UNANG
HAKBANG
NI ISKO UNANG
HAKBANG
NI ISKO UNANG
HAKBANG
NI ISKO
“Iskolar ng bayan,
lagi’t lagi para sa bayan.”
Test Reviewer and Guide
for S&T Scholarship
Prepared by
DOST Scholars’ Association in
Region 7 - DOST SA SIETE
Test Reviewer and Guide for S&T Scholarship
“Iskolar ng bayan,
lagi’t lagi para sa bayan.”
UNANG
UNANG
HAKBANG
HAKBANG
NI NIISKO
ISKOUNANG
UNANG
HAKBANG
HAKBANG
NI
ISKO
UNANG
NI ISKO
HAKBANG
UNANG
NIHAKBANG
ISKO
NI ISKO
Test Reviewer and Guide
for S&T Scholarship
Prepared by
DOST Scholars’ Association in
Region 7Prepared
- DOST SA
by SIETE
DOST Scholars’ Association in
Region 7 - DOST SA SIETE
cvads.dostregion7@gmail.com
/dostsaregion7
Message from DOST SA SIETE
Greetings, future iskos and iskas!
Taking your first step toward becoming a Department of
Science and Technology (DOST) scholar begins here,
with this reviewer in hand. As part of our mission at
DOST SA SIETE, we are committed to guiding future
scientists and innovators like you through the
challenging yet rewarding path of the S&T
Undergraduate Scholarship.
This reviewer is a symbol of your dedication and
ambition to excel in the field of science and technology.
It’s the foundation for what lies ahead in your journey,
where passion meets opportunity, and preparation
leads to success.
Embrace this chance, for every page you turn and
every problem you solve brings you closer to the doors
of countless possibilities in science and technology.
The future of our nation’s progress lies in the hands of
young scholars like you. So give it your all, and let this
reviewer be the first of many milestones on your road to
becoming a proud iskolar ng agham.
Mga iskolar ng bayan, lagi't lagi para sa bayan!
Authors
Erika Niña S. Cotiangco
Editor
Yaghnna Ainein T. Yankin
Co-Editor
Contributors:
Logical Reasoning
Maria Khazandra C. Abonin
English
Maria Khazandra C. Abonin
Science
Erika Niña S. Cotiangco
Dave Justine L. Bantilan
John Matthieu M. Maghanoy
Mechanical-Technical
Yaghnna Ainein T. Yankin
Mathematics
Lee Lhouine Kaidz M. Lirazan II
Izaak Tristan G. Cabigon
Fredireck N. Benitez
Tips
Erika Niña S. Cotiangco
Yaghnna Ainein T. Yankin
Cover Design
John Carlo Payawal
Table of Contents
DOST Scholars' Association in Region 7
DOST SA SIETE
I.
Knowing the DOST Undergraduate
Scholarship Program
II.
REVIEW QUESTIONS
III.
1
Logical Reasoning
4
English
5
Science
7
Mathematics
15
Mechanical-Technical
19
ANSWERS AND EXPLANATIONS
Logical Reasoning
21
English
21
Science
22
Mathematics
38
Mechanical-Technical
49
IV.
KEY REFERENCES
51
V.
GENERAL TIPS
53
Tips in Taking the Exam
Answer & Blank Sheets
I. Knowing the DOST Undergraduate
Scholarship Program
What is the S&T Undergraduate Scholarships?
The S&T Undergraduate Scholarships Program aims to stimulate and
entice talented Filipino youths to pursue lifetime productive careers in
science and technology and ensure a steady, adequate supply of
qualified S&T human resources that can steer the country towards
national progress.
Types of S&T Undergraduate Scholarships:
RA 7687 - also known as the “Science and Technology Scholarship
Act of 1994”, provides for scholarships to talented and deserving
students whose families’ socio-economic status does not exceed
the set cut-off values of certain indicators. Qualifiers must pursue
priority fields of study in the basic sciences, engineering, other
applied sciences, and science and mathematics teaching.
MERIT - formerly known as the NSDB or NSTA Scholarship under RA
No. 2067, is awarded to students with high aptitude in science and
mathematics, and are willing to pursue careers in the fields of
science and technology.
What are the benefits?
Tuition and other school fees: Actual fees up to ₱40,000/AY
Learning Materials and/or Connectivity Allowance: ₱10,000/AY
Monthly Living Allowance: ₱8,000/month of the AY
Clothing Allowance: ₱1,000 (1st Sem of 1st Year only)
Transportation Allowance: 1 economy-class roundtrip fare (for those
studying outside of home province)
Group Accident and Health Insurance: Premium
Thesis Allowance: ₱10,000
Graduation Allowance: ₱1,000
What are the qualified courses?
see this link:
https://www.facebook.com/share/p/6f5dzjzjTez38Fef/
1
Who's eligible to apply?
1. Must be a natural-born Filipino citizen.
2. All graduating Grade 12 students in the school year or graduate of
Grade 12 before the school year and did not enroll in college yet:
• STEM STRAND - All students belonging to the STEM class.
• NON-STEM STRAND - Must be in the top 5% of the graduating class.
3. Graduates of high school before the K-12 program who belong to the
top 5% of the graduating class.
4. Must be of good moral character and in good health.
5. May have applied to the DOST-SEI Undergraduate Scholarship but did
not qualify.
6. May have qualified for the DOST-SEI Undergraduate Scholarship but
did not avail of the award.
7. Must not have earned any post-secondary (college or vocational) units.
How to prepare for the exam?
Review the subjects covered in the scholarship exam. Before answering
any questions, read the exam instructions thoroughly. The test includes
the following domains and discuss some topics:
Part 1:
Logical Reasoning (verbal and nonverbal reasoning)
- Verbal Reasoning: tests your ability to understand, analyze and
interpret information. It also measures your ability to extract
meaning from complex information and to think logically and
analytically. There are 5 items in this reviewer.
- Nonverbal Reasoning: measure your abilities to visualize and
transform images in your mind, recreate visual experiences and
reasoning about shape, measurement, depiction and navigation;
and mentally rotate and manipulate two and three dimensional
spaces. There are 5 items in this reviewer.
Part 2:
English: apply the rules of the English language, specifically on
grammar and syntax, vocabulary, and reading comprehension. There
are 10 items in this reviewer.
Science: consists of problem-items in Earth Science, Astronomy,
Biology, Chemistry, and Physics that will test your ability in
accomplishing various important scientific tasks. There are 40 items
in this reviewer.
2
Mathematics: performing tasks that will measure your ability to
comprehend quantitative relationships and their representations.
There are 30 items in this reviewer.
Mechanical-Technical: measure your ability to acquire information
about everyday physics and to comprehend mechanical
relationships. It consists of mechanical and electrical problems, as
well as items that deal with physical forces. There are 10 items in this
reviewer.
Part 3:
Self-Inventory: This consists of short statements which you are asked
to evaluate or describe yourself.
For more details, visit:
https://sei.dost.gov.ph
https://www.science-scholarships.ph
https://ugrad.science-scholarships.ph/#/faq
Note: This reviewer has a total 100 questions but the total number of questions
during the exam may vary up to 200 items.
3
II. Review Questions
A. Logical Reasoning
Verbal Reasoning
1. AZY, BYW, CXU, ___?
a. DWS
b. DTW
c. DWT
d. SWD
2.
Inference:
a. More students will be
able to afford higher
education.
b. Interest rates will rise
again in the future.
c. The quality of higher
____ .
a.
b.
c.
d.
education will
decrease.
2/16
2/12
3/16
3/12
d. Fewer students will
need loans in the
future.
Nonverbal Reasoning
3.
a.
b.
c.
d.
5
6
4
3
6. If the following figure is
folded along the dotted lines,
what would be the result?
4. April, August, ______, ______,
January, July, June
a. December, February
b. February, December
c. October, September
d. September, October
5. Statement: The government
has announced a reduction in
the interest rate for student
a.
c.
b.
d.
7. Which one is the odd one
out?
loans
to
make
higher
education more accessible.
a.
4
b.
c.
d.
B. English
8. What follows the series of
figures below?
a.
b.
c.
d.
1. The CEO reassured the
team, "You can express your
concerns without fear of
repercussion," meaning she
tried to:
a. Encourage
transparency
b. Downplay dissent
c. Incite rebellion
d. Promote skepticism
9. Which of the following
figures below contain the
following given figure?
2. The Illiad : Homer :: ___:___
a. Tractacus LogicoPhilosophicus :
Wittgenstein
b. Critique of Pure Reason
: Aurelius
c. The Phenomenology of
Spirit : Sartre
d. Beyond Good and Evil :
Machiavelli
Given:
a.
b.
c.
d.
10.
3. Which of the words below
is synonymous with
EPHEMERAL?
a. Timeless
b. Sempiternal
c. Fleeting
d. Perpetual
a.
b.
c.
d.
4. Find the antonymous word
of the capitalized word.
A QUIXOTIC plan.
a. Idealistic
b. Practical
c. Foolhardy
d. Romantic
5
5. Public transportation and
private vehicles serve as two
primary modes of transport,
each with distinct advantages
and
drawbacks.
Public
transportation, such as buses
and trains, offers a more
environmentally friendly option,
reducing traffic congestion and
lowering
greenhouse
gas
emissions. In contrast, private
vehicles provide convenience
and privacy, allowing individuals
to travel on their own
schedules and to more remote
locations.
However,
the
widespread use of personal
cars contributes to urban traffic
and pollution, whereas public
transit systems can alleviate
these issues, especially in
densely populated areas. While
private cars offer flexibility,
public transportation systems
are generally more costeffective
and
promote
sustainable
urban
growth
(Litman, 2020).
What pattern of paragraph
development is evident in the
passage?
a. Problem-Solution
b. Cause and Effect
c. Compare and Contrast
d. Description
6. The actor with slicked back
hair and hunter eyes starring
in the movie was filled with
_______________.
a. Penury
b. Lugubriousness
c. Ostentation
d. Debonair
7. The scholar’s arguments
were so recondite that only
those
with
a
profound
understanding of the subject
could grasp the full extent of
his ideas, leaving the rest
bewildered and confused.
What is the meaning of the
underlined word?
a. Simple
b. Superficial
c. Obscure
d. Humorous
8. What is the error of the
following sentence?
Neither the manager nor the
employees was aware of the
changes until the last minute.
a. was
b. aware
c. until
d. No Error
9. Correct the underlined part
of the sentence.
The committee members, as
well as the chairperson, were
responsible for the project's
completion.
6
C. Science
a. will be responsible for
completing the project
b. is responsible for the
1. Alex argues that bacteria
are living organisms, while
Sam insists that they are not.
Who is correct and why?
a. Sam, because bacteria
are smaller than
eukaryotic cells.
b. Sam, because bacteria
do not contain a
nucleus.
c. Alex, because bacteria
cannot survive without
a host.
d. Alex, because bacteria
can metabolize
nutrients and reproduce
on their own.
project’s completion.
c. have been responsible
for completing the
project.
d. The sentence is
grammatically correct.
10. Identify the underlined
phrase with an error.
Beside the assignment that
a
. teacher gave us,
our
b.
she also sent some
c.
reading materials.
2. Siblings, though they come
from the same parents, are
not identical to each other.
Which stage of cell division is
mainly responsible for this
genetic variability?
a. anaphase II
b. telophase II
c. metaphase I
d. prophase I
No error.
d.
3.
A
woman
who
is
homozygous dominant for
brown eyes (BB) marries a
man who is heterozygous for
brown eyes (Bb). What is the
probability that their child will
have blue eyes (bb)?
7
a. 75%
b. 50%
c. 25%
a. Covalent bonds
b. Hydrogen bonds
c. Hydrophobic
interactions
d. Van der Waals
interactions
d. 0%
4. Sarah is a biology student
working
on
a
genetics
experiment involving fruit flies.
She wants to list down its
phenotype. Which of the
following should she NOT
record?
a. Blue and brown eye
color
b. Long and short hair
length
c. Homozygous for blood
type
d. Purple and white flower
color
5. If a DNA strand with a
sequence of 5' ... GCT ACG TTA
... 3' undergoes transcription,
which is its correct mRNA
complementary strand?
a. 5'...GCT ACG TTA...3'
b. 3'...CGA UGC AAU...5'
c. 3'...CGA TGC AAT...5'
d. 5'...CGA UGC AAU...3'
6. Each nucleotide in DNA and
RNA has an aromatic base.
What is the principal force that
keeps the bases in a polymer
from interacting with water?
7. _______________ are fairly small
organelles that provide a safe
place within the cell to carry
out
certain
biochemical
reactions
that
generate
harmful,
highly
reactive
oxygen
species.
These
chemicals are both generated
and broken down in the same
location.
a. Nucleosomes
b. Peroxisomes
c. Lysosomes
d. Endosomes
8. Dolphins and sharks both
have streamlined bodies and
dorsal fins that help them
move
efficiently
through
water. However, dolphins are
mammals, while sharks are
fish. What can be inferred
from these similarities?
a. These features are
said to be analogous.
b. These features are
said to be homologous.
c. These features are
said to be vestigial.
d. These features are
said to evolve
dependently.
8
9. An organism is discovered
in a salty environment. It has a
cell wall but lacks
d. warm temperatures;
very moist
peptidoglycan and survives in
extreme conditions. Which
kingdom does it belong to?
a. Eubacteria
12.
Which
term
best
describes those processes
that move weathered rock
materials
and
soils
downslope?
a. talus transfer
b. mass wasting
c. slope sheeting
d. haloclasty
b. Plantae
c. Archaebacteria
d. Animalia
10. What are Earth’s layers
from densest to least dense?
a. lithosphere,
13. Which of these did Alfred
Wegener use to support his
continental drift theory?
a. similar rocks and
similar fossils on
different continents
b. convection currents in
the asthenosphere and
seafloor spreading
c. seafloor spreading and
similar rocks on
different continents
d. fossils from ancient
organisms and
convection currents in
the asthenosphere
asthenosphere, outer
core, inner core
b. lithosphere,
asthenosphere, inner
core, outer core
c. inner core, outer core,
asthenosphere,
lithosphere
d. outer core, inner core,
lithosphere,
asthenosphere
11. What two factors speed up
rates of chemical reaction
and weathering in rocks and
soils?
a. low temperatures; very
dry
b. low temperatures; very
moist
c. high temperatures;
very dry
14. Some constellations are
named after animals and
figures
from
mythology.
Which of these analogies is
incorrect?
a. Pisces: The Fishes
b. Hydra: The Water
Serpent
9
c. Ursa Minor: The Little
Horse
d. Phoenix: The Mythical
Bird
15. Imagine you are observing
a full Moon from Earth. At the
same time, an astronaut on
the Moon is observing Earth.
What phase will Earth appear
to be from the astronaut’s
vantage point?
a. Full Earth
b. New Earth
c. First Quarter Earth
d. Third Quarter Earth
16. The Kuiper Belt is a region
of the solar system beyond
Neptune. What type of
celestial bodies are primarily
found in the Kuiper Belt?
a. Asteroids
b. Comets
c. Meteors
d. Meteorites
17. John is driving a car when a
man suddenly crosses the
road. He honks his horn and 3
seconds later, John hears the
echo from a nearby wall. If the
speed of sound is 343 m/s,
how far away is the wall?
a. 212.5 meters
b. 313.5 meters
c. 414.5 meters
d 514.5 meters.
18. Jenna releases two
identical stones from a roof at
the same time. She threw one
stone upwards, while the
other was simply dropped.
Both of them will:
a. Reach the ground at
the same time?
b. Have the same velocity
when they reach the
ground?
c. Have the same
acceleration when
reaching the ground.
d. None of the above
19. A painter is standing on a
scaffold that is supported at
both ends by ropes. The
painter moves from the
center
of
the
scaffold
towards one end. At what
point will one of the ropes
experience zero force, and
why?
a. It is when the painter is
directly above one of
the ropes.
b. It is when the painter is
exactly at the center of
the scaffold.
c. It is when the painter is
halfway between the
center and one end of
the scaffold.
d. It is when the painter
moves past one of the
ropes and stands
beyond the scaffold.
10
20. Ron is driving on a
highway. He knows that
recently, the speed limit was
a. True, the ball floats
because its density is
equal to the density of
increased from 50 km/h to 70
km/h. How much time will be
saved on a 120-kilometer trip
if the driver travels at the
water.
b. False, the ball floats
because the weight of
the displaced water is
maximum allowed speed?
greater than the ball's
a. 32 minutes
b. 42 minutes
c. 52 minutes
volume.
c. True, the ball floats
because the buoyant
d. 62 minutes
force is always greater
than the weight of the
ball.
21. A 1,600-kg truck is initially
moving at 18000 m/h. How
much force is needed to
accelerate the truck to a
speed of 72 km/h in 15
seconds?
a. 1,600 N
b. 1,800 N
c. 2,000 N
d. 2,200 N
22. Alex has a small, hollow
metal ball that he carefully
places in a tub filled with
water. To his surprise, the ball
floats halfway submerged. He
thinks that since the ball
floats in water, it must be
because the buoyant force is
greater than the weight of the
ball. Is Alex’s statement
correct?
11
d. False, the ball floats
because the buoyant
force is equal to the
weight of the ball, not
greater than it.
23. In a complex electrical
system,
five
wires
are
connected to a junction. Wire
A carries 8A of current going
into the junction, while wire B
carries 3A of current going
out. Wire C carries 4A going
in, and wire D carries 5A going
out. What does wire E carry?
a. Wire E carries 2 A
going into the junction.
b. Wire E carries 2 A
going out of the
junction.
c. Wire E carries 4 A
going into the junction.
d. Wire E carries 4 A
going out of the
junction.
24. Sarah is trying to open a
locked room using a wrench.
She tries to apply force at
different areas of the wrench.
How much force must Sarah
apply at a perpendicular
distance of 0.25 meters from
the pivot to generate a torque
of 400 Nm on a wrench?
a. 1,200 N
b. 1,600 N
c. 1,800 N
d. 2,000 N
Refer to the figure below for
25-26.
https://www.varsitytutors.com/ap_physics_1-help/ohm-s-law
25. John is setting up a new
lighting system in his home
workshop and connects four
different resistors in parallel
to ensure the lights operate at
the same voltage. The
resistors have the following
values R1 = 10 ohms, R2 = 20
ohms, R3 = 30 ohms, R4 = 40
ohms. Find the equivalent
resistance of all resistors
a. 2.7 Ω
b. 3.5 Ω
c. 4.8 Ω
d. 5.6 Ω
26. Which of the following is
true regarding the current of
the circuit shown above?
a. The current through R1
is the largest because it
has the smallest
resistance.
b. The current through R4
is the largest because
it has the largest
resistance.
c. All resistors have the
same current because
they are connected in
parallel.
d. The current through R3
is the largest because
it is the middle value of
resistance.
27. Harold has a condition
called myopia. He can see
things that are near better
than those afar. His doctor
recommended using glasses
to correct his eyesight. What
is the best type of lens to use
to correct his eyesight?
a. Convex lens
b. Concave lens
c. Bifocal lens
d. Cylindrical lens
28. Tania is working with a
gas that initially is at the
standard temperature and
pressure
(STP)
then
it
undergoes a change where
12
its pressure is increased to
four times and its temperature
is reduced to half. What
d. To a greater extent than
any other element,
carbon can bond to
happens to the volume of the
gas during this process?
a. The volume is reduced
to one-fourth.
itself to form straight
chains, branched chains
and rings.
b. The volume is reduced
31. Significant figures play a
by a factor of eight.
c. The volume has
increased to four times
crucial role in scientific and
mathematical calculations as
they reflect the precision and
its original value.
d. The volume remains
the same.
accuracy of numerical values.
Consider the number 17.030 mL.
How many significant figures
29. It is an insoluble solid
formed
by
a
chemical
reaction in solution.
a. Precipitate
b. Powder
c. Salt
d. Grain
30. What makes carbon such
a versatile element?
a. Carbon forms covalent
bonds rather than ionic
bonds.
b. Elemental carbon
comes in two forms,
diamond and graphite.
c. Carbon forms four
bonds, although the
ground state
configuration would
predict the formation
of fewer bonds.
does it contain?
a. 3
b. 4
c. 5
d. 6
32. Jose is trying out different
salts in a bunsen burner to
produce
different
colored
flames. She wants to produce a
lilac, pinkish-colored flame.
What salt does she need to put
in a bunsen burner to produce
the said color?
a. NaCl
b. CuCl 2
c. KCl
d. SrCl 2
33. “When filling degenerate
orbitals, the lowest energy is
attained when the number of
13
electrons having the same
spin is maximized.”
a. Aufbau principle
b. Pauli exclusion
principle
c. Hund’s rule
d. None of these
34. Tiffany wants to separate
the pigments in a leaf extract.
Which technique should she
use?
a. Filtration
b. Distillation
c. Decantation
d. Chromatography
35. Arrange each of the
following sets of compounds
in order of increasing boiling
point temperature:
a. CH4 < HI < H2O
b. HI < CH4 < H2 O
c. H2O < HI < CH4
d. H2 O < CH4 < HI
36. What is the molar mass of
benzene(C6H6)?
(Atomic mass of Carbon: 12.011
g/mol; Atomic mass of Hydrogen:
1.0080 g/mol)
a.
b.
c.
d.
75.45 g/mol
76.22 g/mol
78.11 g/mol
77.77 g/mol
38. Nikki is in the laboratory.
She compressed a 2.00000L
container into 1.00000L at
20.0000°C. She noticed a
sudden drop in temperature.
What is the new temperature?
(Express your answer in Kelvin;
conversion of Celsius to Kelvin: x°C +
273.15)
a. 147.575 K
b. 146.575 K
c. 147.755 K
d. 146.755 K
39. Carol, a student chemist, is
preparing a basic solution. She
diluted five (5.000) grams of
NaOH (molar mass: 40.00
g/mol) to 100.00 mL water.
Find its molarity (M)?
a. 2.150 M NaOH
b. 2.152 M NaOH
c. 1.250 M NaOH
d. 1.252 M NaOH
40. Andrea, the laboratory
partner of Carol, is now diluting
the NaOH sample for titration
to 0.10000 M NaOH solution.
How much water does she
need to add in order to get the
desired diluted concentration?
(Express your answer in mL)
a. 1250.0 mL
b. 1500.0 mL
c. 1750.0 mL
d. 2000.0 mL
37.
Balance the following
stoichiometric equation:
14
D. Mathematics
1. Roll a pair of dice two
times. What is the probability
that the product of two
numbers is 6?
a. ½
c. 1/9
b. ¼
d. 2/3
5. Find the focus of the parabola
(x-1)2 = 10y.
a. (1, 2.5)
c. (-1, 2.5)
b. (1, -2.5)
d. (-1, -2.5)
6. The table below shows the
number of computers sold daily
at a local computer shop and its
corresponding probabilities.
2. Evaluate the limit of the
function:
a. 164
b. 165
c. 166
d. 167
3. The sum of Php 50, 000
was deposited in a fund
earning interest at 6% per
annum compounded annually.
What was the amount in the
fund at the end of 4 years?
a.
b.
c.
d.
4. Find the equation of the
line with a slope of 15 and an
x-intercept of -9.
a. y = 15x + 9
b. y = 15x + 135
c. y = 9x -15
d. y = 135x – 15
15
Find the mean of the distribution.
a. 1.87
c. 2.87
b. 2.77
d. 1.77
7. Find the equation of an ellipse
if its vertex is (3, 6) and its foci
are located at (3,12) and (3, 2).
a.
b.
c.
d.
8. The polynomial x3 +4x2 -3x+8
is divided by x-8. What is the
remainder?
a. 541
b. 408
c. 752
d. 635
9. A line passes through the
points (-5, 2) and (1, 9). Find
the slope of the line.
a. 6/7
c. 7/8
b. 7/6
d. 8/7
14. Find the area of a circle
inscribed in a triangle whose
sides are 5, 8 and 9 units,
respectively.
10. What is the derivative of
the function
?
a.
15. What is the horizontal
asymptote of the function
b.
c.
a. 2/3
b. 3/2
c. 0
d. No horizontal asymptote
d.
11. What is the median of the
following set of numbers?
3, 5, 6, 4, 3, 8, 3, 5, 9, 7, 2, 4
a. 5.5
b. 5
c. 4.5
d. 4
12. The sum of 8 consecutive
integers is 5932. Find the
third integer.
a. 430
c. 690
b. 520
d. 740
13. Simplify this expression :
a. cos a
b. sin 2a
c. sin a
d. cos 2a
16. In how many ways can five
people line up to pay their
electric bills if two particular
persons refuse to follow each
other?
a. 120
c. 90
b. 72
d. 140
17. In how many ways can we
seat 7 people in a round table
with a certain three people not
in consecutive order?
a. 576
b. 390
c. 5320
d. 689
16
18. If the surface area of the
sphere is increased by 21%
its volume is increased by:
a.
b.
c.
d.
22. An airplane flying with the
wind, took 2 hours to travel
1000km and 2.5 hours in flying
back. What was the wind
velocity in kph?
a. 50
c. 70
b. 60
d. 40
13.31%
33.1%
21%
30%
19. From the digits (1, 2, 3, 4,
5, 6, 7), how many odd
numbers of different 3 digits
23. Once a month, a man puts
some money into a cookie jar.
Each month he puts 50 centavos
more into the jar than the month
before. After 12 years, he
counted his money, he had Php
5,436. How much money did he
put in the jar in the last month?
a. Php 70.50
each can be formed?
a. 120
b. 240
c. 360
d. 210
20. A piece of wire is shaped
to enclose a square whose
area is 169 cm2. it is then
reshaped to enclose a
rectangle whose length is 15
cm. The area of the rectangle
is:
a. 165 cm2
b. 175 cm2
c. 170 cm 2
d. 156 cm2
b. Php 75.50
c. Php 73.50
d. Php 72.50
24. A coin is tossed 3 times.
What is the probability of getting
3 tails up?
a. 7/8
c. ¼
b. 1/16
d. 1/8
25. In a multiple-choice test,
each question is to be answered
by selecting 1 out of 5 choices,
of which only 1 is right. If there
are 10 questions in a test, what is
the probability of getting a 6 right
of pure guesswork?
a. 10%
c. 0.44%
b. 6%
d. 0.55%
21. If the length of the major
and the minor axes of an
ellipse in 10 cm and 8 cm,
respectively, what is the
eccentricity of the ellipse?
a. 0.5
c. 0.7
b. 0.6
d. 0.8
17
26. If x, y, and z are sides of a
triangle, and x = 13 and y = 17,
which of the following
numbers is a possible value
of z?
a. 29
b. 31
c. 33
d. 35
30. Mary is making a triangular
wall with building blocks. The
top row has three blocks, the
second row has five, and the
third has seven, and so on.
How many rows can he make
with a set of 120 blocks?
27. A DVD player with a list
price of ₱100 is marked down
30%. If John gets an
employee discount of 20%
off the sale price, how much
does John pay for the DVD
player?
a. ₱44.00
b. ₱77.60
c. ₱86.00
d. ₱56.00
a.
b.
c.
d.
28. Which of the following
defines a one-to-one
function?
a.
b.
c.
d.
29. What is the domain of
the function defined by
f(x) = x 2 -1?
a. ( - , -1] U [1, + )
b. [-1, 1]
c. (-1, 1)
d. (- , -1) U (1, + )
18
11
10
13
15
E. MechanicalTechnical
The diameters of the gears are
5 inches, 10 inches, and 15
inches, respectively. If gear A is
turning at 30 revolutions per
minute (RPM), what is the
turning rate of gear C?
a. 6 RPM
b. 10 RPM
c. 15 RPM
d. 50 RPM
1. Consider the 4 gears
shown below. Which of the
following happens when gear
2 turns counter-clockwise?
4. A block slides down a
frictionless incline at an angle
of 30 degrees. If it starts from
rest, what is the speed of the
block after 3 seconds?
a. 14.7 m/s
b. 9.8 m/s
c. 5.1 m/s
d. 10.2 m/s
a. Gears 1 and 4 turn
clockwise.
b. Gears 1 and 3 turn
clockwise.
c. Gear 1 turns
counterclockwise.
d. Gear 3 turns
counterclockwise.
5. In an ideal gas container,
what happens to the pressure
inside the container if the
temperature is doubled while
the volume is kept constant?
a. It is halved
b. It remains constant
c. It is doubled
d. It quadruples
2. A ball is released from a
height of 20 feet above the
ground. After the fourth
bounce, it rebounds to a
height of 3 feet. If the ball
always bounces up to the
same fraction of the height
from the previous bounce,
what is this fraction?
a. 1/5
c. 1/3
b. 1/4
d. 1/2
6. You are playing with a ball on
an uneven surface, as shown in
the figure. If the ball travels
from point A to point D along
the surface, what is the change
in gravitational potential energy
between point A and point B?
3. In the figure shown below,
gears A, B, and C are
connected by a chain.
19
a.
b.
c.
d.
a. The lowest potential
energy is located at
point A.
b. The lowest potential
energy is located at
point B.
c. The potential energy
at A is greater than the
potential energy at B.
d. The potential energy
at B is greater than the
potential energy at A.
7. A car moves around a
curve of radius 100m at a
constant speed of 20 m/s.
What is the magnitude of the
car’s acceleration?
a. 4 m/s²
b. 6 m/s²
c. 8 m/s²
d. 10 m/s²
8. Ming calculated the
average velocity of a vehicle
to be 26.82 ± 0.20 m/s. Four
other students also provided
estimates for the vehicle's
average velocity, which are
listed in the table. Which of
these estimates aligns with
Ming's calculation?
Student 1
Student 2
Student 3
Student 4
9. A solid disk and a hollow
ring of the same mass and
radius roll down an inclined
plane. Which one reaches the
bottom first?
a. The disk
b. The ring
c. Both reach at the same
time
d. Depends on the
material of the objects
10. A heavy-duty crane lifts a
500-kg load vertically upward.
If the crane accelerates the
load from rest to a velocity of
10 m/s in 5 seconds, what is
the net force acting on the
load during this time?
a. 4900 N
b. 1000 N
c. 5900 N
d. 9000 N
20
A. 1. LOGICAL REASONING – VERBAL
Item Answer
Explanation
The series starts with the first and the last letters of the
1
C
alphabet, then subtracted by where the first letter falls in
alphabetical order, then so on. AZY – A (first letter), Z (last
letter), Z being the 26th letter, subtracted by the order of
A, being the 1st letter. 26-1=25th letter of the alphabet, Y.
BYW – B (second letter), Y (25th letter), Y being the 25th
letter, subtracted by the order of B, being the 2 nd letter. 252=23rd letter of the alphabet, W. Then so on, until you get
DWT.
Simplifying the fractions, we get: 1/3, 1/4, and 1/5. We
2
B
must find the fraction that gives us 1/6 if simplified.
The number before the square-rooted number is divided
3
C
into the number before it, resulting in the number under
the square root.
The months are arranged in alphabetical order.
4
A
The statement indicates that the government is reducing
5
A
student loan interest rates to make higher education
more accessible. Lower interest rates will reduce the total
cost of borrowing, making it less expensive for students
to take out and repay loans. Consequently, this financial
relief may make higher education more affordable for a
greater number of students.
A. 2. LOGICAL REASONING – NONVERBAL
6
B
The other letters contain only three strokes, while W has
7
D
four.
8
C
9
D
10
B
B. ENGLISH
The CEO is encouraging the team to openly share their
1
A
thoughts, ideas, or concerns without worrying about
negative consequences. This indicates that the CEO wants
an environment where communication is open and
honest, promoting transparency within the team.
Choice B: Critique of Pure Reason : Kant
2
A
Choice C: The Phenomenology of Spirit : Hegel
21
3
C
4
B
5
6
C
D
7
C
8
A
9
A
10
A
C. Science
1
D
2
D
Choice D: Beyond Good and Evil : Nietzsche
Ephemeral means something that is short-lived or lasts
for a very brief time, fleeting.
Choice A: endures through all time
Choice B: eternal or everlasting
Choice D: indefinitely or lasts forever
Quixotic means overly idealistic, impractical, or
unrealistic. Therefore, its antonym is practical, which
refers to something grounded and achievable.
Choice A: unrealistic
Choice B: recklessly bold
Choice D: dreamy and idealistic
The word “While” is a signal of compare and contrast.
Context Clues. Debonair is used to describe a handsome
male.
Context Clues. Recondite is synonymous with obscure,
meaning complex.
When a compound subject is joined by "neither...nor" the
verb should agree with the part of the subject closest to
it. In this case, "the employees" (which is plural) is closest
to the verb, so the verb should be plural.
The sentence is grammatically correct because the
subject "The committee members" is plural, and the verb
"were" correctly agreeing with this plural subject, despite
the additional phrase "as well as the chairperson."
Must be “Besides”. Besides is used to mean "in addition
to" or "apart from," which is the appropriate choice for
adding extra information.
Bacteria are considered living organisms because they
exhibit all the characteristics of life. They can metabolize
nutrients, grow, respond to stimuli, and reproduce
independently by binary fission. Unlike viruses, which
require a host cell for replication, bacteria can carry out
all necessary life processes on their own.
During prophase I, homologous chromosomes (one from
each parent) pair up in a process called synapsis. This
pairing allows for crossing-over, where sections of
chromatids are exchanged between homologous
chromosomes. This exchange of genetic material creates
new combinations of genes on each chromosome,
contributing to genetic diversity.
22
Mitosis - process of cell division that results in two genetically
identical daughter cells, each with the same number of
chromosomes as the parent cell. It is essential for growth, repair,
and asexual reproduction in organisms.
Stages of Mitosis:
• Prophase: Chromosomes condense and become visible. The
nuclear envelope breaks down, and spindle fibers begin to
form.
• Metaphase: Chromosomes align at the cell's equatorial plane,
known as the metaphase plate.
• Anaphase: Sister chromatids are pulled apart toward opposite
poles of the cell by the spindle fibers.
• Telophase: Chromatids reach the poles, and new nuclear
envelopes form around each set of chromosomes. The
chromosomes begin to de-condense.
• Cytokinesis: The cytoplasm divides, resulting in two separate
daughter cells.
Meiosis - a specialized form of cell division that reduces the
chromosome number by half, producing four genetically diverse
gametes (sperm or eggs) for sexual reproduction. It consists of
two rounds of division: Meiosis I and Meiosis II.
Stages of Meiosis I:
• Prophase I: Chromosomes condense and homologous
chromosomes pair up (synapsis). Crossing-over (exchange of
genetic material) occurs between homologous chromosomes.
• Metaphase I: Homologous chromosome pairs align at the
metaphase plate.
• Anaphase I: Homologous chromosomes are pulled to opposite
poles of the cell.
• Telophase I: Chromosomes reach the poles, and the cell divides
into two haploid cells (each with half the original number of
chromosomes).
Stages of Meiosis II:
• Prophase II: Chromosomes condense again in each haploid
cell, and a new spindle apparatus forms.
• Metaphase II: Chromosomes align at the metaphase plate in
each haploid cell.
• Anaphase II: Sister chromatids are pulled apart toward
opposite poles of each cell.
• Telophase II: Chromatids reach the poles, and the nuclear
envelope reforms around each set of chromosomes. The cells
divide, resulting in four genetically unique haploid gametes.
3
A
As shown in the diagram, none of the offspring can have
the bb genotype, so the probability of having a child with
23
blue eyes is 0%. The woman can
only pass on the B allele, and the
man can pass on either B or b.
However, since the child must
inherit a B allele from the mother,
it is impossible for the child to
have the genotype bb and
therefore have blue eyes.
4
C
5
B
6
C
7
B
A phenotype refers to the observable physical traits or
characteristics of an organism, such as eye color, hair
length, or flower color. "Homozygous for blood type"
refers to a genotype, which is the genetic makeup of an
organism, not an observable trait. Therefore, it is not an
example of a phenotype.
During transcription, RNA polymerase reads the DNA
template strand in the 3' to 5' direction and synthesizes
an mRNA strand in the 5' to 3' direction. The mRNA
strand is complementary to the DNA template strand,
with uracil (U) replacing thymine (T).
Protein synthesis involves two major processes:
• Transcription: This occurs in the nucleus, where RNA
is synthesized by copying the DNA template in the 3'
to 5' direction.
• Translation: This takes place in the cytoplasm,
specifically in the ribosomes, where amino acids are
assembled into proteins. This process is guided by
mRNA and tRNA.
Hydrophobic interactions are the principal force that
keeps the aromatic bases in DNA and RNA from
interacting with water, by causing the bases to cluster
away from water and stay inside the helix.
• Covalent bonds: Strong bonds where atoms share
electrons, holding the DNA/RNA backbone together.
• Hydrogen bonds: Weak bonds between hydrogen and
electronegative atoms, linking DNA/RNA bases.
• Van der Waals interactions: Weak forces between close
atoms/molecules, adding to DNA helix stability.
Among these, peroxisomes are specifically responsible
for handling and neutralizing reactive oxygen species,
making them the correct answer.
24
Basic Parts of a Cell:
Nucleus: The control center of the cell, which contains the cell's
DNA and manages activities like growth, metabolism, and
reproduction.
Cytoplasm: The gel-like substance
inside the cell that contains all
organelles and cell parts. It
provides
a
medium
for
biochemical
reactions
and
supports organelles.
Cell Membrane: The outer layer of
the cell that controls what enters
and exits the cell. It provides
structure and protects the cell.
Mitochondria: Known as the powerhouse of the cell,
mitochondria generate ATP through cellular respiration,
providing energy for the cell's activities.
Ribosomes: Small structures that synthesize proteins by
translating genetic information from mRNA.
Endoplasmic Reticulum (ER): A network of membranes that
helps in the production, processing, and transport of proteins
and lipids. The rough ER has ribosomes attached, aiding in
protein synthesis, while the smooth ER is involved in lipid
synthesis.
Golgi Apparatus: An organelle that modifies, sorts, and packages
proteins and lipids for transport to other parts of the cell or
outside the cell.
Lysosomes: Organelles containing digestive enzymes that break
down waste materials, cellular debris, and foreign invaders.
Peroxisomes: Small organelles that contain enzymes to break
down fatty acids and detoxify harmful substances, including
reactive oxygen species.
Cytoskeleton: A network of protein fibers that maintain cell
shape, secure organelles in specific positions, allow cytoplasm
and vesicles to move within the cell, and enable cells to move in
response to stimuli.
8
A
9
C
The streamlined bodies and dorsal fins in dolphins and
sharks are examples of analogous structures, which
evolved independently in different lineages due to similar
environmental pressures, not because of a common
evolutionary origin.
Archaebacteria are known for surviving in extreme
environments, such as high salinity, and they lack
peptidoglycan in their cell walls, distinguishing them
from Eubacteria.
25
10
C
11
D
6 Kingdoms of Life:
1. Animalia: A kingdom of multicellular, eukaryotic
organisms that are typically motile, heterotrophic
(obtain food by ingestion), and lack cell walls.
2. Fungi: A kingdom of mostly multicellular, eukaryotic
organisms that are heterotrophic, have cell walls
made of chitin, and obtain nutrients through
absorption, often as decomposers.
3. Eubacteria: A kingdom of unicellular, prokaryotic
organisms with cell walls containing peptidoglycan,
which are found in various environments and can be
either beneficial or pathogenic.
4. Plantae: A kingdom of multicellular, eukaryotic
organisms that are primarily autotrophic, have cell
walls made of cellulose, and carry out photosynthesis
to produce energy.
5. Protista: A diverse kingdom of mostly unicellular,
eukaryotic organisms that can be autotrophic or
heterotrophic and are often found in aquatic
environments.
6. Archaebacteria: A kingdom of unicellular, prokaryotic
organisms that lack peptidoglycan in their cell walls
and often live in extreme environments, such as hot
springs or salt lakes.
The Earth's layers are arranged by density, with the
densest material at the center and the least dense at the
surface. The inner core is the densest, composed
primarily of iron and nickel in a solid state. Surrounding
it is the outer core, also made of iron and nickel, but in a
liquid state, making it slightly less dense than the inner
core. Above the core lies the asthenosphere, a semi-solid
layer within the upper mantle that behaves plastically
and allows for tectonic plate movement. The lithosphere
is the outermost layer, including the Earth's crust and the
uppermost part of the mantle; it is the least dense layer
and is solid and rigid.
Chemical reactions and weathering processes in rocks
and soils are significantly influenced by temperature and
moisture. Warm temperatures increase the rate of
chemical reactions because higher temperatures provide
more energy for the reactions to occur. Moisture is also
crucial, as water acts as a medium for chemical reactions,
26
12
B
facilitating processes like hydrolysis, oxidation, and
dissolution, which are key in weathering. Therefore,
environments with warm temperatures and sufficient
moisture (very moist) are most conducive to speeding up
chemical weathering and other related reactions in rocks
and soils.
Mass wasting is the term that best describes the
processes that move weathered rock materials and soils
downslope under the influence of gravity. It includes a
variety of movements such as landslides, rockfalls, and
mudflows. These processes are responsible for the
transfer of sediments from higher elevations to lower
areas, reshaping the landscape.
Talus Transfer: Refers to the accumulation and movement of
rock fragments, typically found at the base of steep slopes or
cliffs, due to gravity.
Slope Sheeting: Describes the process where large sheets or
slabs of rock peel off from a slope or cliff, often due to pressure
release or exfoliation.
Haloclasty: A weathering process where salt crystals grow in the
cracks of rocks, leading to the breakdown of the rock material,
commonly found in coastal environments.
13
A
14
C
15
B
Wegener supported his continental drift theory with
evidence of similar fossils and similar rock formations
found on different continents that are now separated by
oceans. This suggested that these continents were once
joined together, forming a supercontinent called
Pangaea. The idea was that as continents drifted apart,
the similar fossils and rock types were left on different
landmasses.
Ursa Minor is known as "The Little Bear," not "The Little
Horse." The other names are correctly associated with
their constellations.
When the Moon is in its full
phase as viewed from Earth, the
Earth would be in its new phase
as viewed from the Moon. This
is because the positions are
complementary: when the
Moon is fully illuminated from
the Earth’s perspective, the
Earth is in shadow from the Moon’s perspective. This
27
16
B
17
D
means the side of Earth facing the Moon is dark, leading
to a "New Earth" phase for the astronaut on the Moon.
The Kuiper Belt is home to many icy bodies and dwarf
planets, including comets that originate from this region.
Meteorite: A fragment of a meteoroid that survives its
passage through Earth’s atmosphere and lands on the
surface.
Meteor: The streak of light produced when a meteoroid
enters Earth’s atmosphere and burns up, commonly
known as a “shooting star.”
Meteoroid: A small rocky or metallic body in outer space,
typically smaller than an asteroid, that can become a
meteor if it enters Earth’s atmosphere.
Comet: An icy body that releases gas and dust, forming a
glowing coma and tail when near the sun.
GIVEN:
t = 3 sec
vsound = 343 m/s
ASKED:
d= ?
FORMULA: d= v × t
SOLUTION:
An echo occurs when a sound wave travels from the
source, hits an obstacle (the wall), and is reflected
to the source. The total time taken for John to hear
the echo is the time for the sound to travel to the
wall and return to him.
2d= v × t
Substitute the values:
𝑚
2d = (343 𝑠 × 3𝑠)
343
𝑚
d= ( 2 𝑠 × 3𝑠)
d= 514.5 meters
18
D
19
B
Jenna releases two identical stones simultaneously—one
is thrown upwards, and the other is simply dropped. Both
experience the same gravitational acceleration, but the
stone thrown upwards takes longer to fall since it must
first overcome its upward motion. Consequently, they
will not reach the ground at the same time or with the
same velocity, making the correct answer "None of the
above."
Initially, the scaffold and painter are in equilibrium, with
the sum of vertical forces and torques equaling zero. As
28
the painter moves toward one end, the nearby rope
supports more weight while the farther rope supports
less. When the painter is directly above one rope, all the
weight is supported by that rope, and the tension in the
other rope becomes zero.
20
B
21
A
29
22
D
According to Archimedes' Principle, the buoyant force
acting on an object submerged in a fluid is equal to the
weight of the fluid displaced by the object. There are two
primary forces acting on the ball:
1. The weight of the ball (gravitational force): This force
pulls the ball downward, trying to sink it.
2. The buoyant force: This is the upward force exerted
by the displaced fluid, which pushes the ball upward.
For an object to float, these two forces must be equal in
magnitude. If the buoyant force were greater than the
weight of the object, the object would rise completely
above the water. If the weight were greater, the object
would sink.
In this case, the ball is partially submerged, meaning the
buoyant force and the weight of the ball are in perfect
balance. The ball displaces just enough water to create a
buoyant
force
that
equals
its
weight.
30
23
C
24
B
31
25
C
26
A
27
B
In a parallel circuit, the voltage across each resistor is the
same, and current is inversely proportional to resistance.
Therefore, the smallest resistance (R1 = 10 ohms) will
have the largest current, while the largest resistance (R4
= 40 ohms) will have the least current. Hence, the current
through R1 is the largest due to its smallest resistance.
Myopia, or nearsightedness, occurs when the eye focuses
light in front of the retina, making distant objects appear
blurry. A concave lens is used to correct this by diverging
light rays, shifting the focal point onto the retina, allowing
clear vision of distant objects. Thus, the best lens for
Harold’s myopia is a concave lens.
32
28
B
29
A
30
D
A precipitate is an insoluble solid formed by a reaction in
solution.
Carbon's versatility comes from its ability to form strong
covalent bonds with other carbon atoms, creating
structures like chains and rings, which are the foundation
of organic molecules. This property, called catenation, is
more pronounced in carbon than in any other element,
leading to a vast array of organic compounds. Carbon can
also form up to four covalent bonds, allowing it to bond
33
with many other elements, enhancing its bonding
flexibility.
31
C
All non-zero digits and any zeros between them or after
the decimal point are significant, so 17.030 has 5
significant figures.
Rules on Significant Figures:
1. All non-zero digits (1-9) are always significant.
Examples:
924 143 has 6 significant figures
2. Zeroes in between significant numbers are always
significant.
Examples:
3 050 030 021 - has 10 significant figures
3. Zeroes at the beginning of a number are not significant;
they only indicate the position of the decimal point.
Examples:
0.0213 has 3 significant figures
4. Trailing zeros to the right of the decimal ARE
significant. There are FOUR significant figures in 92.00.
5. Trailing zeros in a whole number with the decimal
shown ARE significant. Placing a decimal at the end of a
number is usually not done. By convention, however, this
decimal indicates a significant zero. For example, "540."
indicates that the trailing zero IS significant; there are
THREE significant figures in this value.
6. Trailing zeros in a whole number with no decimal
shown are NOT significant. Writing just "540" indicates
that the zero is NOT significant, and there are only TWO
significant figures in this value.
7. Exact numbers have an INFINITE number of significant
figures. This rule applies to numbers that are definitions.
For example, 1 meter = 1.00 meters = 1.0000 meters =
1.0000000000000000000 meters, etc.
8. For a number in scientific notation: N x 10x, all digits
comprising N ARE significant by the first 6 rules; "10" and
34
32
C
33
C
34
D
35
A
"x" are NOT significant. 5.02 x 104 has THREE significant
figures: "5.02." "10 and "4" are not significant.
When you excite an atom or an ion by very strong heating,
electrons can be promoted from their normal unexcited
state into higher orbitals. As they fall back down to lower
levels (either in one go or in several steps), energy is
released as light. Each of these jumps involves a specific
amount of energy being released as light energy, and each
corresponds to a particular wavelength (or frequency).
As a result of all these jumps, a spectrum of lines will be
produced, some of which will be in the visible part of the
spectrum. The color you see will be a combination of all
these individual colors.
Hund’s rule states that when filling degenerate orbitals,
the lowest energy is attained when the number of
electrons having the same spin is maximized.
Chromatography is a technique used to separate
components of a mixture based on their movement
through a medium.
Methods of separating mixtures into their component
substances:
• Chromatography: A mixture is passed through a
medium where the components move at different rates.
• Distillation: A method for separating mixtures of two or
more pure liquids.
• Evaporation: A technique for separating a soluble solid
from a liquid.
• Filtration: A method for separating pure substances in
mixtures of particles.
• Sieving: A technique for separating a mixture of fine
sand and pebbles by passing the mixture through a
sieve.
• Centrifugation: A technique for separating suspension
mixtures, such as toothpaste, concrete, and clay.
The boiling point of the compound depends on their
intramolecular forces. There are four intramolecular
forces in total, which are arranged from weakest to
strongest. These are: London Dispersion forces, DipoleDipole interactions, Hydrogen Bonding (which is a
special case of Dipole-Dipole), and ion-ion interactions.
The stronger the force, the higher its boiling point.
35
36
37
38
C
B
A
Molar mass is calculated by adding the atomic masses of
a given compound. The periodic table provides the mass
of each individual element, denoted beneath the
element's symbol. By adding the atomic masses taken
from the periodic table, the molar mass can be
determined.
Molar mass of benzene (C6H6)
C = 12.011 (6) = 72.066
H = 1.0080 (6) = 6.048
C6H6
= 78.114 g/mol or 78.11 g/mol
To construct a balanced chemical equation we start by
writing the formulas for the reactants on the left-hand
side of the arrow and the products on the right-hand side.
Next we balance the equation by determining the
coefficients that provide equal numbers of each type of
atom on both sides of the equation. For most purposes, a
balanced equation should contain the smallest possible
whole-number coefficients. In balancing an equation, you
need to understand the difference between coefficients
and subscripts. Never change subscripts when balancing
an equation. In contrast, placing a coefficient in front of a
formula changes only the amount of the substance and
not its identity.
Zn + 2 HCl => ZnCl2 + H2
Zn = 1
Zn = 1
H = 1 (2) = 2
H =2
Cl = 1 (2) = 2
Cl = 2
Gases are interesting cases in the world of science. It does
not have a definite volume like solids and liquids.
However, scientists developed a number of laws in gases
over the course of time. These laws are the following:
Boyle’s Law: “The volume of a fixed quantity of gas
maintained at constant temperature is inversely
proportional to the pressure.” V = constant * 1/P or PV
= constant.
Charles's Law: “The volume of a fixed amount of gas
maintained at constant pressure is directly proportional
to its absolute temperature.” V = constant * T or V/T =
constant.
36
Avogadro’s Law: “The volume of a gas maintained at
constant temperature and pressure is directly
proportional to the number of moles of the gas.” V =
constant * n or V/n = constant.
Ideal Gas Law: A hypothetical gas whose pressure,
volume, and temperature relationships are described
completely by one equation. PV=nRT.
39
C
V1/T1 = V2/T2
(20 + 273.15 = 293.15) / 2.00000L = (1.00000L) / T2
146.575 K = T2
The formula for Molarity is moles of solute over liters of
solution. Since we are given 100 grams of NaOH here, we
need to convert it to moles using the molar mass of NaOH
that was given in the question. And, we are also given 100
mL here which means, we need to convert it to liters so
that we can proceed to get the molar concentration.
1 𝑚𝑜𝑙 𝑁𝑎𝑂𝐻
5.000𝑔 𝑁𝑎𝑂𝐻 (40.000𝑔 𝑁𝑎𝑂𝐻)
1𝐿
100.00 𝑚𝐿 𝐻2𝑂 (1000𝑚𝐿)
0.125 𝑚𝑜𝑙 𝑁𝑎𝑂𝐻
0.100L H2O
40
B
= 1.250 M NaOH
The equation of determining the new concentration and
dilution of the solution is derived by remembering that
the number of moles of solute is the same in both the
concentrated and dilute solutions and that moles =
molarity * liters:
37
D. Mathematics
1
C
2
A
3
C
To find the probability of rolling a pair of dice twice and
getting a product of 6, we need to consider the possible
outcomes.
First Roll: There are 6 possible outcomes for each die, so
6 * 6 = 36 possible outcomes for the first roll.
Second Roll: There are, again, 36 possible outcomes for
the second roll.
Total Possible Outcomes: Since we're rolling the dice
twice, the total possible outcomes are 36 * 36 = 1296.
Favorable Outcomes: To get a product of 6, the possible
combinations are:
•
1*6
•
2*3
•
3*2
•
6*1
For each combination, the second roll has 36 possible
outcomes. Thus, there are 4 * 36 = 144 favourable
outcomes.
Probability: The probability is the number of favourable
outcomes divided by the total possible outcomes:
Probability = Favorable Outcomes / Total Possible
Outcomes
Substituting the values, we get:
Probability = 144 / 1296 = 1/9
Therefore, the probability of rolling a pair of dice twice
and getting a product of 6 is 1/9.
x=3
5(3)3-2(3)2+9(3)+20 = 164
The limit of the function is 164.
To calculate the amount in the fund at the end of 4 years,
we can use the compound interest formula:
A = P(1 + r/n)nt
Where:
• A is the final amount
• P is the principal amount (initial deposit)
• r is the annual interest rate (as a decimal)
• n is the number of times interest is compounded per
year
• t is the number of years
In this case:
38
4
B
5
A
6
D
• P = Php 50,000
• r = 6% = 0.06
• n = 1 (compounded annually)
• t = 4 years
Plugging these values into the formula:
A = 50,000(1 + 0.06/1)1(4)
A = 50,000(1.06)4
Therefore, the amount in the fund at the end of 4 years is
A = 50,000(1.06)4.
The equation of a line in slope-intercept form is y = mx +
b, where m is the slope and b is the y-intercept.
We are given the slope (m) is 15. To find the y-intercept
(b), we can use the fact that the x-intercept is -9. This
means that when x = -9, y = 0.
Substituting these values into the equation, we get:
0 = 15(-9) + b
0 = -135 + b
b = 135
Therefore, the equation of the line is y = 15x + 135.
The given equation is in the standard form of a parabola:
(x - h)2 = 4ay
Where:
(h, k) is the vertex of the parabola
a is the focal length
Comparing the given equation to the standard form, we
can see that:
h=1
k=0
4a = 10
Solving for p, we get:
a = 10 / 4 = 2.5
The focus of the parabola is located at a distance of p units
above the vertex. So, the coordinates of the focus are:
(h, k + a) = (1, 0 + 2.5) = (1, 2.5)
Therefore, the focus of the parabola (x - 1)2 = 10y is (1,
2.5).
To find the mean, you need to multiply each number of
computers sold by its corresponding probability and then
sum the results.
Mean = Σ[X * P(X)]
Where:
Σ = summation
39
7
C
X = number of computers sold
P(X) = probability of selling X computers
Calculation:
Mean = (1 * 0.25) + (2 * 0.36) + (3 * 0.18) + (4 * 0.04)
+ (5 * 0.02)
Mean = 0.25 + 0.72 + 0.54 + 0.16 + 0.10
Mean = 1.77
Therefore, the mean is 1.77.
To find the equation of the ellipse, we need to determine
its center, major axis length, and minor axis length.
Center: The center of the ellipse is the midpoint between
the two foci. Using the midpoint formula:
Center = ((3 + 3)/2, (4 + 2)/2) = (3, 3)
Major Axis: The major axis is the line segment connecting
the two vertices. The length of the major axis is twice the
distance between the center and one vertex.
Major Axis Length = 2 * (6 - 3) = 2 * 3 = 6
Minor Axis: The minor axis is perpendicular to the major
axis and passes through the center. Its length can be
found using the relationship between the major axis
length (a) and the minor axis length (b):
40
8
C
9
B
10
A
41
11
C
12
D
Arrange the set in ascending order: 2, 3, 3, 3, 4, 4, 5, 5, 6,
7, 8, 9,
Since the total number of observations is even, we will
utilize the formula for the median:
42
13
D
14
B
43
15
C
16
B
17
A
18
B
No of ways 5 people can line up in any order:
N1 = 5! = 120
No. of ways 2 people can be together: N2 = (2! x 4!) = 48
Total no. of ways = 120-48 = 72 ways
No of ways 5 people can be seated in any order:
(7-1)! = 720
No of ways 3 people can be seated together:
3! (5-1)! = 144
Total no. of ways = 720 – 144 = 576
Since all the spheres are similar, then:
44
19
A
20
A
21
B
22
A
Three-digit number = Hundreds Tens Unit
Only four digits are qualified in the unit’s digit,
N = 4 x 6 x 5 = 120 odd numbers
For the square: A = x2 = 169, x = 13cm
Perimeter = 4x = 4(13) = 52 cm
For the rectangle: Perimeter = 30 + 2y = 52
y = 11
Area = 15y = 15(11) = 165 sq. cm
Major axis = 2a = 10; a = 5
Minor axis = 2b = 8; b = 4.
a 2 = b2 + c2
52 = 42 + c2; c = 3
Eccentricity, e = c/a = 3/5 = 0.6
Let: V1= velocity of airplane
V2 = velocity of wind
1000
𝑉1 + 𝑉2 =
= 500 (1)
2
1000
𝑉1 − 𝑉2 = 2.5 = 500 (2)
Subtract (2) from (1):
(𝑉1 + 𝑉2 ) − (𝑉1 − 𝑉2 ) = 500 − 400
2𝑉2 = 100
𝑉2 = 50 𝑘𝑝ℎ
23
C
Given: d=0.50; n=12(12) = 144
𝑛
𝑆 = [(2𝑎1 + (𝑛 − 1)𝑑]
2
144
5436 =
[(2𝑎1 + (143 − 1)0.50]
2
5436 = 144𝑎1 + 5148
45
24
D
25
D
𝑎1 = 2
𝑎144 = 𝑎1 + 143𝑑
𝑎144 = 2 + 143(2)
𝑎144 = ₱73.50
Let: P = probability of getting 6 correct answers
from 10 questions.
26
A
Using Triangle Inequality Theorem
(This condition is always true since 𝑧 is positive)
27
D
From the given problem:
100(0.70) = 70 is the amount that would be paid if the
DVD was marked down 30%, but there is another
46
discount of 20%, so the price is going to be 80% of the
marked-down price. The price will be 70(0.80) = 56.
28
C
29
A
47
30
B
48
E. Mechanical-Technical
Adjacent gears move reversibly: 1 and 3 are clockwise
1
B
while 2 and 4 are counterclockwise.
The ball initially drops from a height of 20 feet. After the
2
A
fourth bounce, it rises to 3 feet. The ratio between the
heights of consecutive bounces is constant. To find this
ratio, you can set up an equation where the height after
each bounce is a fraction (f) of the previous height. After
4 bounces, the height is 20 × 𝑓 4 = 3.
3
3 1
𝑓4 =
= ( )4
20
20
1
𝑓≈
5
Gear C is 3 times the diameter of gear A.
3
B
Since the gears are all connected by a chain, the tip
velocity of all the gears must be the same; otherwise, the
chain would slip off the gears. Therefore, if the tip
velocity is to be the same for all gears and gear C is 3 times
larger than gear A, then gear C must be turning 3 times
slower than gear A. Thirty RPM divided by 3 equals 10
RPM.
The acceleration of the block is
4
A
𝑚
𝑎 = 𝑔𝑠𝑖𝑛𝜃, 𝑤ℎ𝑒𝑟𝑒 𝑔 = 9.8 𝑠2 and 𝜃 = 30°.
𝑇ℎ𝑢𝑠, 𝑎 = 9.8 × 0.5 = 4.9 𝑚/𝑠 2 .
Using v = u + at, with u=0 m/s, a=4.9 𝑚/𝑠 2, and t=3s,
v=0+(4.9×3)= 14.7 m/s.
According to the ideal gas law PV=nRT, if the volume V
5
C
is constant and the temperature T is doubled, the
pressure P is directly proportional to the temperature.
Therefore, the pressure also doubles.
Gravitational potential energy is determined by height
6
C
(PE = mgh). Since point A is positioned at a higher
elevation than point B, the potential energy at point A is
higher compared to that at point B.
49
7
A
𝑣2
In circular motion, the centripetal acceleration 𝑎𝑐 = ,
𝑟
where v is the velocity and r is the radius. Substituting
(20)2
8
C
9
A
10
B
v = 20 m/s and r = 100m, 𝑎𝑐 =
= 4 𝑚/𝑠 2
100
The measurement falls within the range provided by
students 2, 3, and 4. Comparing the mean values, student
3’s estimate is closest to Ming’s measured velocity,
making student 3’s estimate the most consistent with
Ming’s. Additionally, student 1’s estimate is the most
precise, as it has the smallest deviation from the mean,
indicated by a minimal error value.
The moment of inertia for the disk is less than that of the
ring because the disk’s mass is distributed closer to the
center. Objects with lower moment of inertia accelerate
faster, so the disk reaches the bottom first.
To solve for the net force, first calculate the acceleration
𝑣−𝑢
using the formula 𝑎 = 𝑡 , 𝑢 = 0 𝑚/𝑠, 𝑎𝑛𝑑 𝑡 = 5𝑠. The
acceleration is 𝑎 = 2𝑚/𝑠 2 . The net force is the sum of
gravitational force and the force requires to accelerate
the load.
Gravitational force = 500 𝑘𝑔 × 9.8 𝑚/𝑠 2 = 4900 N
An upward force needed = 500 𝑘𝑔 × 2 𝑚/𝑠 2 = 1000 N
Thus, the net force = 4900 N + 1000 N = 5900 N.
50
IV. Key References
Logical Reasoning
Online
Logical
Reasoning
Test.
(n.d.).
IndiaBix.
https://www.indiabix.com/online-test/logical-reasoning-test/41
English
Victoria Transport Public Institute. (n.d.). Victoria Transport Institute main page. https://www.vtpi.org/
Science
Tarbuck, Edward J & Lutgens, Frederick K (2015), 14th ed. Earth
Science ISBN-10: 0-321-92809-1; ISBN-13: 978-0-321-92809-2
Alberts, Bruce; Bray, Dennis; Hopkin, Karen; Johnson, Alexander;
Lewis, Julian; Raff, Martin; Roberts. Keith; Walter, Peter (2019).
Essential Cell Biology. 5 th Edition. Garland Science, Taylor and
Francis Group, New York, USA.
Brown, T. L., LeMay, H. E., Bursten, B. E., Murphy, C., Woodward, P., &
Stoltzfus, M. (2018). Chemistry: The Central Science (14th ed.).
Pearson.
Chemistry LibreText (2023). Flame Test.
https://chem.libretexts.org/Bookshelves/Inorganic_Chemistry/Supplemental_Mo
dules_and_Websites_(Inorganic_Chemistry)/Descriptive_Chemistry/Elements_Or
ganized_by_Block/1_sBlock_Elements/Group__1%3A_The_Alkali_Metals/2Reactions_of_the_Group_1_Ele
ments/Flame_Tests
General Physics - STEM - Senior High School
General Chemistry - STEM - Senior High School
General Biology - STEM - Senior High School
Earth Science - STEM - Senior High School
Mathematics
Wheater, C. (2019). Easy Pre-Calculus STEP-BY-STEP (2nd ed.).
McGraw-Hill Education.
Belecina, R., Baccay, E., & Mateo, E. (2016). Statistics and probability
(1st ed.). Rex Book Store, Inc.
Magcuyao, D. A. (2016). General Mathematics (1st ed.). JFS
PUBLISHING SERVICES.
51
IV. Key References
Mechanical-Technical
Department of Science and Technology. (2013). Syensiya-bilidad:
Developing One’s Skills in Testing. Slide Share.
https://www.slideshare.net/slideshow/dost-seischolarship-examreviewer/80064876#45
YouTube Channels
enginerdmath
(https://youtube.com/@enginerdmath?si=mG7hYYtNaRPlt9DA)
The Organic Chemistry Tutor
(https://youtube.com/@theorganicchemistrytutor?
si=P3NAekkHy11N5qTe)
CrashCourse
(https://www.youtube.com/@crashcourse)
Professor Dave Explains
(https://www.youtube.com/@ProfessorDaveExplains)
Osmosis from Elsevier
https://www.youtube.com/@osmosis
For more reviewer samples, you may visit this website:
https://drive.google.com/drive/folders/1GMt
ZQr4xVRBXKmcKUNS3VZkSjg639LFj?
usp=drive_link
52
V. General Tips
1
Understand the Exam Coverage
Join study groups.
Practice with previous exam papers or sample questions.
Organize a study plan that allocates time for each subject.
Stick to it daily to avoid cramming.
Ensure you're sleeping well leading up to the exam.
2
During the exam proper
Get to the exam venue ahead of time to reduce stress and settle
down before the test starts.
Maintain your calm. Remember to fill out your details first and read
instructions carefully.
Tackle the easier questions to gain confidence and secure points
early. Come back to the challenging ones later.
If you have time left, review your answers to catch any mistakes or
unanswered questions.
Use the process of elimination or make an educated guess if you're
uncertain of an answer.
3
For Science and Mathematics
Tips from University of the Philippines Learning Resource Center
Practice solving questions by refining your basic math skills.
Addition
Subtraction
Division
Fractions
Multiplication
Familiarize the basic formulas and understand how they were
derived.
Understand how and why the theorems or laws are used.
Internalize concepts and apply them in real world application.
Review your high school notes.
53
You can practice answering by using these bubble sheet.
A. Logical Reasoning
A
B
C
D
1
A
B
C
D
2
A
B
C
3
A
B
4
A
5
B. English
A
B
C
D
1
A
B
C
D
D
2
A
B
C
D
C
D
3
A
B
C
D
B
C
D
4
A
B
C
D
A
B
C
D
5
A
B
C
D
6
A
B
C
D
6
A
B
C
D
7
A
B
C
D
7
A
B
C
D
8
A
B
C
D
8
A
B
C
D
9
A
B
C
D
9
A
B
C
D
10
A
B
C
D
10
A
B
C
D
A
B
C
D
C. Science
A
B
C
D
1
A
B
C
D
3
A
B
C
D
2
A
B
C
D
4
A
B
C
D
You can practice answering by using these bubble sheet.
A
B
C
D
A
B
C
D
5
A
B
C
D
23
A
B
C
D
6
A
B
C
D
24
A
B
C
D
7
A
B
C
D
25
A
B
C
D
8
A
B
C
D
26
A
B
C
D
9
A
B
C
D
27
A
B
C
D
10
A
B
C
D
28
A
B
C
D
11
A
B
C
D
29
A
B
C
D
12
A
B
C
D
30
A
B
C
D
13
A
B
C
D
31
A
B
C
D
14
A
B
C
D
32
A
B
C
D
15
A
B
C
D
33
A
B
C
D
16
A
B
C
D
34
A
B
C
D
17
A
B
C
D
35
A
B
C
D
18
A
B
C
D
36
A
B
C
D
19
A
B
C
D
37
A
B
C
D
20
A
B
C
D
38
A
B
C
D
21
A
B
C
D
39
A
B
C
D
22
A
B
C
D
40
A
B
C
D
You can practice answering by using these bubble sheet.
D. Mathematics
A
B
C
D
A
B
C
D
1
A
B
C
D
16
A
B
C
D
2
A
B
C
D
17
A
B
C
D
3
A
B
C
D
18
A
B
C
D
4
A
B
C
D
19
A
B
C
D
5
A
B
C
D
20
A
B
C
D
6
A
B
C
D
21
A
B
C
D
7
A
B
C
D
22
A
B
C
D
8
A
B
C
D
23
A
B
C
D
9
A
B
C
D
24
A
B
C
D
10
A
B
C
D
25
A
B
C
D
11
A
B
C
D
26
A
B
C
D
12
A
B
C
D
27
A
B
C
D
13
A
B
C
D
28
A
B
C
D
14
A
B
C
D
29
A
B
C
D
15
A
B
C
D
30
A
B
C
D
You can practice answering by using these bubble sheet.
E. Mechanical-Technical
A
B
C
D
A
B
C
D
1
A
B
C
D
6
A
B
C
D
2
A
B
C
D
7
A
B
C
D
3
A
B
C
D
8
A
B
C
D
4
A
B
C
D
9
A
B
C
D
5
A
B
C
D
10
A
B
C
D
You can use this page for solutions.
You can use this page for solutions.
You can use this page for solutions.
You can use this page for solutions.
Test Reviewer and Guide for S&T Scholarship
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HAKBANG
NI ISKO
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lagi’t lagi para sa bayan.”
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