PMA Entrance Exam cheat sheet

Percent change = (new − old) ÷ old × 100; a 20% increase followed by a 20% decrease leaves 96% of the original value.

For a right triangle: a² + b² = c², where c is the hypotenuse; the 3-4-5 and 5-12-13 triples are common test values.

Slope of a line through (x₁,y₁) and (x₂,y₂) is m = (y₂ − y₁)/(x₂ − x₁); parallel lines share m, perpendicular lines have m₁·m₂ = −1.

Average = sum ÷ count; if a set of n numbers has mean m, the sum is n·m, which lets you recover a missing value.

Distance = rate × time; for two objects moving toward each other, combined speed = sum of rates, and time to meet = distance ÷ combined speed.

Area formulas: triangle ½bh, circle πr², trapezoid ½(b₁+b₂)h, rectangle lw; volume of a cylinder is πr²h.

Order of operations: parentheses, exponents, multiplication/division left to right, then addition/subtraction left to right.

Probability of an event = favorable outcomes ÷ total equally likely outcomes; independent events multiply, so P(A and B) = P(A)·P(B).

To solve a system of two linear equations, substitute one variable or add/subtract the equations to eliminate a variable, then back-substitute.

Subject-verb agreement: a singular subject takes a singular verb; phrases between subject and verb ("the box of pens") do not change the verb number.

Use "who" for people and "which/that" for things; "whom" is used when the pronoun is an object (after a preposition or as a direct object).

Its = possessive; it's = it is/has. Their = possessive; there = place; they're = they are.

Comma rules: separate independent clauses with a comma plus a coordinating conjunction (and, but, or, nor, for, so, yet); do not join two clauses with a comma alone.

A semicolon joins two related independent clauses and cannot be followed by a coordinating conjunction.

Use the comparative (-er, more) for two items and the superlative (-est, most) for three or more; do not double-mark ("more better").

Dangling modifiers: an introductory modifier must describe the subject of the main clause that immediately follows it.

Apostrophes mark possession (singular: 's; plural: s') and contractions; they never form a plural of a plain noun.

Newton's second law: F = ma; weight is the force of gravity, W = mg, and mass does not change with location while weight does.

Kinetic energy = ½mv², gravitational potential energy = mgh; energy is conserved but converted among forms.

The cell is the basic unit of life; mitochondria carry out cellular respiration, chloroplasts carry out photosynthesis, and ribosomes build proteins.

Photosynthesis: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts and producing glucose and oxygen.

DNA is a double helix of nucleotides with bases A-T and C-G; RNA substitutes uracil for thymine.

Atomic number = number of protons and identifies the element; mass number = protons + neutrons.

In a series circuit current is the same through all components and resistance adds; in a parallel circuit voltage is the same across branches.

The pH scale runs 0–14: below 7 is acidic, above 7 is basic, 7 is neutral, and each unit is a tenfold change in hydrogen ion concentration.

Main idea = the author's central point; it is broader than any single supporting detail and is often stated in the first or last sentence.

Inference questions require a conclusion that the passage supports but does not state directly; reject choices needing outside information.

Tone and attitude questions are answered by word choice (connotation), not by the topic alone; look for evaluative adjectives.

"According to the passage" questions are answered only from explicit text; do not import outside knowledge even if it is true.

Cause-and-effect structure is signalled by words such as because, therefore, as a result, and consequently.

Compare-and-contrast structure is signalled by however, unlike, in contrast, similarly, and whereas.

For vocabulary-in-context, substitute each answer choice into the sentence and check that the passage's meaning is preserved.

An answer choice that is too extreme (always, never, all) is usually wrong when the passage uses hedged language (often, may, some).

Sequence questions: map each event to a paragraph, then order by the passage's chronology rather than by real-world assumptions.

Analogy rule: state the relationship in a sentence ("A is a type of B", "A is the tool used by B"), then apply the same sentence to the answer choices.

Common analogy relationships: part-to-whole, cause-to-effect, function-to-object, degree (warm : hot :: cool : cold), and category-to-member.

Keep the direction of the analogy: if the first pair goes category → member, the answer must too, not member → category.

For odd-one-out items, find the shared property of all but one item; the outlier may differ by category, function, or scale.

Syllogism: "All A are B" and "All B are C" implies "All A are C"; "All A are B" does not imply "All B are A".

For letter series, check differences between consecutive positions (e.g., +2, +3, +4) and alternating patterns in odd and even positions.

Antonym and synonym items hinge on precise meaning; distinguish near-synonyms by intensity, formality, or usage.

Word-association groups: classify each word by part of speech and category before deciding which does not belong.

Rotation preserves size and shape; reflection reverses orientation, so check whether a figure is mirrored rather than merely turned.

Count elements systematically (sides, dots, intersections, line segments) across the series to find the arithmetic rule.

Common series rules: +1 element per step, alternating increase/decrease, doubling, or a repeating cycle of period 2 or 3.

In matrix problems, test each row and each column separately; the rule often holds horizontally and vertically.

Position rules: an element may move clockwise one corner per step, or alternate between two positions.

For folded-paper and punch-hole items, unfold step by step and mirror the hole across each fold line.

Net-folding items: identify opposite faces (they never share an edge) before checking which cube is possible.

Figure classification: find the invariant shared by the given set (e.g., all have an odd number of sides) and exclude any choice that breaks it.

Shading and line-type changes often encode a binary rule (filled/unfilled, solid/dashed) alternating between steps.