PA State Trooper cheat sheet

Main idea: locate the topic sentence, most often the first or last sentence of a paragraph; every other sentence supplies who, what, when, where, why, or how.

An inference must be supported by the text; if a choice requires outside knowledge or an unstated leap, it is wrong even when it sounds reasonable.

For EXCEPT and NOT questions, test all four choices against the passage: three are confirmed, one contradicts or lacks support.

Author's tone comes from connotation of adjectives and verbs, not from the topic itself; common labels are positive, negative, neutral, critical, and humorous.

Cause-and-effect items hinge on signal words: because, since, therefore, thus, consequently, as a result, due to, and leads to.

Vocabulary in context: substitute each option into the sentence and re-read; the correct choice preserves the sentence's original logic.

Sequence questions are answered by chronological markers: first, then, next, after, meanwhile, finally, and by verb tense changes.

On paired-passage sets, identify where the two authors agree and disagree before answering relationship or 'would agree' items.

Distractor patterns: true but not answering the question, extreme wording (always, never, all, none), and reversal of cause and effect.

Subject-verb agreement: the verb agrees with the subject, not with a noun inside an intervening prepositional phrase ('the box of files is').

Pronoun case: use subject pronouns (I, he, she, they, who) for subjects and object pronouns (me, him, her, them, whom) after prepositions and verbs.

Who vs. whom: substitute he or him; if 'he' fits the slot use who, if 'him' fits use whom.

Comma splice: two independent clauses joined by only a comma; repair with a period, a semicolon, or a comma plus and/but/or/so/yet.

A semicolon joins two independent clauses without a conjunction and separates list items that already contain commas; it never introduces a dependent clause.

Apostrophes: singular possessive adds 's, plural possessive adds ' after the final s, 'its' is possessive, and 'it's' means it is or it has.

Dangling modifier: the introductory phrase must describe the subject of the main clause, which follows immediately after the comma.

Parallel structure: items joined by and, or, not only...but also, or in a comparison must share the same grammatical form.

Frequently confused pairs: affect (verb) vs. effect (noun), lie (recline) vs. lay (place something), then (time) vs. than (comparison), fewer (countable) vs. less (mass).

Percent change = (new value − old value) ÷ old value × 100; the divisor is always the original amount, and a negative result is a decrease.

Part = percent × whole; whole = part ÷ percent; percent = part ÷ whole, converted to a decimal before multiplying.

Average = sum ÷ count; missing value = (average × count) − sum of the known values.

Proportions: set up a/b = c/d and cross-multiply (ad = bc); keep like units in the same position on both sides.

Distance = rate × time; rate = distance ÷ time; time = distance ÷ rate. Convert minutes to hours before multiplying by an hourly rate.

Combined work rate: 1/t = 1/a + 1/b; the combined time t is always less than the faster worker's individual time.

Area and perimeter: rectangle A = lw, triangle A = ½bh, circle A = πr² and C = 2πr; a triangle's height is perpendicular to its base.

Pythagorean theorem a² + b² = c², where c is the hypotenuse; common triples are 3-4-5, 5-12-13, 8-15-17, 7-24-25, and their multiples.

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

Contrapositive: 'If P then Q' is logically equivalent to 'If not Q then not P'; the converse ('if Q then P') and inverse are not equivalent.

Necessary condition must hold for the result to occur; sufficient condition guarantees the result. Confusing the two is the standard flaw tested in conditional items.

Syllogism chain: All A are B, all B are C, therefore all A are C. Follow the arrows in one direction only; the reverse is not valid.

Ordering and grouping puzzles: draw slots or a diagram, place the most constrained item first, and eliminate any answer choice that violates a single stated rule.

Weaken an argument by attacking the hidden assumption linking evidence to conclusion or by offering an alternative explanation; strengthen by confirming that assumption.

Analogies: state the precise relationship in a sentence (part to whole, cause to effect, degree, function) before evaluating the choices.

Number and letter series: check successive differences, then ratios, then alternating subsequences, squares, primes, and alphabet positions (A = 1).

Percent and rate word problems: identify the whole, the part, and the unknown before computing; answer the question actually asked, not an intermediate value.

Data-sufficiency style items: test each statement alone, then together; only a statement that pins down a single value is sufficient.

Short-term memory holds roughly four to seven items for about 15 to 30 seconds without rehearsal; chunking raises the effective amount.

Chunking groups separate items into meaningful units, such as splitting a ten-digit number into a three-three-four pattern.

Serial position effect: first (primacy) and last (recency) items in a list are recalled best, while middle items are weakest.

Spacing effect: several short rehearsal sessions over time outperform the same total time massed into a single session.

Method of loci attaches each item to a landmark along a familiar route and retrieves them by mentally walking the route in order.

Change blindness: unattended details change without being noticed, so compare a scene systematically (left to right, top to bottom) rather than staring at one point.

Record observable facts when describing a person or vehicle: relative height against a fixed object, clothing colors top to bottom, direction and speed of travel, not conclusions.

Recognition (choosing from options) is generally more accurate than free recall (describing from memory), so photo arrays and lineups exploit a stronger memory process.