PMA Cadet Entrance Test cheat sheet

Order of operations: evaluate grouping symbols, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Percent change = (new − old) ÷ old × 100; a 20% increase followed by a 20% decrease yields a net 4% decrease, not zero.

Slope of a line through (x1, y1) and (x2, y2) is (y2 − y1)/(x2 − x1); parallel lines share a slope, perpendicular slopes multiply to −1.

Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a for ax² + bx + c = 0; the discriminant b² − 4ac gives 2, 1, or 0 real roots.

Area formulas: triangle ½bh, circle πr², trapezoid ½(b1 + b2)h; circumference 2πr and volume of a cylinder πr²h.

Pythagorean theorem a² + b² = c² for right triangles; common triples are 3-4-5, 5-12-13, and 8-15-17 or their multiples.

Average (mean) = sum ÷ count; median is the middle value of an ordered list, and mode is the most frequent value.

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

Work and rate rule: combined rate equals the sum of individual rates, so two workers at 1/6 and 1/3 job per hour finish in 1 ÷ (1/6 + 1/3) = 2 hours.

Subject-verb agreement: a singular subject takes a singular verb even when a prepositional phrase intervenes, as in 'The box of tools is heavy.'

Indefinite pronouns each, everyone, neither, and nobody are singular and take singular verbs and pronouns.

Its is possessive; it's means 'it is.' Their is possessive; there shows place; they're means 'they are.'

A pronoun must agree with its antecedent in number and gender; collective nouns like team take a singular pronoun when acting as one unit.

Dangling modifiers must be repaired by naming the actor right after the comma: 'Walking home, she saw the rain,' not 'Walking home, the rain was seen.'

Parallel structure requires matching grammatical forms in a list: 'reading, writing, and swimming,' not 'reading, writing, and to swim.'

Comma splices join two independent clauses with only a comma; fix with a semicolon, a period, or a coordinating conjunction.

Affect is usually a verb meaning to influence; effect is usually a noun meaning result.

Active voice puts the doer first ('The cadet raised the flag'); passive voice puts the receiver first ('The flag was raised by the cadet').

Newton's second law F = ma; weight equals mass times gravitational acceleration, about 9.8 m/s² near Earth's surface.

Speed = distance ÷ time; acceleration = change in velocity ÷ time, and velocity includes direction while speed does not.

Kinetic energy = ½mv²; gravitational potential energy = mgh, and energy is conserved but transforms between forms.

Ohm's law V = IR; power P = VI, and series resistors add while parallel branches share voltage.

Density = mass ÷ volume; an object floats in a fluid when its density is less than the fluid's density.

Photosynthesis converts carbon dioxide and water into glucose and oxygen using light energy captured by chlorophyll.

The cell is the basic unit of life; mitochondria release energy from glucose, and the nucleus holds genetic material in DNA.

DNA bases pair adenine with thymine and guanine with cytosine; humans carry 46 chromosomes in 23 pairs.

Water's pH of 7 is neutral; values below 7 are acidic and above 7 are basic, and litmus turns red in acid and blue in base.

In number series, check differences first, then ratios, then alternating or two interleaved sequences.

Letter series follow alphabet positions: A=1 through Z=26, so a +3 pattern maps A→D→G→J.

Shape rotation rules: track a single feature such as a dot or arrow across frames rather than the whole figure.

Counting rules for matrices: count sides, enclosed regions, intersections, or line segments before guessing a pattern.

Analogy form A is to B as C is to D: identify the transformation applied to A, then apply the same transformation to C.

Odd-one-out items usually break one shared property such as symmetry, number of sides, or open versus closed figures.

Fold-and-punch items mirror the hole across each fold line; the number of holes doubles with each fold through the punched region.

Mirror images reverse left and right but not top and bottom; water images reverse top and bottom instead.

The Philippine Military Academy is located in Fort del Pilar, Baguio City, and its cadets are called cavaliers.

The PMA cadet corps is organized into a Corps of Cadets led by the Corps Commander, with companies and battalions beneath.

The Armed Forces of the Philippines has three main branches: the Army, the Navy (including the Marine Corps), and the Air Force.

The Philippine Constitution's Bill of Rights protects due process, speech, and protection against unreasonable searches and seizures.

The three branches of the Philippine government are the executive, legislative (Senate and House of Representatives), and judiciary.

The United Nations was founded in 1945 and its principal organs include the General Assembly and the Security Council.

ASEAN was established in 1967 with the Bangkok Declaration, and the Philippines is a founding member.

The Philippine flag's blue stripe stands for peace and justice, red for patriotism, and the three stars represent Luzon, Visayas, and Mindanao.