PSAT/NMSQT key terms

The main point a passage communicates about its topic, stated or implied. Questions often ask you to choose the statement that best captures the whole text rather than one detail.

The reason an author wrote a text, such as to explain, persuade, or describe. It differs from the central idea because it names the author's goal rather than the content of the message.

A specific fact, example, or statistic used to back up a broader claim. Identifying which detail supports which claim is a common Reading and Writing task.

A conclusion drawn from evidence in the text plus reasonable reasoning, rather than stated outright. Correct inferences must be tightly supported by the passage, not merely plausible in real life.

Information stated directly in the text, leaving no need for interpretation. Contrasted with implied meaning, which the reader must construct from clues the author provides.

A meaning suggested but not directly stated, often signaled by word choice, sentence order, or what the author leaves out. Recognizing implications supports questions about the author's attitude or intent.

An assertion that is supported by specific data, quotations, or findings cited in the passage. Questions may ask which piece of evidence best strengthens or weakens such a claim.

A position that opposes the main argument, often acknowledged and then rebutted by the author. Recognizing it helps you track the structure of an argumentative passage.

An acknowledgment that part of an opposing view is valid, usually followed by a qualification or rebuttal. Concessions often appear after words like although, granted, or admittedly.

A limitation or narrowing of a claim, such as adding only under certain conditions. Qualified claims are usually more defensible than absolute ones and are often the correct answer in reasoning questions.

A claim stated too broadly to be accurate, often marked by words like all, always, never, or everyone. Recognizing overgeneralization helps you eliminate wrong answer choices.

Wording that softens a claim, such as may, tends to, often, or suggests. Hedged statements are usually easier to defend and appear frequently in correct answer choices.

The author's attitude toward the subject, conveyed through word choice and sentence structure. Tone words include critical, nostalgic, cautious, and enthusiastic, and must match the whole passage's feel.

An author's choice of words, especially the connotation and precision of that choice. Analyzing diction helps explain why a passage feels formal, informal, technical, or emotionally charged.

The associations or emotional coloring a word carries beyond its literal meaning. For example, thrifty and stingy share a denotation but differ sharply in connotation.

The literal, dictionary meaning of a word, independent of emotional associations. Distinguishing denotation from connotation is essential for precision questions and word-choice items.

A word or phrase that signals the logical relationship between ideas, such as however, therefore, or similarly. Choosing the correct transition requires identifying whether ideas contrast, cause, or add.

The way sentences and paragraphs connect smoothly through pronouns, repeated terms, and transitions. Cohesion questions ask which revision best links ideas without introducing confusion.

The combination of speaker, audience, purpose, context, and message that shapes a text. Understanding it helps you judge whether a passage's approach suits its intended readers.

A strategy used to persuade, commonly classified as appeals to logic, character, or emotion. Identifying which appeal an author uses supports questions about how an argument works.

A flaw in reasoning that weakens an argument, such as attacking a person instead of a claim or assuming a cause from mere correlation. Spotting fallacies helps evaluate argument quality.

An unstated belief an argument depends on to reach its conclusion. Questions may ask which assumption, if false, would most weaken the reasoning in a passage.

The rule that a verb must match its subject in number, as in the dog runs versus the dogs run. Interrupting phrases between subject and verb often hide agreement errors on the test.

The requirement that a pronoun match the noun it refers to in number and person. Singular nouns such as each or team take singular pronouns, which trips up many test takers.

A pronoun whose referent is unclear because more than one noun could fit. Revising for clarity often means replacing the pronoun with a specific noun.

The position of descriptive words or phrases so they clearly attach to the intended word. A misplaced or dangling modifier creates confusing or unintended meaning in a sentence.

An incomplete sentence missing a subject, a verb, or a complete thought. On the test, fragments often appear as tempting choices in sentence-boundary questions.

Two or more independent clauses joined without correct punctuation or a conjunction. Fixes include a period, a semicolon, or a comma plus a coordinating conjunction.

A specific run-on error in which a comma alone joins two independent clauses. Replacing the comma with a semicolon or adding a conjunction corrects it.

A group of words containing a subject and verb that can stand alone as a complete sentence. Recognizing it is central to punctuation questions involving commas, semicolons, and colons.

The use of matching grammatical forms for items in a list or comparison, such as hiking, swimming, and biking. Parallelism makes sentences clearer and is frequently tested in revision items.

An equation whose graph is a straight line, typically written as y = mx + b, where m is the slope and b is the y-intercept. It represents a constant rate of change.

The measure of a line's steepness, calculated as the change in y divided by the change in x between two points. It also equals the constant rate of change in a linear relationship.

The point where a graph crosses the y-axis, occurring when x equals zero. In a linear equation y = mx + b, the value b is the y-intercept.

The point where a graph crosses the x-axis, found by setting y equal to zero. In word problems it often represents the input value that makes an output reach zero.

Two or more equations considered together, whose solution satisfies all of them at once. Solutions can be found by substitution, elimination, or graphing the equations.

A situation in which a system of equations has no point satisfying every equation, occurring when lines are parallel. For linear equations, this means equal slopes but different y-intercepts.

A situation in which every point on one line also lies on the other, so the equations describe the same line. This occurs when equations are equivalent after simplification.

How much one quantity changes relative to another, often expressed as a ratio of change in output to change in input. In linear contexts it equals the slope.

A relationship in which two quantities vary at a constant ratio, graphed as a line through the origin. It can be written as y = kx, where k is the constant of proportionality.

An equation of degree two, commonly written as ax² + bx + c = 0 with a not equal to zero. Its graph is a parabola, and it can have zero, one, or two real solutions.

The U-shaped curve that is the graph of a quadratic function. It opens upward when the leading coefficient is positive and downward when it is negative.

The highest or lowest point of a parabola, located on its axis of symmetry. In vertex form y = a(x − h)² + k, the vertex is the point (h, k).

The vertical line that divides a parabola into mirror-image halves, given by x = −b/(2a) in standard form. It passes through the vertex of the parabola.

Rewriting an expression as a product of simpler expressions, such as turning x² − 9 into (x − 3)(x + 3). It is a key method for solving quadratic equations.

The rule that if a product equals zero, then at least one factor must equal zero. It allows you to solve factored equations by setting each factor to zero.

An input value for which the function's output equals zero, also called a root or x-intercept. Zeros correspond to where the graph crosses the x-axis.

A pattern in which a quantity increases by a constant percentage over each interval, modeled by y = a(1 + r)^t. The graph curves upward and grows faster as the input increases.

A pattern in which a quantity decreases by a constant percentage over each interval, modeled by y = a(1 − r)^t with a base between zero and one. It approaches zero without reaching it.

A function in which the variable appears in the exponent, generally written as y = a·b^x with b positive and not equal to one. It models repeated percentage change.

A way of writing a function's output for a given input, such as f(3) = 7. It lets you substitute values and interpret functions in applied contexts.

The set of all allowable input values for a function and the set of all resulting output values. In word problems, the domain is often restricted by real-world limits such as nonnegative time.

A function that reverses another function's effect, so applying one and then the other returns the original input. Its graph is a reflection across the line y = x.

Expressions that produce the same value for every allowable input, even though they look different. Skills like distributing, combining like terms, and factoring create equivalent forms.

A rate expressed per single unit of a quantity, such as miles per one hour or dollars per one item. Unit rates simplify comparisons and often appear in ratio word problems.

The size of a change expressed as a percentage of the original amount, calculated as the change divided by the original value times 100. It is used in discount, markup, and growth problems.

The use of sine, cosine, and tangent ratios to relate the angles and side lengths of right triangles. These ratios compare sides such as opposite over hypotenuse.

The relationship a² + b² = c² for right triangles, where c is the hypotenuse. It is used to find unknown side lengths and distances in coordinate geometry.

Triangles with equal corresponding angles and proportional corresponding side lengths. Their proportional sides let you set up equations to find missing measurements.

The equation (x − h)² + (y − k)² = r² describing a circle with center (h, k) and radius r. Completing the square converts a general equation into this useful form.