GEN ED: ENGLISH

CLASSIFICATION OF ENGLISH VERBS

These verbs do not have complements, i.e., they are not followed by noun or adjective
Intransitive phrases, since they indicate actions done by the subject, involving no one or nothing else
Example: The lame walked.
These verbs are followed by noun phrases as their direct object.
Transitive
Example: The congressman bought an island
They are also known as linking verbs, copular or copulative verbs, or verbs of incomplete
Ascriptive predication. They ascribe as an identity, and quality.
Example: The time is now.
These verbs occur before the main verb and denote modification of the basic meaning of
Modal the main verb, in terms of attitude, conditionality of the action, and the like.
Example: must (necessity), may (permission), can (ability)
These verbs are used to complete the verb phrase in certain constructions such as the
Auxiliary emphatic, the negative, the passive, or the perfect and progressive aspects.
Example: Light does have like a particle or a wave.

VERB
A word or group of words that expresses time while showing an action, a condition, or the fact that something
exists.
a) A statement held to be generally true at the moment of speaking
Example: The moon is made of the same materials as earth.
Present Tense
b) A statement of a habit or usual activity
Example: Bicolanos cook many dishes with coconut and chili.
a) A statement which was true in the past but no longer, or not necessarily, true at the
moment of speaking
Example: The young Mozart was the darling of Europe
Past Tense
b) A statement which became true in the past, le, the action or state referred to by
the verb: happened in the past.
Example: An asteroid impacted in the bay of Mexico at the close of the Jurassic period
a) An action just completed.
Present-Perfect Example: We have just arrived from Angono,
Tense b) An action which began in the past and which continues to the present
Example: They have exhibited the paintings for 6 months now.
A statement which was true, or an action which was completed before another past
Past-Perfect Tense action or past time reference.
Example: The mail arrived right after you had gone.
A statement which will be completed before another future action or future time
Future-Perfect Tense
reference
Phrasal Verb is verb followed by a preposition (stand for), or a verb followed by an adverb (slow down), or a
verb followed by both adverb and preposition (watch out for). It has an idiomatic meaning that is often quite
different from the literal meaning of the individual words: take up-start a new hobby (Sam has taken up jogging.
He likes it.).

take after-resemble in character or appearance. (He takes after his father.)

take in-to understand (It was difficult to take in all he said.)

ADVERB
Modifies verbs, adjectives, and adverbs
Manner [how?] well, automatically, with care
Frequency [how often?] never, sometime, occasionally, seldom, often, daily, always, every
Place [where?] here, there, inside, outside, near, nearby
Time [when?] now, later, tomorrow, earlier, yesterday, as soon as possible
Degree [to what immensely, completely, partly, mainly, rather, fairly, too, so
extent?]
Negotiation not, never, by no means

2
 SEQUENCE OF ADVERBS
Subject Verb Manner Place Frequency Time Purpose
Beth swims enthusiastically in the pool every morning before dawn to keep in shape

PRONOUNS
A word that can function by itself as a noun phrase and that refers either to the participants in the
discourse (e.g., 1, you) or to someone or something mentioned elsewhere in the discourse (e.g., she,
it)
TYPES OF PRONOUNS
1. Personal Pronouns Take note of the cases, person, gender and number
Subjective Objective Possessive
Singular 1st Person I me my/mine
2nd Person you you your/yours
3rd Person - masculine he him his
3rd Person - feminine she her her/hers
3rd Person - neuter it it its
Plural 1st Person we us our/ours
2nd Person you you your/yours
3rd Person they them their/theirs.
d1 - this and these - near the speaker/
2. Demonstrative Pronouns
d2 - that those -far from the speaker)
3. Interrogative Pronouns who, whom, whose, that, and which.
Singular: someone, anyone, no one, somebody, anybody, nobody,
something, someone, everyone, everybody
4. Indefinite Pronouns
Plural: both, many, few, several, others
Singular or plural - according to sense: all, most some
Are used to refer back to the subject - as the form of the object if
5. Reflexive Pronouns the object is the same person as the Subject (ends in -self or-selves).
She found herself in a difficult situation

RULES FOR FORMING PLURAL OF NOUNS

Regular Add 's' (ex: cat-cats]
S, CH, SH, X, Z Add 'es' [ex: brush-brushes]
F/FE Change to 've [ex: knife - knives]
Vowel + O Add 's' [ex radio - radios]
Consonant + O Add 'es' [ex: hero - heroes]
Vowel + Y Add 's' [ex: day-days]
Consonant+Y Change y to T [ex: city-cities]
Irregular Spell change [ex: goose - geese]
No change [ex: Sheep Sheep]
RULES FOR FORMING POSSESSIVE NOUNS
Singular Nouns ending in -s Add [ex: Tess - Tess']
Singular Nouns not ending in s Add 's' [ex: Rey - Rey's]
Plural Nouns ending in s Change [ex boy-boys]
Plural Nouns not ending in s Add 's' [ex: children - children's]
3
Joint ownership Last-'s [ex: mom and dad's room]
Separate ownership Each 's [ex: teacher's and principal's office]

No subject and verb.

Fragment
Example: ate the cake.
With subject and verb. They can or cannot stand
Clause
Example: after he ate
With subject and verb. Complete in thought
Sentence
Example: He ate the cake.
TYPES OF SENTENCE
(Structure)
Subject and verb: Complete thought
1. Simple.
Example: He ate his cake.
Two independent clauses; coordinating conjunctions.
2. Compound
Example: He ate, and he danced.
One independent clause, and once or more dependent clauses;
3. Complex subordinating conjunctions.
Example: After he ate, he slept.
Two independent clauses, and one or more dependent clauses;
4. Compound Complex coordinating and subordinating conjunctions.
Example: After he ate, he slept and (he) dreamt of her.
NOUNS
Names of PERSONS, PLACES, THINGS, or EVENTS
KINDS OF NOUNS
Common – general Proper – specific Abstract – emotions, qualities,
[ex: Artist] [ex: JAYB] idea
[ex: love]
Collective – names of groups Count – counted individually Mass – measured only
[ex: audience] [ex. bottle] [ex: water]

4
 GEN ED: BIOLOGICAL SCIENCE
EVOLUTION
Series of changes in a group of organisms in terms of its structures and functions.
Microevolution - changes in a smaller scale of population in terms of its allele frequencies. This may
happen through:
BOTTLENECK EFFECT FOUNDER EFFECT
When a natural disaster struck a certain a When a certain part of a population is separated
population causing a decrease of number of the on their group and discovered a suitable place to
organisms. thrive.
VARIATIONS BASED ON POPULATION PHENOTYPE POPULATION
Stabilizing Selection Intermediate phenotype is highly favored in the environment
Directional Selection One extreme phenotype is highly favored in the environment
Disruptive Selection Two extreme phenotypes are highly favored in the environment
SPECIATION – process of making new species
Allopatric speciation Sympatric speciation
due to geographical isolation due to genetical isolation

REPRODUCTION
SEXUAL ASEXUAL
Needs gametes and fertilization. No gametes, no fertilization
Involves a single parent only Involves two parents
Sex cells are not produced Sex cells are produced
Offspring is identical to the parent Offspring has genetic variation
Mitosis-cell division Sex cells - through mitosis;
Zygote- through meiosis
Asexual Reproduction in Animals
Budding Outgrowth from the parent cell (e.g. hydra, yeast)
Binary Fission Living organism splits into two (e.g. bacteria)
Fragmentation Breaking of parent cell into many parts (e.g. planaria)
Regeneration The ability of a simple organism to regrow its lost parts (eg starfish,
lizard)
Parthenogenesis An egg develops into a complete individual without being fertilized

COMPARISON OF KINGDOMS UNDER THE SIX KINGDOM SYSTEM OF CLASSIFICATION

MODE OF MODE OF
KINGDOM TYPE OF CELL ORGANIZATION
REPRODUCTION NUTRITION
Autotroph or
Archaeabacteria Prokaryotic Unicellular Asexual
Heterotroph
Autotroph or
Eubacteria Prokaryotic Unicellular Asexual
Heterotroph
All unicellular except Autotroph or
Protista Eukaryotic Asexual
for algae Heterotroph
All multicellular
Fungi Eukaryotic Asexual Saprophyte
except for yeast
Plantae Eukaryotic Multicellular Sexual or asexual Autotroph
 Animalia Eukaryotic Multicellular Sexual or asexual Heterotroph
Kingdom Archaebacteria is further divided into different phyla depending on the kind of environment do
they live while organisms under Kingdom Eubacteria are grouped based on their shapes and how do they
obtain nutrition.
Kingdom Protista (also known as the animal-like, plant-like or fungi-like organisms) is divided into
different phyla with main consideration of their locomotory organ for the animal-like protists and based
on the pigment present in the plant-like ones, while the only fungi like ones are the water molds and
the slime molds.
Kingdom Fungi, on the other hand, is divided into different phyla based on the type of spores that they
produce for reproduction.
Most organisms which we are familiar of, belongs to either Kingdom Plantae or Kingdom Animalia.
The main difference between the two is that plants are sessile yet can make their own food and
animals are the exact opposite
Kingdom Plantae is divided into three phyla. Take note that in Kingdom Plantae, Phyla is also called as
Division. Plants are divided based on the presence of the conducting tissues-xylem and phloem, body
differentiation and the part of their body which they use for reproduction.

TAXONOMY
Taxonomy is the science of naming, classifying, and identifying organisms. It is a branch of science
that deals with giving universally accepted names to organisms to avoid confusion among people with
different types of languages.

A Swedish naturalist and explorer. Carl von Linne, widely known as Carolus Linnaeus proposed binomial
nomenclature as a systematic way of naming organisms. It includes the use of two names: genus and
species which is written in italicized form and is expressed in Latin language Linnaeus also pioneered
the use of taxa in classifying organisms such that the groupings are based with regards on their
similarities in structure, form, and genetic composition. Because of such work, he is proclaimed as the
Father of modern Taxonomy

Taxa (singular taxan) are the unit used in classifying organisms. It is arranged hierarchical from the
most general to the most specific one. The complete units of classification are as follows

Domain
Kingdom
Phylum
Class
Order
Family
Genus
Order
COMPARISON OF DOMAINS UNDER THE THREE DOMAIN SYSTEM OF CLASSIFICATION
DOMAIN TYPE OF CELL ORGANIZATION MODE OF REPRODUCTION
Archaea Prokaryotic Unicellular Asexual
Bacteria Prokaryotic Unicellular Asexual
Eukarya Eukaryotic Unicellular or Multicellular Asexual or sexual

6
The main difference between Domains Archaea and Bacteria is that the organisms belonging to Domain
Archaea are also known as extremophiles because they can live in extreme environment. Moreover,
archaeans don't have peptidoglycan in their cell wall in contrast with bacteria. Also, the genetic
composition of archaeans is said to be more similar with eukaryotes than with bacteria.

The next unit is Kingdom. There are different Kingdom Systems depending on naturalists that proposed
them but the most acceptable of them is the Six Kingdom System (The six kingdoms are Eubacteria,
Archae, Protista, Fungi, Plantae, and Animalia.) which is proposed by Grey and Doolittle which is based
on Whittaker's Five Kingdom System.

CELLULAR RESPIRATION
• Conversion of glucose to ATP
• Composed of series of reactions such as:
KREB'S CYCLE/ CITRIC ACID
ELECTRON TRANSORT CHAIN/
GLYCOLYSIS CYCLE/ TRICARBOXYLIC ACID
OXIDATIVE PHOSPHORYLATION
CYCLE
Happens in the cytoplasm • Requires oxygen to proceed • Happens in the inner
In every molecule of glucose, • Happens in mitochondrial membrane of mitochondria
glycolysis produces a net of 2 matrix. (cristae)
ATP, 2 NADH and 2 molecules of • Supplies ETC with electrons • Series of electron carrier
pyruvate from NADH and FADH₂ transports that yields NADH
a) If oxygen is absent, • Carbon molecules from acetyl and FADH2 to deposit their
NADH transfers it COA are converted into electrons until the electrons
electrons directly to carbon dioxide releasing ATP reach oxygen
pyruvate yielding lactate • For every 1 molecule of • Oxygen is the final electron
(lactic acid fermentation) acetyl CoA. net products are acceptor This process yields
or ethyl alcohol (alcohol 1 ATP, 3 NADH and 1 FADH₂ up to 36 ATP (eukaryotes)
fermentation)
b) If oxygen present, the 2
molecules of pyruvate will
be oxidized forming 2
molecules of acetyl CoA.
All in all, in every molecule of glucose, cellular respiration yields 38 ATP in eukaryotes, and 36 ATP
in prokaryotes

BIOLOGY
The study of living things It deals with the characteristics of life and how it is maintained.
This field of study consists of a number of specializations.
BRANCHES OF BIOLOGY
Anatomy Bacteriology Biochemistry Botany
study of internal study of bacteria study chemical reactions study of plants
structures of living things inside body of living
things
Cytology Ecology Embryology Endocrinology
study of cell. structure study of the relationship
and function or interaction. between
7
 living things and it's study of developmental study of endocrine glands
environment. patterns of an organism and their corresponding
from zygote to birth hormones
Entomology Genetics Helminthology Herpetology
study of insects study of genes and study of parasitic worms study of reptiles and
heredity amphibians
Histology Ichthyology Malacology Mammalogy
study of tissues study of fishes study of mollusks (shell study of mammals
animals)
Morphology Mycology Ornithology Paleontology
study of shapes and forms study of fungi study of birds study of fossils
of living organisms
Pathology Physiology Virology Zoology
study of different diseases study of function of study of viruses study of animals
organs and body systems
PLANT TISSUES
Protects the plant from water loss, regulated gas
DERMAL TISSUE
exchange and absorbs nutrients and minerals
Transport food and water internally throughout the
plant
VASCULAR TISSUE
Xylem - for water transport
Phloem - for food transport
a. Parenchyma-function is for repair, photosynthesis,
and storage:
b. Collenchyma - for mechanical support and
GROUND TISSUE elasticity
c. Sclerenchyma - for mechanical support and aids in
the water and food transport

PLANT HORMONES
Apical dominance, affect root growth differentiation and branching; retard leaf
AUXIN abscission, stimulate stem elongation; development of fruit, phototropism, and
gravitropism
Stimulate germination, delay leaf aging, stimulate cell division and growth; affect
CYTOKININ
root growth and differentiation.
Stimulate flowering, fruit development and seed germination: promote bud
GIBBERELLINS
development, stem elongation and leaf growth.
Promote leaf aging, closes stomata during dry spells: helps maintain seed dormancy,
ABSCISIC ACID (ABA)
inhibit growth.
Promotes flowers in some species; opposes some auxin effects, promotes fruit
ETHYLENE
ripening and abscission. promotes root formation.
CELLULAR PROCESSES
PHOTOSYNTHESIS
• Food making process of plants
• Requires water, carbon dioxide and sunlight
a. Water enters through the xylem
b. Carbon dioxide enters through the stomata and exits as oxygen
8
 c. Sunlight is absorbed by chlorophyll in units called as photons.
LIGHT DEPENDENT PHASE LIGHT INDEPENDENT PHASE/CALVIN CYCLE
• Happens in the thylakoid membranes • Happens in the stroma
• Captures light energy and stores it as ATP and • Uses the chemical energy (ATP and NADPH) from the
NADPH in a series of chemical light dependent phase
• Reactions through four protein complexes • To form glucose from carbon dioxide
(Photosystem I. Cytochrome
• Complex, Photosystem II and ATP Synthase)
• Water is split into oxygen and hydrogen ions
• Products are ATP. NADPH, and oxygen

9
 GEN ED: FILIPINO
PANITIKAN
Ayon kay Bro. Azarias ang panitikan ay ang pagpapahayag ng damdamin ng tao sa lipunan, sa pamahalaan,
kapaligiran, kapwa at sa Dakilang Lumikha.
12 AKDANG NAKA-IMPLUWENSIYA SA BUONG DAIGDIG
Bibliya Koran Canterbury Tales Iliad at Odyssey
El Cid Compeador Awit ni Rolando Aklat ng mga Patay Aklat ng mga Araw
Isang Libo't Isang Gabi Divina Comedial Uncle Tom's Cabin Ang Mahabharata
MGA PILING AKDA SA PILIPINAS
Doctrina Christiana Nuestra Señora Del Rosario Barlaan at Josaphat
Unang aklat na nalimbag Ikalawang aklat na nalimbag Unang nobelang binigyan ng
pagsasalin sa tagalog ni Fray
Antonio de Borja
Nena at Neneng Urbana at Feliza Banaag at Sikat
Unang tagalog na nobela ni Modesto de Castro Lope K. Santos
Valeriano. Peña
MGA AMA NG PANITIKAN
Maikling Kwentong may Banghay
Deogracias Rosario
Aloha
Pinakadakilang Makata
Francisco Balagtas Florante at Laura
Demosthenes ng Pilipinas
Graciano Lopez Jaena Pinakamahusay na Orador
100 Talumpati at Fray Botod
Hari ng Balagtasan
Jose Corazon de Jesus Ang Pamana at Isang Punongkahoy
Ama ng Panitikang Pampango
Crisostomo Soto
Bb. Pathupats

PAGSASALIN NG WIKA
Ang pagsasalin ay maaaring maisagawa sa pamamagitan ng pagtutumbas sa ideyang nasa likod ng pananalita
(Theodore H. Savory, 1968).

Ang pagsasalin ay muling pagbubuo sa tumatanggap na wika ng tekstong naghahatid ng kahalintulad na mensahe
sa simulaang wika subalit gumagamit ng mga piling tuntuning gramatikal at leksikal ng tumatanggap na wika
(Mildred L Larson, 1984).

Ang pagsasalin ay isang pagsasanay na binubuo ng pagtatangkang palitan ang isang nakasulat na mensahe sa
isang wika ng gayon ding mensahe sa ibang wika (Peter Newmark, 1988).
MGA URI NG PAGSASALIN
1. Salita sa Salita Literal o katumbas na kahulugan at salita
2. Naturalisasyon Mga hiram na salitang iniba ang baybay sa Filipino
3. Leksikal Ibinibigay ang pinakamalapit at pinakaangkop na salita
4. Kultural Binibigyang pansin ang mga tradisyon/kultura sa pagsasalin
5. Adaptasyon Hiram na salitang hindi na iniiba ang baybay
6. Idyomatiko Figure of speech na mayroon o walang katumbas na paghahalintulad sa Filipino
 Walang kontrol na uri ng pagsasalin kung saan maaaring magdagdag o magbawas ng
7. Malaya
salita (hindi literal)

ANTAS NG WIKA
Ang wika ay nahahati sa iba't-ibang kategorya sa antas na ginagamit ng tao batay sa kanyang
pagkatao, sa lipunang kanyang ginagalawan. lugar na tinitirhan, panahon, katayuan at okasyong
dinadaluhan.
PORMAL
Ito ay antas ng wika na istandard at kinikilala/ginagamit ng nakararami.
Pambansa • Ito ay ginagamit ng karaniwang manunulat sa aklat at pambalarila para
sa paaralan at pamahalaan.
• Mga salitang ginagamit sa mga aklat at babasasahing ipinalalabas sa
buong kapuluan at lahat ng paaralan.
• Ang wikang ginagamit ng pamahalaan at wikang panturo sa mga
nagsisipag-aral.
Halimbawa: Asawa, Anak, Tahanan
Pampanitikan Panretorika • Ito ay ginagamit ng mga malikhain manunulat.
• Ang mga salita ay karaniwang malalim, makulay at masining.
Halimbawa: Pambansa-Kapatid: Pampanitikan - Kapusod
IMPORMAL
Ito ay antas ng wika na karaniwan, palasak, pang araw-araw, madalas gamitin sa pakikipag-usap at
pakikipagtalastasan
Lalawiganin (Provincialism) • Mga salitang kilala at saklaw lamang ng pook na pinaggagamitan nito.
• May kakaibang bigkas at tono.
Halimbawa:
Pambansa - Ina,
Bikol - Mamay:
Bisaya-lloy;
Ilokano - Nanang
Kolokyal (Colloquial) Mga salitang ginagamit sa pang-araw-araw na pakikipagtalastasan ngunit
may kagaspangan at pagkabulgar, bagama't may anyong repinado at malinis
ayon sa kung sino ang nagsasabi.
Halimbawa:
Pormal - Aywan;
Impormal - Ewan
Balbal (Slang) • Sa Ingles ito ay slang. Nagkakaroon ng sariling codes, mababa ang antas
na ito; ikalawa sa antas bulgar
• Una ay hindi tinatanggap ng mga matatanda at mga may pinag-aralan
dahil hindi raw maganda pakinggan
• Kilala rin bilang salitang kanto o salitang kalye
Halimbawa:
Pormal-Tatay o Ama;
Balbal - Erpat

BARAYTI NG WIKA
11
Kilala rin sa Ingles na 'variety, ito ang sanhi ng pagkakaiba ng uri ng lipunan nating ginagalawan,
heograpiya, edukasyon, okupasyon, edad, kasarian, at kung minsan, ang uri ng pangkat etniko
• Bahagi o subordineyt ng isang wikang sinasalita sa isang lugar o rehiyon.
• Ayon kay Dayag, ito ang baryti ng wikang ginagamit na partikular na pangkat ng mga tao
sa isang lugar tulad ng lalawigan, rehiyon o bayan. Maaaring gumamit ang mga tao ng
isang wikang katulad ng sa iba pang lugar ngunit naiiba sa punto o tono, may
magkakaibang katawagan para sa isang kahulugan, iba ang gamit ng salita para sa isang
Dayalekto bagay, o magkakaiba ang pagbuo ng mga pangungusap na siyang magpapaiba sa dayalek ng
lufar sa iba pang lugar.
Halimbawa:
Tagalog - "Mahal kita"
Hiligaynon - "Langga ta gd ka
Bikolano – “Namumutan ta ka”
• Ginagamit ayon sa relasyong sosyal.
• Ayon kay Dayag. Ito ay barayti ng Wikang nakabatay sa katayuan o antas panlipunan o
dimensyong sosyal ng mga taong gumagamit ng wika
Sosyolek Halimbawa:
Te meg, shat ta? (Pare, mag-inuman tayo)
Oh my God! It's so mainit naman dito. (Naku, ang init naman dito!)
Wag kang snobber (Huwag kang maging suplado)
• Personal na paggamit sa wika, katangian ng pagsasalita.
• Ayon kay Dayag, ito ay pansariling paraang ng pagbigkas o pagsasalita ng bawat isa kahit
isang dayalek ang gamit.
Halimbawa:
Idyolek "Magandang Gabi Bayan - Noli de Castro
"Hoy Gising" - Ted Failon
"Hindi ka namin tatantanan - Mike Enriquez
Di umano'y - Jessica Soho
Tanging bokabularyo ng isang pangkat
Jargon
Halimbawa: Wikang ginagamit ng mga inhenyiro, doktor at iba pang propesyonal
Isang bagong wika na nabubuo mula sa dalawang taong may magkaibang unang wika na
nagtatangkang mag-usap ngunit hindi magkaintindihan, na siyang nagbubunga ng tinatawag na
makeshift language.
Pidgin Wala itong pormal na estraktura, at nasa proseso pa lang ito ng pagkalinang at paglaganap.
Halimbawa: Ako punta banyo - Pupunta muna ako sa banyo.
Hindi ikaw galing kanta - Hindi ka magaling kumanta.
Sali ako laro ulan - Sasali akong maglaro sa ulan.
Wikang nagsimula sa pagiging Pidgin ngunit paglaon ay nalinang at lumaganap sa isang lugar
hanggang ito na ang maging unang wika
Creole Halimbawa: Mi nombre - Ang pangalan ko
Yu ting yu wan, a? - Akala mo espesyal ka o ano?
I gat planti kain kain abus long bikbus - Marami akong uri ng mga hayop sa gubatan

MGA KATANGIAN NG WIKA

Ang ibig sabihin ng katangiang ito ay isinaayos ang mga tunog sa
ANG WIKA AY MASISTEMANG
sistematikong paraan para makabuo ng makahulugang bahagi tulad
BALANGKAS
ng salita, parirala, pangungusap at panayam.

12
 Ito ay sinasalita na galing sa magkasunud-sunod na tunog na
humuhugis sa paraan ng mga iba't ibang kasangkapan sa
ANG WIKA AY SINASALITANG TUNOG
pagsasalita na tinatawag na mga bahagi ng pagsasalita o speech
organs
Sa katangiang ito, ang mga salita ay tumututok sa mga salitang
ANG WIKA AY ARBITRARYON SIMBOLO
simbolo. Napapaloob sa katawagang ito ang dualismo na isang
NG MGA TUNOG
pananagaisag at isang kahulugan
ito ay kasangkapan ng komunikasyon ng dalawa o higit pang nag-
uusap na mga tao. Sa ganitong paraan, maipapahayag ang mga
ANG WIKA AY KOMUNIKASYON
damdamin, kaisipan, pangarap, imahinasyon, layunin, at
pangangailangan ng tao.
Ang wika ay isang eksklusibong pag-aari ng mga tao nga sila
ANG WIKA AY PANTAO mismong lumikha at sila rin ang gumagamit. Dala-dala ng mga tao
nito bilang kasangkapan ng pakikipagtalastasan
Taglay nito ang kultura ng lipunang pinagmumulan nito. Ang sining,
ANG WIKA AY KAUGNAY NG KULTURA panitikan, karunungan, kaugalian, kinagawain at paniniwala ng
mamamayan ang bumubuo ng kultura.
Kailangan itong gamitin na instrumento sa komunikasyon. Unti-
ANG WIKA AY GINAGAMIT
unting mawawala ito kapag hindi ginagamit.
May kaibahan ang bawat wika sa ibang wika. Walng dalawang wika
na magkatulad. Ang bawat wika ay may sariling sistema ng
ANG WIKA AY NATATANGI
palatunugan, palabuuan, at palaugnayan; at may sariling set ng
mga bahagi.
Ito ay buhay at patuloy sa pagbabago nang dahil sa patuloy rin na
ANG WIKA AY DINAMIKO nagbabago ang pamumuhay ng tao at iniangkop ang wika sa mabilis
na tkbo ng buhay na dulot ng agham at teknolohiya.
Ang anumang wika ay may abilidad na makabuo ng walang
ANG WIKA AY MALIKHAIN
katapusang dami ng pangungusap.

KASAYSAYAN NG ALPABETONG FILIPINO

Bago pa man dumating ang mga Kastila, tayo ay mayroon nang kinikilalang
isang uri ng alpabeto. Ito ang tinatawag nating Alibata, isang uri ng
ALIBATA palaybaybayang hatid na atin ng mga Malayo at Polinesyo.

Tinuruan ng mga kastila na sumulat ang mga Pilipino sa pamamagitan ng

palatitikang Romano upang mabisa nilang mapalaganap ang Doctrina Christiana.
ABECEDARIO
Ang mga titik Romano gaya ng alam na natin, ay iba sa mga simbolong ginagamit
sa pagsulat sa wikang Hapon o sa wikang Intsik
Bunga ito ng batas na bago ipahayag ang napiling batayan ng wikang pambansa
ay kailangang mayroon na munang magagamit na aklat panggramatika sa
ABAKADA paaralan. Si Lope K. Santos, isa sa mga kagawad noon ng. Surian ng Wikang
Pambansa, ang sumulat ng nasabing gramatika na nakilala sa tawag na Balarila
ng Wikang Pambansa.
ALFABETONG FILIPINO Ang alfabetong Filipino ay binubuo ng 28 letra. Ang tawag sa mga letra ay
ayon sa bigkas-Ingles ng mga Pilipino maliban sa ñ (enye) na tawag-Kastila.
13
Ang walong (8) letra na dagdag ay galing sa mga umiiral na wika ng Pilipinas
at sa mga iba pang wika

14
 GEN ED: PHYSICAL SCIENCE
CHEMISTRY
A branch of science that involves the study of the composition, structure and properties of matter. It is sometimes
called the central science because it bridges physics with other natural sciences, such as geology and biology. It
has four branches:
1. Organic Chemistry Mostly concerned with the study of chemicals containing the element
carbon.
2. Inorganic Chemistry The study of all elements of compounds other than organic compounds.
3. Analytical Chemistry The study of qualitative and quantitative analysis of elements and
compounds.
4. Physical Chemistry The study of reaction rates, mechanisms, bonding and structure
MATTER AND ITS PROPERTIES
Matter is anything that occupies space and has mass. At a minimum, matter requires at least one
subatomic particle, although most matter consists of atoms.
STATES OF MATTER
SOLID LIQUID GAS
composed of tightly packed particles. made of more loosely packed composed of particles packed so
It can retain its shape; the particles particles. It will take the shape of loosely that it has neither a defined
are not free to move around but they its container. Particles can move shape nor a defined volume. A gas
can only vibrate about within a liquid, but they are can be compressed
packed densely enough that volume
is maintained.
PLASMA BOSE-EINSTEIN CONDENSATE
often thought of as a subset of gases, but the two states formed when a gas of bosons at low densities is cooled
behave very differently Like gases, plasmas have no fixed to temperatures very close to absolute zero ( 273.15
shape or volume, and are less dense than solids or liquids. °C).
But unlike ordinary gases, plasmas are made up of atoms
in which some or all of the electrons have been stripped Examples: superfluids (cold liquid helium),
away and positively charged nuclei, called ions, roam superconductor
freely.

Examples: lightning, solar wind, tail of a comet, Earth's

ionosphere

ATOMS, MOLECULES, AND IONS

ATOM is the smallest possible amount of matter which still retains its identity as a chemical element, consisting
of a nucleus surrounded by electrons. It is composed of two regions: the nucleus, which is in the center of the
atom and contains protons and neutrons, and the outer region of the atom, which holds its electrons orbit around
the nucleus.
PROTON NEUTRON ELECTRON
positively charged subatomic particle subatomic particle forming part of negatively charged subatomic.
forming part of the nucleus of an the nucleus of an atom. It has no particle orbiting around the nucleus.
atom and determining the atomic charge.
number of an element.
HISTORY OF ATOMIC STRUCTURE
SCIENTIST MODEL CONTRIBUTION
Proposes that the indivisible unit of an element is
John Dalton (1803) "Billiard Ball”
the atom
JJ Thomson (1904) "Plum Pudding” Discovered electrons
Ernest Rutherford (1911) “Rutherford Model” Discovered protons.
Discovered that electrons travel around the
nucleus and that the number of electrons in the
Niels Bohr (1913) “Bohr Model”
outer orbit determines the properties of an
element.
Shows electrons do not move around the nucleus in
Erwin Schrödinger (1926) "Electron Cloud" orbits, but in clouds where their position is
uncertain,
MOLECULE is formed when two or more atoms form chemical bonds with each other. It doesn't matter if the
atoms are the same or are different from each other. It is neutral and do not carry any charge.
ISOMERS are molecules that have the same molecular formula but have a different arrangement of the atoms in
space. That excludes any different arrangements which are simply due to the molecule rotating as a whole or
rotating about particular bonds. Example of this is pentane, which has a molecular formula of CsH2, has three
different chain isomers.
IONS are formed when the number of protons in an atom does not equal the number of electrons. They are highly
reactive species and generally found in a gaseous state and do not occur in abundance on Earth. They are repelled
by like electric charges and are attracted to opposite charges.
CATION formed when there are more protons than ANION formed when there are more electrons than
electrons present in an atom. protons present in an atom

PERIODIC TABLE OF ELEMENTS

PERIODIC TABLE OF ELEMENTS is a tabular arrangement of chemical elements that is arranged by increasing
atomic number and groups elements according to recurring properties. It is organized so scientists can quickly
discern the properties of individual elements such as their mass, electron number, electron configuration and their
unique chemical properties.
DMITRI IVANOVICH MENDELEEV is the father of periodic table. He realized that the physical and chemical
properties of elements were related to their atomic mass in a 'periodic way and arranged them so that groups of
elements with similar properties fell into vertical columns in his table.
MAIN PARTS OF THE PERIODIC TABLE
Located in the left-hand side of the periodic table. It has the following characteristics
• Metallic luster
• High electrical and thermal conductivity
• Usual hard solids (mercury is liquid)
METALS • Usually ductile (capable of being drawn into a wire) and malleable (capable of being
hammered into thin sheets)
• Most have high melting points
• Readily lose electrons (low electron affinity)
• Low ionization energies
Zig-zag line toward the right side of the periodic table that acts as a sort of border
between metals and nonmetals. Elements on either side of this line exhibit some
properties of metals and some of the nonmetals. It has the following properties:
METALLOIDS
• Metalloids have multiple forms or allotropes
• Can be made to conduct electricity under special conditions (semiconductors)

Located at the right-hand side of the periodic table. It has the following characteristics:
NON-METALS • Usually, poor conductors of heat and electricity
• Lack metallic luster

16
 • Often liquids or gases at room temperature and pressure
• Readily gain electrons (high electron affinity)
• High ionization energy

PERIODIC TABLE TRENDS

Atom's ability to attract electrons. Metals have lower electronegativity value
ELECTRONEGATIVITY
because they tend to lose. electrons. The most electronegative element is
Fluorine (F) and the least electronegative element is Francium (Fr)
Energy needed to remove an electron from an atom and form ion. Fluorine
IONIZATION ENERGY (F) has the highest value of ionization energy while Francium (Fr) has the
lowest value of ionization energy.
Ability of an atom to accept an electron. Fluorine (F) has the most electron
ELECTRON AFFINITY
affinity value while Francium (Fr) has the lowest electron affinity value.
One-half the distance between the nuclei of two atoms. The element with
ATOMIC RADIUS largest atomic radius is Francium (Fr) and the element with smallest atomic
radius is Helium (He).
Can be defined as how readily an atom can lose an electron. The most
METALLIC CHARACTER
metallic element is Francium (Fr) while the least metallic is Helium (He).
PHYSICS
a natural science that involves the study of matter and its motion through space and time, along with related
concepts such as energy and force. More broadly, it is the study of nature in an attempt to understand how the
universe behaves
Determination of the size or magnitude of something. There are two major standards of
MEASUREMENT measurement English System (Imperial Unit) and Metric System International System
of Units (SI)
Fundamental Quantities - do not depend on other quantities (mass, volume)
Derived Quantities - depend on other quantities (density, momentum)
QUANTITIES
Scalar Quantities - magnitude only (distance, speed)
Vector Quantities - magnitude with direction (displacement, velocity)
NEWTON'S THREE LAWS OF MOTION
LAW OF INERTIA LAW OF ACCELERATION LAW OF INTERACTION
a body at rest will remain at rest (a when a force acts. on an object, the in every action, there is an equal
body in motion will remain in motion) object accelerates in the direction of and opposite reaction.
unless it is acted upon by an the force. If F is applied to a particle
unbalanced force. mass m, it may be expressed Examples: gun firing, punching
mathematically as F=ma. the wall
Examples: motion of a kite when
the wind changes, ball falling Examples: kicking a ball, pushing
down through the atmosphere a car

WORK, ENERGY AND POWER

WORK happens when a force exerted on the system has a component in the direction of motion. It is the transfer
of energy by a force acting on an object as it is displaced. It is a product of the force times the distance through
which the force acts.
Note that there is only work done if:
1. There is a component of the force in the direction of motion.
2. The object has to move a certain distance parallel to the force.
17
3. There is a force acting on the object.
TYPES OF FORCES
NORMAL FORCE (N) FRICTION (F) TENSION (T)
perpendicular force exerted by a opposing force between two surfaces force that is transmitted through a
surface to an object placed to it. in contact. rope, string or wire when pulled by
• STATIC forces acting from opposite sides.
FRICTION
exists between stationary object
and surface
• KINETIC
FRICTION
exist between moving object and
surface
ENERGY is the ability to do work. Work shifts energy from one place to another. It can exist in many
forms (thermal energy, electrical energy, etc.). These different forms can be categorized into two:
Potential Energy and Kinetic Energy
POTENTIAL ENERGY KINETIC ENERGY
Associated with position relative to some other object. It The energy of motion regardless of it's vertical or
is often associated with restoring forces such as a spring horizontal motion
or the force of gravity.
POWER (P) is the rate which the work is done. It is the amount of energy consumed per unit time.
Mathematically:

where P is power. W is work; t is the time while doing work. It can be express in joules per second
(J/s) or Watts (W)

WAVES
a motion that transfers energy from one point to another, usually without permanent displacement of the particles
of the medium (matter through which a wave travels).
CLASSIFICATION OF WAVES
DEPENDS ON THE MEDIUM DEPENDS ON THE DIRECTION
MECHANICAL WAVES TRANSVERSE WAVES
require a medium. which occur at right angles or perpendicular to
Examples of this are sound waves and water waves the direction of the wave. This moves up and
ELECTROMECHANICAL WAVES down.
do not require a medium Example of this is light waves.
Example of this is light waves LONGITUDINAL WAVES
which occur parallel to the direction of the wave.
It is compression (denser region) and rarefaction
(less dense).
Example of this is sound waves.
SOUND is produced by vibration. It is a mechanical and longitudinal wave. When an object is vibrating,
it produces periodic sound waves (ex: human vocal cords, musical instruments, etc.)
INFRASONIC Frequencies below the range of human hearing (18-20 Hz)
ULTRASONIC Frequencies above the range of human hearing (18-20 kHz)

18
LOUDNESS Intensity of a sound wave which is proportional to the square of its amplitude. The unit
used to measure this is decibels (dB) (logarithmic scale),
PITCH Quality that makes it possible to judge sounds as "higher" (high frequency) and "lower"
(low frequency) in the sense associated with musical melodies

19
 GEN ED: SOCIAL SCIENCE
PHILIPPINE HISTORY
Era Pre-colonial
Year Before 1565
General Condition The Philippines is composed of different barangay in Luzon and in Visayas while in
Mindanao and some part of Manila had Sultanate. Each barangay had autonomy and
to avoid being annexed to other big barangay, they created confederation. Hence
there is no centralized government which govern the barangays. The economy is
subsistence, and the trading system is barter
TERMS TO REMEMBER
DATU SULTAN UMALOHOCAN
The chief executive, the head of The chief executive, the head of The town crier or the announcer
the legislative and the highest the legislative and the highest of the new laws
judge in the judiciary in the judge in the judiciary in the
baranganic society. sultanate.
MAGINOO MAHARLIKA ALIPIN OR ORIPUN
The council of elders who The highest social class tax The lowest social class and the
assisted the Datu in making laws exempted and the ruling class social class of the workers
BARTER BABAYLAN CATALONAN TIMAWA
The product-to-product The lady priest in The lady priest in Luzon The middle class and
exchange and means of Visayas the taxpayers
trading

Era Spanish Era

Year 1565-1898
General Conditions The Spaniards unified the different islands under a centralized government. The
main goals for colonization can be summarized to 3G or God, Gold and Glory.
Since based on their observations, the natives are religious, they Catholicism as
means of colonization and pacification. They imposed different policies which
transform the subsistence economy to feudalism. The inter-marriage of the
Spaniards to the natives resulted to the emergence of the creoles who will
encourage the Indios to unite and end the Spanish Dominance in the Philippines.

TERMS TO REMEMBER
TREATY OF TORDESILLAS FERDINAND MAGELLAN HUMABON
the treaty which divided the earth the leader of the Spanish expedition, the rajah of Cebu who welcome
for exploration for Portugal and which was able to reach Homonhon, Magellan
Spain. The western part belongs to Samar and proven that the earth is
Spain while the eastern part was a sphere.
given to Portugal
LIMASAWA BATTLE OF MACTAN RUY LOPEZ DE VILLALOBOS
the venue of the first mass (March the battle headed by Lapulapu and the leader of the 4th expedition who
31, 1521) the first triumph of the Asians named our country as Las Islas de
against the Western powers (April Felipinas to honored king Felipe of
27, 1521) Spain
ENCONMIENDA CABEZA DE BARANGAY ROYAL AUDIENCIA
the system of land owning the head of the barangay
 the Supreme Court during the
Spanish Era
MIGUEL LOPEZ DE LEGASPI POLO Y SERVICIOS GALLEON TRADE
the first Spanish govemor general in the forced labor imposed to male 16 the trading initiated by the Spanish
the Philippines and also known as to 60 years old. The polistas are government. The trading route is
Adelantado de Filipino obliged to render their service for limited to Manila, Philippines and
40 days However the people who can Acapulco, Spain. Since this is
afford to pay for Falla can be monopoly in terms of trading only the
exempted. people who can afford to pay Boleta
or ticket for the Galleon can join the
international trading.
GOVERNOR GENERAL ALCALDE MAYOR GOBERNADORCILLOS
the highest executive official in the the head of the province and the head of the town or pueblo. The
country, appointed i by the Viceroy. appointed from the obernadorcillos. only elected position in the country.
He had the power of cumplace or the
power of the governor general to
choose the laws that he will
implement in the country. He also
had the fiscal power and power to
grant pardon.
PENINSULARES INSULARES CREOLES ILLUSTRADO
the highest social class, the Spanish born in the the mixed blood the well-educated Filipinos
the Spanish born in Spain Philippines
INDIO PEDRO PELAEZ LA SOLIDARIDAD
the Natives the Father of Secularization the newspaper founded by the
Filipinos in Madrid
LA LIGA FILIPINA KKK KARTILYA
the civic society founded by Jose the secret society founded by Andres the code of conduct of the
Rizal which aimed for Unity, Reform Bonifacio which aimed for Katipuneros
and Equality. independence of the Philippines
KALAYAAN EMILIO JACINTO APOLINARIO MABINI
the newspaper of KKK the brain of KKK The brain of Revolution
MARIANO ALVAREZ BALDOMERO AGUINALDO TREATY OF BIAK NA BATO
the head of the Magdiwang faction the head of the Magdalo Faction of the treaty which ended the Filipino-
of KKK KKK Spanish war and the voluntary exile
of Emilio Aguinaldo to Hongkong
after the payment of 400, 000
Mexican peso.

SIGNIFICANT DATES
March 16, 1521 The arrival of Ferdinand Magellan and his troops in Homonhon, Eastern, Samar.
March 31, 1521 The first Mass in the country
April 27, 1521 The Battle of Mactan
February 03, 1565 The arrival of Miguel Lopez de Legaspi in Cebu
January 20, 1872 The Cavite Mutiny
February 17, 1872 The Execution of GomBurZa
July 03, 1892 The Founding of La Liga Filipina
July 07, 1892 The Founding of KKK
21
August 19, 1896 The discovery of KKK
August 23, 1896 The start of Philippine Revolution
December 30, 1896 The execution of Dr. Jose Rizal
March 22, 1897 The Tejeros Convention
May 10, 1897 The Execution of Andres Bonifacio
December 15, 1897 The Treaty of Biak na Bato

Era American Era

Year 1898-1946
General Conditions The American was able to intercede in Filipino- Spanish war and became one of
the world powers in the 20th century. The new colonizer used education and local
government as an instrument of pacification under their Benevolent assimilation
principle. They created different infrastructures and made the Philippines as the
center of trade and commerce in the Pacific. However, they also imposed different
rules which will create a dominant impact to the country even after gaining
independence in July 4, 1946.

TERMS TO REMEMBER
FRANCIS BURTON CAYETANO ARELLANO TREATY OF PARIS THOMASITES
HARRISON The first Filipino Chief the treaty which ceded the American trained
the Pro Filipino Justice the Philippines to teachers
American Civil Governor Americans
RECONCENTRATION ACT PAYNE ALDRICH ACT JONES ACT OF 1916
the policy imposed by the Americans the trading law int 1909 which The law which transform the
which created zone for the Filipino implemented partial free trade legislative body into Bicameral
communities for easy administration between the Philippines and the legislature, thus it created the
Americans. senate.
WILLIAM HOWARD TAFT UNDERWOOD SIMMONS WILLIAM MCKINLEY
the First American Civil Governor in the trading law in 1913 which the President of United States
the Philippines and the architect of implemented full free trade. during their colonization
US colonization between the Americans. Philippines
and the
HARE-HAWES CUTTING LAW TYDINGS-MCDUFFIE LAW MACARIO SAKAY
Independence bill resulted from the Independence. law which gave The founder of the Republikang
OSROX Mission. the Philippines a partial Tagalog and one of the last generals
independence from the Americans. It to surrender to the Americans
also leads to the creation of
commonwealth government

SIGNIFICANT DATES
May 01, 1898 The Battle of Manila Bay
June 12, 1898 The Declaration of Independence against Spain
September 15, 1898 Malolos Congress
December 10, 1898 Ratification of Treaty of Paris
February 04, 1899 San Juan del Monte Incident, Start of US-Philippine War

22
June 15, 1899 Death of Gen. Antonio Luna
December 02, 1899 Battle of Pasong Tirad
March 23, 1901 Captivity of Emilio Aguinaldo

23
Era Japanese Era
Year 1942-1945
General Conditions The Second World War started in 1939 when Adolf Hitler invaded Poland. The Pacific
became part of WWII after the invasion of Japan to Pearl Harbor and Manila. The Allied
Powers became active in freeing Europe from the Axis Powers, so the American forces
leave Philippines for almos hree years. In the midst of war, the Filipino continue their
loyalty to the American. And this resulted to the destruction of the infrastructures and
death of many Filipinos.
TERMS TO REMEMBER
GEN. DOUGLAS JOSE P. LAUREL AXIS POWERS ALLIED POWERS
MACARTHUR the President of the Germany and Italy Great Britain, France,
the field Marshall of Second Republic USSR and USA
the USAFFE
PEARL HARBOR MANUEL L. QUEZON KALIBAPI
the biggest military bases of the the president of Commonwealth Kapisanan sa Paglilingkod sa Bagong
Americans in the Pacific government during the WWII Pilipinas, the only political party in
the Philippines during the Japanese
Era
KEMPEITAI CORREGIDOR JONATHAN WAINRIGHT
The Japanese Military Police The last US military Bases in Asia to the head of the US forces in
surrender to the Japanese Corregidor when they surrender to
Japanese forces.

SIGNIFICANT DATES
December 07, 1941 The bombing of Pearl Harbor
December 08, 1941 The invasion of Manila, Manila declared as Open City
April 09, 1942 The fall of Bataan
May 06, 1942 The fall of Corregidor
January 23, 1943 The second Republic
October 20, 1944 The Leyte Landing the return of Douglas MacArthur
August 06, 1945 Bombing of Hiroshima
August 09, 1945 Bombing of Nagasaki
August 15, 1945 The surrender of Japan

24
 PROF ED: Teaching Profession
BASIC CONCEPTS
A quantity that represents a distance along a line
REAL NUMBERS
All the numbers on the number line.
Numbers which are non-terminating and non-repeating
IRRATIONAL NUMBERS
Cannot be written as a fraction
Terminating
RATIONAL NUMBERS Can be written as a fraction
Non-terminating yet repeating
NON-INTEGER Positive and negative fractions
INTEGER Numbers with no decimal part, it may be positive or negative
NEGATIVE INTEGERS Negative numbers with no decimal part (fraction)
WHOLE NUMBERS Includes Zero and all positive integers
It represents nothing in counting
ZERO
The only integer that is neither positive (+) nor negative (-)
Also known as Counting Numbers
NATURAL NUMBERS
This includes all integers greater than 0.

BASIC ALGEBRA
Word Meaning Examples
VARIABLE An unknown value that is represented by a C=2mr
letter or a symbol Where C and r are variables
EXPRESSION An algebraic form consisting of numbers, 2x + y – 7 ;
variables, and operation signs
EQUATION An algebraic form which contains an * = " sign 2x + y = 7 ;
TERMS Algebraic forms which are separated by "+" or " 2x + y 7 has 3 terms. These
signs, the signs being included are 2x, y and -7
LIKE TERMS Terms with exactly the same variable form In 2x + y – 7 – 3x
(variable and index) only 2x and 3x are like terms.
CONSTANT TERM A term which does not contain a variable In 2x + y – 7 – 3x,
-7 is the constant term
COEFFICIENT The number factor of an algebraic term In y – 7 – 3x,
3 is the coefficient of x
1 is the coefficient of y

POLYNOMIALS
A polynomial is a special algebraic expression with terms that consist of real number coefficients and variable
factors with whole number exponents.
COLLECTING LIKE TERMS
Algebraic expressions can often be simplified by adding or subtracting like terms. We call this collecting like
(similar) terms.
EXPRESSION TO BE SIMPLIFIED SIMPLIFIED EXPRESSION
2a²-4a + 5a² + 4a² + 3a 2a² and 5a² are like terms=2a² + 5a² = 7a²
-4a and 3a are like terms=-4a + 3a = -a
=7a² = a + 4a³
FACTORING
We just studied the expansion of algebraic factors. In this part of our study, we will do the reverse. Instead of
finding the product this time from the product we will find the factors, which is the process called factorization.
 Law or Rule What to do Example(s)
1. REMOVAL OF THE COMMON Divide all the terms by the GCF, 2x² + 3x = x(2x + 3)
FACTOR (GCF) express them as products -2x² - 6x = -2x(x+3)

2. DIFFERENCE OF TWO Since (a + b)(a - b) =a²-b² 25-y²=(5+y)(5-y)

SQUARES then a²-b² = (a + b)(a-b) y²-36= (y+6)(y-6)
3. SUM AND PRODUCT x² + (p + q)x+ pq = (x + x² + 5x + 6 = (x+3)(x+2)
p)(x+q) x²-x-6=(x + 2)(x-3)

PROBABILITY
a measure of the possibility of the event occurring as the result of an experiment. A numerical representation of
events ranging from 0 to 1. The probability of an event E is the sum of the weights of all sample points in E
Thus 0 ≤ P(E) ≤ 1, P(Ø)=0, and P(S) = 1
SUBJECTIVE PROBABILITY Based on one's expertise
EMPIRICAL PROBABILITY Based on observable experience
CLASSICAL PROBABILITY

THE MULTIPLICATION PRINCIPLE

Suppose k events E₁, E₂…,Ek are to be performed in order in such way that each event is independent of the
others. If event E, can be performed in n(E₁) ways, event E₂ in n(E₂) ways, and so on, then the total number of
ways of performing all k events is given by the product
N=n(E₁)n(E₂)…n(Ek)
Note: The fundamental principle of counting often referred to as the multiplication rule.

If n is a positive integer, the product of the numbers 1, 2,..., n is denote by n! (read "n factorial"). Also, 0! is
defined to be 1. That is,
n!= n(n-1)(n-2)...3 •2 •1 and 0!= 1
Note: It is used when all things/objects are different or distinct and repetition of things /object are not allowed

PERMUTATION
• A rearrangement of objects in which the order of selection is important.
• A permutation of n objects taken rat a time is an ordered arrangement of r of the n objects selected without
repetition. The total number of these arrangements is denoted by nPr and is given by

Note: P =nl
n n

(Circular Permutation)
(Permutation with identical object)

Where: n₁ + n₂ +…+ nk = n and n₁ = number of type1 identical things n₂ = number of type 2 identical things
etc.

COMBINATION
• A rearrangement of objects in which the order of selection is not important.

26
 • A combination of n objects taken r at a time is a subset of r objects selected without regard to order from
a collection of n objects. The total number of such combinations is denoted by nCr and is given by

Note: nPn – r = nCr for r = 0, 1, 2.. n

If A and B are any two events, then P(A U B) = P(A) + P(B) - P(A ∩B)

If the events happen to be mutually exclusive, then P(A ∩B) = 0

If A₁. A₂... An are mutually exclusive, then P(A₁UA₂U-UAn) = P(A₁) + P(A₂)+…+P(An)

If A and A' are complementary events, then P(A) + P(A’) = 1

BUSINESS MATH
PERCENTAGE, BASE AND RATE
BASE Denoted B, is the whole in a problem. It is the standard used for comparison.
PERCENTAGE Percentage or the amount, denoted P, is the part of the whole being compared to the base.
RATE Denoted R, is the ratio of the amount to the base. It is written as a percent
FORMULAS:
Percentage (P) Base (B) x Rate (R)
Base (B) = P / R
Rate (R) = P/B

INTEREST
INTEREST Defined as the cost of borrowing money as in the case of interest charged
on a loan balance. Conversely, interest can also be the rate paid for
money on deposit as in the case of a certificate of deposit. Interest can
be calculated in two ways, simple interest or compound interest
SIMPLE INTEREST Calculated on the principal, or original, amount of a loan.
COMPOUND INTEREST Calculated on the principal amount and also on the accumulated interest
of previous periods, and can thus be regarded as "interest on interest"
SIMPLE INTEREST COMPOUND INTEREST
I = Prt
where
I = Interest F = Final value
P = Principal P = Principal
r = interest rate r = interest rate
t = term of the loan n = the number of compounding a year
t = term or loan period

STATISTICS
Measures of Central Tendency
MEAN OR ARITHMETIC MEAN Set of data is the sum of the data values divided by the number of observations.
This measurement can only be used if the level of data is interval or ratio.
Take note that there is only mean in a set of data. In computing the mean all
values in the data set should be included. The mean is most appropriate in
27
 symmetrical data. The disadvantage of using the mean is that, the mean is
affected by the extreme values (relatively small or large values on and a data
set) and the mean cannot be computed for the data in a frequency distribution
with an open ended class. The formula is given below for population and sample
mean of ungrouped data

Where N and in represent the number of data idx represent the numerical
values of the observation.

Furthermore, for the mean of grouped data we will be using this formula

Note that in the actual study, if raw data is/are available, the ungrouped
treatment is highly recommended

Another type of mean is what we called the WEIGHTED MEAN. This is useful
when several types of data make different contributions to the mean, then
each type of data should be assigned a weight proportional to its importance
prior to calculation of the mean. If this is done, the formula for the weighted
mean

MEDIAN Denoted by x, is the middle most observation of a set of observations that are
arrange in an ascending or descending order. If the number of sample size is
an odd number, the median is simply the middle observation. Can be used if
the level of data is ordinal, interval and ratio. Take note that the median of a
data set is unique. Median is not affected by the extreme values and median
can be computed even for open ended frequency distribution. It is most
appropriate in a skewed data
MODE If it exist, is the most frequently occurring value. It can be used for any
type of level of measurement (nominal, ordinal, interval, and ratio). It is the
easiest average to compute. It is possible to have more than one mode or no
mode at all for a given data set. Not suggested for continuous data. And the
mode is not affected by extreme values.

28