MASTERY PROBLEM 3
1. If a bug moves a distance of 3 pi cm along a circular arc and if this arc subtends a central angle of
45 degrees, what is the radius of the circle?
Answer: 12 cm
2. A man rows upstream and back in 12 hours. If the rate of the current is 1.5 kph, and that of the
man in still water is 4 kph, what was the time spent downstream?
Answer: 3.75 hours
3. The area of the rhombus is 264 sq. m. if one of the diagonals is 24 m long, calculate the length of
the other diagonal.
Answer: 22 m
4. A ship is sailing due east when a light is observed to have a bearing of N 62 deg 10 mins E. After
the ship has traveled 2250 m, the light bears N 48 degrees 25 minutes E. If the course is
continued, how close will the ship approach the light?
Answer: 2934 m
5. An observer at sea is 30 feet above the surface of the water, how much of the ocean can he see?
Answer: 124.80 miles^2
6. A bus leaves Manila at 12 noon for Baguio 250 miles away, traveling an average of 55 mph. At
the same time, another bus leaves Baguio for Manila 65 mph. At what distance from Manila will
they meet?
Answer: 114.58 miles
7. Michael is four times as old as his son Carlos. If Michael was 18 years old when Carlos was born,
how old is Michael now?
Answer: 24 y/o
8. In an arithmetic sequence whose first term is 5, the sum of 8 terms is 208. What is the common
difference?
Answer: d = 6
9. An observer wishes to determine the height of the tower. He takes sights at the top of the tower
from A and B, which are 50 ft apart at the same elevation on a direct line with the tower. The
vertical pole at point A is 30 degrees and at point B is 40 degrees. Find the height of the tower.
Answer: 92.54 ft
10. Two complementary angles measures x and y respectively. The difference of three times x and
two times y is 40 degrees, then the smaller angle measures:
Answer: 44 degrees
11. In triangle ABC, AB = 40 in, BC = 60 in and AC = 80 in. How far from A will the other end of the
bisector of angle B located along the line AC?
Answer: 32 in
12. To build a dam, 60 men must work 72 days. If all 60 men are employed at the start but the
number is decreased by 5 men at the end of each 12-day period, how long will it take to
complete the dam?
Answer: 108 days
13. The sides of a triangle are 8 cm, 10 cm and 14 cm. Determine the radius of the inscribed circle.
Answer: 2.45 cm
14. In triangle XYZ, Z = 70 deg and X = 45 deg, XY = 40 ft. What is the length of the median drawn
from vertex X to side XYZ?
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Answer: 36.3 ft
The sides of a triangle are 8 m, 10 m and 14 m. Determine the radius of the circumscribed circle.
Answer: 39.19 m
The distance between the centers of the three circles which are externally tangent to each other
externally are 10, 12, and 14 yards. The area of the smallest circle is:
Answer: 16 pi square yards
Determine the unit’s digit of the expansion 3 raised to 856.
Answer: 1
The sum of all even numbers from 0 to 420 is:
Answer: 44310
There are nine arithmetic terms between 11 and 51. The sum of the progression is ______.
Answer: 341
If y, 4y + 8, 30y + 24 are in geometric progression, what will be the common ratio?
Answer: 6
If one-third of the air is removed by each stroke of an air pump, what fractional part of the total
air is removed in 6 strokes?
Answer: 0.9122 of the total air
The sides of a right triangle is an arithmetic progression whose difference is 6 units. Its area is:
Answer: 216 square units
The side of a triangle are 18 cm, 24 cm, and 34 cm, respectively. Find the length of the median
to the 24-cm side, in cm.
Answer: 24.41 cm
If the sides of the parallelogram and an included angle are 6, 10 and 100 degrees, respectively,
find the length of the shorter diagonal.
Answer: 10.73 units
How many diagonals are there in a pentadecagon?
Answer: 60 diagonals
-ENDSo whether you eat or drink, or whatever you do, do it all for the glory of God.
-1 Corinthians 10:31-