- Main idea
- The central point a passage conveys — what the whole text is mostly about.
- Supporting detail
- A fact, example, statistic, or reason that explains or develops the main idea.
- Theme
- The underlying message or insight about life that a literary text explores.
- Topic sentence
- The sentence (often first) that states a paragraph's main point.
- Inference
- A logical conclusion drawn from textual evidence plus reasoning — not stated outright.
- Textual evidence
- Specific words or lines from a passage used to support a claim or answer.
- Command of evidence
- Choosing the detail or line that best supports a given conclusion.
- Word in context
- A word's meaning as it is actually used in a sentence, not just its dictionary definition.
- Connotation
- The implied or emotional meaning of a word beyond its literal definition.
- Denotation
- The literal, dictionary meaning of a word.
- Author's purpose
- The reason a text was written — to inform, persuade, entertain, or explain.
- Tone
- The author's attitude toward the subject, shown through word choice.
- Mood
- The feeling or atmosphere a text creates in the reader.
- Point of view
- The perspective from which a text is told or argued.
- Synthesis
- Combining ideas across two or more texts to reach a broader conclusion.
- Paired passages
- Two related passages compared on the same topic on the Reading test.
- Cross-text connection
- A relationship (agreement, disagreement, extension) between two passages.
- Literary text
- Imaginative writing such as fiction, poetry, and drama.
- Informational text
- Nonfiction such as essays, articles, editorials, and documents.
- Figurative language
- Language meaning something beyond the literal — metaphor, simile, personification.
- Metaphor
- A comparison that states one thing IS another ("time is money").
- Simile
- A comparison using "like" or "as" ("brave as a lion").
- Text structure
- How a text is organized — cause/effect, compare/contrast, sequence, problem/solution.
- Cause and effect
- A structure linking events to their results.
- Compare and contrast
- A structure showing similarities and differences between ideas.
- Sequence
- A structure presenting events or steps in order.
- Summarize
- Restate a passage's main points briefly in your own words.
- Paraphrase
- Restate a specific idea in different words while keeping its meaning.
- Context clues
- Hints in surrounding text — definitions, examples, contrasts — that reveal a word's meaning.
- Central idea
- The most important point a passage makes; the ACCUPLACER term for main idea.
- Claim
- A debatable position an author argues for.
- Counterargument
- A point that opposes the author's claim, often addressed to strengthen it.
- Rhetorical question
- A question asked for effect, not for an answer.
- Implication
- Something a text suggests without stating directly.
- Explicit information
- Information stated directly in the text.
- Implicit information
- Information implied or suggested, requiring inference.
- Information and Ideas
- An ACCUPLACER Reading category: central ideas, evidence, and inferences.
- Craft and Structure
- An ACCUPLACER Reading category: word meaning, text structure, purpose, and point of view.
- Vocabulary item
- A single-sentence ACCUPLACER Reading question about a word's meaning in context.
- Analyze
- Break a text into parts to examine how they work and what they mean.
- Evaluate
- Judge the quality, strength, or logic of an argument or evidence.
- Bias
- A one-sided perspective that can color how a text presents information.
- Objective writing
- Writing that presents facts without personal opinion.
- Subjective writing
- Writing that expresses personal opinions or feelings.
- Narrator
- The voice telling a story in a literary text.
- Genre
- A category of text, such as fiction, poetry, essay, or editorial.
- Argument
- A claim supported by reasons and evidence in a text.
- Evidence-based answer
- An answer choice you can prove with a specific line in the passage.
- Drawing conclusions
- Combining stated facts to reach a logical end point.
- Primary source
- A firsthand account or original document.
- Secondary source
- A work that analyzes or interprets primary sources.
- Persuasive text
- Writing that aims to convince the reader of a position.
- Audience
- The intended readers a text is written for.
- Expression of Ideas
- An ACCUPLACER Writing category: development, organization, and effective language use.
- Standard English Conventions
- An ACCUPLACER Writing category: sentence structure, usage, and punctuation.
- Development
- Stating a clear point and supporting it with relevant detail.
- Organization
- Arranging ideas in a logical order with effective openings and closings.
- Effective language use
- Choosing concise, precise words that fit the style and tone.
- Concision
- Expressing an idea in as few words as needed; cutting wordiness.
- Subject-verb agreement
- A singular subject takes a singular verb; a plural subject takes a plural verb.
- Pronoun-antecedent agreement
- A pronoun must match the noun it refers to in number and gender.
- Pronoun case
- Using the correct subjective (I, he) or objective (me, him) pronoun form.
- Verb tense
- The form of a verb showing time; keep it consistent unless the time changes.
- Parallel structure
- Using the same grammatical form for items in a list, pair, or comparison.
- Modifier
- A word or phrase that describes another; place it next to what it modifies.
- Dangling modifier
- A modifier with no clear word to describe, creating confusion.
- Misplaced modifier
- A modifier positioned so it seems to describe the wrong word.
- Sentence fragment
- An incomplete sentence missing a subject, verb, or complete thought.
- Run-on sentence
- Two complete sentences joined without proper punctuation or a conjunction.
- Comma splice
- Joining two complete sentences with only a comma — a kind of run-on.
- Independent clause
- A group of words with a subject and verb that can stand alone as a sentence.
- Dependent clause
- A clause with a subject and verb that cannot stand alone.
- Coordinating conjunction
- A joining word — for, and, nor, but, or, yet, so (FANBOYS).
- Subordinating conjunction
- A word (because, although, when) that begins a dependent clause.
- Transition
- A word or phrase signaling the logical relationship between ideas.
- Contrast transition
- However, but, although — signals an opposing idea.
- Cause/effect transition
- Therefore, because, consequently — signals a result or reason.
- Addition transition
- Furthermore, moreover, also — signals an added point.
- Example transition
- For instance, for example — signals an illustration.
- Comma
- Punctuation separating items, clauses, or introductory elements.
- Semicolon
- Punctuation joining two closely related independent clauses.
- Colon
- Punctuation introducing a list, explanation, or quotation.
- Apostrophe
- Punctuation showing possession (Maria's) or contraction (don't).
- Its vs. it's
- "Its" shows possession; "it's" is the contraction of "it is."
- Their/there/they're
- "Their" = possession; "there" = place; "they're" = they are.
- Your vs. you're
- "Your" shows possession; "you're" is the contraction of "you are."
- Affect vs. effect
- "Affect" is usually a verb (to influence); "effect" is usually a noun (a result).
- Accept vs. except
- "Accept" means to receive; "except" means to exclude.
- Active voice
- The subject performs the action ("The team won the game").
- Passive voice
- The subject receives the action ("The game was won by the team").
- Redundancy
- Needless repetition of an idea; ACCUPLACER rewards cutting it.
- Wordiness
- Using more words than needed; choose the most concise correct option.
- Thesis
- The central claim or position an essay argues, stated near the start.
- WritePlacer
- The ACCUPLACER essay test, scored 1–8 on six criteria.
- Purpose and Focus
- A WritePlacer criterion: a clear, sustained position.
- Organization and Structure
- A WritePlacer criterion: logical arrangement of ideas.
- Development and Support
- A WritePlacer criterion: reasons and examples that develop the thesis.
- Sentence Variety and Style
- A WritePlacer criterion: varied sentences and precise word choice.
- Mechanical Conventions
- A WritePlacer criterion: grammar, usage, punctuation, and spelling.
- Critical Thinking
- A WritePlacer criterion: reasoning and insight in the argument.
- Topic sentence (writing)
- A sentence stating a paragraph's main idea, supporting the thesis.
- Conclusion
- The final paragraph that restates the position and wraps up the argument.
- Verb form
- The correct form of a verb (tense, agreement, participle) for the sentence.
- Antecedent
- The noun a pronoun refers back to.
- Comparative form
- The -er or 'more' form comparing two things (faster, more careful).
- Superlative form
- The -est or 'most' form comparing three or more (fastest, most careful).
- Then vs. than
- "Then" relates to time; "than" is used in comparisons.
- Quotation marks
- Punctuation marking exact words spoken or quoted.
- Capitalization
- Begin sentences and proper nouns with a capital letter.
- Idiom
- A standard expression whose meaning isn't literal ("interested in," not "interested on").
- Whole number
- A non-negative number with no fraction or decimal part (0, 1, 2, 3, …).
- Place value
- The value of a digit based on its position (tens, hundreds, …).
- Numerator
- The top number of a fraction — how many parts you have.
- Denominator
- The bottom number of a fraction — how many equal parts in the whole.
- Proper fraction
- A fraction less than 1 (numerator smaller than denominator).
- Improper fraction
- A fraction equal to or greater than 1 (numerator ≥ denominator).
- Mixed number
- A whole number combined with a fraction, such as 2½.
- Common denominator
- A shared denominator used to add or subtract fractions.
- Least common denominator
- The smallest common denominator for two or more fractions.
- Adding fractions
- Use a common denominator, then add the numerators.
- Multiplying fractions
- Multiply numerators together and denominators together, then simplify.
- Dividing fractions
- Multiply by the reciprocal of the second fraction (flip and multiply).
- Reciprocal
- A fraction flipped upside down; ¾ becomes 4⁄3.
- Simplify a fraction
- Divide numerator and denominator by their greatest common factor.
- Decimal
- A number using a decimal point to show parts of a whole (0.75).
- Adding decimals
- Line up the decimal points, then add.
- Multiplying decimals
- Multiply as whole numbers, then place the decimal by counting decimal places.
- Rounding
- Replacing a number with a nearby simpler value to a given place.
- Percent
- A part per hundred; convert to a decimal by dividing by 100 (25% = 0.25).
- Percent of a number
- Convert the percent to a decimal and multiply (20% of 80 = 0.20 × 80 = 16).
- Percent increase
- Multiply by (1 + rate); a 25% increase is × 1.25.
- Percent decrease
- Multiply by (1 − rate); a 30% discount is × 0.70.
- Percent change
- (new − old) ÷ old × 100.
- Finding the whole
- If a part is a percent of a number, divide the part by the decimal form.
- Equivalent forms
- The same value as a fraction, decimal, and percent (½ = 0.5 = 50%).
- Order of operations
- PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract.
- Factor
- A number that divides evenly into another number.
- Multiple
- The product of a number and an integer (multiples of 4: 4, 8, 12, …).
- Greatest common factor
- The largest factor shared by two or more numbers.
- Least common multiple
- The smallest multiple shared by two or more numbers.
- Prime number
- A whole number greater than 1 divisible only by 1 and itself.
- Composite number
- A whole number with more than two factors.
- Integer
- A whole number or its negative (… −2, −1, 0, 1, 2 …).
- Absolute value
- A number's distance from 0, always non-negative (|−5| = 5).
- Estimating
- Rounding to friendly numbers to get a quick approximate answer.
- Ratio
- A comparison of two quantities, written 3:4 or 3⁄4.
- Number comparisons
- Ordering values by converting them to one common form first.
- Decimal to fraction
- Write the decimal over its place value and simplify (0.25 = 25⁄100 = ¼).
- Fraction to decimal
- Divide the numerator by the denominator (¾ = 3 ÷ 4 = 0.75).
- Negative numbers
- Values less than 0; subtracting a negative is the same as adding.
- Markup
- An amount added to a cost to set a selling price.
- Discount
- An amount subtracted from a price; often a percent off.
- Sales tax
- A percent added to a purchase price.
- Tip
- A percent of a bill added for service.
- Sum
- The result of addition.
- Difference
- The result of subtraction.
- Product
- The result of multiplication.
- Quotient
- The result of division.
- Average
- The mean — add the values and divide by how many there are.
- Square (number)
- A number multiplied by itself (5² = 25).
- Square root
- A value that, multiplied by itself, gives the number (√25 = 5).
- Scientific notation
- Writing a number as a digit times a power of 10 (3.2 × 10⁴).
- Divisibility
- Whether one number divides into another with no remainder.
- Remainder
- What is left over after division.
- Rational number
- Any number that can be written as a fraction of two integers.
- Irrational number
- A number that cannot be written as a fraction (√2, π).
- Proportion
- An equation stating two ratios are equal; solved by cross-multiplying.
- Cross-multiplying
- Multiplying across an equals sign to solve a proportion.
- Unit rate
- A ratio per single unit, such as miles per hour or cost per item.
- Proportional relationship
- Two quantities that change at a constant ratio.
- Exponent
- A raised number showing repeated multiplication (2³ = 8).
- Product rule (exponents)
- Same base: add the exponents (xᵃ · xᵇ = xᵃ⁺ᵇ).
- Quotient rule (exponents)
- Same base: subtract the exponents (xᵃ ÷ xᵇ = xᵃ⁻ᵇ).
- Power of a power
- Multiply the exponents: (xᵃ)ᵇ = xᵃᵇ.
- Zero exponent
- Any nonzero base to the 0 power equals 1.
- Negative exponent
- x⁻ⁿ equals 1 ÷ xⁿ.
- Algebraic expression
- A combination of numbers, variables, and operations with no equals sign.
- Variable
- A letter standing for an unknown number.
- Coefficient
- The number multiplying a variable (in 5x, 5 is the coefficient).
- Like terms
- Terms with the same variable and exponent that can be combined.
- Distributive property
- a(b + c) = ab + ac.
- Linear equation
- An equation whose graph is a straight line; variables to the first power.
- Solving equations
- Isolate the variable using inverse operations on both sides.
- Slope
- Rise over run = (y₂ − y₁)/(x₂ − x₁); the m in y = mx + b.
- Y-intercept
- Where a line crosses the y-axis (x = 0); the b in y = mx + b.
- Slope-intercept form
- y = mx + b, where m is slope and b is the y-intercept.
- X-intercept
- Where a line crosses the x-axis (y = 0).
- Linear inequality
- Like a linear equation but with <, >, ≤, or ≥.
- Flipping the inequality
- Reverse the sign when multiplying or dividing by a negative.
- Coordinate plane
- A grid formed by a horizontal x-axis and vertical y-axis.
- Ordered pair
- A point's coordinates written (x, y).
- Set
- A collection of distinct objects or numbers.
- Union
- All elements in either set, written A ∪ B.
- Intersection
- Elements common to both sets, written A ∩ B.
- Probability
- Favorable outcomes ÷ total outcomes — a number from 0 to 1.
- Independent events
- Events where one outcome does not affect the other.
- Mean
- The average — sum of values divided by how many there are.
- Median
- The middle value of a data set in order.
- Mode
- The value that appears most often in a data set.
- Range (statistics)
- The highest value minus the lowest value.
- Outlier
- A value far from the others that can skew the mean.
- Scatterplot
- A graph of paired data points showing a relationship.
- Positive correlation
- As one variable rises, the other tends to rise.
- Negative correlation
- As one variable rises, the other tends to fall.
- Line of best fit
- A trend line through a scatterplot summarizing the data.
- Box plot
- A graph showing the median, quartiles, and range of data.
- Histogram
- A bar graph of frequencies across value ranges.
- Area
- The space inside a 2D figure; rectangle area = length × width.
- Perimeter
- The distance around a 2D figure.
- Circumference
- The distance around a circle, 2πr.
- Volume
- The space inside a 3D solid.
- Pythagorean theorem
- In a right triangle, a² + b² = c² (c is the hypotenuse).
- Geometry concepts
- Area, perimeter, volume, angles, and the Pythagorean theorem on QAS and AAF.
- Factoring
- Rewriting an expression as a product of simpler factors.
- Greatest common factor (algebra)
- Factor out the largest factor shared by every term first.
- Trinomial
- A polynomial with three terms, such as x² + 5x + 6.
- Factoring a trinomial
- Find two numbers that multiply to the constant and add to the middle coefficient.
- Difference of squares
- a² − b² = (a − b)(a + b).
- Perfect-square trinomial
- a² + 2ab + b² = (a + b)².
- Quadratic equation
- An equation with a squared variable: ax² + bx + c = 0.
- Parabola
- The U-shaped graph of a quadratic function.
- Zero-product property
- If a product is 0, at least one factor is 0 — used to solve factored quadratics.
- Quadratic formula
- x = (−b ± √(b² − 4ac)) ÷ 2a.
- Discriminant
- b² − 4ac; its sign tells how many real solutions a quadratic has.
- Function
- A rule assigning exactly one output to each input; written f(x).
- Function notation
- f(x) names the output of a function for input x.
- Evaluating a function
- Substitute the input: if f(x) = 2x + 1, then f(3) = 7.
- Domain
- The set of all allowed input values (x) of a function.
- Range (functions)
- The set of all possible output values (y) of a function.
- Vertical-line test
- A graph is a function if no vertical line crosses it more than once.
- Linear function
- A function whose graph is a straight line, f(x) = mx + b.
- Quadratic function
- A function of the form f(x) = ax² + bx + c.
- Vertex
- The highest or lowest point of a parabola.
- Axis of symmetry
- The vertical line through a parabola's vertex that mirrors it.
- Radical
- A root expression, such as a square root √x.
- Radical equation
- An equation with a variable under a radical.
- Solving radical equations
- Isolate the radical, then square both sides; check for extraneous roots.
- Extraneous solution
- A solution introduced by squaring that doesn't satisfy the original equation.
- Rational expression
- A fraction whose numerator and denominator are polynomials.
- Rational equation
- An equation containing rational expressions; clear denominators to solve.
- Polynomial
- An expression of terms with whole-number exponents (3x³ − 2x + 1).
- Degree of a polynomial
- The highest exponent in the polynomial.
- Leading coefficient
- The coefficient of the highest-degree term.
- Exponential equation
- An equation with a variable in the exponent; models growth and decay.
- Exponential growth
- A quantity increasing by a constant percent over equal intervals.
- Exponential decay
- A quantity decreasing by a constant percent over equal intervals.
- Logarithm
- The inverse of an exponent: logₐ(b) asks 'a to what power gives b?'
- Log-exponent conversion
- logₐ(b) = c means aᶜ = b.
- Common logarithm
- A logarithm with base 10, written log(x).
- Natural logarithm
- A logarithm with base e, written ln(x).
- Trigonometry
- The study of relationships between angles and sides in triangles.
- Sine
- In a right triangle, opposite ÷ hypotenuse (SOH).
- Cosine
- In a right triangle, adjacent ÷ hypotenuse (CAH).
- Tangent
- In a right triangle, opposite ÷ adjacent (TOA).
- SOH-CAH-TOA
- Mnemonic for sine, cosine, and tangent ratios.
- Hypotenuse
- The longest side of a right triangle, opposite the right angle.
- Right triangle
- A triangle with one 90° angle.
- System of equations
- Two or more equations solved together by substitution or elimination.
- Substitution method
- Solve one equation for a variable and substitute into the other.
- Elimination method
- Add or subtract equations to cancel a variable.
- Linear application
- A real-world problem modeled with a linear equation (shared QAS/AAF topic).
- Geometry concepts (AAF)
- Area, volume, angles, and the Pythagorean theorem appearing on AAF.
