MATHEMATICS – SET A FIELD OF SPECIALIZATION (MAJOR IN: MATHEMATICS) MULTIPLE CHOICE 1. Which of the following numbers is divisible by 11? A. 23, 234, 212 B. 2, 243, 121
C. 454,595,064 D. 1,576,123
2. What is the LEAST COMMON MULTIPLE (LCM) of 24 and 36? A. 72 B. 24
C. 36 D. 96
3. Three brothers inherited a cash amount of Php 120,000 and they divided it among themselves in the ratio of 5:2:1. How much more is the largest share than the smallest share? A. Php 15 000 B. Php 60, 000
C. Php 30, 000 D. Php 75, 000
4. If a and b are integers and the sum of ab and b is odd, which of the following could be TRUE? I. II. III.
a is even and b is odd a and b are both odd a is odd and b is even
A. III only B. I and II
C. II only D. I only
5. What is the 10th number in the series whose first 4 terms are 1,2,4, and 8? A. 512 B. 128
C. 256 D. 80
6. How many factors does 80 have? A. 10 B. 6 7. The expression
C. 9 D. 8 1 1 1 + + 100 25 1000
is equal to _____________.
A. 0.006
C. 0.051
1
MATHEMATICS – SET A B. 0.51
D. 0.0051
8. Which of the following expressions has the largest value? A.
43
B.
(2+2+2)2
[(2+2)2 ]
C. D. 2 +
22
2
2 + (2+2)
9. A piece of jewelry is marked 20% from its wholesale price. During a sale, the retail price is reduced by 15%. What percent higher is the sale price than the whole price? A. 2% B. 8%
C. 4% D. 6%
10. If a box medicine is sufficient to support 12 patients in 10 days, how many days will the medicine last for 3 patients? A. 2.5 B. 5
C. 90 D. 120
11. What is the smallest number which can be exactly divided by the first five counting numbers? A. 80 B. 60
C. 40 D. 120
12.
From the huge roll of cloth 200 m long, school girls’ uniforms are 1 2 made. Each blouse takes 1 4 m and each skirt 1 3 m. How much cloth is left after cutting and making 60 sets of such uniform? A. 45 meters B. 25 meters
C. 15 meters D. 55 meters
13. What number subtracted from each of 71 and 58 will result in two perfect squares? A. 35 B. 22 14.
C. 33 D. 42 The average adult man has a mass of about ________________.
A. 700 kg B. 70 kg
C. 700 mg D. 70 g
2
MATHEMATICS – SET A 15. What is the largest 2-digit number which leaves a remainder of 1 when it is divided by either 3 or 5? A. 88 B. 91
C. 96 D. 81
16. In a Mathematics Test, 35 students passed and 30% failed. How many students took the test? A. 40 B. 50
C. 60 D. 30
17. How many cubic meters of concrete will be required to construct a road 10 km long, 5 meters wide, and 0.2 meters thick? A. 10, 000 cu. m B. 90, 900 cu. m
C. 90, 000 cu. m D. 100, 000 cu. m
18. The product of 2 whole numbers is 36, and their ratio is 1:4. Which of these is the smallest number? A. 12 B. 2 19.
C. 3 D. 9 What is the reciprocal of
9
5 13 ?
A.
5 117
C.
9 65
B.
3 45
D.
13 122
20. A class has 24 students. Which of the following could not be the ratio of the girls to the boys? A. 1:4 B. 1:3 21.
If
C. 1: 5 D. 3: 5 x3
is odd, which statement is/are TRUE? I.
x is odd
3
MATHEMATICS – SET A x
II.
2
is odd
2
x +1
III.
is odd
A. I only B. I and III only 22.
C. I and II only D. II only
Which statement is TRUE? I. II. III. IV.
1 1 1 1
mm is longer than 1 in m is longer than 1 km gallon is heavier than 1 lb. gallon is more than 1 liter
A. I and IV B. III and IV
C. I only D. II and III
23. On its anniversary, Mister Dunkin offered a free donut for every 6th customer and a free tumbler for every 8th customer. What is the least number of customers that Mister Dunkin had if 5 customers enjoyed both free donut and tumbler? A. 24 B. 48 24.
C. 120 D. 72 8−(−4 )2
Simplify the following
x 3 + 9 ÷ (-3)
A. -27 B. -11 25.
C. -43 D. 32
If x > 1, which of the following decreases as x decreases? 2
I.
x+ x
II.
2 x −x
III.
1 x +1
2
A. I and II only B. I only 26. A.
C. III only D. II only
Which of the equation below has roots 0, 2 and -3? x 3+ x 2−6 x =0
C. 4
x 3+ x 2 +6 x=0
MATHEMATICS – SET A B.
3
2
x −x + 6 x =0
3
2
x −x −6 x=0
D.
27. In how many ways can a 5 member committee of 3 women and 2 men be chosen from a group consisting of 5 women and 4 men? A. 120 B. 20 28.
Simplify
A.
2 a2 +2 b2
B.
−3 a 2+ 3 b2
C. 30 D. 60 (a+2 b)2−(2 a+b)2 . C.
3 a2 +2 b2
2 a2 +ab+b 2
D.
29. The pitch of a roof is the ratio of its rise (height) to its span (width). What is the pitch of a roof that has height of 30ft and a width of 45ft? A. 3:2 B. 3:5 30.
C. 5:3 D. 2:3
If 2x - 5 is a multiple of 3, what is the next greater multiple of 3?
A. 3x – 6 B. 2x -2
C. 2x + 6 D. 2x – 8
The 4th power of the 9th root of x can be written as
31.
4 3
A.
x
B.
x9
C.
( x 4 )9
D.
x4
4
32.
9
What is the sum of the solutions of
2
6 x +3=11 x ?
A.
1 2
C.
11 6
B.
7 6
D.
3 5
33. If the variance of a distribution is 36, then the standard deviation is __________. 5
MATHEMATICS – SET A A. Ogive B. Pie 34. by
C. Bar D. Histogram
What is the remainder when 3
3 x5 −8 x 4−5 x 3+ 26 x2 −33 x +26
x −2 x −4 x +8 ?
A. 29x + 2 B. -5x + 2 35.
A.
is divided
2
C. 5x + 50 D. 5x – 2
Rationalize and simplify
√3 3 ax
√3 4 a2
3
a √ 12 x
.
C. 4a
B. 2x
D.
√3 6 a 2 x 2a
36. A container holds about 4.75 liters of orange juice. How many milliliters is that? A. 47.5 B. 4, 750
37.
C. 47, 500 D. 475
If x + 6 = 9, then 3X + 1 = _____________.
A. 10 B. 3
38.
C. 9 D. 34
Evaluate:
log (¿¿ 2 32) log 5 ¿
A. 5 B. 3
C. 16 D. 1
39. The first three elements of an arithmetic sequence are 20, 16 and 12. Which element is -96? A. 10th B. 40th
C. 30th D. 20th 6
MATHEMATICS – SET A 40. d)?
Which of the following will always give the same value as a(b + c -
A. ab + ac – ad B. abc – d 41.
C. abcd D. ab – ac + ad
What is the difference when (b – a) is subtracted from (a – b)?
A. 2(a – b) B. 2a + 2b
C. 2(b – a) D. 0
42. Jess can mow the lawn in 5 hours, while Jeff can mow the same lawn in 4 hours. How long will it take them to mow the lawn together? A.
4
B.
4
43.
1 2
hours
C. 5 hours
hours
D.
The simplest form of
C. 5 D. 4
√3 8+ √3 64−√3 27 is:
A. 5 B. 2 45.
2 9 hours
If X = Y = 2Z and XYZ = 1000, what is the value of Z?
A. 10 B. 2.5 44.
2
C. 4 D. 3 Actual number of days from Feb. 3, 2008 to April 18, 2008
A. 74 B. 75
C. 76 D. 73
46. How much money was borrowed at 15% simple interest for 18 months if the interest paid was Php 3, 000. A. P 13, 000 B. P 13, 333.33 47.
C. P 133, 333.33 D. P130.00
The graph of the function f(x) =
vertex at
7
x 2−6 x+ 3
is a parabola with
MATHEMATICS – SET A A. (-3,-6) B. (6,-3) 48.
C. (3, -6) D. (-3, 6) 3 x =81
If
and
4 y =64 , what is (x-y)?
A. 1 B. -1 49.
C. 17 D. 0 x 4 = y z , then
If
16 y 2
equals __________.
2
A.
x 16
B.
x 2 z2 16
50.
C.
Subtract
D. 4 y 2−5 y+ 2
2 y +5 y−3
B.
10 y −5 y−3
3
x z
6 y 2−5 .
from
2
A.
x2 z2
2
2
C.
2 y +5 y−7
D.
10 y +5 y −7
2
51.
The same number is subtracted from the numerator and 8 denominator of the fraction 11 . If the resulting fraction is equivalent to 2 3 , what I the number subtracted? A. 6 B. 4
52.
C. 3 D. 2 Which expression gives the nth term of the sequence 1,4,7,10,…?
A. 3n – 5 C. 3n B. 3n – 2 D 3n + 1 53. Which congruence statement is true about this pair of triangles?
8
MATHEMATICS – SET A
A.
∆ ABC ≅ ∆ MNO
C.
∆ ABC ≅ ∆ NOM
B.
∆ ABC ≅ ∆ NMO
D.
∆ ABC ≅ ∆ MON
54. One circle has a radius of m, and another circle has a radius of 2m. The area of the larger circle is how many times the area of the smaller circle? A. 3 B. 2 55.
C. 1.5 D. 4 2 If the area of square is 81 x , what will represent the perimeter of
the square? 2 C. 18 x
A. 36x 2 B. 9 x
D. 81 x
56. The floor area of a square room is given as 18x. Which of the following could be the value of x if the side of the square is a whole number? A. 6 B. 8
C. 7 D. 9
57. Five equal squares are joined together to form a rectangle whose perimeter is 372 cm. What is the area of one square? A. 961 sq. cm. B. 72 sq. cm.
C. 124 sq. cm. D. 900 sq. cm.
58. An equilateral triangle 8 cm on each side is divided into smaller equilateral triangles 2 cm on each side. What is the maximum number of such triangles that can be formed? A. 36 B. 24
C. 16 D. 20
59. The sum of the measures of the interior angles of a convex polygon is 1260 degrees. The number of sides of this polygon is ________________. 9
MATHEMATICS – SET A A. 7 C. 9 B. 8 D. 10 60. Which of the following CANNOT be the ratio of the sides of a triangle? A. 10:15:20 B. 2:2:3
C. 2:5:5 D. 1:1:2
61. A road runs 1200 ft. from A to B, and then makes a right angle going to C, a distance of 500 ft. A new road is being built directly from A to C. How much shorter will the new road be? A. 400 ft. B. 850 ft.
C. 609 ft. D. 600 ft.
62. Find two positive numbers, whose product is 64, and whose sum is a minimum. A. 8 and 8 B. 16 and 4
C. 32 and 2 D. 8 and 12
63. If each square in the figure has a side of length 1, what is the perimeter of the figure? A. B. C. D. 64.
8 16 14 12
What fractional part of a circle is the arc measures 270°?
A.
2 3
C.
1 4
B.
3 4
D.
4 9
65. The minute hand of a clock is 5 cm long. Find the distance its tip travels in 15 minutes. A. 12 cm B. 7.5 cm
C. 7.85 cm D. 9.25 cm
66. The difference of two polynomials is 6m + 5n – 5p, if the second polynomial is 2m – 3n + 2p , what is the first polynomial? 10
MATHEMATICS – SET A A. 4m + 8n – 7p B. 8m + 2n – 3p
C. -8m – 8n – 3p D. –m – 8n + 7p
67. In a university, 2 out of 7 students work their way through college. If the school has an enrollment of 11, 758, about how many are working students? A. 3, 401 B. 3, 359
C. 1, 680 D. 1, 790
68. If all sides of a square are doubled, the area of that square ________________. A. is doubled B. remains the same
C. is tripled D. is multiplied by 4
69. Which of the following theorems states that “two triangles with corresponding angles equal are similar”? A. ASA B. SAS Similarity Theorem
C. AAA D. Right Triangle
70. If two coplanar lines are cut by a transversal, which of the following guarantee that these lines are parallel? A. The alternate interior angles are complementary B. The alternate interior angles and corresponding angles are congruent C. A pair of interior angles on the same side of the transversal are complementary D. The corresponding angles are supplementary 71. The perimeter of a rectangle is 96 cm. If its width is 1/3 its length, what is the area of the rectangle? A. 768 sq. cm. B. 108 sq. cm.
C. 1, 728 sq. cm. D. 432 sq. cm.
72. If the sides of a quadrilateral are tangent to a circle, then the quadrilateral is __________. I. II. III.
an inscribed quadrilateral a subset of the circle a circumscribed quadrilateral
A. II only
C. I only 11
MATHEMATICS – SET A B. I and II
D. III only
73. Which of the following can be an equation of a line that is equivalent from the line equation y = 2x – 1? 1 2 x−2
A. 3y = 6x + 5
C. y =
B. 5y = 8x – 5
D. y = 4x – 1
74.
The graph of 1/x – y = 3 in the x-y plane is a/an _________________.
A. ellipse B. hyperbola
C. circle D. straight line
75. Which of the following quadratic functions will have a graph which opens downward? A. y = -4(2 -
x 2 ) + 5x
C. y = 5x(x – 1) + 3
2 B. y = 7x - (5 x +1 )
x2 )
D. y = 1 – (3x -
76. What is the sum of all integers on the number line starting from -20 to +20? A. 400 B. 0 77.
C. 210 D. 420
Where will the line 3x – 8y + 24 = 0 cut the x-axis?
A. at x = -3 B. at x = 8 78.
C. at x = 3 D. at x = -8
Find the value of x which satisfies
A. 2005 B. 2004 79.
2004
2
2004
+2
+2
2004
2004
+2
=2
x
.
C. 2006 D. 2007
What is the area bounded by y =
x 2 , x = 1 and x= 3, and the x-
axis? A. 7
C.
12
28 3
MATHEMATICS – SET A B.
22 3
D.
26 3
80. Find an equation of the line with slope 2 that passes through the midpoint of the line segment connecting (3, -2) and (4, 7). A. 4x – 2y – 9 = 0 B. 4x + 2y + 9 = 0 81.
C. 4x – 2y + 9 = 0 D. 4x + 2y – 9 = 0
What is the sum of the roots of
6 x 2+3=11 x ?
A.
1 2
C.
3 5
B.
7 6
D.
11 6
82. Which of the following lines is perpendicular to the line with equation 2x – 3y = 4? A. y = 2x + 2 B. y =
2x 3
+2
C. y =
−3 x 2
D. y =
3x 2
+2 +2
83.
The monthly profit in pesos from the sale of x cellphones for a 2 3 company is given by P(x) = 800 - x + 0.2 x . Determine the rate of change in the monthly profit for cellphones. A. P 12, 800.00 C. P 5, 800.00 B. P 7, 200.00 D. P 6, 800.00
84.
Find the equation of the tangent to the parabola
2 x 2−3 x +2 y−4=0
at point (-2, -5). A. 2x – 11y – 12 = 0 B. 11x – 2y + 12 = 0
C. 2x – y – 3 = 0 D. x + 2y + 12 = 0
85. A square is inscribed in a circle with radius r. Find the area of the shaped region. A. (2 –
π )
r2
13
MATHEMATICS – SET A B. ( π −2 ) C.
π −2
D.
π r −2
r r
2
2
2
86. The total length of fencing needed to enclose a rectangular area of 46 feet by 34 feet is _______. A. 48 yd. 1 B. 53 3 yd.
C. 52 yd. 2 ft. D. 26 yd. 1 ft.
87. What is the equation of a straight line with a gradient -1 and yintercept 4? A. y = 2x + 5 B. 2y = x + 4
C. y = -x + 4 D. 4y = x + 1
88. One end of a line segment is (1,-2). If the midpoint of the segment is (4,3), find the coordinate of the other endpoint of the segment. A. (6,7) B. (6,9)
C. (7,8) D. (5,8)
89. Which of the following is the equation of a line perpendicular to 2x + 4y = -5? A. 2x – 4y = 5 B. 4x – 2y = 3 90.
Evaluate
C. 3x – 6y = 4 D. 6x + 3y = 7 lim (3 x3 −4 x +1) x→ 2
.
A. 33 B. 15 91.
C. 209 D. 17 In how many ways can six people be seated at a round table?
A. 240 B. 120 92.
If
2 11
C. 60 D. 100 is the probability that an event will happen, what is the
probability that it will NOT occur?
14
MATHEMATICS – SET A A. 9/11 B. 9/13
C. 2/13 D. 7/11
93. In a school, 40% of the students major in Math, 25% major in Science and 15% major both Science and Math. A student is selected at random from the school. If he majors Science, what is the probability that he does not major in Math? A. 3/8 B. ½
C. 2/5 D. ¾
94. Barbara is twice as old as Maria and Janice is three times as old as Barbara. Their mean age is 36. How old is Barbara? A. 72 B. 12
C. 36 D. 24
95. In how many ways can the first, second and third places be chosen from a group of 10 candidates? A. 1000 B. 70
C. 27 D. 720
96. What is the value of x in the set (10, 30, 50, x) if the mean, mode and median of the set are equal? A. 70 B. 80
C. 40 D. 30
97. Given that X and Y are mutually exclusive events, which of the following is NOT correct? A. P(A) = 1 – P(A) B. P(A and B) = 1
C. P (A and B) = 0 D. P (A or B) = P(A) + P(B)
98. Lito’s average grade in subjects is 82. If his lowest grade is disregarded, his average grade for the remaining subjects is 84. What is the lowest grade? A. 70 B. 72
C. 74 D. 80
99. A committee of 5 chosen by lot from a group of 5 seniors and 4 juniors. What is the probability that the committee will have 3 seniors and 2 juniors? A. 10/21
C. 3/21 15
MATHEMATICS – SET A B. 5/21
D. 8/21
100.The probability that a man will live 10 more years is ¼ and the probability that his wife will live 10 more years is 1/3. What is the probability that both still live 10 years hence? A. 2/3 B. 1/12
C. 1/6 D. 7/12
101.If a letter is chosen at random from the English alphabet, find the probability that the letter is somewhere after the letter g? A. 19/26 B. 5/26
C. 11/26 D. 9/26
102.Two different committees of five are to be formed from a group of ten people. In how many ways can these two committees be formed if no person should be on both committees? A. 420 B. 125
C. 252 D. 210
103.Which of the following CANNOT be a probability value?
( 0.5 )−1
A.
0.994
C.
B.
√3 0.59
D. 83/100
104.A clerk lost one of the 6 slips for purchases made in the last hour. The mean value of all 6 slips was Php 860.50, and the remaining 5 slips had the values Php 445.50, Php 925.30, Php 1275.00, Php 867.20 and Php 1050.00. What is the amount stated in the slip that was lost? A. P 800.00 B. P 600.00 105.What is the exact value of
C. P 720.00 D. 550.00 sin 2 x , if sin x = 4/5 and 0 < x <
A. ½ B. 8/5
π /2 ?
C. 16/25 D. 8/10
106.The total surface area of a cube with volume 8 cubic centimeters. A. 8 sq. cm. B. 24 sq. cm.
C. 12 sq. cm. D. 36 sq. cm.
16
MATHEMATICS – SET A 107.The marked priced of a suitcase was P 3, 485.00. This was reduced by 15% and 4% at a sale. What was the sale price? A. P 2, 943.76 B. P 2, 962.25
C. P 2, 762.50 D. P 2, 843.76
108.The construction of a new production facility costs P 250,000.00 for materials and P 50,300.00 for labor. What percent of the total cost was the cost of labor? A. 25.19% B. 8.33%
C. 20.12% D. 16.03%
109.If triangle ABC is labeled conventionally, and a = 8, b = 12, and angle c = 48 degrees, the triangle can be solved using the _______________. A. Sine function B. Law of Cosines
C. Law of Sines D. Tangent function
110.What will be the area of the triangle which the line 3y = 9x – 36 forms with the coordinate axes? A. 24 sq. units B. 30 sq. units 111.Change
5π 6
C. 65 sq. units D. 45 sq. units radians to degrees
A. 77 degrees B. 150 degrees
C. 24 degrees D. 15 degrees
112.If you borrow P 50,000.00and pay P 69, 500.00 after 6 years, what is the rate of interest? A. 7% B. 6.5%
C. 5% D. 75%
113.What is 135 degrees in radians? A.
5π 8
C.
3π 4
B.
3 4π
D.
2π 3
114.Change 600° to radian 17
MATHEMATICS – SET A
A.
10 π 3
C.
3π 2
B.
5π 3
D.
8π 3
115.What is the exact value of sin 75°?
√ 2−√ 6
A.
C.
4
√ 6+ √ 2
B.
D.
4
√ 3−√ 3 4
√3−√ 6 4
116.Find the measure of the arc intercepted by the angle with measure 2 π in a circle with radius 9m. A. 3 π
C. 9 π
m
B. 12 π
m
D. 6 π
m
m
117.Which of these identities is TRUE? 2
2
A.
cos T −sin T =1
C. 1 +
B.
cot T =csc T
D.
118.What is TRUE about the graph of y = I. II. III. A. B. C. D.
csc 2 T=−sec 2 T
sin 2 x + cos 2 x ?
It is a line parallel to the x-axis It is y-intercept in 1 It is a curve
II and III only III only I and II only II only
119.Find dy/dx at x = 2 for
2
2 x 2 +1 ?
A. 2 B. 8
C. 9 D. 3
18
2
tan T =sec T
MATHEMATICS – SET A 120.Which function has graph which intersects the x –axis but not the yaxis? A. y = sec x B. y = tan x
C. y =cot x D. y = csc x
ANSWER KEY 1. C 2. A 3. B 4. D 5. A 6. A 7. C 8. C 9. A 10. C 11. B 12. B 13. B 14. B 15. B 16. B 17. A 18. C 19. D 20. A 21. B 22. B 23. C 24. C 25. A 26. A 27. D 28. B 29. D 30. B 31. B
32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62.
C A B D B A D C A A D A D B B C A C C D B C D A B A C C D A A
63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93.
19
D B C B B D C B D D A D B B D C D A D C C B B B C C B D B A C
MATHEMATICS – SET A 94. D 95. D 96. A 97. D 98. D 99. A 100.B 101.A 102.C 103.C
104.B 105.C 106.B 107.D 108.C 109.C 110.B 111.B 112.B 113.C
114.A 115.B 116.C 117.C 118.C 119.B 120.B 121.
20
122.
