Lessons
A short lesson for every CLT skill
Each one takes about two minutes: what the skill asks, how to do it, an example and the traps.
Subject-verb agreementA verb must match its subject in number: one subject takes a singular verb, two or more take a plural verb.PronounsA pronoun must point clearly to one noun and match it in number, and it must take the right case: subject (I, he, who) or object (me, him, whom).Verb tenseTense places an action in time.Sentence boundariesTwo complete sentences cannot be joined with only a comma (a comma splice) or with nothing at all (a run-on), and a piece of a sentence cannot stand alone (a fragment).PunctuationCommas, colons, dashes and apostrophes each have a few jobs.Parallel structureItems in a list or a comparison must have the same grammatical form: all nouns, all "-ing" words, all "to" verbs, all clauses.ModifiersA describing phrase must sit next to the thing it describes.Word choiceThe right word has the exact meaning, the right tone for the passage, and the right idiom (the preposition that goes with it).ConcisionIf two choices are both correct, the shorter one is right, as long as it keeps the meaning.TransitionsA transition word tells the reader how two ideas relate: contrast, cause, addition, example or sequence.RelevanceSome questions ask whether a sentence should be added or deleted.OrganizationOrganization questions ask where a sentence belongs, or which sentence best opens or closes a paragraph.
Main idea and purposeThese questions ask what the whole passage is mainly saying, or why the author wrote it.Vocabulary in contextYou are asked what a word means as it is used in one sentence.InferenceAn inference is what the passage strongly suggests without saying it outright.DetailDetail questions ask what the passage actually says.Tone and attitudeTone questions ask how the author feels about the subject: admiring, skeptical, ironic, urgent, detached.Function of a partThese questions ask why the author included a sentence, a quotation, an example or a paragraph.AnalogyAnalogy questions ask which situation is most like one in the passage.Argument and evidenceThese questions ask what an author claims, what supports it, and what would strengthen or weaken it.RhetoricRhetoric questions ask about how a writer persuades: repetition, rhetorical questions, metaphor, contrast, appeals to shared values, and the effect of word choices.StructureStructure questions ask how the passage is organized: problem and solution, claim and support, chronology, comparison, objection and reply.ComparisonPaired passages, or two views inside one passage, are compared: where the authors agree, where they differ, and how one would answer the other.Data and the textEvery CLT reading section has a science passage with a table or graph.Precision of meaningThese questions ask which word or phrase states the author's idea most exactly, or what a phrase means precisely in context.
Linear equationsSolve for the unknown by doing the same thing to both sides until it stands alone.Systems of equationsTwo equations, two unknowns.PercentsA percent is a fraction of 100.Ratios and proportionsA ratio compares parts.Exponents and radicalsExponent rules let you simplify without computing: multiply means add exponents, divide means subtract, a power of a power means multiply.QuadraticsA quadratic has an x² term.FunctionsA function takes an input and gives one output.Lines and slopeSlope is rise over run: (y₂ − y₁) ÷ (x₂ − x₁).TrianglesKnow the angle sum (180°), the Pythagorean theorem, the common right triangles, and that similar triangles have proportional sides.Angles and polygonsAngles on a straight line add to 180°, around a point to 360°.CirclesArea is πr², circumference is 2πr.Area and volumeKnow the area of rectangles, triangles (½bh) and circles, and the volume of boxes (lwh) and cylinders (πr²h).AveragesAverage = sum ÷ count.Number propertiesQuestions on odd and even, primes, factors, multiples, divisibility and remainders.SequencesAn arithmetic sequence adds the same number each time; a geometric sequence multiplies by the same number.Counting and probabilityProbability is favorable outcomes ÷ possible outcomes.Rates and workDistance = rate × time, and work = rate × time.InequalitiesSolve inequalities like equations, with one rule: multiplying or dividing by a negative number flips the sign.TrigonometryIn a right triangle, sine = opposite ÷ hypotenuse, cosine = adjacent ÷ hypotenuse, tangent = opposite ÷ adjacent (SOH CAH TOA).LogicLogic questions test what must follow from given statements.