General Education Professional Education Review Notes 2025

Mathematics and Numerical Analysis

Passing Percentage Calculation: In a Licensure Examination for Teachers, only $83,152$ examinees passed out of a total of $228,963$ . To find the passing percentage: $(83,152 / 228,963) \times 100 = 36.316...\%$ , which rounds to $36.32\%$ .
Prime Numbers: A prime number is a natural number greater than $1$ that has no positive divisors other than $1$ and itself.
- Examples of prime numbers: $61$ , $71$ , and $31$ .
- The number $51$ is NOT prime because it is divisible by $3$ ( $3 \times 17 = 51$ ).
Discount Calculations: If a bottle of perfume costs $P10,000$ and a discount of $10\%$ is applied, the savings amount to $P1,000$ . The final cost is: $P10,000 - P1,000 = P9,000$ .
Percentage of a Number: To determine what percent $35$ is of $560$ , use the formula: $\frac{35}{560} = 0.0625$ $0.0625 \times 100 = 6.25\%$ .
Algebraic Expressions and Operations:
- Literal Coefficient: In the term $-7x^3m^2n$ , the literal coefficient consists of the variable part, which is $x^3m^2n$ . The numerical coefficient is $-7$ .
- Simplification ( $1$ ): $3x - (2y - 4x) + 6y$ simplifies by distributing the negative sign: $3x - 2y + 4x + 6y = 7x + 4y$ .
- Simplification ( $2$ ): $x - (2y + 3x) - 2y$ simplifies to: $x - 2y - 3x - 2y = -2x - 4y$ .
Interest Calculations: The total amount after adding $8\%$ interest for $3$ months on a principal of $P6,000$ is calculated using the simple interest formula $I = P \times r \times t$ : $I = 6,000 \times 0.08 \times \frac{3}{12} = 120$ Total Amount = $P6,000 + P120 = P6,120$ .
Exponential Form: The estimated area of Luzon, which is $100,000\,square\,kilometers$ , is expressed in exponential form as $10^5$ .
Volume and Geometry:
- Volume: The volume of an aquarium with dimensions $10\,cm$ , $8\,cm$ , and $6\,cm$ is calculated as: $V = l \times w \times h = 10 \times 8 \times 6 = 480\,cm^3$ .
- Perimeter and Area: A square with an area of $144\,square\,meters$ has a side length ( $s$ ) of: $s = \sqrt{144} = 12\,m$ . Perimeter ( $P$ ) is $4s = 4 \times 12 = 48\,m$ .
Ratios and Proportions:
- Time Allocation: If review hours for Algebra, Chemistry, and English are in a ratio of $4:3:1$ for a total of $24\,hours$ , the parts are $4 + 3 + 1 = 8$ . Each part is $24 / 8 = 3\,hours$ . Chemistry ( $3$ parts) equals $3 \times 3 = 9\,hours$ .
- Proportion Solving: In the proportion $x : 8 = 4 : 16$ , solve for $x$ by cross-multiplying: $16x = 32$ , thus $x = 2$ .
Consecutive Integers:
- The sum of three consecutive integers is $96$ . Let the integers be $n$ , $n+1$ , and $n+2$ . $3n + 3 = 96 \rightarrow 3n = 93 \rightarrow n = 31$ . The integers are $31, 32, 33$ .
- The sum of two consecutive even integers is $34$ . Let them be $n$ and $n+2$ . $2n + 2 = 34 \rightarrow 2n = 32 \rightarrow n = 16$ . The integers are $16$ and $18$ .
Number Theory and Factoring:
- GCF: The largest common factor of two or more numbers is called the Greatest Common Factor (GCF).
- Prime Factorization: The prime factorization of the number $154$ is calculated as: $154 = 2 \times 77 = 2 \times 7 \times 11$ .

Jose Rizal: Life, Works, and Philosophy

Character and Traits: Jose Rizal is described as courageous, intelligent, and audacious. He was specifically NOT pessimistic.
Literary Works:
- Notable Pieces: To The Filipino Youth, Touch Me Not (English title of Noli Me Tangere), and The Reign of the Greed (English title of El Filibusterismo).
- Exceptions: The Daughter of a Friar is not a work of Rizal.
- "Our Mother Tongue": Rizal wrote the poem Sa Aking Mga Kabata (Our Mother Tongue) at the age of $8$ .
- "Mi Ultimo Adios": Written the night before his execution, this poem is classified as an elegy (a poem of serious reflection, typically a lament for the dead). It expresses the beauty of the Philippines and his hope for current and future generations.
Novels and Characters:
- Noli Me Tangere: Features characters like Sisa, the symbol of the abused Filipino mother, and Donya Pia Alba, who died due to difficulties during childbirth. Pilosopo Tasyo in the novel is said to personify Rizal’s older brother, Paciano, in real life.
- The Reign of Greed (El Filibusterismo): This novel was first published in $1891$ in Ghent, Belgium.
- Symbolism: The characters in Rizal's novels symbolize the varied reactions of Filipinos toward the colonizers from Spain.
- Famous Quote: "I shall die without seeing the dawn break upon my homeland" was a statement made by the character Elias.
Education and Polymathy:
- Rizal was a polymath, demonstrating genius in both sciences and arts.
- He was a polyglot, conversant in approximately $22$ languages.
- He continued his medical studies in Spain and earned his degree in medicine in $1884$ at the Universidad Central de Madrid.
Family and Legal Struggles:
- Surname Change: All siblings used "Mercado," but Rizal used his father's second surname ("Rizal") to travel and study freely because the Mercado family members were blacklisted and suspected as anti-government.
- Teodora Alonso (Mother): She chose imprisonment and a $50\,km$ walk rather than accepting a trumped-up charge from a Spanish official, showing she was a woman of conviction.
Legislation and Art:
- RA 1425: The Republic Act requiring the compulsory teaching of the Rizal Course and the lives of other Filipino patriots.
- Sculpture: The Triumph of Science over Death is a famous sculpture by Rizal.
- Museums: Buildings like the Rizal Shrine were built in homage (honor/respect) to him.

Philippine History and Social Sciences

Discovery and Early Resistance:
- The Philippines was discovered by Portuguese explorer Ferdinand Magellan (sailing for Spain) in $1521$ .
- Tirad Pass: General Gregorio del Pilar (known as G. del Pilar) lost his life defending the pass.
Pre-colonial and Spanish Era:
- Barter System: The system used for business transactions in pre-colonial trade.
- Ilustrados: Europe-educated Filipinos from affluent middle-class families during the Spanish regime (e.g., Jose Rizal, Marcelo H. del Pilar, Graciano Lopez Jaena). Andres Bonifacio was notably NOT an Ilustrado.
- Early Culture: Antonio de Morga’s Sucesos de las Islas Filipinas describes early Filipinos as having their own culture, army, and navy with advanced weapons like Kris and Kampilan.
19th and 20th Century Conflicts:
- Declaration of War: The discovery of the Katipunan marked the declaration of war against Spain.
- 1986 People Power Revolution: This model of non-violence ended dictatorial rule and gained international admiration.
- WWII: Manila fell to the Imperial Japanese Army in $1942$ under Commander General Masaharu Homma.
Government and Law:
- Taxation: The unlawful act of escaping from the payment of taxes is known as Tax Evasion.
- Sustainable Development: Defined by the Brundtland Commission as development that meets current needs without compromising the ability of future generations to meet theirs.
Geography and ASEAN:
- Mindanao: It is the second biggest island in the country (Luzon is the biggest).
- ASEAN Members: Members include Singapore, Indonesia, Myanmar, Laos, the Philippines, Cambodia, and others. China and India are not members.
- Natural Disasters: Due to its location on the Pacific Ring of Fire, the Philippines is highly prone to earthquakes.

Natural Sciences: Biology, Chemistry, and Physics

Biology and Taxonomy:
- Levels of Taxonomy: There are $8$ levels in the hierarchy of biological taxonomy.
- Aristotle: Known as the "father of ancient taxonomy".
- Genetics: The branch of biology studying heredity and the inheritance of characters. Gregor Mendel is credited with studying the laws of heredity.
- Biological Classification:
  - Fungal cell walls are composed of chitins, proteins, and sugar.
  - Classification Hierarchy: Mammalia is to class as Primate is to Order.
  - Zebra, horse, and donkey belong to the same genus.
- Phylogenetics: Used to classify plants based on their evolutionary sequence.
Reproduction and Health:
- Fertilization: The combination of an ovum and sperm.
  - In vitro: Fertilization occurring in a test tube (outside the body).
  - In vivo: Fertilization within the living organism.
- Hemophilia: A sex-linked recessive disorder. If a man is hemophiliac, he inherited the disease from his mother because the X chromosome comes from the mother.
- Recessive Genes: These only have phenotypic expression if the genotype is homozygous.
Ecology:
- Ecosystem: Soil is an ecosystem because it consists of both biotic and abiotic components.
- Biodiversity: The Tropics (terrestrial biome) house the greatest biodiversity.
- Ecological Succession:
  - Secondary Succession: Occurs when a disturbance (like a wildfire) destroys vegetation but leave the soil viable, allowing life to return.
- Symbiotic Relationships:
  - Commensalism: One organism benefits (e.g., an orchid on a mango tree) while the other is unaffected.
  - Competition: Two organisms (e.g., an avocado tree and a sampaguita plant) vying for the same resources.
  - Predation: One organism kills and eats another (e.g., a hunter shooting a duck).
Physics and Chemistry:
- Energy Types:
  - Potential Energy: Stored energy. Gravitational potential energy is found in a child at the top of a slide or a book on a table.
  - Chemical Energy: Energy transfer stored in a battery or power bank.
- Atomic Structure: Silicon has an atomic number of $14$ and a mass number of $28$ . The number of protons is equal to the atomic number ( $14$ ).
- pH Scale: A pH below 7 indicates acidity.
- Optical Illusion: A mirage is an optical illusion caused by the refraction of light and optical focus issues related to temperature gradients in the air.
- Ammonia: A gaseous compound ( $NH_3$ ) produced by the combination of nitrogen and hydrogen.

Language and Literature (English and Filipino)

Filipino Language (Wika):
- Morpema: Ang pinakapayak na yunit ng isang salita na nagtataglay ng kahulugan.
- Salitang Ugat: Pinakapayak na anyo ng salita na walang panlapi.
- Bantas: Ang gitling ang ginagamit sa paghihiwalay ng dalawang salita na nagkakaroon ng ibang kahulugan.
- Baybay (Spelling): Ang wastong baybay sa mga nabanggit ay gamugamo.
- Malayuning Komunikasyon: Tungkol sa pagsulat, pagsasalita, at presentasyon para sa iba-ibang layunin.
English Literature and Literary Devices:
- Allegory: A piece that expresses truth through symbolic people and events.
- Idiomatic Expression: "Piece of cake" describes an easy task.
- Specific Authors and Works:
  - Edgar Allan Poe: American writer of "The Raven" and "The Fall of the House of Usher".
  - Henry Wadsworth Longfellow: Author of The Song of Hiawatha.
  - Christopher Marlowe: Noted English playwright from the Elizabethan era.
  - Carlos Bulosan: Author of My Father Goes To Court.
  - Herman Melville: Wrote Moby-Dick, which famously opens with "Call me Ishmael".
  - Elizabeth Barrett Browning: Wrote "How do I love thee, let me count the ways".
  - Aesop: Ancient Greek storyteller famous for fables.

Information and Communication Technology (ICT)

Online and Distance Learning: Distance education made possible by computers is known as Online Learning.
Web and Internet:
- Tim Berners-Lee: He invented the World Wide Web (WWW) in $1989$ .
- Modem: The device required to connect a computer to the internet.
- Webinar: A seminar or presentation that takes place on the internet.
- Search Engines: Google, Yahoo, and MSN are search engines; Windows is an operating system.
Computer Components:
- Byte: Known as the storage unit of data.
- Cursor: Indicates the position of the mouse on the screen.
- Password: A secret word required for access to information.
- Word Processing: The productivity tool used for writing letters.

Arts, Ethics, and General Knowledge

Sports: EJ Obiena is a world-renowned athlete in Pole Vault.
Ethics: Socrates is considered the father of ethics and is attributed with the dictum: "A life unexamined is not worth living."
Fine Arts:
- Wassily Kandinsky: Known as the "Father of abstract painting".
- Principles of Art: Balance, emphasis, movement, proportion, rhythm, unity, and variety.
- Juan Luna & Felix Resurreccion-Hidalgo: Famous Filipino painters; Hidalgo painted Virgin Exposed to the Populace.
Astronomy:
- Mercury: The closest planet to the Sun.
- Mars: Classified as a terrestrial (rocky) planet.
- Revolution: Planets generally revolve in a west to east direction.
Health (COVID-19):
- Transmission: Person-to-person transmission.
- San Lazaro Hospital: The first institution to handle the first Covid-19 case in the Philippines.
- Contact Tracing: The process of identifying individuals who have come into close contact with someone infected with Covid-19.