ACET (Philippines University Entrance Tests) cheat sheet

Subject-verb agreement: a singular subject takes a singular verb; intervening phrases ("along with", "as well as") do not change the subject's number.

Pronoun case: use the subjective form after "than" or "as" when it is the subject of an implied verb ("She is taller than I [am]").

Comma splice: two independent clauses joined only by a comma is an error; fix with a semicolon, a coordinating conjunction, or a period.

Dangling modifier: an introductory participial phrase must modify the subject of the main clause, not an object or absent noun.

Parallelism: items in a list or comparison must share grammatical form (all nouns, all infinitives, or all gerunds).

Affect is a verb (to influence); effect is usually a noun (a result). Lie = recline (intransitive); lay = place (transitive, takes an object).

Reading comprehension: main-idea answers must cover the whole passage; scope too narrow or too broad is a distractor signal.

Inference questions: the correct answer is necessarily true given the passage, not merely plausible or consistent with outside knowledge.

Quadratic formula: for ax^2 + bx + c = 0, x = (-b +/- sqrt(b^2 - 4ac)) / (2a); discriminant b^2 - 4ac > 0 gives two real roots.

Percent change = (new - old) / old x 100; successive percent changes multiply, they do not add.

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

Circle: area = pir^2, circumference = 2pi*r; sphere volume = (4/3)pir^3.

Triangle: area = (1/2)baseheight; Pythagorean theorem a^2 + b^2 = c^2 applies only to right triangles.

Arithmetic sequence nth term = a + (n-1)d; geometric sequence nth term = a*r^(n-1).

Average (mean) = sum / count; for evenly spaced sets, mean = median = (first + last)/2.

Probability of independent events = product of individual probabilities; P(not A) = 1 - P(A).

Newton's second law: F = ma; net force and acceleration point in the same direction, and mass resists acceleration.

Speed = distance/time; acceleration = change in velocity/time; velocity is a vector (magnitude plus direction).

Kinetic energy = (1/2)mv^2; gravitational potential energy near Earth = mgh.

Ohm's law: V = IR; in a series circuit current is constant and resistances add; in parallel, voltage is constant across branches.

Photosynthesis: 6CO2 + 6H2O + light -> C6H12O6 + 6O2, occurring in chloroplasts using chlorophyll.

DNA bases pair A-T and G-C; RNA substitutes uracil for thymine.

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

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

Count elements first: number of sides, dots, or shapes often changes by a constant increment across the sequence.

Track rotation direction and step: a shape rotating 90 degrees clockwise each frame returns to its start after four frames.

Alternating patterns: odd-positioned figures may follow one rule while even-positioned figures follow another.

Reflection versus rotation: a reflected figure cannot be rotated into its mirror image unless it is symmetric.

Positional movement: elements often shift one place clockwise per step, with wraparound at the edge.

Size and shading rules frequently toggle: filled becomes unfilled, large becomes small, on alternating steps.

Odd-one-out items: identify the property shared by all but one figure (symmetry, closed shape, line count).

Number-series figures: check differences, then ratios, then alternating sub-sequences before assuming a complex rule.