FTCE GK cheat sheet

The essay is timed at 30 minutes and scored holistically by trained readers, so overall clarity, focus, and development outweigh isolated mechanical errors.

A defensible thesis names the position plus the two or three reasons the essay will develop; it appears in the introduction and is restated in the conclusion.

One body paragraph per reason: topic sentence, specific evidence or example, then an explanatory sentence linking the evidence back to the thesis.

Concede the strongest opposing view and refute it; an acknowledged counterargument with a rebuttal scores higher than ignoring objections.

Conclusions introduce no new evidence; they restate the thesis in fresh wording and state the larger implication.

Transitional markers signal relationships: addition (furthermore), contrast (however), cause (therefore), example (for instance).

Formal academic register excludes second person 'you', contractions, slang, and rhetorical questions.

Suggested time split: about 5 minutes planning and outlining, 20 minutes drafting, 5 minutes proofreading for fragments, run-ons, and agreement.

Off-topic or underdeveloped responses score lower regardless of mechanics; every paragraph must serve the stated thesis.

Subject-verb agreement ignores prepositional phrases between subject and verb: 'The list of items is long,' not 'are.'

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

Two independent clauses require a period, a semicolon, or a comma plus one of the seven coordinating conjunctions (for, and, nor, but, or, yet, so).

A semicolon joins independent clauses without a conjunction or separates series items that already contain internal commas.

Nonessential clauses and appositives take commas; essential ones do not: 'The book that I lost was new.'

An introductory participial phrase must describe the subject of the main clause; otherwise the modifier dangles.

Parallelism: items joined by and, or, or correlative pairs (not only … but also, either … or) must share grammatical form.

Possessive singular adds 's; a plural ending in s adds only an apostrophe; its is possessive, while it's means it is.

Test who/whom by substituting he/him; use between for two items and among for three or more.

Main idea equals topic plus the author's point about it; supporting details only explain or prove that point.

An inference must be supported by textual evidence; any answer requiring outside knowledge is incorrect.

Vocabulary in context: substitute each option into the sentence and test connotation, not just the dictionary's first sense.

Tone is the author's attitude, inferred from adjectives, verbs, and connotation; mood is the feeling created in the reader.

Purpose signals: inform (facts, neutral tone), persuade (opinion, loaded language, call to action), entertain (narrative, figurative), explain (steps, causes).

Organizational patterns carry signal words: sequence (first, then), comparison (similarly, unlike), cause-effect (because, therefore), problem-solution.

Fact claims are verifiable by evidence; opinion claims contain value terms (should, best, beautiful) or predictions.

Bias indicators include loaded words, sweeping generalizations, one-sided evidence, and omitted counterpoints.

Eliminate choices that are true but do not answer the specific question asked, and choices overstated by always or never.

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

Percent relationships: part = rate × whole; percent change = (new − original) ÷ original × 100.

Linear relations: slope m = (y2 − y1)/(x2 − x1); y = mx + b; parallel lines share a slope, perpendicular slopes are negative reciprocals.

Geometry: rectangle A = lw; triangle A = ½bh; circle A = πr² and C = 2πr; rectangular prism V = lwh; cylinder V = πr²h.

Right triangles: a² + b² = c²; 45-45-90 sides are x, x, x√2; 30-60-90 sides are x, x√3, 2x.

Quadratic formula: x = [−b ± √(b² − 4ac)] ÷ (2a), for ax² + bx + c = 0.

Statistics: mean = sum ÷ count; median = middle of ordered data; mode = most frequent value; the median resists outliers.

Probability: P(event) = favorable ÷ total; P(A and B) = P(A)·P(B) for independent events; P(not A) = 1 − P(A).

Rate problems: distance = rate × time; simple interest I = Prt; arrange unit conversions so unwanted units cancel.