PUPCET cheat sheet

Quadratic formula: for ax² + bx + c = 0 (a ≠ 0), x = [−b ± √(b² − 4ac)] / (2a).

Discriminant b² − 4ac: positive gives two distinct real roots, zero gives one repeated real root, negative gives no real roots.

Slope m = (y₂ − y₁)/(x₂ − x₁); parallel lines have equal slopes, perpendicular lines have slopes whose product is −1.

Sum of interior angles of an n-sided polygon = (n − 2) × 180°; each interior angle of a regular n-gon = (n − 2) × 180° ÷ n.

Arithmetic sequence: aₙ = a₁ + (n − 1)d, Sₙ = n/2 × (a₁ + aₙ); geometric sequence: aₙ = a₁rⁿ⁻¹.

Probability: P(event) = favorable outcomes ÷ total outcomes; P(A or B) = P(A) + P(B) − P(A and B); for independent events P(A and B) = P(A) × P(B).

Circle: area = πr², circumference = 2πr; sector area = (θ/360) × πr².

Exponent rules: aᵐ · aⁿ = aᵐ⁺ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁻ⁿ = 1/aⁿ; a⁰ = 1 when a ≠ 0.

Percent change = (new − old) ÷ old × 100; successive percent changes are multiplied as factors, not added.

Subject-verb agreement: a singular subject takes a singular verb and a plural subject takes a plural verb; prepositional phrases between them do not affect the verb.

Indefinite pronouns each, either, neither, everyone, somebody, and nobody are singular; both, few, many, and several are plural.

Pronoun case: use subject pronouns (I, he, she, we, they) for subjects and object pronouns (me, him, her, us, them) after prepositions or as objects.

Active voice: the subject performs the action; passive voice: the subject receives the action and the verb uses be + past participle.

Main idea answers what the passage is mostly about; detail questions are answered by explicit statements; inferences must be supported by the text but are not directly stated.

Transition signals: contrast (however, nevertheless), cause-effect (therefore, consequently), addition (moreover, furthermore), example (for instance).

Parallel structure: items in a list or joined by and/or must share the same grammatical form, such as all gerunds, all infinitives, or all nouns.

A misplaced modifier must be moved next to the word it describes; a dangling modifier has no logical word to modify.

Context clues include definition, synonym or restatement, contrast or antonym, and example.

Newton's laws: an object stays at rest or in uniform motion unless a net external force acts; F = ma; every action has an equal and opposite reaction.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts containing chlorophyll.

Cellular respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP, occurring mainly in mitochondria.

DNA base pairing: adenine–thymine and cytosine–guanine; in RNA, adenine pairs with uracil.

pH below 7 is acidic, 7 is neutral, above 7 is basic; each unit represents a tenfold change in hydrogen-ion concentration.

Mitosis produces two identical diploid cells for growth and repair; meiosis produces four genetically varied haploid gametes.

Cell organelles: nucleus controls activity, ribosomes make protein, mitochondria release ATP, chloroplasts carry out photosynthesis, membrane is selectively permeable.

Energy pyramids lose roughly 90% of energy at each trophic level, so producers form the broad base and top consumers are fewest.

Periodic table: group number relates to valence electrons, period number to electron shells; metals lie left, nonmetals right.

Number series: test constant differences, constant ratios, alternating two-step patterns, squares, cubes, and primes before choosing the next term.

Letter series: convert letters to positions (A = 1 … Z = 26) and check for constant, increasing, or alternating shifts.

Analogy: name the relationship (part–whole, cause–effect, function, synonym, worker–tool) and apply the identical relationship to the second pair.

Valid syllogism: 'All A are B; X is A; therefore X is B' is valid. 'All A are B; X is B; therefore X is A' is invalid.

Odd-one-out: classify each option by a shared property; the option lacking the property common to the others is the answer.

Matrix puzzles: track row transformations and column transformations separately, then combine them.

Coding–decoding: identify the letter shift, reversal, or substitution rule using a known word, then apply it to the target word.

Ordering puzzles: draw positions on a line and apply before/after constraints one at a time to fix the sequence.

Mga bahagi ng pananalita: pangngalan, panghalip, pandiwa, pang-uri, pang-abay, pang-ukol, pangatnig, pandamdam.

Aspekto ng pandiwa: perpektibo (tapos na), imperpektibo (nagaganap), kontemplatibo (gaganapin), perpektibong katatapos (katatapos pa lamang).

Pokus ng pandiwa: aktor (gumaganap), layon (tinatanggap), ganapan (lugar), instrumento (gamit), sanhi (dahilan).

Mga tayutay: simili (gaya ng, kapara), metapora (tuwirang paghahambing), personipikasyon, hyperbole, onomatopeya.

Sawikain o idyoma ay may di-tuwirang kahulugan; halimbawa, 'kumukulo ang dugo' ay nangangahulugang galit.

Sanhi at bunga: sanhi ang dahilan, bunga ang resulta; hudyat nito ang dahil, sapagkat, kaya, kung kaya.

Pagbuo ng salita: paglalapi (unlapi, gitlapi, hulapi), pag-uulit (ganap o parsyal), at pagtatambal.

Wastong baybay: gamitin ang limang patinig (a, e, i, o, u) at mga katinig; sundin ang KWF sa hiram na salita.

Pagpapantig: bawat pantig ay may isang patinig; karaniwang anyo ay katinig-patinig (CV) o katinig-patinig-katinig (CVC).