 140o D. 130o
A. Vertical pairs of angles are supplementary.
B. Vertical pairs of angles are congruent.
C. Linear pairs of angles are congruent.
610. ∠A and ∠C are consecutive angles in a
D. Linear pairs of angles are complementary.
parallelogram. If m∠A = 60o, what is m∠C?
A. 40o B. 50o C. 150o D. 120o
602. How many line segments can be made from
28 non-collinear points?
611. Two parallel lines are cut by a transversal,
A. 378 B. 394
forming ∠R and ∠V. If the two angles are
C. 412 D. 422
corresponding angles, what is the measure of ∠R
if the measure of ∠V is 70o?
603. The vertex angle of an isosceles triangle is A. 35o B. 70o
70°. What is the measure of one of the base C. 160 o D. 110o
angles?
A. 45° B. 50° C. 55° D. 60°
612. If the sum of the supplement and the
complement of an angle is 100 degrees, what is
604. A shoebox measures 20 inches by 15 inches the angle?
by 9 inches. What is its volume in cubic inches? A. 65o B. 70o C. 75o D. 85o
A. 900 B. 1350
C. 1650 D. 2700

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1000 MMR Author: Victor A. Tondo Jr., LPT
613. It is the perpendicular bisector of a regular 620. In the figure, A is the center of the circle.
polygon’s side, passing through the center. What is the measure of ∠BDC?
A. side B. apothem A. 160o B. 80o C. 40o D. 20o
C. asymptote D. diagonal

614. In the figure, 𝐴𝐵 //𝐶𝐷. If m∠AFE = 130o,

find the measure of ∠CGH.

621. Find the measure of ∠E using the figure of

parallelogram WENA below.

A. 50o B. 130o C. 65o D. 25o

615. The measure of each interior angle of a A. 15 B. 65 C. 115 D. 85

regular polygon is 170o. How many vertices does
it have?
A. 36 B. 24 C. 12 D. 10 622. In parallelogram
MATH, m∠A = 7x – 32 and
m∠T = 5x + 32. Find m∠A.
616. How many diagonals does a regular A. 15 B. 63
dodecahedron have? C. 73 D. 117
A. 45 B. 54 C. 60 D. 66

623. The diagonal of a rectangular prism is 17

617. Find the area of a square whose perimeter cm long. If it is 9 cm thick and 12 cm long, how
is 480 cm. wide is it?
A. 14400 cm2 B. 28800 cm2 A. 15 cm B. 10 cm
C. 57600 cm2 D. 270400 cm2 C.8√3 cm D. 8 cm

618. A circle has a diameter of 34 cm. What is its 624. Statement 1: A square is a rhombus.
area? Statement 2: A square is a rectangle.
A. 17 π cm2 B. 34 π cm2 A. Only the first statement is true.
C. 289 π cm2 D. 1156 π cm2 B. Only the second statement is true.
C. Both statements are true.
D. Both statements are false.
619. The perimeter of a rectangle is 84. If its
length is 29 cm, find its area.
A. 377 cm2 B. 1218 cm2 625. Which of the following has its incenter,
C. 2436 cm2 D. 4872 cm2 circumcenter, centroid, and orthocenter in just
one point?
A. Equilateral Triangle B. Right Triangle
C. Scalene Triangle D. Obtuse Triangle

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1000 MMR Author: Victor A. Tondo Jr., LPT
626. In triangles, this line segment is drawn from 634. Find the volume of a rectangular pyramid
midpoint of one side to its opposite vertex. given that its base has length 21 cm and width 10
A. Median B. Altitude cm, and its height is 15 cm.
C. Bisector D. Longitude A. 700 cm3 B. 1050 cm3
C. 1575 cm 3 D. 1400 cm3

627. The radius of a cone measures 12 cm and its

height is 15 cm. Find its volume. 635. The diameter of a cylinder is 24 cm. If its
A. 240 π cm3 B. 360 π cm3 height is 40 cm, find its surface area.
C. 480 π cm3 D. 720 π cm3 A. 312 π cm2 B. 624 π cm2
C. 936 π cm 2 D. 1248 π cm2

628. This is located at the intersection of the

perpendicular bisectors of a triangle. 636. In the figure, AC is a diagonal of rhombus
A. Centroid B. Circumcenter ABCD. If m∠B = 118o, what is m∠CAD?
C. Incenter D. Orthocenter A. 124o B. 118o C. 62o D. 31o

629. The radius of a cylinder measures 9 cm and

its height is 15 cm. Find its volume.
A. 1215 π cm3 B. 810 π cm3
C. 540 π cm3 D. 360 π cm3

637. A rhombus has diagonals measuring 20 cm

630. What is the measure of each exterior angle and 30 cm. What is its area?
of a regular decagon? A. 75 cm2 B. 150 cm2
A. 108o B. 72o C. 60o D. 36o C. 300 cm2 D. 600 cm2

631. Find the area of an isosceles trapezoid given 638. A rhombus as diagonals measuring 30 cm
bases measuring 20 cm and 30 cm, with each of and 16 cm. What is its perimeter?
the congruent slants measuring 13 cm. A. 136 cm B. 92 cm
A. 250 cm2 B. 275 cm2 C. 68 cm D. 46 cm
C. 300 cm 2 D. 325 cm2

639. Find the approximate distance around a

632. Which of the following side lengths belong semicircular park with radius 100m.
to an acute triangle? A. ~1028 m B. ~771 m
A. 5 cm, 7 cm, 9 cm B. 6 cm, 8 cm, 10 cm C. ~514 m D. ~257 m
C. 6 cm, 9 cm, 12 cm D. 7 cm, 9 cm, 11 cm

640. Find the equation of the line perpendicular

633. A prism has a right triangle as its base. The to 7x + 4y = 12, passing through (-2, 9).
two legs of the right triangular base are 6 cm and A. 4x – 7y = -71 B. 4x + 7y = 71
8 cm long. If the prism is 2 cm thick, find its C. 4x – 7y = 71 D. 4x + 7y = -71
lateral surface area.
A. 24 cm2 B. 48 cm2
C. 56 cm 2 D. 72 cm2

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1000 MMR Author: Victor A. Tondo Jr., LPT
641. Find the equation of the line perpendicular 646. In the figure below, m∠CAB = 2x + 4, while
to 9x –7y = -6, passing through (4, -3). m∠COB = 5x – 7. Find x.
A. 7x + 9y = 1 B. 7x + 9y = -1
C. 7x – 9y = 1 D. 7x – 9y = -1

642. A rectangle is drawn with dimensions 28 cm

by 42 cm. A larger rectangle is drawn by adding
5 cm margins from each side of the original 11 7
A. B. -2 C. 5 D. 15
rectangle. What is the area of the larger 3
rectangle?
A. 1456 cm2 B. 1551 cm2
C. 1556 cm 2 D. 1976 cm2 647. In the figure below, 𝐴𝐵 // 𝐶𝐷. If m∠AGE =
7x + 11 and m∠CHF = 5x + 1, what is m∠AGE?

643. Find the length of the diagonals of a

rectangular prism 6 cm thick, 15 cm long, and 10
cm wide.
A. 17√3 cm B. 18√2 cm
C. 19 cm D. 20√5 cm

A. 119o B. 109o C. 71o D. 61o

644. Find the volume of the following pool.

648. Find the sum of all interior angles of a

regular 15-sided polygon.
A. 5400o B. 2700o
C. 2340 o D. 1170o

649. If each square in the figure has an area of 36

A. 700 m3 B. 1050 m3 square cm, find the perimeter of the figure.
C. 1400 m3 D. 2800 m3

645. What is the slope of the line defined by the

equation 3x + 5y = 11?
−3 −5
A. 5 B. 3 C. 3 D. 5 A. 864 cm B. 792 cm
C. 144 cm D. 132 cm

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1000 MMR Author: Victor A. Tondo Jr., LPT
650. Find the area of the shaded part of the 656. Find the equation of the line passing
circle. through (2, -7) with a slope of -3.
A. y = -3x – 1 B. y = -3x + 1
C. y = -3x – 2 C. y = -3x + 2

657. A square has a diagonal measuring 28 cm.

Find its area.
A. 9720 π cm2 B. 972 π cm2 A. 784 cm2 B. 392 cm2
C. 540 π cm2 D. 270 π cm2 C. 196 cm2 D. 98 cm2

̂ = 120o and m∠E = 28o.

651. In the figure, 𝐴𝐶 658. Symbol for line.
̂.
Find 𝐵𝐶 A. B.
C. D.

659. Symbol for ray.

A. B.
A. 46o B. 54o C. 64o D. 72o C. D.

652. Find the volume of a cone whose radius is 660. Find the volume of the swimming pool
30 cm and height is 170 cm. drawn below.
A. 289,000 π B. 153,000 π A. 2000 cu. ft. B. 2100 cu. ft.
C. 51,000 π D. 17,000 π C. 2250 cu. ft. D. 2500 cu. ft.

653. Find the center of a circle given one of its

longest chords has endpoints at M(-11,8) and
N(23,-24).
A. (12, -16) B. (6, -8)
C. (-17,16) D. (17, -16)

654. Find the radius of a circle if its diameter has

endpoints at M(3,5) and N(-12,13).
A. 8 B. 8.5 C. 9 D. 9.5
661. Which geometric figure extends indefinitely
in two opposite directions?
655. Find the equation of the line passing A. angle B. ray
through (7, 5) and (5, 1). C. line D. line segment
A. y = 2x + 9 B. y = 2x – 9
C. y = ½ x + 9 D. y = ½ x – 9

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1000 MMR Author: Victor A. Tondo Jr., LPT
662. In the figure, ∠ACB is formed by the 670. Find the equation of a circle if its diameter
tangents AC and BC. If m∠ACB = 34o, what is the has endpoints at M(3,5) and N(-12,13).
measure of the minor intercepted arc? A. (x + 4.5)2 + (y + 9)2 = 72.25
B. (x – 4.5)2 + (y + 9)2 = 72.25
C. (x + 4.5)2 + (y – 9)2 = 72.25
D. (x – 4.5)2 + (y – 9)2 = 72.25

A. 112o B. 146o C. 68o D. 34o 671. A bicycle’s wheel is 24 inches in diameter. If

it revolves 625 times, how far does the bicycle
travel?
663. X(7,9) is the midpoint of A(1,2) and B. Find A. 7,500 π B. 15,000 π
the coordinates of B. C. 30,000 π D. 60,000 π
A (-13, -16) B. (13, -16)
C. (-13, 16) D. (13, 16)
672. A right triangle is inscribed in a circle. If the
triangle’s legs are 16 cm and 30 cm, what is the
664. Point O is two-thirds the way from A(-4,5) area of the circle?
to B(8,-10). Find the coordinates of point O. A. 289 π cm2 B. 480 cm2
A. (0, 0) B. (4, -5) C. 480 π cm2 D. 1156 π cm2
C. (3, -6) D. (3, -4)

673. In the figure, a rectangle is

665. ∠H and ∠K form a vertical pair. If m∠H = inscribed in a circle. If the rectangle
4x + 20 and m∠K = 6x – 10, find x. is 20 cm by 48 cm, what is the area of
A. 13 B. 15 C. 17 D. 19 the shaded figure?
A. 676π – 960 cm2 B. 1352π – 960 cm2
C. 2304π – 960 cm 2 D. insufficient data
No item #666, as requested by many subscribers.

674. What is the area of the red trapezium in the

667. ∠F and ∠G form a linear pair. If m∠F = given figure?
4x + 20 and m∠G = 6x – 10, find x.
A. 13 B. 15 C. 17 D. 19

668. Point C is two-fifths the way from M(-3,4) to

N(7,-11). Find the coordinates of point C.
A. (0, 0) B. (2, -1)
C. (1, -2) D. (1, -1) A. 23 sq. units B. 24 sq. units
C. 25 sq. units D. 26 sq. units

669. Find the slope of the line 5x – 6y = 7.

5 6 −5 −6
A. 6 B. 5 C. 6 D. 5

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1000 MMR Author: Victor A. Tondo Jr., LPT
675. Which of the following are not congruent? 682. Which of the following is false?
A. Corresponding angles formed by two parallel A. Radii of the same circle are always congruent.
lines cut by a transversal. B. Any two right angles are congruent.
B. Alternate exterior angles formed by two C. An inscribed right angle always intercepts a
parallel lines cut by a transversal. semicircle.
C. Pairs of vertical angles. D. There are infinitely many lines that may be
D. Interior angles on the same side of the drawn parallel to a given line passing through a
transversal cutting two parallel lines. given point.

676. A rectangle is 24 cm long. If its diagonal is 683. The volume of a cube is 343 cm3. What is its
25 cm, what is its perimeter in cm? surface area?
A. 49 B. 62 C. 64 D. 98 A. 24 cm2 B. 24√3 cm2
C. 48 √13 cm2 D. 294 cm2

677. Square FACE is drawn such that one of its

sides AC is the diagonal of a rectangle, ABCD. If 684. Find the volume of a rectangular plank of
AB = 20 and BC = 43, find the area of FACE. wood that is half-inch thick, six inches wide, and
6 feet long.
A. 2209 cm2 B. 2229 cm2 A. 18 cubic inches B. 36 cubic inches
C. 2249 cm2 D. 2269 cm2 C. 108 cubic inches D. 216 cubic inches

678. If the vertex angle of an isosceles triangle is 685. In the following figure, O is the center of the
50o, what is the measure of each base angle? circle. If m∠CAB = 36o, what is m∠DBA?
A. 130o B. 80o C. 65o D. 25o

679. Which of the following is a square?

A. VCTR whose sides measure 20 cm each
B. LUVS whose angles are 90o each
C. RWNA whose diagonals are 50 cm each A. 18o B. 36o C. 54o D. 72o
D. AYIE whose congruent diagonals
perpendicularly bisect each other
686. What is the measure of each interior angle
of a regular nonagon?
680. The following are measures of sides of four A. 135o B. 140o
triangles. Which of them are taken from an C. 144 o D. 145o
obtuse triangle?
A. 20, 20, 29 B. 20, 21, 29
C. 20, 22, 28 D. 20, 23, 30 687. Find the surface area of a ball whose radius
is 24 cm.
A. 576 π cm2 B. 1152 π cm2
681. Find the length of the intercepted arc of a C. 2304 π cm 2 D. 4608 π cm2
central angle measuring 60o given that the radius
of the circle is 12 cm.
A. 4 π cm B. 6 π cm
C. 8 π cm D. 12 π cm

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1000 MMR Author: Victor A. Tondo Jr., LPT
688. Give the converse of the conditional 693. How many diagonals does a regular
statement “If two angles are vertical angles, then decagon have?
they are congruent.” A. 30 B. 35 C. 40 D. 45
A. “If they are are congruent, then two angles are
vertical angles.”
B. “If two angles not vertical angles, then they are 694. Each side of a regular hexagon is 256 cm
not congruent.” long. Find the distance around it.
C. “If they are not congruent, then two angles are A. 1536 cm B. 1280 cm
not vertical angles.” C. 1024 cm D. 718 cm
D. “If two angles are linear angles, then they are
supplementary.”
695. What can be said about these statements?
i. Any rectangle has two congruent diagonals.
689. Give the inverse of the conditional ii. Any rhombus has two perpendicular
statement “If two angles are vertical angles, then diagonals.
they are congruent.” A. Only the first statement is true.
A. “If they are are congruent, then two angles are B. Only the second statement is true.
vertical angles.” C. Both statements are true.
B. “If two angles not vertical angles, then they are D. Both statements are false.
not congruent.”
C. “If they are not congruent, then two angles are
not vertical angles.” 696. In the figure, A is the midpoint of 𝐵𝐸 and
D. “If two angles are linear angles, then they are 𝐷𝐶. By which triangle congruence postulate can
supplementary.” we prove that △CAB ≅ △DAE?

690. In which geometry do two distinct lines

intersect in two points?
A. Euclidean Geometry
B. Hyperbolic Geometry
C. Elliptic Geometry
D. Plane Geometry

691. In which geometry can the sum of the A. SSS Congruence Postulate
measures of the angles of a triangle be less than B. SAS Congruence Postulate
180 degrees? C. ASA Congruence Postulate
A. Euclidean Geometry D. ASS Congruence Postulate
B. Hyperbolic Geometry
C. Elliptic Geometry
D. Plane Geometry 697. Find the circumference of a coin whose
radius is 13 cm.
A. 13 π cm B. 26 π cm
692. In which geometry are the summit angles of C. 169 π cm D. 676 π cm
a Saccheri quadrilateral obtuse angles?
A. Euclidean Geometry
B. Hyperbolic Geometry
C. Elliptic Geometry
D. Plane Geometry
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1000 MMR Author: Victor A. Tondo Jr., LPT
698. Find the area of a square whose perimeter 707. The longest side in a 30-60-90 triangle is
is 280 cm. 480 cm. How long is the shortest side?
A. 1120 cm2 B. 4900 cm2 A. 120 cm B. 160 cm
C. 19600cm2 D. 78400 cm2 C. 240 cm D. 360 cm

699. Find the altitude to the hypotenuse of a 708. If the hypotenuse of a 45-45-90 triangle is
right triangle whose legs are 60 cm and 80 cm. 50 cm long, how long is a leg?
A. 40 cm B. 48 cm A. 25 cm B. 25√2 cm
C. 96 cm D. 100 cm C. 25√3 cm D. 50√2 cm

700. This is formed by two rays with a common 709. Which of the ff. is coterminal with 143o?
end point. A. 2403o B. 2303o
A. polygon B. angle C. 2103o D. 2003o
C. line D. line segment

710. What is the measure of the smaller angle

7𝜋
701. Convert rad to degrees. formed by the hands of the clock at 5:55?
6
A. 210o B. 420o A. 180o B. 174.75o
C. 630o D. 840o C. 163.625o D. 152.5o

702. What is the reference angle of 212o? 711. What is the measure of the smaller angle
A. 32o B. 68o C. 106o D. 12o formed by the hands of the clock at 3:50?
A. 185o B. 175o
C. 170o D. 165o
703. A negative sine and a positive cosine are
properties of angles in which quadrant?
A. QI B. QII C. QIII D. QIV 712. Which of the following is false?
sin θ
A. tan θ = cos θ
cot θ
B. csc θ = cos θ
704. Which of the following equal to sec 50o?
tan θ
A. sin 40o B. cos 40o C. sec θ = sin θ
C. csc 40o D. cot 40o cot θ
D. sin θ = cos θ

705. Which of the ff. is coterminal with 2019o?

A. 219o B. 209o 714. If sin x = 0.936, which of the following could
C. 199o D. 189o be cos x?
A. 0.064 B. 0.8
C. 0.016 D. -0.352
706. The angle of elevation to the top of a
building is 30o. If the observer is 50√3 meters
away from the building, how tall is the building?
A. 25 m B. 25√3 m
C. 50 m D. 100 m

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1000 MMR Author: Victor A. Tondo Jr., LPT
715. A man stands 20 meters away from a 724. A sniper is on top of a 20-meter cliff. He
building. If the angle of elevation to the top of the spots a target at an angle of depression of 30o.
building is 60o, how tall is the building? How far must his bullet travel to hit the target?
A. 20√2 m B. 20√3 m A. 20 meters B. 20 √2 meters
C. 40 m D. 20√5 m C. 20 √3 meters D. 40 meters

−13 725. A meter stick leans to a wall and reaches a

716. If csc x = , what is sin x?
5
12 13 −5 −13 point 50 cm away from the wall. What is the
A. 13 B. 12 C. 13 D. measure of the angle formed by the meter stick
12
and the wall?
A. 30o B. 45o C. 60o D. 75o
5
717. If sec x = 4, which of the following could be
sin x?
−3 4 −4 3 726. A tight rope connects the top of a 500 cm
A. 5 B. 5 C. 5 D. 4
pole to the ground. If the angle formed by the
ground and the tight rope is 45o, how long is the
tight rope?
718. Which of the following is false? A. 500 cm B. 500√2 cm
A. cos A (tan A) = sin A
C. 500√3 cm D. 500√5 cm
B. csc A (cos A) = cot A
C. sin A (sec A) = tan A
D. tan A (csc A) = cos A
727. Which of the
following can be used
to solve for x in the
719. Which of the ff. is coterminal with 63o?
figure?
A. 7503o B. 7303o 𝐴
C. 7103o D. 6903o A. sin 𝐶
𝐴
B. cos 𝐶
𝐴
C. arcsin 𝐶
720. Convert 160oto radians.
16 8 4 2 𝐴
A. 9 π B. 9 π C. 9 π D. 9 π D. arccos 𝐶

721. What is the reference angle of 156o? 728. Evaluate: 2 sin 30 – 4 cos 60 + 3 tan 45.
A. 14o B. 24o C. 56o D. 66o A. -10.2378 B. -12.1426
C. 2 D. 1

722. In which quadrants is the sine function

negative? 729. Which of the following is true?
A. QI and QII B. QII and QIII A. sin x = sin (-x) B. cos x = cos (90 – x)
C. QIII and QIV D. QIV and QI C. –sin x = sin (-x) D. tan x = (sin x)(cos x)

723. What is the reference angle if 2019o?

A. 19o B. 39o C. 51o D. 59o

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1000 MMR Author: Victor A. Tondo Jr., LPT
730. Which of the following is true? A. x | x 𝜖ℝ B. x ≠ 1, 9
A. sin x = csc (90 – x) C. x > -81 D. x ≥ -81
B. cos x = csc (90 – x) 740. Give the range of f(x) = 2020.
C. tan x = cot (90 – x) A. y | y 𝜖ℝ B. y ≠ 2020
D. sec x = cos (90 – x) C. y = 2020 D. y = { }

2𝑥+3
731. Evaluate: lim 2019 741. Give the range of f(x) = 3𝑥−6
𝑥→0
A. 2019 B. -2019 2
A. y | y 𝜖ℝ B. y ≠ 3
C. 0 D. 1
C. y ≠ 2 D. y ≠ -2

732. Evaluate: lim(20𝑥 – 5x2)

𝑥→1 742. Give the range of f(x) = 20x – 20.
A. 1 B. 15 C. -15 D. 10 A. y | y 𝜖ℝ B. y ≠ 1
C. y = 20 D. y = { }

733. Evaluate: lim(𝑥3 – 5x2)

𝑥→3
A. 3 B. 18 C. -18 D. 72 743. Give the range of f(x) = x125.
A. y | y 𝜖ℝ B. y > 0
C. y ≠ 2019 D. y = { }
𝑥 2 −4
734. Evaluate: lim
𝑥→2 𝑥−2
A. LDNE B. 2 C. 4 D. 0 744. Give the range of f(x) = 6𝑥+7
5𝑥−4

5
A. y | y 𝜖ℝ B. y ≠ 6
2𝑥 3 −4𝑥+9 −7
735. Evaluate: lim C. y ≠ D. y ≠ -2
𝑥→+∞ 𝑥+3 6
A. +∞ B. -∞ C. LDNE D. 2

745. Give the range of f(x) = x2019.

5𝑥 3 −10𝑥+8 A. y | y 𝜖ℝ B. y > 0
736. Evaluate: lim
𝑥→+∞ 8𝑥 3 +2𝑥−3 C. y ≠ 2019 D. y = { }
5
A. +∞ B. -∞ C. LDNE D. 8

746. Give the range of f(x) = 2019x – 2019.

2𝑥+3 A. y | y 𝜖ℝ B. y ≠ 1
737. Give the domain of f(x) = 3𝑥−6
2 C. y = 2019 D. y = { }
A. x | x 𝜖ℝ B. x ≠ 3
C. x ≠ 2 D. x ≠ -2
7𝑥−9
747. Give the range of f(x) = 8𝑥+11
−11
A. y | y 𝜖ℝ B. y ≠
738. Give the domain of f(x) = √2018𝑥 − 2019. 8
2019 9 7
A. x | x 𝜖ℝ B. x ≠ 2018 C. y ≠ 7 D. y ≠ 8
2019
C. x > 0 D. x ≥ 2018
5𝑥−10
748. Give the domain of f(x) = 3𝑥+9
5
739. Give the domain of f(x) = x2 – 20x + 19. A. x | x 𝜖ℝ B. x ≠ 3

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1000 MMR Author: Victor A. Tondo Jr., LPT
C. x ≠ 2 D. x ≠ -3 757. Find the slope of the line tangent to
y = 3x5 – 4x3 + 5x2 – 10x + 9 at x = 2.
749. What is 0! equal to? A. 50.5 B. 101 C. 151.5 D. 202
A. 0 B. 1 758. Find the remainder when 1998! is divided
C. undefined D. +∞ by 2000.
A. 1024 B. 256 C. 64 D. 0

750. Give the range of f(x) = 2019x + 2020.

A. y | y 𝜖ℝ B. y > 2020 759. In Mathematics, what does the delta ∆
C. y ≠ 2019 D. y ≠ 2020 symbol mean or refer to?
A. the change in B. the summation of
C. therefore D. belonging to
751. Find the first derivative: f(x) = (2x + 3)5.
A. f ’(x)= 5 (2x + 3)4
B. f ’(x)= 10 (2x + 3)4 760. In Mathematics, what does the sigma Σ
C. f ’(x)= 15 (2x + 3)4 symbol mean or refer to?
D. f ’(x)= 20 (2x + 3)4 A. the change in B. the summation of
C. therefore D. belonging to

752. Find f ‘(x) given f(x) = (3x2 – 2x + 1 )7.

A. f ’(x)= (42x – 14) (3x2 – 2x + 1)6 761. In Mathematics, what does the epsilon ∈
B. f ’(x)= (42x – 28) (3x2 – 2x + 1)6 symbol mean or refer to?
C. f ’(x)= (42x + 14) (3x2 – 2x + 1)6 A. such that B. element of
D. f ’(x)= (42x + 28) (3x2 – 2x + 1)6 C. therefore D. ergo

753. Find the maximum area that can be 762. In set theory, what does the symbol ∅ mean
enclosed by a rectangle given its perimeter or refer to?
should only be 202 meters. A. not O B. not zero
A. 2550 m2 B. 2550.25 m2 C. does not D. empty
C. 2550.5 m2 D. 2550.75 m2

763. Which of the following is ALWAYS an odd

754. Find the lowest possible value of the number?
function f(x) = x2 – 8x + 7. A. The difference of two odd numbers.
A. -10 B. -9 C. -8 D. -7 B. The sum of two odd numbers.
C. The product of two odd numbers.
D. The product of two even numbers.
755. Find the instantaneous rate of change for
f(x) = 5x3 – 2x2 + 7x – 9 at x = 2.
A. 37 B. 48 C. 59 D. 70 764. Given 2x + 2x = 2y, express y in terms of x.
A. y = 2x B. y = x2
C. y = x + 2 D. y = x + 1
756. Find the instantaneous rate of change for
f(x) = 4x3 + 5x2 – 7x – 11 at x = 1.
A. -15 B. 0 C. 15 D. 30 765. In set theory, what does the symbol ∩ mean
or refer to?
A. no elements B. common elements
C. all elements D. half of the elements
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1000 MMR Author: Victor A. Tondo Jr., LPT
C. A – B D. B – A
774. Which of the
766. In Mathematics, what does the symbol ∴ following
mean? represents the
A. since B. prove shaded region in
C. therefore D. previously the Venn diagram?
A. A’ ∪ B’
B. A’ ∩ B’
767. Which of the following is the Geometric C. (A ∩ B)’
symbol for congruent? D. (A ∪ B)’
A. ≅ B. ≈ C. ≡ D. //

775. In a class of 50, there are 20 students who

768. Which of the following is the obelus sign? excel in Math, 24 who excel in Science, and 4 who
A. ! B. ÷ C. ⊙ D. θ excel in both Math and Science. How many of
them excel in neither?
A. 2 B. 4 C. 7 D. 10
769. Given X = {1, 4, 16, 64} and Y = {1, 2, 3, 4},
find X ∩ Y.
A. {1, 4} B. {16, 64} 776. There are 50 students in a class. 39 of them
C. {2, 3} D. {1, 2, 3, 4, 16, 64} have a cellphone, 17 of them have a laptop, and 5
of them have neither. How many have both a
cellphone and a laptop?
770. Given X = {1, 2, 4, 8} and Y = {1, 2, 3, 4}, find A. 6 B. 7 C. 9 D. 11
X – Y.
A. {1, 4, 8} B. {8}
C. {3, 8} D. {1, 2, 3, 4, 8} 777. Rayon has 10 shirts, 5 pairs of pants, and 4
pairs of shoes. How many ways can he pick what
to wear for today?
771. Given X = {1, 2, 4, 8} and Y = {1, 2, 3, 4}, find A. 19 B. 20 C. 190 D. 200
Y – X.
A. {1, 4, 8} B. {3}
C. {3, 8} D. {1, 2, 3, 4, 8} 778. Using the digits 1, 2, 3, 4, 5, and 6 without
repetition, how many 3-digit numbers can be
made?
772. Given X = {6, 5, 4, 3} and Y = {1, 2, 3, 4}, find A. 480 B. 240 C. 120 D. 60
X ∪ Y.
A. {3, 4} B. {6, 5}
C. {1, 2} D. {1, 2, 3, 4, 5, 6} 779. Using the digits 1, 2, 3, 4, 5, 6, and 7 without
repetition, how many 4-digit numbers can be
made?
A. 1680 B. 840 C. 420 D. 210

773. Which of the

following 780. Using the digits 0, 1, 2, 3, 4, 5, and 6 without
represents the repetition, how many 3-digit numbers can be
shaded region in made?
the Venn diagram? A. 360 B. 180 C. 90 D. 45
A. A ∩ B B. A ∪ B
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1000 MMR Author: Victor A. Tondo Jr., LPT

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1000 MMR Author: Victor A. Tondo Jr., LPT
781. Using the digits 0, 1, 2, 3, 4, 5, 6, and 7 789. Evaluate: log6 8 + 3 log6 3.
without repetition, how many 4-digit numbers A. 24 B. 14 C. 9.5 D. 3
can be made?
A. 1680 B. 1470 C. 840 D. 735
790. How many ways can the word ABABA be
rearranged?
782. Using the digits 0, 1, 2, 3, 4, 5, 6, and 7 A. 120 B. 60 C. 20 D. 10
without repetition, how many 3-digit numbers
can be made?
A. 672 B. 588 C. 336 D. 294 791. There are 10 different beads and a locking
mechanism to be used in making a bracelet. How
many different bracelet patterns can be made?
783. Using the digits 0, 1, 2, 3, 4, 5, and 6 without A. 3,628,800 B. 362,880
repetition, how many odd 3-digit numbers can C. 1,814,400 D. 181,440
be made?
A. 180 B. 150 C. 90 D. 75
792. There are six different Math books, four
different Science books, and two different
784. Using the digits 0, 1, 2, 3, 4, 5, 6, and 7 English books to be arranged on a shelf. How
without repetition, how many odd 4-digit many ways can this be done?
numbers can be made? A. 12C3 B. 12! C. 48 D. 3!
A. 1470 B. 1440 C. 735 D. 720

793. There are six different Math books, four

785. Using the digits 0, 1, 2, 3, 4, 5, 6, and 7 different Science books, and two different
without repetition, how many odd 3-digit English books to be arranged on a shelf. If books
numbers can be made? of the same subject must be together, how many
A. 336 B. 288 C. 168 D. 144 ways can this be done?
A. 479,001,600 B. 207,360
C. 34560 D. 144
786. Using the digits 0, 1, 2, 3, 4, 5, 6, and 7
without repetition, how many even 3-digit
numbers can be made? 794. There are six people to be seated on a bench
A. 162 B. 156 C. 150 D. 144 for a picture. A certain couple, Vic and Rowena,
are to be seated next to each other. How many
ways can this be done?
787. Using the digits 0, 1, 2, 3, 4, 5, 6, and 7 A. 120 B. 240 C. 360 D. 720
without repetition, how many even 4-digit
numbers can be made?
A. 765 B. 750 C. 735 D. 720 795. There are six people to be seated on a bench
for a picture. A certain trio, Vic, Rayon, and Aira,
do not want to be separated. How many ways
788. Using the digits 0, 1, 2, 3, 4, 5, and 6 without can this be done?
repetition, how many even 3-digit numbers can A. 60 B. 72 C. 144 D. 180
be made?
A. 120 B. 105 C. 90 D. 75

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1000 MMR Author: Victor A. Tondo Jr., LPT
796. TNB Gaming has five “carry” players, four 804. There are ten red, nine blue, and six black
“offlane” players, and six “support” players. If a pens in a bag. If a pen is randomly drawn from
game calls for two carry, one offlane, and two the bag, what is the probability that it is red?
2 2 3 4
support players, how many possible lineups do A. 5 B. 3 C. 4 D. 5
they have?
A. 1200 B. 600 C. 300 D. 150
805. There are ten red, nine blue, and six black
pens in a bag. If a pen is randomly drawn from
797. If today is a Sunday, what day is 125 days
the bag, what is the probability that it is black?
from now?
A. 0.06 B. 0.6 C. 0.24 D. 0.7
A. Friday B. Saturday
C. Sunday D. Monday
806. What does a probability of 0 pertain to?
A. an impossible event
798. If today is a Monday, what day is 200 days
B. a very unlikely event
from now?
C. a very likely event
A. Friday B. Saturday
D. a sure event
C. Sunday D. Monday

799. If three-fourths of a number is 33 more than 807. Simplify: √10 + 2√21.

one-fifth of itself, then what is the number? A. √2 + √5 B. √3 + √7
A. 80 B. 60 C. 40 D. 20 C. √3 − √2 D. √5 − √2

800. What time is 2019 hours after 3:00PM? 808. Simplify: √11 − 2√30.
A. 6:00 AM B. 12:00 NN
A. √6 − √5 B. √6 + √5
C. 6:00 PM D. 12:00 MN
C. √3 − 2√2 D. 1

801. In a certain fastfood chain, soft drinks are

served in Small, Medium, and Large cups. 809. ∫(3𝑥 + 4)5 dx
1 1
What level of data is this? A. 6 (3x + 4)6+ c B. 2
(3x + 4)6+ c
A. Nominal B. Ordinal 1
C. 5(3x + 4)4+ c D. 18 (3x + 4)6+ c
C. Interval D. Ratio

810. ∫(6𝑥 2 + 6𝑥 − 6) dx
802. The prime factorization of a number is
given as 23 x 52 x 133. How many factors does it A. 2x3 + 3x2 + 6x + c B. 2x3 – 3x2 + 6x + c
have? C. 2x3 + 3x2 – 6x + c D. 2x3 – 3x2 – 6x + c
A. 96 B. 48 C. 36 D. 18
1
811. ∫ 𝑥 2 dx
803. The prime factorization of a number is 1 2
A. 𝑥 + c B. 𝑥 + c
given as 22 x 32 x 7 x 11. How many factors does −1 −2
it have? C. 𝑥
+c D. 𝑥
+c
A. 96 B. 48 C. 36 D. 18

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1000 MMR Author: Victor A. Tondo Jr., LPT
1 𝑑
812. ∫ 𝑥 3 dx 818. 𝑑𝑥 (x2 + 3x – 2)4 = _________
−1 1
A. 2𝑥 2 + c B. 2𝑥 2 + c A. (x2 + 3x – 2)3
2 −2 B. 4(x2 + 3x – 2)3
C. 𝑥 2 + c D. 𝑥 2 + c C. (8x + 12) (x2 + 3x – 2)3
D. (2x + 3) (x2 + 3x – 2)3

813. Mr. dela Cruz is going to present the growth

of a certain plant over a span of 10 weeks. Which 𝑑
819. 𝑑𝑥 √𝑥 3 − 2𝑥 + 3 = _________
graph would be best suited for this?
A. bar graph B. line graph 1 −2
A. B. √𝑥 3
C. pie graph D. pictograph 2√𝑥 3 −2𝑥+3 −2𝑥+3
3𝑥 2 −2 3𝑥 2 −2
C. √𝑥 3 D.
−2𝑥+3 2√𝑥 3 −2𝑥+3

814. Rayon is going to present the sales of six

different teams in the company from January to 820. (2x + 3)(4x – 5) = _________
June. Which graph would be best suited for this? A. 8x2 + 2x + 15 B. 8x2 + 2x – 15
A. bar graph B. line graph C. 8x – 2x – 15
2 D. 8x2 – 2x + 15
C. pie graph D. pictograph

𝑑 2𝑥+1
821. 𝑑𝑥 (3𝑥−4) = _________
815. Ms. Rowena is tasked to send 8 randomly 1 11
selected students from her class of 40 to the A. (3x−4)2 B. (3x−4)2
clinic for drug test. She decides to let the −11 −10
C. (3x−4)2 D. (3x−4)2
students count off from 1 to 5, after which she
randomly picks a number from 1 to 5. All
students whose number is that which she picked
will be sent to the clinic. What sampling method 822. There are 17 red bags, 19 green bags, and
did Ms. Rowena use? 14 blue bags in a store. What percent of the bags
A. cluster B. systematic is blue?
C. stratified D. quota A. 38% B. 34%
C. 28% D. 27%

816. What is the 7th decile of the following data?

14 15 16 20 24 823. Which of the following is true?
25 26 26 27 29 A. (sin x) (cot x) = sec x
31 33 34 34 35 B. (cos x) (csc x) = tan x
C. (tan x) (csc x) = sec x
A. 31 B. 31.4 C. 31.5 D. 32 D. (cot x) (sec x) = cos x

817. Find the remainder when f(x) is divided by 824. Which of the following could be the value of
(x – 3) given f(x) = x3 – 3x2 + 5x – 13. x if x ≅ 4 (mod 10)?
A. 1 B. 2 C. 3 D. 4 A. 46 B. 49 C. 52 D. 54

825. Which of the following could be the value of

x if x ≅ 7 (mod 9)?
A. 146 B. 149 C. 151 D. 154

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1000 MMR Author: Victor A. Tondo Jr., LPT
826. Given ̅̅̅̅
BF bisects ∠ABC and m∠ABF = 34o, 834. Fifteen guests shake hands with each other.
find m∠ABC. If each guest is to shake hands with all the other
A. 17o B. 34o C. 51o D. 68o guests, how many handshakes will be made?
A. 105 B. 150 C. 210 D. 225

827. If f(x) = x2 – 2x + 3 and g(x) = x + 1, find

fog(x). 835. The salary of 5 men for 6 days is P9,000.
A. x2 – 1 B. x2 – 2x + 4 How much is the salary of 7 men for 8 days?
C. x – 3x + 5
2 D. x2 + 2 A. P15,000 B. P15,600
C. P16,800 D. P17,400

828. How many 3-digit numbers can be formed

using the digits 0, 1, 2, 3, 4, 5, and 6 if repetition 836. The average grade of eleven students is 84.
is not allowed? If the average of seven of these students is 82,
A. 160 B. 180 C. 200 D. 210 what is the average of the other four students?
A. 88 B. 87.5 C. 86.5 D. 86

829. What is the longest side of ∆VAC if m∠V =

45o and m∠C = 65o? 837. A radius of a circle is 25 cm long. How long
A. ̅̅̅̅
VC B. ̅̅̅̅
AC C. ̅̅̅̅
VA D. ̅̅̅̅
CA is its longest chord?
A. 20√2 cm B. 40 cm
C. 50 cm D. It depends,
830. Which quadrilateral has two congruent
diagonals that are perpendicular to each other?
A. kite B. isosceles trapezoid 838. Find the largest area of a rectangular piece
C. rectangle D. rhombus of land that can be enclosed with 800 meters of
fencing material.
A. 40,000 m2 B. 56,250 m2
831. If the length of a rectangle is increased by C. 62,500 m 2 D. 80,000 m2
30% while the width is decreased by 30%, what
will happen to its area?
A. It stays the same. 839. Which statistical test is used for testing for
B. It is increased by 9%. relationship between two variables?
C. It is decreased by 9%. A. ANOVA B. t-test
D. It is decreased by 6%. C. Pearson R D. Chi Square

832. Rayon had an average of 93 on his first five 2𝑥 + 4; 𝑥 < 5

Math tests. After taking the next test, his average 840. Given 𝑓(𝑥) = { 5; 𝑥 = 5,
increased to 94. Find his most recent grade. 𝑥 2 − 9; 𝑥 > 5
A. 96 B. 97 C. 98 D. 99 find lim 𝑓(𝑥).
𝑥→5
A. 5 B. 14
C. 16 D. limit does not exist
833. A bus drove for 7 hours at 73 kph and 3
hours at 88 kph. What was its average speed?
A. 75.5 kph B. 76.5 kph 841. Find the equation of the line passing
C. 77.5 kph D. 78.5 kph through (3, 7) and (-3, -5).

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1000 MMR Author: Victor A. Tondo Jr., LPT
A. y = 2x + 1 B. y = 3x + 1 849. The sum of two numbers is 73 and their
C. y = 2x – 1 D. y = 3x – 1 difference is 41. What is the larger number?
842. In which non-Euclidean model for geometry A. 65 B. 61
can we have any given line ℓ and a point A which C. 57 D. 53
is not on ℓ, wherein all lines through A will
intersect ℓ?
A. hyperbolic B. elliptic 850. An item is sold for P7,280 after being
C. Saccheri D. Pythagorean marked down by 30%. What was its original
price?
A. P11,400 B. P10,900
843. If A is at (-9, 11) and B is at (6,-9), find C if C C. P10,400 D. P9,900
is three-fifths the way from A to B.
A. (1, -1) B. (0, 1)
C. (1, 1) D. (0, -1) 851. Which of the following lines passes through
the point (-4, 5)?
A. y = x + 1 B. y = 2x – 3
844. Find the vertex of y = 5x2 – 4x – 7.
1 39 1 −39
C. y = 1 – x D. y = 3 – 2x
A. (5 , 5 ) B. (5 , 5 )
2 39 2 −39
C. (5 , 5 ) D. (5 , )
5 852. Which of the following is outside the circle
defined by the equation (x + 2)2 + y2 = 50?
A. (-9, 1) B. (-7, 5)
845. Mr. G sold 70% of his chickens and still had C. (-5, 7) D. (2, 4)
129 chickens left. How many chickens did he
have originally?
A. 344 B. 430 853. Which of the following equations pertain to
C. 598 D. 860 a parabola?
A. y2 – 5y = x2 + 4
B. x2 + 5x – 4y = 13
846. Find the average rate of change of (𝑥+3)2 (𝑦−5)2
y = x3 – 6x2 + 5x – 20 from x = 1 to x = 6. C. + =1
36 25
A. 5 B. 6 (𝑥+7)2 (𝑦+1)2
D. − =1
C. 7 D. 8 16 9

854. Which of the following equations pertain to

847. What is the remainder when
a parabola that opens to the left?
534,214,557,989,215 is divided by 4?
A. -2(y + 7) = (x – 3)2
A. 1 B. 2 C. 3 D. 0
B. 5(y – 9) = (x – 5)2
C. (y – 4)2 = 2(x + 7)
D. (y + 3)2 = -3(x + 4)
848. What do you call an equation in which only
integer solutions are allowed?
A. Diophantine equations
855. The lengths of two sides of a triangle are 7
B. Euclidean equations
inches and 15 inches. Which of the following
C. Fibonacci equations
represents x, the possible length in inches of the
D. Newtonian equations
remaining side of the triangle?
A. 8 < x < 22 B. 8 ≤ x ≤ 22
C. x < 8 or x > 22 D. x ≤ 8 or x ≥ 22
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1000 MMR Author: Victor A. Tondo Jr., LPT
856. Rayon has 46 coins in P1 and P5 865. Which of the following Mathematicians had
denominations for a total worth of P186. How a method “Sieve” for identifying prime numbers?
many P5 coins does he have? A. Pythagoras B. Euclid
A. 25 B. 30 C. 35 D. 40 C. Eratosthenes D. Archimedes

857. If x = 2 and y = 3, what is x2 – y2 + 3xy? 866. Which Mathematician developed a formula

A. 31 B. 13 C. -5 D. -13 for finding the area of a triangle using its side
lengths?
A. Hipparchus B. Pythagoras
858. In an arithmetic sequence, the first term is C. Heron D. Euclid
200 and the common difference is -3. What is the
64th term?
A. 20 B. 17 C. 14 D. 11 867. Who refined and perfected the decimal
place value number system?
A. Greeks B. Romans
859. In an arithmetic sequence, the 23rd term is C. Chinese D. Indians
157 and the common difference is -4. What is the
34th term?
A. 113 B. 117 C. 121 D. 125 868. This Mathematician invented natural
logarithms.
A. Isaac Newton B. John Napier
860. Find the inverse of y = x2 – 6x + 5. C. Marin Mersenne D. Rene Descartes
A. √𝑥 + 4 + 3 B. √𝑥 + 4 – 3
C. √𝑥 − 4 + 3 D. √𝑥 − 4 – 3
869. Prime numbers that are 1 less than a power
of 2 are called ______.
861. ln e4 = _____ A. Pythagorean Primes B. Mersenne Primes
A. 24.1295 B. 12.06475 C. Fermat Primes D. Pascal Primes
C. 6.032375 D. 4

870. Which Mathematician developed the

862. eln 5 = _____ triangle of binomial coefficients?
A. 5 B. 6.25 C. 12.5 D. 25 A. Gottfried Leibniz B. Isaac Newton
C. Blaise Pascal D. Johann Bernoulli

863. What is ln e?
A. 0 B. 1 C. e D. 10 871. Two Mathematicians are known for the
theory of hyperbolic geometry although they
worked independently from each other. Who are
864. Who are the first to use papyrus? these Mathematicians?
A. Sumerians B. Egyptians A. Euclid and Pythagoras
C. Chinese D. Greeks B. Euclid and Descartes
C. Lobachevsky and Bolyai
D. Babbage and Bolyai

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1000 MMR Author: Victor A. Tondo Jr., LPT
7𝜋
872. Which Mathematician developed the use of 879. Convert 12 rad to degrees.
AND, OR, and NOT operators in Algebra?
A. 70o B. 105o
A. George Boole C. 210o D. 420o
B. Janos Bolyai
C. Charles Babbage
D. August Mobius
880. Find the volume of a cylinder whose radius
is 50 cm and height is 24 cm.
A. 20,000 π cm3 B. 30,000 π cm3
873. Which Mathematician is known for his last
C. 45,000 π cm3 D. 60,000 π cm3
theorem?
A. Andrew Wiles
B. Pierre de Fermat 881. Find the altitude to the hypotenuse of a
C. John Wallis
right triangle whose legs measure 16 cm and 30
D. Rene Descartes
cm.
240
A. 17 cm B. 240 cm
874. Who have the first fully-developed base-10 C. 34√2 cm D. 24√3 cm
number system in use?
A. Romans B. Egyptians
C. Indians D. Sumerians 882. How many line segments can be made from
25 non-collinear points?
A. 900 B. 600 C. 450 D. 300
875. Notched tally bones proved their use of
Mathematics around 35000 BCE.
A. Africans B. Asians 883. Dividing by 0.25 is the same as multiplying
C. Europeans D. Americans by which number?
A. 2 B. 4 C. 5 D. 16

876. Which sampling method is best used when

the population has subgroups? 884. Find the surface area of a sphere whose
A. systematic sampling radius is 24 cm.
B. stratified sampling A. 192 π cm2 B. 768 π cm2
C. quota sampling C. 1152 π cm2 D. 2304 π cm2
D. cluster sampling

885. Which of the following is the reference

877. Mr. Lazada drove for 2 hours at a speed of angle of 295o?
48 kph, 3 hours at 58 kph, and then 5 hours at 64 A. 25o B. 45o C. 65o D. 75o
kph. What was his average speed?
A. 57 kph B. 58 kph
C. 59 kph D. 60 kph 886. Which numerical system is sexagesimal
(base-60)?
A. Roman B. Babylonian
878. Find the domain of y = 3x. C. Mayan D. Hindu-Arabic
A. x | x 𝜖ℝ B. x ≠ 0
C. x ≠ 3 D. x > 0

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1000 MMR Author: Victor A. Tondo Jr., LPT
887. In solid geometry, what do you call a solid 894. The amount of money you have falls under
bound by polygons? what level of data?
A. tessellation B. multigon A. nominal B. ordinal
C. polyhedron D. soligon C. interval D. ratio

888. Two triangles have a pair of congruent 895. To study tooth decay a researcher takes a
angles. Which of the following is true about these sample at random but with the stipulation that
triangles? all age groups are represented proportionally.
A. They are isosceles triangles. What sampling method did the researcher use?
B. They are equilateral triangles. A. systematic B. cluster
C. They are congruent triangles. C. stratified D. convenience
D. They are similar triangles.

896. By what property do we say that when

889. Rayon deposited an amount of P500,000 in A = B and B = C, then A = C?
a bank that offers 4% interest compounded per A. reflexive B. symmetrical
annum. How much will he have in his account C. transitive D. closure
after 3 years?
A. P720,000 B. P600,000
C. P560,000 D. P562,432 897. In number theory, what do we call a
polynomial equation with integer coefficients
that also allows the variables and solutions to be
890. Find the range of the following scores: integers only?
37 40 44 45 41 39 48 A. Integral equations
B. Differential equations
A. 7 B. 9 C. 10 D. 11
C. Diophantine equations
D. Bolyai-Lobachevsky equations
891. What is the 9th decile of the following data?
13 15 17 19 21
898. How long is the latus rectum of the parabola
23 24 26 28 29
defined by (y + 3)2 = 20x – 196?
30 33 35 36 40
A. 3 B. 12 C. 20 D. 19
A. 34 B. 35.5 C. 37.6 D. 38

899. In the set of real numbers, what do we call

892. -20192 is NOT equal to ___. the set that includes only the counting numbers
A. (-2019)2 C. (-20192) and zero?
B. –(2019 x 2019) D. –(2019)2 A. rational numbers B. integers
C. whole numbers D. irrational numbers

893. The product of two numbers is 1425. If each

of the two numbers is doubled, the product of 900. Find the sum of the first 60 counting even
these larger numbers is _____. numbers.
A. 2,850 B. 5,700 A. 3660 B. 3600 C. 1830 D. 900
C. 8,550 D. 11.400

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1000 MMR Author: Victor A. Tondo Jr., LPT
901. If M and N are complementary angles, 908. Find the radius of x2 + y2 + 12x – 14y = 36.
which of the following is true? A. 6 B. 7 C. 11 D. 13
A. cos M = sec N B. sin M = cos N
C. tan M = csc N D. sec M = -cos N
909. Find the instantaneous rate of change for
f(x) = 4x3 + 7x2 – 27x – 49 at x = 1.
902. The top ten students of a graduating class A. -2 B. -1 C. 1 D. 2
got the following scores in their final
examination in Calculus:
89 84 83 89 89 910. log3 24 – 3 log3 2 = _____
85 88 93 83 98 A. 1 B. 0 C. -1 D. e
What is their mean score?
A. 87.4 B. 87.5 C. 88.1 D. 89.3
911. After using one-sixth of her budget on bills,
two-fifths on groceries, and P1700 on books and
903. The top ten students of a graduating class magazines, Mrs. Lazada still had P7400 left. How
got the following scores in their final much was her budget?
examination in Calculus: A. P20,000 B. P21,000
89 84 83 89 89 C. P22,500 D. P30,000
85 88 93 83 98
What is the modal score?
A. 83 B. 85 C. 89 D. 98 912. An assistant’s response times were
recorded on the table below. What is her average
response time in minutes?
904. The sum of five consecutive integers is 980. Response Time Frequency
What is the value of the greatest integer? 1 minute 3
A. 192 B. 194 C. 196 D. 198 2 minutes 7
3 minutes 11
4 minutes 9
905. x varies directly as y and inversely as z. If 5 minutes 5
x = 20 when y = 10 and z = 3, what is x when 6 minutes 3
y = 15 and z = 9? 7 minutes 2
A. 10 B. 15 C. 25 D. 30
A. 3.625 B. 3.575 C. 3.525 D. 3.5

906. Factorize 15x2 – 13x – 20.

A. (5x – 4)(3x – 5) B. (5x – 4)(3x + 5) 913. The average grade of 22 students in Section
C. (5x + 4)(3x – 5) D. (5x + 4)(3x + 5) Abaca is 95, while the average grade of 28
students in Section Acacia is 89. What is the
average grade of all 50 students in both sections?
907. Which of the following is the axis of A. 92.36 B. 91.64 C. 90.72 D. 89.8
symmetry of the parabola defined by the
equation y = x2 – 6x + 5?
A. x = 5 B. x = -5
C. x = 3 D. x = -3

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1000 MMR Author: Victor A. Tondo Jr., LPT
914. Find the slope of 2x – 6y = 13. 922. If x = 10, which of the following is equal to
1 −1
A. 3 B. C. -3 D. 219?
3 3
A. 23x – 1 B. 2x2 + 5x + 5
C. 2x2 + 2x – 1 D. x2 + x + 2
915. Find the intersection of y = -3x – 2 and
y = 2x + 23.
923. In the equation 3x – 4y = 25, what is x when
A. (5, 13) B. (-5, -13)
y is 5?
C. (5, -13) D. (-5, 13)
A. 18 B. 15 C. 12 D. 9

916. A book was sold for P630 after a 10%

924. What is the measure of each interior angle
discount was given. How much was the book
of a regular 30-sided polygon?
originally?
A. 158o B. 162o
A. P800 B. P750
C. 165 o D. 168o
C. P700 D. P690

1−cos 𝑥
917. If the sum of the supplement and the 925. Simplify: sin 𝑥
complement of an angle is 146, what is the A. csc x – tan x B. csc x + tan x
angle? C. csc x – cot x D. csc x + cot x
A. 61 B. 62 C. 63 D. 64

𝑥 2 𝑦 −3 𝑦4
926. Simplify: x 𝑥3𝑧
918. A bag contains some marbles. When the 𝑧 −2
𝑥𝑦 𝑥𝑧 𝑥 𝑦𝑧
marbles are grouped by 2, 3, 4, 5, or 6, there is A. B. C. 𝑦𝑧 D.
𝑧 𝑦 𝑥
always one marble left. Which of the following
could be the number of marbles in the bag?
A. 31 B. 41 C. 51 D. 61 927. Which of the following is a diagonal matrix?
1 6 9 0 2 4
A. [−2 2 6] B. [1 0 5]
919. Amitaf, Bernard, and Chloe share a total of 3 4 3 2 3 0
P2,460 in the ratio 3:5:4 respectively. How much 4 0 0 3 2 3
is Amitaf’s share? C. [0 5 0 ] D. [2 3 6]
A. P600 B. P615 0 0 −6 1 4 3
C. P630 D. P660

928. Which of the following is a scalar matrix?

920. Fifty-four kilometers per hour is equal to 5 −7 9 0 2 3
how many meters per second? A. [ 2 8 6 ] B. [ 4 0 7]
A. 15 B. 30 C. 54 D. 60 −3 4 3 3 −8 0
7 0 0 7 0 0
C. [0 −5 0] D. [0 7 0]
930 0 0 6 0 0 7
921. Simplify 360.
3 2
A. 1 B. 2 C. 3 D. 2

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1000 MMR Author: Victor A. Tondo Jr., LPT
929. Which of the following is an identity matrix? 936. Which of the following graphs have a
1 0 0 0 5 3 positive leading coefficient and an even degree?
A. [0 1 0] B. [−4 0 9]
0 0 1 7 10 0
6 1 1 0 1 1
C. [1 12 1 ] D. [1 0 1]
1 1 18 1 1 0
A.

930. Which of the following is the transposition

1 4 3
of A = [ ]?
5 10 15
5 10 15 4 5 15 B.
A. AT = [ ] B. AT = [ ]
1 4 3 10 1 3
1 5 1 4 3
C. AT = [4 10] B. AT = [5 10 15]
3 15 1 1 1

931. When dealing with matrices A, B, and C,

which of the following is always true?
A. AB = BA
B. If AB = 0, then A = 0 or B = 0 C.
C. If AB = AC, then B = C
D. None of the above.

932. If the numbers x-1, x+2 and 2x+4 are

consecutive terms of a geometric sequence, what
is x?
A. 1 B. 2 C. 4 D. 8
D.
933. What are the zeros of 12x2 – x – 35?
4 −3 −4 3
A. 7 and 5 B. 7 and 5
7 −5 −7 5
C. 4 and D. and 3
3 4

934. What is the sum of the interior angles of a

regular dodecagon?
A. 1620o B. 1800o
C. 1980o D. 2160o

𝑑
935. 𝑑𝑥 45x – 20 = _____.
A. 45x – 20 B. 5(45x – 20)
C. 20(4 5x – 20) D. (5x – 20)(45x – 20)

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1000 MMR Author: Victor A. Tondo Jr., LPT
937. Which of the following graphs have a 939. What can be said about the equation f(x) of
negative leading coefficient and an odd degree? the following graph?

A.
A. The leading coefficient is positive.
B. The constant is positive.
C. The degree is 4.
D. The function is logarithmic.

B.
𝑥 2 + 1; 𝑥 < 4
940. If 𝑓(𝑥) {2𝑥 + 1; 𝑥 = 4 , find lim 𝑓(𝑥).
𝑥→4
5𝑥 − 3; 𝑥 > 4
A. Limit does not exist. B. 9
C. 13 D. 17

2𝑥 + 1; 𝑥<3
C. 941. If 𝑓(𝑥) { 7 ; 𝑥 = 3 , find lim 𝑓(𝑥).
2 𝑥→3
𝑥 − 3; 𝑥>3
A. 3 B. 6
C. 7 D. Limit does not exist.

942. Give the domain of f(x) = √8𝑥 + 24.

A. x | x 𝜖ℝ B. x ≠ -3
C. x > 24 D. x ≥ -3

D.
943. What is the 3rd term in the expansion of
(A + B)5?
938. Given f(x) = (x + 2)(x – 1)(2x – 3)(x – 5), A. 5A4B B. 10A3B2
where can we find f(3)? C. 10A B
2 3 C. 5A3B2
A. On the x-axis.
B. Above the x-axis.
C. Below the x-axis. 944. Find the remainder when
D. On the intersection of the x- and y-axis. 2x4 – 5x3 + 3x2 – 5x + 7 is divided by (x – 1).
A. 1 B. 2 C. 4 D. 7

3𝑥+4
945. Give the range of f(x) = 5𝑥−8
8
A. y | y 𝜖ℝ B. y ≠ 5
3
C. y ≠ 5 D. y ≠ 0

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1000 MMR Author: Victor A. Tondo Jr., LPT
946. In the arithmetic sequence -2, 1, 4, 7, …, 954. The freezing temperature of water is 0o
which term is 100? Celsius. What level of data is temperature in
A. 34th B. 35th C. 36th D. 37th Celsius?
A. nominal B. ordinal
C. interval D. ratio
947. Find the length of the intercepted arc of a
central angle measuring 45o given the radius is
80 cm. 955. Factorize: x3 + 5x2 – 9x – 45
A. 20 π cm B. 30 π cm A. (x + 1)(x + 9)(x – 5)
C. 40 π cm D. 50 π cm B. (x + 1)(x – 9)(x + 5)
C. (x + 3)(x + 3)(x – 5)
D. (x + 3)(x – 3)(x + 5)
948. If f(x) = 5x2 – 4x + 9, find the average rate
of change from x = 1 to x = 4.
A. 20 B. 21 C. 22 D. 23 956. Which of these is equal to A-1 + B-1?
1 1 1
A. B. +
−(𝐴+𝐵) 𝐴 𝐵

949. If f(x) = 4x2 + x – 5, find the instantaneous 1 −1

C. 𝐴+𝐵 D. 𝐴+𝐵
rate of change at x = 5.
A. 39 B. 40 C. 41 D. 42
957. Find the equation of the line with slope 3,
passing through (2, 5).
950. How is 67500 written in scientific notation?
A. y = 3x – 2 B. y = 3x – 1
A. 67.5 x 103 B. 6.75 x 103
C. y = 3x + 1 D. y = 3x + 2
C. 67.5 x 104 D. 6.75 x 104

958. Find the distance of the point (7, 8) from

951. Find the mean of the following data:
the line 2x – 3y + 4 = 0
24 24 25 26 28 29 6√13 6√73
A. B.
A. 24 B. 25.5 C. 26 D. 29 13 73
C. 4√73 D. 5√13

952. Rayon’s Social Security System (SSS) ID

number is 02-2525255-2. What level of data is 959. Find the distance between the parallel lines
the SSS ID? y = 2x – 1 and y = 2x + 4.
A. nominal B. ordinal A. 5 B. 2√5 C. √5 D. ½
C. interval D. ratio

960. There are 80 cows and ducks in a farm, all

953. A tree is 4 meters tall, while the flagpole is 8 of which are healthy. If there are 190 legs in
meters tall. What level of data is used? total, how many cows are there?
A. nominal B. ordinal A. 5 B. 10 C. 15 D. 20
C. interval D. ratio

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1000 MMR Author: Victor A. Tondo Jr., LPT
961. Which of the following angles in standard 970. The distance D of a
position is coterminal with 150o? projectile from the
A. 2570o B. 5490o ground t seconds
C. 7830o D. 9870o after launch is given as
D = 8t – t2. How
many seconds
962. Which of the following is false? after launch does
1 1
A. sin x = cos 𝑥 B. tan x = cot 𝑥 the projectile hit
1 1 the ground?
C. cos x = sec 𝑥 D. csc x = sin 𝑥 A. 4 B. 6 C. 7 D. 8

963. ∠V and ∠R form a vertical pair. If m∠V = 7x 971. The distance D of a projectile from the
and m∠R = 3x + 60, find m∠V. ground t seconds after launch is given as
A. 105o B. 84o C. 20o D. 15o D = 14t – t2. How many seconds after launch
does it attain its peak?
A. 4 B. 6 C. 7 D. 8
964. ∠V and ∠R form a linear pair. If m∠V = 13x
and m∠R = 5x + 72, find m∠R.
A. 112o B. 102o C. 78o D. 68o 972. The distance D of a projectile (in meters)
from the ground t seconds after launch is given
as D = 16t – 2t2. What is its maximum height?
965. Evaluate: tan 45o – sin 60o + cos 30o A. 16 m B. 24 m
A. -1 B. 0 C. 1 D. 2 C. 32 m D. 40 m

𝑥 3 −27 973. Find the slope of the line tangent to the

966. Evaluate: lim
𝑥→3 𝑥−3 graph of f(x) = x3 – 3x2 + 5x – 1 at x = 1.
A. LDNE B. undefined C. 0 D. 27
A. -1 B. 0 C. 1 D. 2

967. Which of the following circles is concentric

974. Which of the following is a diagonal matrix?
with x2 + y2 – 7x + 9y = 25? −9 0 0 0 1 −4
A. (x – 3)2 + (y + 5)2 = 25 A. [ 0 3 0] B. [−1 0 −7]
B. (x – 7)2 + (y + 9)2 = 50 0 0 6 2 3 0
C. (x + 3.5)2 + (y – 4.5)2 = 100
7 6 9 −4 2 9
D. (x – 3.5)2 + (y + 4.5)2 = 125
C. [4 −3 8] D. [ 1 8 7]
5 4 5 2 −4 6
968. Find k such that (x + 2) is a factor of the
polynomial 5x3 + 11x2 – kx + 12. 975. Which of the following is a scalar matrix?
A. 11 B. 7 C. -3 D. -8 −5 1 2 −5 0 0
A. [ 4 −9 10 ] B. [ 0 −5 0 ]
8 5 −3 0 0 −5
969. If P = 4S and A = S2, express A in terms of P.
𝑃2 𝑃2
7 1 1 0 2 −5
A. A = 16 B. A = 4 C. [1 −5 1] D. [−9 0 1]
C. A = 16P2 D. A = 4P2 1 1 6 1 −8 0

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1000 MMR Author: Victor A. Tondo Jr., LPT
976. Which of the following is an identity matrix? 983. A whole number is 3 more than another
4 1 1 0 6 −3 number. The sum of their squares is 4145. Find
A. [1 8 1 ] B. [ 4 0 2 ] the larger number.
1 1 12 −7 9 0 A. 47 B. 46 C. 45 D. 44
1 0 0 0 1 1
B. [0 1 0] D. [1 0 1]
0 0 1 1 1 0 984. The numbers x, y, z, and w have an average
of 30. If x, y and z have an average 35, what is w?
A. 5 B. 10 C. 15 D. 20
977. Find the quotient when the polynomial
7x5 – 3x3 + 2x2 – 9x + 3 is divided by x – 1.
A. 7x4 + 7x3 + 4x2 + 6x – 3 985. A is a constant. Find A such that the
B. 7x4 + 7x3 + 4x2 – 6x – 3 equation 2x + 1 = 2A + 3(x + A) has a solution
C. 7x4 + 7x3 – 4x2 – 6x – 3 at x = 2.
D. 7x4 – 7x3 – 4x2 – 6x – 3 A. -0.4 B. -0.2 C. 0 D. 0.2

978. Find k such that 9x2 + 36x + k = 0 has only 986. It takes 4 men 9 days to build 2 houses. How
one unique root. many days will it take 6 men to build 5 houses?
A. 4 B. 16 C. 18 D. 36 A. 12 B. 13 C. 14 D. 15

979. There are 210 candies in a jar. The ratio of 987. If 860 = 32x, what is x?
red candies to blue is 2:3, and the ratio of blue to A. 18 B. 24 C. 20 D. 36
yellow is 4:5. How many yellow candies are
there?
A. 35 B. 45 C. 60 D. 90 988. In a certain university, a student’s grade is
computed as the sum of 25% of his prelims
grade, 30% of his midterms grade, and 45% of
980. A certain bacteria doubles its population his finals grade. He knows that his prelims grade
after 3 minutes. If the bacteria in a petri dish is is 72 and his midterms grade is 70. What is his
512,000 at 8:45 AM, at what time was its grade for the finals if he got a grade of 75 in
population count 125? Calculus?
A. 6:30 AM B. 7:15 AM A. 75 B. 77 C. 79 D. 80
C. 8:09 AM D. 9:21 AM

989. Mr. Lazada bought 75 pieces of Elunium for

981. A square picture was framed and given 3 cm 𝒵8,000 per piece and sold them for a total of
margins. If the total area of the margin is 324 𝒵720,000. What is his mark-up rate?
cm2, what is the area of the picture? A. 20% B. 25%
A. 441 cm2 B. 576 cm2 C. 32.5% D. 40%
C. 729 cm 2 D. 900 cm2

990. Triangular numbers are numbers that can

982. Given f(x) = x2 + 10x + 25 and be shown by triangular arrangements of dots.
g(x) = 3x + 1, find f(g(x)). The triangular numbers are 1, 3, 6, 10, 15, 21, …
A. 3x2 + 30x + 26 B. 9x2 + 36x + 36 What is the 20th triangular number?
C. 9x + 30x + 26
2 D. 3x2 + 36x + 36 A. 200 B. 205 C. 210 D. 220

This is a free reviewer. All rights reserved.

1000 MMR Author: Victor A. Tondo Jr., LPT
991. What is a pattern of shapes that covers a 999. A certain Math challenge gives the
surface completely without overlaps or gaps? competitors a score of 4 for each correct answer,
A. translation B. tessellation and a deduction of 1 point for each wrong
C. constellation D. transposition answer. If a contestant answered all 100 items
and got a score of 200, how many items did the
contestant answer correctly?
992. Find the equation of the line perpendicular A. 45 B. 50 C. 60 D. 35
to 5x + 3y = 12, passing through (3, -7).
A. 3x – 5y = -44 B. 3x + 5y = 44
C. 3x – 5y = 44 D. 3x + 5y = -44 1000. What is 111011012 in decimal?
A. 257 B. 237
C. 217 D. 197
993. Point V is two-fifths the way from A(9, -7)
to B(-6, 13). Find the coordinates of point V.
A. (2, 2) B. (2, 0)
C. (3, 1) D. (3, 2)

994. Find the angle of inclination of the line

passing through V(5, -5) and T(2, 4)
A. 88.145o B. 92.429o
C. 97.593o D. 108.435o ⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯

995. The first term of an arithmetic sequence is 3

and the 20th term is 98. What is the 25th term?
A. 108 B. 115 C. 118 D. 123

End of 1000MMR.
996. An educational psychologist classifies
students as high, medium and low intelligence.
What kind of scale is being used?
A. nominal scale B. ordinal scale
C. interval scale D. ratio scale

997. The GCF of two numbers is 8 and their LCM

is 80. What is their product? Congratulations!!
A. 80 B. 160 D. 320 D. 640

998. If c1.5 – 4 = 7, what is c3?

A. 784 B. 121 C. 49 D. 16

This is a free reviewer. All rights reserved.