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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 *
18. Find the volume of a right circular cylinder whose lateral area is 25.918 sq. m and base area of 7.068 sq. m.
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 *
18. Find the volume of a right circular cylinder whose lateral area is 25.918 sq. m and base area of 7.068 sq. m.
