HSPT cheat sheet

Analogies: state the relationship in a sentence (e.g., 'A glove covers a hand'), then apply the same sentence to the answer choices.

Common analogy bridges: part-to-whole, cause-to-effect, synonym, antonym, category-to-member, tool-to-user, function.

Antonym items: eliminate answer choices that are synonyms of the stem word before choosing.

Synonym items: choose the closest meaning in context, not the most common meaning of the word.

Word classification: a valid group needs one shared property that excludes every other option; test each option against the rule.

Logic/ordering puzzles: draw positions as blank slots and fill only what each clue forces, then test remaining options.

Prefixes that flip meaning: un-, in-/im-/il-/ir-, dis-, non-, anti-, mis-.

Root clues: -dict- (say), -spect- (look), -port- (carry), -scrib-/-script- (write), -cred- (believe), -bene- (good).

If two answer choices both seem correct, prefer the narrower, more specific relationship over a loose one.

Percent change = (new − old) ÷ old × 100; a 20% increase then 20% decrease yields 96% of the original, not 100%.

Percent of a number: part = percent × whole; convert percent to decimal by dividing by 100.

Average (mean) = sum ÷ count; sum = average × count, so a missing value = (target sum) − (known sum).

Ratio a:b with total T: each share = (its ratio part ÷ total ratio parts) × T.

Work/rate: combined rate = 1/a + 1/b per unit time; time together = ab ÷ (a + b).

Distance = rate × time; for average speed over equal distances, average speed = 2xy ÷ (x + y).

Number-series items: check differences first, then ratios, then alternating or two interleaved sequences.

Probability of a single event = favorable outcomes ÷ total outcomes; probabilities of all outcomes sum to 1.

Estimate before computing: rounding operands often identifies the only plausible answer choice.

Main idea = what the whole passage is about; a detail answer is wrong even if it is stated in the text.

Supporting details must be traceable to a specific sentence; if it requires outside knowledge, it is not supported.

Inference answers must be forced by the text - if a reasonable person could disagree, it is too strong.

Tone/attitude words: objective, critical, enthusiastic, nostalgic, skeptical, neutral; match the author's word choices.

Sequence questions: locate time-order words (first, then, after, finally) and map events to them.

Vocabulary in context: substitute each answer choice into the sentence and keep the one preserving the passage's meaning.

Passage organization: cause-effect, compare-contrast, chronological, problem-solution, or main idea plus examples.

Words like all, never, always, only, must signal overstatement and usually mark a wrong answer.

Author's purpose verbs: to persuade, to inform, to entertain, to describe, to compare - tie the verb to the text's structure.

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

Fractions: a/b + c/d uses common denominator bd; a/b ÷ c/d = a/b × d/c.

Percent ↔ decimal ↔ fraction: 45% = 0.45 = 9/20.

Area: rectangle lw, triangle ½bh, circle πr²; circumference = 2πr or πd.

Volume: rectangular prism lwh; cylinder πr²h.

Angles: straight line = 180°, triangle interior = 180°, quadrilateral interior = 360°.

Mean vs. median: median is the middle value of an ordered list; with an even count, average the two middle values.

Integer rules: negative × negative = positive; negative × positive = negative; subtracting a negative adds.

Solve for x by undoing operations in reverse order, applying the same operation to both sides.

Subject-verb agreement: ignore prepositional phrases between subject and verb; singular subject takes singular verb.

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

Comma rules: separate items in a series, set off introductory phrases, and join two independent clauses only with a conjunction.

Run-on fix options: period, semicolon, or comma plus coordinating conjunction (for, and, nor, but, or, yet, so).

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

Comparative/superlative: two items use -er/more; three or more use -est/most.

Dangling modifier: the noun right after an introductory phrase must be the one performing the action.

Capitalize proper nouns, the first word of a sentence, and titles before names; do not capitalize seasons or general subjects.

Choose the answer that keeps the sentence grammatically complete: every clause needs a subject and a working verb.

Pattern completion: test one rule at a time (add, subtract, multiply, alternate) against all given terms before choosing.

Analogous-figure items: identify the transformation (rotation, reflection, size change, shading) and apply the identical transformation.

Classification: the correct group shares a rule that every other option violates by at least one feature.

Ordering/sequencing: convert clues into inequalities (A before B) and chain them; the item forced into one slot is the anchor.

Memory/attention items: chunk information into groups of 3-4 rather than rehearsing item by item.

If-then logic: 'if P then Q' forbids P with not-Q; it does not forbid Q without P.

Elimination beats certainty: remove options that violate a stated constraint, then choose among survivors.

Spatial reasoning: track orientation separately from position; a shape can move without rotating.