Algebra 2
1. Holes are drilled 35.7 mm apart in a metal plate. If a row of 26 holes is drilled, determine the distance,
in centimeters, between the centers of the first and last hole.
a. 106.7 mm
b. 89.25 cm
c. 91.30 m
d. 613.4 nm
Answer: a. 89.25 cm
2. Two times the father’s age is 8 more than six times his son’s age. Ten years ago, the sum of their ages
was 44. The age of the son is:
a. 49
b. 15
c. 20
d. 18
Answer: b. 15
3. 2000 kg of steel containing 8% nickel is to be made by mixing a steel containing 14% nickel with
another steel containing 6% nickel. How much of the steel containing 14% nickel is needed?
a. 1500 kg
b. 800 kg
c. 750 kg
d. 500 kg
Answer: d. 500 kg
4. A father and his son can dig a well if the father works 6 hours and his son works 12 hours or they can
do it if the father works 9 hours and the son works 8 hours. How long will it take for the son to dig the
well alone?
a. 5 hours
b. 10 hours
c. 15 hours
d. 20 hours
Answer: d. 20 hours
5. Three times the first of three consecutive odd integers are three more than twice the third. Find the
integer.
a. 9
b. 11
c. 13
d. 15
Answer: d. 15
6. A 100-kg salt solution originally 4% by weight. Salt in water is boiled to reduce the water content until
the concentration is 5% by weight salt. How much water is evaporated?
a. 10 kg
b. 15 kg
c. 20 kg
d. 25 kg
Answer: 20 kg
7. A pipe can fill up a tank with the drain open in three hours. If the pipe runs with the drain open for one
hour and then the drain is closed, it will take 45 more minutes for the pipe to fill the tank. If the drain
will be closed right at the start of filling, how long will it take for the pipe to fill the tank?
a. 1.15 hrs
b. 1.125 hrs
c. 1.325 hrs
d. 1.525 hrs
Answer: b. 1.125 hrs
8. A 40 gram alloy containing 35% gold is to be melted with a 20 gram alloy containing 50 % gold. How
much percentage of gold is the resulting alloy?
a. 40 %
b. 30%
c. 45 %
d. 35 %
Answer: a. 40 %
9. 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
Answer: d. 5
10. The product of three consecutive integers is 9240. Find the third integer.
a. 20
b. 21
c. 22
d. 23
Answer: c. 22
Engineering Mathematics
1. Calculate the diameter of a solid cylinder which has a height of 82.0 cm and a total surface area of 2.0 𝑚2.
a. 57.5 𝑐𝑚
b. 50 cm
c. 51.25 cm
d. 43.2 cm
Answer: a. 57.5 cm
2. Solve for the missing angle in the given figure.
a. 84 degrees
b. 83 degrees
c. 82 degrees
d. 81 degrees
Answer: 83 degrees
3. Find the value of the missing angle in the given figure.
a. 91 degrees
b. 95 degrees
c. 102 degrees
d. 30 degrees
Answer: a. 91 degrees
4. Determine the value of angle 𝛽 in the given figure.
a.
b.
c.
d.
50 degrees
47 degrees
43 degrees
81 degrees
Answer: b. 47 degrees
5. Determine the value of angle 𝜃 in the figure.
a. 59 degrees 26 minutes
b. 60 degrees 2 minutes
c. 81 degrees 54 minutes
d. 90 degrees
Answer: a. 59 degrees 26 minutes
6. Determine angles c and d in the given figure.
a.
b.
c.
d.
45 degrees and 165 degrees
43 degrees and 20 degrees
44 degrees and 134 degrees
46 degrees and 101 degrees
Answer: c. 44 degrees and 134 degrees
7. Find the angle 𝛼.
a.
b.
c.
d.
59 degrees 20 minutes
60 degrees 21 minutes
61 degrees 22 minutes
5 degrees 54 minutes
Answer: a. 59 degrees 20 minutes
8. In the figure, find the length of side a.
a.
b.
c.
d.
10.1 cm
12 cm
11.2 cm
10. 61 cm
Answer: d. 10.61 cm
9. A tent peg is 4 m away from a 6 m high tent. What length of rope runs from the top of the tent to the
peg?
a. 7.21 m
b. 8 m
c. 6.34 m
d. 9 m
Answer: a. 7.21 m
10. Two sides of a triangle measures 6 cm and 8cm and their included angle is 40 degrees. Find the third
side.
a. 5.144 cm
b. 5.263 cm
c. 4.256 cm
d. 5.645 cm
Answer: a. 5.144 cm
Physics for Engineers
1. A man fires 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 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. 525 m/s
b. 360 m/s
c. 350 m/s
d. 336 m/s
Answer: a. 525 m/s
2. A man travels in a motorized banca at the rate of 12 kph from his barrio to the población and come
back to his barrio at the rate of 10 kph. If his total time of travel back and forth is 3 hours 10 minutes,
the distance from the barrio to the población is:
a. 17.27 km
b. 17.72 km
c. 12.77 km
d. 17.32 km
Answer: a. 17.27 km
3. It takes Michael 60 seconds to run around a 440-yard track. How long does it take Jordan to run around
the track if they meet in 32 seconds after they start together in a race around the track in opposite
directions?
a. 58.76 s
b. 68.57 s
c. 65.87 s
d. 86.57 s
Answer: b. 68.57 s
4. Juan can walk from his home to his office at the rate of 5 mph and back at the rate of 2mph. What is
his average speed in mph?
a. 2.86
b. 3.56
c. 4.12
d. 5.89
Answer: a. 2.86
5. Kim and Ken 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 Kim walks along the circumference and Ken towards the center, find their distance
after 10 minutes.
a. 193 m
b. 202 m
c. 241 m
d. 258 m
Answer: d. 258 m