1. The angle of elevation of the top of a tower from a point A is 30°15’. From another point B, the angle of elevation of the top of the tower is 52°33’. The points A and B are 332 m apart and on the same horizontal plane as the foot of the tower. The horizontal angle subtended by A and B at the foot of the tower is 90 degrees. Find the height of the tower.
A. 90.6 m B. 176.8 m * C. 89.5 m D. 155.9 m
2. Two jeepney start at the same point but are going in different directions. If jeepney A runs at the rate of 60km/hr and jeepney B at 50km/hr and both start at the same time, when will the two jeepney be 550 km apart?
A. 4 hrs B. 5 hrs * C. 6 hrs D. 7 hrs
3. The probability that A can solve a given problem is 3/5, that B can solve it is 3/4 and that C can solve it is 3/7. If all three try, compute the probability that the problem will be solved.
A. 0.81 B. 0.94 * C. 0.96 D. 0.19
4. Rex and Jason traveled at the same time at the rate of 20 m/min, from the same point on a circular track of radius 600 m. if Rex walks along the circumference and Jason towards the center, find their distance after 10 mins.
A. 193 m B. 202 m C. 241 m D. 258 m *
5. The excess of the sum of the fifth and sixth parts over the difference of the half and third parts of a number is 139. Find the number.
A. 240 B. 695 * C. 420 D. 430
6. A yacht can travel 10 miles downstream in the same amount of time as it goes 6 miles upstream. If the velocity of the river current is 3 MPH, find the speed of the yacht in still water.
A. 12mph* B. 16mph C. 15mph D. 18mph
7. A cubical container that measures 2 inches on a side is tightly packed with 8 marbles and in filled with water. All 8 marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are the same size. What is the volume of the water in the container?
A. 4.9 cu. In C. 3.8 cu. in *
B. 3.5 cu. In D. 4.2 cu. in
8. In probability theory, the set of possible outcomes of an experiment is termed as: A. a sample space * C. a set of random variables
B. a set of random events D. a fuzzy set
9. The locus of a point that moves so that its distance from a fixed point and a fixed line is always equal is known as:
A. parabola * C. ellipse
B. circle D. hyperbola
10. Two cards are drawn at random from a standard deck of 52 cards. What is the probability that both are hearts?
A. 13/52 B. 1/17 * C. 7/13 D. 7/26
11. There are 9 arithmetic means between 6 and 18. What is the common difference?
A. 1.2 * B. 1 C. 1.4 D. 0.8
12. Twenty men can finish the job in 30 days. Twenty-five men started the job. If ten men quitted the job after 18 days, find the total number of days to finish the job.
A. 27 B. 28 * C. 26 D. 29
13. Twelve books consisting of 6 mathematics books, 2 electronics book, and 4 communications books are arranged on a shelf at random. Determine the probability that books of the same kind are all together.
A. 1/2310 * B. 1/5620 C. 1/3810 D. 1/1860
14. A flagpole 3 m high stands at the top of a pedestal 2 m high located at one side of a pathway. At the opposite side of the pathway, directly facing the flagpole, the flagpole subtends the same angle as the pedestal. What is the width of the pathway?
A. 4.47 m * B. 3.21 m C. 6.28 m D. 8.41 m
15. A right regular hexagonal prism is inscribed in a right circular cylinder whose height is 20 cm. the difference between the circumference of the circle and the perimeter of the hexagon is 4 cm. determine the volume of the prism.
A. 9756 cc C. 10857 cc
B. 14752 cc D. 10367 cc *
16. The lateral area of a right circular cone of radius 4 cm is 100.53 sq. cm. Determine the slant height. A. 8 cm * B. 9 cm C. 6 cm D. 10 cm
17. The frustum if a regular triangular pyramid has equilateral triangles for its bases and has an altitude of 8 m. the lower base edge is 9 m. if the volume is 135 cu. m, what is the upper base edge?
A. 2 m B. 5 m C. 4 m D. 3 m *
A. 19.44 cu. m * C. 20.53 cu. m
B. 15.69 cu. m D. 18.12 cu. m
19. Determine the equation of the directrix of the curve x^2 = 16y.
A. x + 4 = 0 C. y – 4 = 0
B. x – 4 = 0 D. y + 4 = 0 *
20. Find the area of the curve x^2 and y^2 + 6x – 2y + 9 = 0
A. 125 sq. units C. 92 sq. units
B. 113 sq. units * D. 138 sq. units
21. Find the distance between the foci of the curve 9x^2 + 25y^2 – 18x + 100y -116 = 0
A. 7 B. 6 C. 8 * D. 12
22. What is the equivalent rectangular coordinate of a point whose polar coordinate is (7, 38 deg.)
A. (3.56, 4.31) C. (5.52, 4.31) *
B. (4.31, 5.52) D. (4.31, 3.56)
23. A line has an equation of 3x-ky-8=0. Find he value of k if this line makes an angle of 45 degrees with the line 2x+5y-17=0.
A. 5 B. 7 * C. 8 D. 6
24. Find the slope of the line having a parametric equations of x=2+t and y=5-3t.
A. 1 B. 1/3 C. -3 * D. -1
25. Find an equation for the hyperbola with foci at (1, 3) and (9, 3), and eccentricity of 2. A. x^2 – 3y^2 – 30x + 6y + 54 = 0
B. 3x^2 – y^2 – 30x + 6y + 54 = 0 C. x^2 – y^2 – 30x + 6y + 54 = 0 * D. 3x^2 – y^2 – 6x + 30y + 54 = 0
26. Find the shortest distance from (3, 8) to the curve x^2 + y^2 + 4x – 6y = 12.
A. 1.21 B. 2.07 * C. 4.09 D. 3.73
27. Find the sum of the first 100 positive integers that is exactly divisible by 7.
A. 35,350 * C. 53,350
B. 25,053 D. 25,536
28. Ship A is 70 km west of ship B and is sailing south at the rate of 25 km/h. Ship B is sailing north at the rate of 45 km/h. How fast is the distance between the two ships changing 2 hours later?
A. 66.21 B. 62.61 * C. 61.26 D. 66.12
29. A baseball diamond is a square whose sides are 90 ft long. If a batter hits a ball and runs to first base at the rate of 20 ft/sec, how fast is his distance from second base changing when he has run 50 ft?
A. -8.08 * B. 8.08 C. -8.38 D. 8.38
30. Two legs of a right triangle are each 70 cm. If one leg grows at the rate of 5 cm/min and the other shrinks at the rate of 5 cm/min, how fast is the hypotenuse of the triangle changing 2 minutes later?
A. 1 * B. 2 C. 3 D. 4
31. Two legs of a right triangle are each 70 cm. If one leg grows at the rate of 5 cm/min and the other shrinks at the rate of 5 cm/min, how fast is the area of the triangle changing 2 minutes later?
A. 50 B. -50 * C. 70 D. -70
32. An open field is bounded by a lake with a straight shoreline. A rectangular enclosure is to be constructed using 500 ft of fencing along three sides and the lake as a natural boundary on the fourth side. What is the maximum area?
A. 62,500 C. 52,500
B. 20,000 D. 31,250 *
33. Ryan has 800 ft of fencing. He wishes to form a rectangular enclosure and then divide it into three sections by running two lengths of fence parallel to one side. What is the maximum area?
A. 40,000 C. 20,000 *
B. 30,000 D. 10,000
34. Simplify the expression: limit of (x^2-16)/(x-4) as x approaches to 4.
A. 1 B. 8 * C. 0 D. 5/2
35. Evaluate the following limit, limit of (x^2 - 1)/(x^2 + 3x – 4) as x approaches 1.
36. The semi – transverse axis of the hyperbola (x^2 / 9) – (y^2 / 4) = 1 is :
A. – 3 B. – 2 C. + 2 D. + 3 *
37. It is a conic section whose discriminant is equal to zero (0).
A. Ellipse B. Parabola *
C. Hyperbola D. Circle
38. A car headlight reflector is cut by a plane along its axis. The section is a parabola having the light center at the focus. If the distance of focus from vertex is 3/4 cm and the diameter of reflector is 10 cm. find its depth.
A. 23/3 B. 25/3 * C. 22/3 D. 27/3 39. Find the equation of the directrix of the parabola y^2 = 16x A. x = -4 * B. x = 4 C. x =-8 D. x = 8
40. The semi-major axis of an ellipse is 4 and its semi-minor axis is 3. The distance from the center to the directrix is
A. 6.047 * B. 6.532 C. 0.6614 D. 6.222
41. A cool drink is removed from a refrigerator on a hot summer day and placed in a room whose temperature is 30 degrees Celsius. According to the law of Physics, the temperature of the drink “t” minutes later is given by the function of the form f(t) = 30 – Ae^(-kt). If the temperature of the drink was 10 degrees Celsius when it left the refrigerator and 15 degrees Celsius after 20 mins, determine the values of A and k. A. 10, 0.0143716 C. 20, 0.0143716* B. 20, 0.0143176 D. 10, 0.0143176 42. Solve for H if
√1−… …. A. 0.723 B. 0.618* C. 0.852 D. 0.453
43. The Roman Numeral MCMXCIV can be found at the main entrance of a museum. We can assume that the museum was built in __________. A. 1994* B. 2974 C. 2174 D. 3974 44. If f(x) = x^2 + x + 1, then f(x) – f(x-1) is equal to ___________. A. 0 B. X C. 2x* D. 3
45. Which of the following is not an identity? A. (x-1)^2 = x^2 – 2x + 1 B. (x+3)(2x-2) = 2 (x^2 + 2x -3) C. x^2 – (x-1)^2 = 2x – 1 D. 2(x – 1) + 3(x+1) = 5x + 4*
46. In the binomial expansion (a + b)^n, find the value of “n” if the coefficients of the 4th and the 13th terms are equal to each other.
A. 12 B. 13 C. 14 D. 15*
47. Find the coefficient of the expansion of (x-y)^15 containing the term x^4 y^11 A. -1365*
B. -1275 C. -1465 D. 01165
48. If 4x^3 – 9x – 8x^2 is divided by (2x-3), the remainder is __________. A. -11*
B. -15 C. 11 D. 15
A. -4 B. -2 C. -5* D. -3
50. Find the value of h in the equation 2x^2 – hx^2 + 4x + 5h = 0 so that the sum of the roots is 2. A. 4*
B. 6 C. 12 D. 18
51. If logx 2 + log2 x = 2, then the value of 2x is __________
A. 1 B. 2 C. 3 D. 4*
52. If the roots of ax^2 + bx + c = 0 are u and v, then the roots of cx^2 + bx + a = 0 are: A. u and v
B. –u and v C. 1/u and 1/v* D. -1/u and -1/v
53. The term involving x^9 in the expansion of (x^2 + 2/x)^12 is ____. A. 25434 x^9
B. 52344 x^9 C. 25344 x^9 * D. 23544 x^9
54. From the given expression (3x – 1)^12, find the sum of the exponents. A. 77
B. 78* C. 79 D. 76
55. If “f” is a polynomial function in one variable, then which of the following statement is wrong? A. x = a is a zero or root of the function “f”
B. x = a is a solution of the equation f(x) = 0 C. (x – a) is a factor of the function f D. (a,0) is a y-intercept of the graph of “f”*
56. How many different signal flags each consisting of 6 flags hung in a vertical line can be formed from 4 identical red flags and 2 identical flags?
A. 20 B. 12 C. 15* D. 18
57. The motion of a particle through a certain medium is such that it moves two thirds as far as each second as in the preceding second. If it moves 6m of the first second, how far will it move before coming to rest?
A. 20 B. 23 C. 18* D. 12
58. In a potato race, 8 potatoes are placed 6 feet apart on a straight line, the first being 6 feet from the basket. A contestant starts from the basket and puts one potato at a time into the basket and puts one potato at a time into the basket. Find the total distance he must run in order to finish the race.
A. 532 ft. B. 432 ft.* C. 342 ft. D. 222 ft.
59. In how many ways can a party of 6 people be seated on a row of 6 seats if 2 refuse to sit next to each other?
A. 240 ways C. 180 ways
B. 480 ways* D. 320 ways
60. Find the sum of the numbers divisible by 6 which lie between 75 and 190.
A. 2508* C. 2058
B. 2580 D. 2850
61. The sum of the parent’s ages is twice the sum of their children’s ages. Five years ago, the sum of the parent’s ages is four times the sum of their children’s ages. In fifteen years, the sum of the parent’s ages will be equal to the sum of their children’s ages. How many children were in the family?
A. 2 B. 3 C. 4 D. 5*
62. A 40-gram alloy containing 35% gold is to be melted with a 20-gram alloy containing 50%. How much percentage of gold is the resulting alloy?
A. 40%* B. 30% C. 45% D. 35%
63. Four positive integers form an arithmetic progression. If the product of the first and last term is 70 and the second and third term is 88, what is the first term?
A. 3 B. 14 C. 5* D. 8
64. How many terms of the progression 3, 5, 7, … should there be so that their sum will be 2600?
A. 54 B. 52 C. 50* D. 55
65. Find the sum of the infinite progression: 2-1 , 2-3, 2-5,…
A. 3/4 B. ½ C. 2/3* D. 1/3
66. In a certain A.P. the first, fourth and eight terms are themselves form a geometric progression. What is the common ratio of the G.P.?
A. 4/3* B. 5/4 C. 4/5 D. ¾
67. A club has 25 members, 4 of whom are ECEs. In how many ways can a committee of 3 be formed so as to include at least one ECE?
A. 543 B. 126 C. 970* D. 314
68. Determine how much water should be evaporated from 50kg of 30% salt solution to produce a 60% salt solution. All percentages are by weight.
A. 25kg* B. 35kg C. 15kg D. 20kg
69. In how many ways can 10 different books be divided among A, B, and C so that A gets 5 books, B 3 books, and C 2 books?
A. 2520* C. 1360800
B. 5040 D. 263
70. There are 4 geometric mean between 3 and 729. Find the sum of the G.P.
A. 1304 C. 2324
B. 1092* D. 1102
71. Renan can finish a certain job in 10 days if Rey will help for 6 days. The same work can be done by Rey in 12 days if Renan helps for 6 days. If they work together, how long will it take for them to do the job?
A. 9 B. 8.4 * C. 9.2 D. 8
72. A boat going across a lake 8 km wide proceeds 2 km at a certain speed and then completes the trip at a speed ½ kph faster. By doing this, the boat arrives 10 minutes earlier than if the original speed had been maintained. Find the original speed of the boat.
A. 4 kph * B. 2 kph C. 6 kph D. 3 kph
73. A man left his home at past 1:00 o’clock PM as indicated in his wall clock. Between three to four hours after, he returned home and noticed that the hands of the clock interchanged. At what time did he left his home?
A. 1:31.47 C. 1:23.54
B. 1:24.52 D. 1:25.59 *
74. A bag contains 20 coins: some pieces of penny, nickel, and dime. There are twice as many pieces of dime as there are pieces of penny. How many pieces of nickel might be there?
A. 7 B. 16 C. 11 * D. 3
75. The digits of a three-digit number form an arithmetic progression. If the hundreds digit is six more than the units digit, and if the tens digit is 3, find the units digit.
A. 6 B. 3 C. 2 D. 0 *
76. In an exam of Math, Electronics, and Communications, 2000 passed in Math, 3000 passed in Electronics, and 1500 passed Communications. There are 40 who passed in Math alone, 60 in Electronics alone, and 30 in Communications alone. There are 800 who passed in all three subjects. If there are 1100 who passed in both Math and Communications, how many did pass in both Communications and Electronics?
A. 2080 * B. 1660 C. 940 D. 2160
77. If 3 balls are drawn in succession from 5 white and 6 black balls in a bag, find the probability that all are of one color, if the 1st ball
drawn is replaced immediately, but the 2nd is not replaced before the 3rd draw.
A. 10/121 C. 2/11
B. 18/121 D. 28/121 *
78. In a shooting game, the probabilities that Jomar and Joel will hit the target is 2/3 and ¾, respectively. What is the probability that the target is hit when both shoot at it once?
A. 10/12 B. 9/12 C. 11/12 * D. 8/12
79. The probability of getting a credit in an examination is 1/3. If three students are selected at random, what is the probability that at least one of them got a credit?
80. A boy intends to arrive at a certain time to a market that is 30 km away from his school. After riding 10 km, he rested for half an hour; as a result he was obliged to ride the rest of the trip 2km/hr faster. What was his original speed?
A. 7 km/hr B. 9 km/hr
C. 10 km/hr D. 8 km/ hr*
81. Peter had wrapped 500 pieces of candies when Billy helped him and together they wrapped 1260 more. Peter worked for a total of 24 minutes. If Peter worked for 24minutes and Billy for 12 minutes, they will be able to wrap 1680 candies. On the average, how many candies can Peter wrap per minute?
A. 25 B. 40 C. 50* D. 75
82. The excess of the sum of the fifth and sixth parts over the difference of the half and third parts of a number is 139. Find the number.
A. 240 B. 695* C. 420 D. 430
83. Twelve books consisting of 6 mathematics books, 2 electronics book, and 4 communications books are arranged on a shelf at random. Determine the probability that books of the same kind are all together.
A. 1/2310* B. 1/5620 C. 1/3810 D. 1/1860
84. Two people are chosen randomly from 4 married couples. What is the probability that they are husband and wife?
A. 1/28 B. 1/14 C. 3/28 D. 1/7 *
85. It is now between 3 and 4 o’clock and in twenty minutes, the minute hand will be ahead as much as the hour hand as it is now behind it. What is the time now?
A. 3:06.36 * B. 3:09.63
C. 3:08.67 D. 3: 07.33
86. Once upon a time, there was a ship coming into a harbor on an unusually high tide. The ship has to pass under the harbor bridge but the captain doesn't know if the ship will fit. He uses a theodolite to measure the angle at an unknown distance from the bridge and then re-measures the angle when he is 300 meters closer. The first angle measured is 2.3 degrees from sea level and the second angle is 3.3 degrees from sea level. If the ships height is 35metres out of the water, will it fit under the bridge.
A. Certainly Yes!* B. Of course Not!
C. Not determinable due lack of enough given. D. Maybe, we cannot truly say.
87. Find A, b, c and D so that function f defined by f(x) = A sin(b x + c) + D has the following properties: the maximum value of f(x) is 7 and f(0) = 7, the minimum value of f(x) is 3, the period of the graph of function f is equal to 2 pi/3. A, b and c are positive and c is less than 2pi.
A. f(x) = 3 sin(3 x + pi/4) – 7 B. f(x) = 4 sin(3 x + pi/4) + 3 C. f(x) = 2 sin(3 x + pi/2) + 5* D.f(x) = sin(3 x + pi/2) – 3
88. A corner lot of land is 35 m on one street and 25 m on the other street. The angle between the two lines of the street being 82O. The other two lines of the lot are respectively perpendicular to the lines of the streets. What is the worth of the lot if its unit price is P2500 per square meter?
A. P1,978,456 C. P2,234,023
B. P1,588,045 D. P1,884,050 *
89. If the angles of the triangle are 2x, x+15, and 2x + 15, find the smallest of the angle in mils.
A. 500 B. 600
C. 800 * D. 900
90. A clock has a dial face of 12 in. radius. The minute hand is 9 in. while the hour hand is 6 in. The plane of rotation of the hour hand is 2 inches about the plane of rotation of the minute hand. Find the distance between tips of the minute hand and hour hand at 5:40 a.m.
A. 7.48 in. B. 6.48 in
C. 9.17 in * D. 10.16 in
91. Two tower are 60 m apart from each other. From the top of the shorter tower, the angle of elevation of the top of the taller tower is 40O. How high is the taller tower if the height of the smaller tower is 40 m.
A. 90* B. 100
C. 80 D. 70
92. A pine tree broken over by the wind forms a right triangle with the ground. If the broken part makes an angle of 50O with the ground and the top of the tree is now 20 ft from its base, how tall was the pine tree?
A. 35 ft. B. 45 ft.
93. A ladder, with its foot in the street, makes an angle of 30O with the street when its top rests on a building on one side of the street and makes an angle of 40O with the street when its top rests on a building on the other side of the street. If the ladder is 50 ft. long, how wide is the street?
A. 96.2 ft B. 81.6 ft *
C. 78.5 ft D. 64.3 ft
94. From a helicopter flying at 30,000 feet, the angles of depression of two cities are 28O and 55O. How far apart are the two cities?
A. 35,415.56 ft. * B. 23, 587.67 ft.
C. 53, 452.67 ft. D. 43,254.76 ft.
95. An airplane flew from Tokyo whose latitude is 14o36’N and longitude of 121o05’E on a course S30OW and maintaining a uniform altitude. How many hours will it take to cross the equator with a constant speed of 550 nautical miles per hour?
A. 2.14 hours B. 2.87 hours
C. 1.83 hours* D. 1.67 hours
96. The angle of elevation of the top of a tower from a point A is 23O30’. From another point B, the angle of elevation of the top of the
tower is 55O30’. The points A and B are 217.45 m apart and on the same horizontal plane as the foot of the tower. The horizontal
angle subtended by A and B at the foot of the tower is 90O. Find the height of the tower.
A. 90.6 m * B. 86.7 m
C. 89.5 m D. 55.9 m
97. A man fires at a target 420 m away and hears the bullet strike 2 seconds after he pulled the trigger. An observer 525 m away from the target and 455 m away from the man heard the bullet strike the target one second after he heard the report of the rifle. Find the velocity of the bullet.
A. 652 m/s C. 525 m/s*
B. 363 m/s D. 350 m/s
98. If sinA = 4/5 and sinB = 7/25, what is sin(A+B) if A is in the third quadrant and B is in the second quadrant?
A. -3/5 C. 3/5*
B. 4/5 D. 2/5
99. A wall is 15 ft high and 10 ft from a building. Find the length of the shortest ladder which will just touch the top of the wall and reach a window 20.5 ft above the ground.
A. 45.54 m* C. 54.45 m
B. 35.54 m D. 47.45 m
100. The probability for the ECE board examinees from a certain school to pass the Mathematics subject is 3/7 and that for
Communications subject is 5/7. If none of the examinees failed both subjects and 4 passed both subjects, how many examinees from the school took the examination?
A. 28* C. 32
B. 27 D. 26
101.A cylindrical water tank which is 35 ft in diameter and 105 ft in length is placed temporarily on an 18.5 degree slope. The filler is located flush with the top of the tank at midpoint. What is the maximum volume of water which can be placed in the tank? A. 90,303.09 ft3 B. 100,455.45 ft3
C. 89,232.56 ft3 D. 90,343.92 ft3*
102.A point P within an equilateral triangle has a distance of 4, 5, and 6 units respectively from the vertices. Determine the length of the equilateral triangle.
A. 9.5 B. 7.55 C. 8.53 * D. 9
103.A circle having an area of 201 cm2 is to be divided into two segments by a chord which is 3 cm from the center of the circle. Compute
the area of the smaller segment. A. 53.65 cm2* B. 68.21 cm2
C. 124.2 cm2 D. 92.15 cm2
104.A piece of wire of length 52 cm is cut into two parts. Each part is then bent to from a square. It is found that total area of the two squares is 97 sq. cm. What is the dimension of the bigger square?
A. 4 B. 3 C. 9 * D. 6
105.A regular hexagon with an area of 93.53 cm2 is inscribed in a circle. The area in the circle not covered by the hexagon is:
A. 18.38 cm2 B. 19.57 cm2 *
C. 16.72 cm2 D. 15.68 cm2
106.A corner lot of land is 35 m on one street and 25 m on the other street. The angle between the two lines of the street being 82O. The
other two lines of the lot are perpendicular to the lines of the streets. What is the worth of the lot if its price is P2500 per square meter?
A. P1,978,456 B. P2,234,023 C. P1,588,045 D. P1,884,050 *
107.A swimming pool is to be constructed in the shape of partially overlapping identical circles. Each of the circles has a radius of 9 m, and each passes through the center of the other. Find the area of the swimming pool.
A. 302.33 m2 B. 362.55 m2
C. 398.99 m2 D. 409.44 m2 *
108.A circle of radius 5 cm has a chord which is 6 cm long. Find the area of the circle concentric to this circle and tangent to the given chord.
A. 14π B. 16 π *
C. 9 π D. 4 π
109.Find the area of the largest circle that can be cut from a triangle whose sides are 10 cm, 18 cm, and 20 cm. A. 11 π B. 12 π
C. 13 π D. 14 π *
110. A closed conical vessel has diameter of 2.4 m across the top and a height of 4.8 m. It contains water at a depth of 2.4 m. If the vessel is inverted, how deep is the water inside?
A. 0.56 m B. 0.21 m *
C. 0.92 m D. 0.45 m
111. A rectangle ABCD which measures 18x24 is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.
A. 18.5 B. 22.5 *
C. 20.5 D. 19.5
112. A quadrilateral has sides equal to 12 cm, 20 cm, 8 cm, and 17 cm respectively. If the sum of the two opposite angles is 225O, find the
area of the parallelogram.
A. 168.18 * B. 78.31
C. 70.73 D. 186.71
113. Three identical circles are tangent to each other externally. If the area of the curvilinear triangle enclosed between the points of tangency of the 3 circles is 16.13 cm2., compute the radius of each circle.
A. 10 cm * B. 13 cm C. 9 cm D. 15 cm
114. A reversed curved on a railroad track consist of two circular arcs. The central angle of one side is 20 degrees with radius 2500 feet, and the central angle of the other is 25 degrees with radius 3000 feet. Find the total length of two arcs.
A. 2912 ft B. 2218 ft
C. 2821 ft D. 2182 ft *
115. Find the volume of the solid common to two cylinders intersecting at 90O angle if radius of cylinders are both 3 cm.
A. 125 cm3 B. 135 cm3
C. 144 cm3 * D. 154 cm3
116. Two vertices of a triangle are (2, 4) and (-2, 3) and the area is 2 sq. units, find the locus of the third vertex. A. 4x – y = 14 B. 4x + 4y = 14
C. x + 4y = 12 D. x – 4y = -18 *
117. Find the coordinates of the point P(2, 4) with respect to the translated axis with origin at (1, 3).
A. (1, -1) B. (-1, -1)
C. (1, 1) * D. (-1, 1)
118. One line passes through the points (1, 9) and (2, 6), another line passes through (3, 3) and (-1, 5). The acute angle between the two lines is:
A. 30 B. 60 C. 45 * D. 135
119. Find the median through (-2, -5) of the triangle whose vertices are (-6,2), (2,-2), and (-2, -5). A. 3 B. 4 C. 5 * D. 6
120.The midpoint of the line segment between point A(x, y) and point B(-2, 4) is (2, -1). Find the coordinate of A. A. (6, -5) B. (5, -6) C. (6, -6) * D. (-6, 6)
121.The equation of a line passing through point A(2,3) and parallel to the line 5x – 3y + 8 = 0 is: A. 5x – 3y = 0 B. 5x – 3y = 1 *
C. 3x + 5y = 21 D. 3x + 5y = 0
122.The distance between points (5, 30O) and (-8, -50O) is:
A. 9.84 B. 10.14 *
123.Find the centroid of a triangle whose vertices are (2,3), (-4,6) and (2,-6).
A. (0,1) * B. (0,-1) C. (1,0) D. (-1,0)
124.The segment from (-1,4) to (2,-2) is extended three times its own length. Find the terminal point.
A. (11,-24) C. (-11,-20)
B. (11,-18) D. (11,-20) *
125.Given 3 vertices of a triangle whose coordinates are A(1,1), B(3,-3) and (5,-3). Find the area of the triangle.
A. 3 B. 4 * C. 5 D. 6
126.The distance between lines x-2y=4 and 2x-4y=7 is _______.
A. 3. B. -3 C. 4.47 D. 0.224 *
127.What is the x-intercept of the line passing through (1,4) and (4,1)?
A. 4.5 B. 5 * C. 6 D. 4
128.The distance between point (4,7,z) and (5,1,6) is 7.28. Find z.
A. 2 * B. 4 C. 6 D. 8
129.Compute the y-intercept of a line passing through point (5,3) and a slope of 3/4.
A. -3/4 * B. -3/5 C. -5/4 D. -4/5
130.The angle of inclination of ascend of a road having 8.25% grade is ________ degrees. A. 0.464 B. 4.72 * C. 4.64 D. 0.472
131.Find the volume of solid revolution formed by rotating the region bounded by the parabola y = x^2 and the lines y = 0 and x = 2 about the x-axis.
A. 40.21 C. 50.27
B. 67.02 D. 20.12 *
132.Compute the volume of the solid obtained by rotating the region bounded by y = x^2, y = 8 – x^2, and the y-axis about the x-axis.
A. 134.04 C. 100.53
B. 201.06 D. 268.08 *
133.A hole of radius 2 is drilled through the axis of a sphere of radius 3. Compute the volume of the remaining solid.
A. 59.69 C. 20.94
B. 46.83 * D. 41.88
134.Find the coordinates of the centroid of the plane area bounded by the parabola y = 4 – x^2 and the x-axis.
A. (0, 1) C. (0, 1.6) *
B. (0, 2) D. (1, 2)
135.Find the length of the arc of the parabola x^2 = 4y from x = -2 to x = 2.
A. 4.2 C. 4.9
B. 4.6 * D. 5.2
136.Suppose that a cylindrical tank has height 10, the radius of the base is 7, and it is half filled with water. Find the amount of work necessary to move all of the water out of the top of the tank. Water weighs 62.5 pounds per cubic foot.
A. 7215845.63 ft-lbs C. 3607922.81 ft-lbs * B. 96211.28 ft-lbs D. 192422.55 ft-lbs
137.The rate of change of a function y with respect to x equals 2 – y and y = 8 when x = 0. Find y when x = ln (2).
A. 2 C. 5 *
B. -2 D. -5
138.The velocity of a body is given by v(t) = sin (t), where the velocity is give in meters per second and “t” is given in seconds. The distance covered in meters between t = 0.25 and o.5 second is closed to:
A. -0.5221 C. -0.2251
B. 0.52221 D. 0.2251 *
139._______ states that the surface area of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of the arc length of the generating curve and the distance traveled by the curve's geometric centroid.
A. First theorem of Pappus * B. Second theorem of Pappus C. Reimann’s Theorem C. Lebesgue integral
140.______ was the first rigorous definition of the integral of a function on an interval. It can be readily evaluated by using the fundamental theorem of calculus or by numerical integration.
A. Lebesgue integral C. Reimann integral * B. Darboux integral D. Leibniz integral 141.Evaluate the integral of sin6xdx from 0 to π/2
A. π/32 C. 3π/32
B. 2π/17 D. 5π/32 *
142.Find the area (in square units) bounded by the parabola x2 – 2y = 0 and x2 + 2y – 8 = 0.
A. 11.7 C. 9.7
B. 4.7 D. 10.7 *
143.Integrate the square root of (1 – cos x)dx.
A. -2(2)1/2 cos x/2 + C * C. (2)1/2 cos x/2 + C
B. -2(2)1/2 cos x + C D. (2)1/2 cos x/ + C
144.Evaluate the integral of dx/(x+2) from -6 to -10.
A. 21/2 C. ln 3
B. 1/2 D. ln 2 *
145.Find the equation of the curve at every point of which the tangent line has a slope of 2x A. x = -y2 + C C. y = x2 + C *
B. y = -x2 + C D. x = y2 + C
146.Find the area of the region bounded by y = x^2 – 5x + 6, the x-axis, and the vertical lines x = 0 and x = 4.
A. 5.33 C. 10.67
B. 5.67 * D. 11.33
147.Determine the area of the region bounded by the parabola y = 9 – x^2 and the line x + y = 7.
A. 4.5 * C. 10/3
B. 3/2 D. 2.17
148.Determine the area of the region bounded by the curve y = x^3 – 4x^2 + 3x and the x-axis, from x = 0 to x = 3
A. 2.25 C. 3.08 *
B. 2.67 D. 2.47
149.What is the integral of (2 sec2 x – sin x)dx
A. 2 cos x + tan x + C C. 2 sin x + cos x + C B. 12 tan x + sin x + C D. 2 tan x cos x + C * 150.Evaluate the integral of 3^(4x)dx
A. 4^(4x) / ln3 + C C. 3^(4x) / ln81 + C * B. 3^(4x) / ln27 + C D. 4^(4x) / ln12 + C
151.Three numbers are in A.P. such that the sum of the first and third is 12 and the product of the first and second is 24. Find the largest of the three numbers.
A. 4 B. 8 * C. 6 D. 10
152.In a potato race, 8 potatoes are placed 6 feet apart on a straight line, the first being 6 ft from the basket. A contestant starts from the basket and puts one potato at a time into the basket. Find the total distance he must run in order to finish the race.
A. 532 ft. B. 432 ft * C. 342 ft D. 222 ft 153.Find the sum of the first 100 positive integers exactly divisible by 7.
A. 35,350 * B. 2,053 C. 53,350 D. 25,536
154.Two workers A and B together can complete a job in 7 days. A works twice as fast as B. How many days would it take B to do the job working alone?
A. 10.5days B. 21days * C. 9 days D. 18 days
155.The first of the three numbers exceeds twice the second number by 4, while the third number is twice the first. If the sum of the three numbers is 54, find the largest of the three numbers.
A. 12 B. 32 * C. 16 D. 6
156.The speed of the plane is 120 mi/hr in a calm. With the wind it can cover a certain distance in 4 hours, but against the wind it can cover only 3/5 of that distance in the same time. Find the velocity of the wind.
A. 10 mi/hr B. 30 mi/hr * C. 20 mi/hr D. 40 mi/hr
157.In the equation
3x m 1 x 24 0
, find m if one of the root is twice the other. A. -19,17 B. -12,18 C. 19,-17 D. 12,-18
158.A carpenter and his helper together can repair a house in 10 days. It takes the helper 5 days longer than the carpenter to do the repair when each works alone. How many days would it take the helper to do the repair if he is to work alone?
A. 22.8 days* B. 7.2 days C. 17.8 days D. 12.2 days
159.Two friends A and B are respectively 5 and 8 years old. In how many years will the ratio of their ages be 3:4?
A. 5 B. 6 C. 4 * D. 7
160.Roy and RR can jog around a circular park in 8 and 12 minutes, respectively. If they start at the same instant from the same place, in how many minutes will they pass each other if they jog around the track in the same direction?
A. 24 min. * B. 20 min. C. 15 min. D. 25 min. 161.Find the term containing x2 in the expansion of [x3+(a/x)]10.
A. 128a7x2 B. 210a6x2 C. 120a7x2 * D. 320a5x2
162.If sinxcosx+sin2x =1, what are the values of x in degrees? A. 32.2,69.3 B. -32.2, 69.3 C. 20.9, 61.9* D. 20.9, -61.9 163.Find the 15th term of the progression 1/4,1/7, 1/10,...
A. 46 B. 1/56 C. 1/46 D. 56
164.Find the geometric mean between -2 and -8.
A. 4 B. 16 C. -4* D. 6
165.In how many minutes after 2 o’clock will the hands of the clock extend in opposite directions for the first time? A. 2: 43min & 0.636 sec C. 2: 43 min & 38 sec *
B. 2: 48.636 sec D. 2: 46 min & 30 sec 166.Which of the following is a factor of x4-4x3-7x2+22x+24.
A. (x-3)* B. (x-2) C. (x-1) D. (x+3)
167.A number is divided into two parts such that when the greater part is divided by the smaller, the quotient is 3 and the remainder is 5. Find the smaller number if the sum of the two numbers is 37.
A. 8* B. 12 C. 32 D. 16
168.What is the probability of getting a 9 exactly once in 3 throws with a pair of dice? A. 0.033 B. 0.263 * C. 0.862 D. 0.751
169.Find the value of A for which the equation A(2x+3)-(x-4) = 3x+10 is an identity.
A. -1 B. 3 C. 2* D. -3
, find the value of versed Sin
A. 0.8 B. 0.3 C. 0.5* D. 0.2
171.A wheel, 5 ft in diameter, rolls up an incline of 18°20’. What is the height of the center of the wheel above the base of the incline when the wheel has rolled up 5 ft up the incline?
A. 3 ft B. 5 ft C. 4 ft * D. 6 ft
172.A tree broken over by the wind forms a right triangle with the ground. If the broken part makes an angle of 50° with the ground and the top of the tree is now 20 ft from its base, how tall was the tree?
A. 55 ft * C. 45 ft
B. 64 ft D. 36 ft
173.Seven carpenters and 5 masons earn a total of 2,300 per day. At the same rate of pay 3 carpenters and 8 masons earn 2,040. What are the wages per day of a carpenter and a mason?
A. 200 & 180* C. 210 & 170 B. 300 & 210 D. 270 & 150
174.A lady started a chain letter by writing to four friends and requesting each to copy the letter and send it to four other friends. If the chain was unbroken until the 5th set of letters was mailed, how much was spent for postage at P8.00 per letter?
A. 12,219 C. 21,435
B. 10,912* D. 11,291
175.Determine how much water should be evaporated from 50kg of 30% salt solution to produce a 60% salt solution. All percentages are by weight.
176.A machine costs P50,000.00 and depreciates 20% of the original cost during the first year, 16% during the second year, 12% during the third year, and so on, for 5 years. What is the value at the end of 5 years?
A. 15,000 C. 30,000
B. 25,000 D. 20,000*
177.A boat going across a lake 8 km wide proceeds 2 km at a certain speed and then completes the trip at a speed of ½ km/hr faster. By doing this, the boat arrives 10 minutes earlier than if the original speed had been maintained. Find the original speed of the boat.
A. 5 km/hr C. 8 km/hr
B. 4 km/hr* D. 6 km/hr
178.z varies directly as x and inversely as y2. If x = 1 and y = 2, then z = 2. Find z when x = 3 and y = 4.
A. 1.5* B. 3 C. 2.5 D. 3.5
179.An audience of 540 people is seated in rows having the same number of persons in each row. If 3 more persons seat in each row, it would require 2 rows less to seat the audience. How many persons were in each row originally?
A. 17 B. 30 C. 27* D. 31
180.A group consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n.
A. 80 B. 110 C. 55 D. 100*
181.If Juan is 10% taller than Pedro and Pedro is 10% taller than Maria, then Juan is taller than Maria by how many percent?
A. 20% B. 18% C. 21%* D. 11%
182.A piece of wire of length 52 cm. is cut into two unequal parts. Each part is then bent to form a square. It is found that the total area of the two squares is 97 cm2. Find the difference between the sides of each square.
A. 3 B. 5* C. 4 D. 9
183.Assuming the earth to be a sphere of radius 3960 mi, find the distance of a point 36 N
latitude from the equator.
A. 2844 mi. C. 2484 mi
B. 2488 mi* D. 4288 mi
184.In how many ways can 10 different books be divided among A, B, and C so that A gets 5 books, B 3 books, and C 2 books?
A. 2,520 * C. 1360800
B. 5040 D. 263
185.From the equation 12x3-8x2+kx+18=0, find the value of k if one root is the negative of the other.
A. -18 B. -12 C. -27* D. -31
186.If one root of 9x^2-6x+k=0 exceeds the other by 2, find the value of k.
A. 8 C. -8*
B. 5 D. -6
187.The arithmetic mean of two numbers is 5, and their harmonic mean is 24/5. Find the numbers.
A. 3 & 5 C. 2 & 6
B. 4 & 6 D. 4 & 4
188.A man has P100,000, part of which he invested at 12% interest and the rest at 18%. He received a total annual interest of P15,300. How much did he invest at 18% interest rate?
A. 45,000 C. 55,000 *
B. 60,000 D. 75,000
189.Simplify the equation Sin2x(1+cot2x).
A. sin2x C. 1*
B. cos2x D. sec2xsin2x
190.A vertical pole consists of two parts, each one half of the whole pole. At a point in the horizontal plane which passes through the foot of the pole and 36 m from it, the upper half of the pole subtend an angle whose tangent is 1/3. How high is the pole?
A. 72* B. 25 C. 46 D. 16
191.ABDE is a square section and BDC is an equilateral triangle with C outside the square. Compute the value of angle ACE.
A. 30 deg.* C. 50 deg.
192.The angle of elevation of the top of a tower from a point A is 23 30 '
. From another point B, the angle of elevation of the top of the tower is
55 30 '
. The points A and B are 217.45 m apart and on the same horizontal plane as the foot of the tower. The horizontal angle subtended by A and B at the foot of the tower is 90 degrees. Find the height of the tower.
A. 90.6 m* C. 89.5 m
B. 86.7 m D. 55.9 m
193.At a meeting, after everyone had shaken hands with everyone else, it was found that 66 handshakes were exchanged. How many were at the meeting?
A. 10* B. 20 C. 12 D. 24
194.A number between 1 and 1000 (inclusive) is randomly selected. What is the probability that it will be divisible by 4 and 5?
A. 0.03 B. 0.05 * C. 0.04 D. 0.06
195.In the series 1, 1, 1/2, 1/6, 1/24,,..., determine the 6th term.
A. 1/28 B. 1/64 C. 1/32 D. 1/120 *
196.A tree broken over by the wind forms a right triangle with the ground. If the broken part makes an angle of 50° with the ground and the top of the tree is now 20 ft from its base, how tall was the tree?
A. 55 ft * B. 64 ft C. 45 ft D. 36 ft 197.Which is identically equal to secx/(cotx+tanx)?
A. cscx B. sinx * C. cosx D. -secx
198.Woodz was four times as old as LC ten years ago. If she is now twice as old as LC, how old is Woodz?
A. 15 B. 20 C. 30* D. 25
199.A boat propelled to move at 25 mi/hr in still water, travels 4.2 miles upstream in the same time that it can travel 5.8 miles downstream. Find the speed of the stream.
A. 4* B. 10 C. 8 D. 12
200.Find the value of x which will satisfy the equation
x 2 x 1
A. 1 B. 1,4 C. 4* D. 0,4
201.Find the sum and product of roots of the equation
x 2x 23x 60 0
. A. -2, 60* B. 2, 17 C. 17, -60 D. 2, 60
202.The probability that A can solve a given problem is 4/5, that B can solve it is 2/3 and that C can solve it is 3/7. If all three try, compute the probability that the problem will be solved.
A. 0.64 B. 0.52 C. 0.96* D. 0.81
203.In how many ways can 9 different books be arranged on a shelf so that 3 of the books are never all 3 together? A. 130,240 B. 332,640 * C. 160,480 D. 260,354
204.Find the equation whose roots are numerically equal but opposite in sign to the roots of the equation x3+7x2+11x+5=0.
A. x3-7x2+11x-5=0 * C. x3+7x2+11x-5=0
B. x3+7x2-11x+5=0 D. x3-7x2-11x+5=0
205.Determine the sum of the first 10 terms of the sequence whose general term is given by
n 3 2 . A. 88225 B. 88552 * C. 88255 D. 88522 206.If 3log x log y 0 , express y in terms of x. A. 3 yx * B. 2 yx C. y x D. y3x
207.Mark has nickels, dimes, and quarters amounting to $1.85. If he has twice as many dimes as quarters, and the number of nickels is two less than twice the number of dimes, how many quarters does he have?
A. 3 * B. 8 C. 6 D. 10
208.An organization has 25 members, 5 of whom are ECE’s. In how many ways can a committee of 3 be formed so as to include at least one ECE?
A. 540 B. 1160 * C. 970 D. 311 209.Solve for x in the following equation:
x 3x 5x 7x ... 49x 625 A. 1/4 B. 1* C. 1/2 D. 3/2 210.If x : y : z4 : 3 : 2 and 2x 4y 3z 20 , find x,y,z. A. 4, -5, 2 B. -8, 6, -4* C. 5, -6, 8 D. 2, -7, 4
211. A Café Mocha Grande contains 16oz of a mixture of coffee and Chocolate which is 40% coffee by volume. How much of the mixture should be removed and replaced by an equal volume of chocolate so that the resulting Café Mocha will be 25% coffee by volume?
A. 7.5 liters B. 4 oz C. 2.4 oz D. 6 oz *
212.If the sides of the triangle are 2x+3, x2+3x+3, and x2+2x, find the greatest angle.
A. 100 deg. C. 120 deg.*
B. 130 deg. D. 110 deg
213.The sum and difference of two angles in a triangle are 90 degrees and 30 degrees, respectively. If the side opposite the smallest angle is 20 cm., find the area of the triangle.
A. 346.4* C. 289.6
B. 231.5 D. 268.4
214.In triangle ABC, angle A=80 deg. and point D is inside the triangle. If BD and CD are bisectors of angle B and C, solve for the angle BDC.
A. 100 deg. C. 120 deg.
B. 130 deg.* D. 140 deg.
215.A statistical clerk submitted the following reports. The average rate of production of radios is 1.5 units for every 1.5 hrs work by 1.5 workers. How many radios were produced in one month by 30 men working 200 hrs during the month?
A. 4000* C. 5000
B. 3800 D. 4200
216.A class of 40 students took examination in Electronics and Communications. If 30 passed in Electronics, 36 passed in Communication and 2 failed in both subjects, how many students passed in both subjects?
A. 28* B. 30 C. 26 D. 32
217.The excess of the sum of the fourth and fifth parts over the difference of the half and third parts of a number is 119. Find the number.
A. 240 C. 420 *
B. 320 D. 430
218.How many terms of the progression 4, 7, 10, 13, . . . must be taken so that the sum will be 69.
A. 6* B. 9 C. 8 D. 12
219.What is the angle measured in degrees clockwise from the north to the direction in which the carrier is traveling.
A. bearing C. direction
B. azimuth D. course *
220.An urn contains 4 white balls and 3 black balls. Another urn contains 3 white balls and 5 black balls. If one ball is drawn from each urn, determine the probability that the balls drawn will be 1 white and 1 black.
A. 27/56 B. 9/56 C. 29/56* D. 5/14
221.Three friends A, B, and C can do a piece of work in t hours working together. Working alone, A can do the work in 6 hours more, B in 1 hour more, and C in twice the time if all working together. How long would it take to finish the work if all working together?
A. 20 mins. B. 30 mins. C. 40 mins.* D. 50 mins
222.A golf ball is dropped from a height of 6 meters. On each rebound it rises 2/3 of the height from which it last fell. What distance has it traveled at the instant it strikes the ground for the 7th time?
A. 27.89 m* C. 20.87 m
B. 19.86 m D. 24.27 m
223.A wheel, 5 ft in diameter, rolls up an incline of 18°20’. What is the height of the center of the wheel above the base of the incline when the wheel has rolled up 5 ft up the incline?
A. 3 ft B. 5 ft C. 4 ft * D. 6 ft
224.The velocity of an airplane in still air is 125 kph. The velocity of the wind due east is 25 kph. If the plane travels east and returns back to its base again in 4 hours, at what distance does the plane travel due east?
A. 240 km.* C. 320 km.
B. 180 km D. 200 km
225.In a racing contest, there are 240 cars which will have provisions that will last for 15 hours. Assuming constant hourly consumption for each car, how long will the fuel provisions last if 8 cars withdraw from the race every hour after the first?
A. 16 B. 18 C. 20 D. 25*
226.The sum of the sides of a triangle is equal to 100 cm. If the angles of the triangle are in the continued proportions of 1:2:4. Compute the shortest side of the triangle.
A. 17.545 C. 18.525
B. 19.806* D. 14.507
227.The sides of a triangular field which contains an area of 2400 sq. cm. are in continued proportion of 3:5:7. Find the smallest side of the triangle.
A. 45.74 C. 95.43
B. 63.62 D. 57.67*
228.What time after 2 o’clock will the hands of the clock extend in opposite directions for the first time? A. 2:43.64* B. 2:43.46 C. 2:34.64 D. 2:34.46
229.Two cities 270 mi apart lie on the same meridian. Find their difference in latitude.
A. 3/44 rad* C. 4/33 rad
B. 3/34 rad D. 4/43 rad
230.It is a set of ordered pairs of numbers.
A. function C. range
B. domain D. relation *
231.The set of points in a plane such that the difference of the distances of each point of the set from two fixed points (foci) in the plane is constant.
A. Parabola C. Circle
B. Hyperbola * D. Ellipse
232.In how many ways can a party of 6 people be seated on a row of 6 seats if a certain 2 refuse to sit next to each other?
A. 240 ways C. 180 ways
B. 480 ways * D. 320 ways
233.Find the real values of x and y satisfying the given equation: (2x+3y)+ i(3x-5y) = 8-i7 .
A. x=1, y=-2 C. x=2, y=1
B. x=-2, y=-1 D. x=2, y=-1*
234.Missy goes to a bake shop to buy some pastries for resale at Book Latte. She spends half her money for Revel Bars, and one-third of what remains for Triple Chocolate Brownies. She spends 150 for other pastries and still has 200 left from the amount she originally had. How much money did she have at the start?
A. 1050* C. 1500
B. 5100 D. 1250
235.Roy met Mark and RR walking hand in hand in Trinoma, and because of jealousy he decided to walk northward away from the two at the rate of 2 m/s while the two went to the east at the rate of 0.5 m/s. after how many minutes will the distance between them be 250 m?
A. 121 mins C. 2 mins
B. 60 mins D. 1 min
236.How many liters of a 25% acid solution must be added to 80 liters of a 40% acid solution to have a solution that is 30% acid?
A. 160 L* B. 90 L C. 100 L D. 120 L
237.Engr. RR walks at the rate of 6 mph to the LRT station. She then takes the LRT to work, averaging at 60 mph. if she spends 15 minutes less time on the LRT than walking, and the distance from her house to work is 29 miles, what is the distance from her house to the LRT station?
A. 3 B. 4* C. 5 D. 6
238.Three friends A, B, and C are in a race. The odds that A will win are 7 to 5, and the odds that B will win are 1 to 3. What are the odds in favor of C?
A. 1 to 4 B. 3 to 2 C. 1 to 5 * D. 2 to 5
239.Two numbers differ by 40 and their arithmetic mean exceeds their geometric mean by 2. What are these numbers? A. 75 & 115 B. 45 & 85 C. 81 & 121* D. 88 &128
240.Which of the following is a prime number?
A. 437 B. 483 C. 417 D. 487 *
241.A and B working together can do a job in 3 days, B and C together can do the same job in 4 days, and A and C in 2.5 days. In how many days can all of them finish the job working together?
A. 1.07 days C. 3.1 days
B. 2.8 days D.2.03 days*
242.Find the mean, median and mode respectively of the following numbers: 13, 13, 14, 12, 11, 10, 9, 11, 8, 11, 5, and 15.
A. 10, 10, 11 C. 10, 11, 11
B. 10, 11, 12 D. 11, 11, 11*
243.The age of Diophantus, a Greek mathematician may be calculated from the epitaph which reads as follows: “Diophantus passed 1/6 of his life in childhood, 1/12 in youth, 1/7 as a bachelor. Five years after his marriage was born a son who died 4 years before his father at half his father’s final age.” How old was Diophantus when he died?
A. 80 C. 78
B. 82 D. 84 *
244.Your father told you “I was your age now when you were born”. If you are 21 years old today, how old is your father?
A. 50 C. 48
B. 42 * D. 44
245.The vibration frequency of a string varies as the square root of the tension and inversely as the product of the length and diameter of the string. If the string is 3 feet long and 0.03 inch in diameter vibrates at 720 times per second under 90 lbs tension, at what frequency will a 2 feet long, 0.025 inch string vibrate under 2500 lbs tension.
A. 6210 C. 6830 *
B. 7514 D. 5645
246.The hypothesis of conditional statement. The "if" part of an "if-then" statement. A. antecedent * C. condition
B. postulate D. theorem
247.A compound statement that says one sentence is true if and only if the other sentence is true. A. dependent statement C. independent statement
B. biconditional statement * D. conditional statement
248.There are 3 copies each of 4 different books. In how many different ways can they be arranged on a shelf? A. 349,800 B. 549,600 C. 469,500 D. 369,600 *
249.The distance passed over by a certain pendulum bob in succeeding swings form the geometric progression 16,12,9,... feet respectively. Calculate the total distance traversed by the bob before coming to rest.
A. 64 ft * B. 75 ft C. 54 ft D. 96 ft
250.At what price should Book Latte mark a book that costs P300 in order that it may offer a discount of 20% on the marked price and still make a profit of 25% on the selling price?