Your FREE PERT Flashcards 2026 – 250+ Cards

Parentheses, Exponents, Multiplication/Division (left→right), Addition/Subtraction (left→right).

Slope = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁); the m in y = mx + b.

y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).

The point where a line crosses the y-axis (where x = 0); the value b in y = mx + b.

The point where a line crosses the x-axis (where y = 0); set y = 0 and solve for x.

An equation whose graph is a straight line; variables appear only to the first power, e.g. y = 2x + 1.

Isolate the variable by doing the same inverse operation to both sides until the variable stands alone.

When you multiply or divide both sides of an inequality by a negative number, reverse the inequality sign.

An equation with several variables; 'solve for' one variable by isolating it in terms of the others (e.g. solve A = lw for w).

An equation of the form ax² + bx + c = 0; its graph is a parabola. Solve by factoring, the square root, or the quadratic formula.

x = (−b ± √(b² − 4ac)) ÷ (2a), which solves any quadratic ax² + bx + c = 0.

b² − 4ac inside the quadratic formula; positive → 2 real roots, zero → 1, negative → no real roots.

Rewrite ax² + bx + c as a product of two binomials; the roots are the values that make each factor 0.

Multiply two binomials by combining First, Outer, Inner, Last terms: (x + 2)(x + 3) = x² + 5x + 6.

a² − b² = (a + b)(a − b); a common PERT factoring pattern, e.g. x² − 9 = (x + 3)(x − 3).

A sum of terms, each a number times a variable raised to a whole-number power, e.g. 3x² − 2x + 5.

Terms with the same variable and exponent; only like terms can be combined (3x + 5x = 8x).

a(b + c) = ab + ac; multiply the outside factor by each term inside the parentheses.

Two or more equations solved together; solve by substitution or elimination to find the values that satisfy all of them.

Solve one equation for a variable, then substitute that expression into the other equation.

Add or subtract the equations so one variable cancels, then solve for the remaining variable.

A rule that assigns exactly one output to each input; written f(x), where f(x) is the output for input x.

Substitute the input value for x: if f(x) = 2x + 1, then f(3) = 2(3) + 1 = 7.

The set of all allowable input (x) values for the function.

The set of all output (y) values the function produces.

xᵃ · xᵇ = xᵃ⁺ᵇ — add exponents when multiplying powers with the same base.

xᵃ ÷ xᵇ = xᵃ⁻ᵇ — subtract exponents when dividing powers with the same base.

(xᵃ)ᵇ = xᵃᵇ — multiply the exponents.

Any nonzero number raised to the 0 power equals 1 (x⁰ = 1).

x⁻ⁿ = 1 ÷ xⁿ — a negative exponent means the reciprocal.

A value that, multiplied by itself, gives the number; √25 = 5. The radical √ asks for the principal (positive) root.

A number that can be written as a fraction of two integers (e.g. ½, 0.75, −3).

A number that cannot be written as a fraction; its decimal never ends or repeats (e.g. √2, π).

Writing a number as a digit between 1 and 10 times a power of 10, e.g. 5,300 = 5.3 × 10³.

The distance of a number from 0 on the number line, always nonnegative; |−7| = 7.

Divide by 100 (or move the decimal two places left): 25% = 0.25.

Convert to a decimal and multiply: 20% of 80 = 0.20 × 80 = 16.

(new − old) ÷ old × 100; positive is an increase, negative a decrease.

An equation stating two ratios are equal; solve by cross-multiplying.

For a/b = c/d, multiply diagonally: a·d = b·c, then solve.

A comparison of two quantities by division, written a:b or a/b.

Add all the values, then divide by how many values there are.

The middle value of a data set arranged in order (average the two middle values if the count is even).

The value that appears most often in a data set.

The highest value minus the lowest value in a data set.

Favorable outcomes ÷ total outcomes, a number from 0 (impossible) to 1 (certain).

Area = length × width.

Area = ½ × base × height.

Area = πr², where r is the radius.

Circumference = 2πr (or πd), where r is the radius and d the diameter.

The total distance around a figure — add the lengths of all its sides.

Volume = length × width × height.

Volume = πr²h, where r is the base radius and h the height.

In a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle).

The radius is the distance from a circle's center to its edge; the diameter is twice the radius (d = 2r).

Two angles whose measures add to 180°.

Two angles whose measures add to 90°.

Opposite angles formed by two intersecting lines; they are equal.

A grid formed by a horizontal x-axis and vertical y-axis; points are written (x, y).

The four regions of the coordinate plane, numbered I–IV counterclockwise starting at the upper right.

The midpoint of two points is ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2).

Distance = √((x₂ − x₁)² + (y₂ − y₁)²); it comes from the Pythagorean theorem.

Lines in the same plane that never meet; they have equal slopes.

Lines that meet at a 90° angle; their slopes are negative reciprocals (e.g. 2 and −½).

Divide numerator and denominator by their greatest common factor.

Find a common denominator, add the numerators, then simplify.

Multiply the numerators together and the denominators together, then simplify.

Multiply by the reciprocal of the second fraction (flip and multiply).

A fraction whose numerator and/or denominator are polynomials; simplify by factoring and canceling common factors.

The largest number (or expression) that divides two values evenly.

The smallest number that two or more numbers both divide into evenly.

A whole number greater than 1 divisible only by 1 and itself (2, 3, 5, 7, 11, …).

A whole number and its opposite, including 0 (…, −2, −1, 0, 1, 2, …).

Operations that undo each other — addition/subtraction, multiplication/division, squaring/square root.

Turn the words into an equation first; 'is' means =, 'of' means ×, 'more than' means +.

y = kx; as x increases, y increases proportionally by the constant k.

A straight line drawn through scatter-plot data to show the trend; its slope is the rate of change.

The median better describes the typical value when a data set has extreme outliers.

Set the matching quantities as equal ratios, then cross-multiply and solve for the unknown.

A rate with a denominator of 1, such as miles per hour or cost per item; divide to find it.

An increase added to a cost: new price = original + (markup% × original).

A reduction in price: sale price = original − (discount% × original), or pay (100% − discount%).

Interest = principal × rate × time (I = Prt), with the rate as a decimal and time in years.

Simple interest earns only on the principal; compound interest earns on the principal plus prior interest.

Round numbers to convenient values to predict the size of the answer and catch calculator slips.

Add or subtract the coefficients of terms with the identical variable part: 4x + 2x = 6x.

Move all variable terms to one side and constants to the other, then isolate the variable.

Graph the boundary line (dashed for < or >, solid for ≤ or ≥), then shade the side that satisfies it.

Zero — a horizontal line has no rise.

Undefined — a vertical line has no run, so you would divide by zero.

The U-shaped graph of a quadratic; it opens up if a > 0 and down if a < 0.

The highest or lowest point of the parabola; the x-value is −b ÷ (2a).

A quantity that increases by a constant percentage each period, modeled by y = a·bˣ with b > 1.

Isolate the radical, square both sides, solve, then check for extraneous solutions.

Eliminate a radical in the denominator by multiplying numerator and denominator by that radical.

Multiply the whole number by the denominator, add the numerator, and keep the denominator.

Multiply by 100 (move the decimal two places right): 0.4 = 40%.

Divide the numerator by the denominator: ¾ = 3 ÷ 4 = 0.75.

Compare the heights or lengths of bars to read and compare category values.

Follow the line to read how a value changes over time or another variable.

Each slice is a share of the whole; the full circle represents 100%.

The total area of all the outer faces of a 3-D solid, measured in square units.

Congruent figures have equal size and shape; similar figures have the same shape but proportional sizes.

The central point a passage makes — what the whole text is mostly about.

A fact, example, statistic, or reason that develops or proves the main idea.

The sentence (often first) that states a paragraph's main idea.

The reason a text was written — to inform, persuade, entertain, or explain.

The author's attitude toward the subject, revealed through word choice (e.g. formal, critical, hopeful).

The feeling a text creates in the reader, set by imagery and word choice.

A logical conclusion drawn from textual evidence plus reasoning — not stated outright.

Combining stated details with reasoning to decide what the text implies.

Surrounding words and sentences that help you figure out an unfamiliar word's meaning.

Determining what a word means as it is actually used in a passage — not just its dictionary definition.

A word's literal, dictionary definition.

The emotional or implied meaning a word carries beyond its literal definition.

Language that means more than the literal words, such as metaphor, simile, and personification.

A comparison using 'like' or 'as' (e.g. 'brave as a lion').

A direct comparison that states one thing is another (e.g. 'time is money').

Giving human qualities to something nonhuman (e.g. 'the wind whispered').

Imaginative writing such as fiction, poetry, and drama.

Nonfiction such as essays, articles, editorials, and documents that present facts and arguments.

How a text is organized — e.g. cause/effect, compare/contrast, sequence, or problem/solution.

A text structure that explains why something happens (cause) and what results (effect).

A structure that examines similarities and differences between ideas or things.

A structure that presents events or steps in order.

A structure that states an issue and then proposes a way to resolve it.

Briefly restating a passage's main points in your own words, leaving out minor details.

Restating a specific passage in your own words while keeping the original meaning.

A debatable position an author argues for.

The facts, examples, data, or expert opinions an author uses to support a claim.

A claim backed by reasoning and evidence intended to persuade the reader.

An opposing view that an author acknowledges and responds to.

An author's slant or prejudice that may distort how a topic is presented.

A fact can be proven true or false; an opinion expresses a belief, judgment, or feeling.

The perspective from which a text is told or an issue is presented.

The underlying message or central insight about life in a literary work.

Combining ideas from two or more texts to reach a broader conclusion.

A firsthand or original record, such as a letter, speech, or diary.

A source that analyzes or interprets primary sources, such as a textbook or review.

Explicit information is stated directly; implicit information is suggested and must be inferred.

A broad statement drawn from specific examples; valid ones are supported by sufficient evidence.

Strategies authors use to convince readers — appeals to emotion, logic, or credibility.

Denotation is a word's literal meaning; connotation is its implied or emotional meaning.

Use nearby words, examples, or contrasts in the sentence to define an unfamiliar word.

A word part added to the front of a root that changes its meaning (e.g. 'un-' means not).

A word part added to the end of a root, often changing its part of speech (e.g. '-ly').

The base part of a word that carries its core meaning.

Examining how a paragraph or whole text is built to understand the author's logic and emphasis.

Anchoring every reading answer to specific words or lines in the passage.

Descriptive words for attitude — e.g. sarcastic, optimistic, somber, objective, urgent.

A main idea that is not stated directly; the reader infers it from the details.

The deliberate choices an author makes — word choice, structure, and devices — to shape meaning.

Using clues in a text to anticipate what will happen or be said next.

Identifying where paired texts agree, disagree, or emphasize different points.

Interpreting a chart, graph, table, or map that accompanies a passage to draw conclusions.

Relevant details support the main idea; irrelevant ones do not and can be set aside.

The intended readers a text is written for, which shapes its tone, word choice, and content.

A PERT Reading skill area: identifying main ideas, supporting details, and what the text states or implies.

A PERT Reading skill area: how word choice, text structure, and point of view shape meaning.

A PERT Reading skill area: evaluating arguments and comparing information across sources.

Asks for information stated directly in the passage; locate the exact line.

A PERT Reading skill: determining the meaning of words and phrases, including academic vocabulary.

Examining how an author's specific words shape meaning, tone, and impact.

A central idea is the main point of informational text; a theme is the underlying message of literary text.

A summary that captures the main points without inserting the reader's own opinions.

Tracing how an author builds a claim with premises and evidence to reach a conclusion.

The viewpoint or attitude that shapes how an author presents a topic.

Specific words, phrases, or lines from a passage that support an answer or inference.

Recognizing how a poem, story, editorial, or report each handles a topic differently.

An idea a text suggests through detail and tone rather than stating directly.

Distinguishing the central points of a passage from minor supporting details.

Questioning an author's claims, evidence, assumptions, and possible bias while you read.

Literal meaning is exact; figurative meaning uses devices like metaphor to imply more.

The feelings or associations a word evokes beyond its dictionary definition.

Words like 'because', 'therefore', 'as a result', and 'since' that signal cause-and-effect relationships.

Words like 'first', 'next', 'then', and 'finally' that signal the order of events.

Words like 'however', 'but', 'on the other hand', and 'whereas' that signal a difference.

Judging whether a claim is supported by sufficient, relevant, and credible evidence.

PERT Reading checks whether you can analyze college-level texts without remediation.

Marking key ideas, transitions, and evidence as you read to answer questions faster.

Choosing the inference the passage's evidence forces, not one merely possible.

A singular subject takes a singular verb and a plural subject takes a plural verb (the dog runs / the dogs run).

A pronoun must match the noun it replaces in number and gender (each student … his or her work).

Use subjective pronouns (I, he, she, they) as subjects and objective pronouns (me, him, her, them) as objects.

The form of a verb that shows time — past, present, or future; keep tense consistent unless the time changes.

An error in which a sentence wrongly switches tenses (e.g. past to present); fix it for consistency.

An incomplete sentence missing a subject, a verb, or a complete thought.

Two independent clauses joined incorrectly without proper punctuation or a conjunction.

A run-on error in which two independent clauses are joined by only a comma.

A group of words with a subject and verb that can stand alone as a sentence.

A clause with a subject and verb that cannot stand alone (begins with words like because, although, when).

A word that joins equal parts — for, and, nor, but, or, yet, so (FANBOYS).

A word that begins a dependent clause (because, although, since, while, if).

Using the same grammatical form for items in a list, pair, or comparison (reading, writing, and editing).

A word or phrase that describes another word in a sentence (adjective, adverb, or phrase).

A modifier placed too far from the word it describes, causing confusion; move it next to that word.

A modifier with no clear word to describe in the sentence; fix it by adding the missing subject.

Use commas between items in a series, after introductory elements, and before a conjunction joining two clauses.

Joins two closely related independent clauses, or separates list items that already contain commas.

Introduces a list, explanation, or quotation after a complete independent clause.

Shows possession (the dog's bone) or marks a contraction (it's = it is); not used for simple plurals.

'Its' is possessive (the cat licked its paw); 'it's' is a contraction of 'it is' or 'it has'.

'Their' shows possession, 'there' indicates place, 'they're' means 'they are'.

'Your' shows possession (your book); 'you're' is a contraction of 'you are'.

'To' is a preposition or infinitive marker, 'too' means also or excessively, 'two' is the number 2.

Capitalize the first word of a sentence, proper nouns, and the pronoun 'I'.

Enclose direct quotations and certain titles; periods and commas go inside them in U.S. usage.

The subject performs the action (The committee approved the plan) — usually clearer and more direct.

The subject receives the action (The plan was approved by the committee) — wordier; prefer active voice.

A sentence that states a paragraph's main idea, usually placed at the beginning.

A word or phrase that signals the relationship between ideas (however, therefore, meanwhile, furthermore).

Arranging a text logically with an effective opening, clear transitions, and a strong closing.

A single sentence that states the central claim or position of an essay.

Using more words than needed; concise, precise writing is preferred on the PERT Writing subtest.

Needlessly repeating the same idea (e.g. 'free gift', 'past history'); eliminate the repeated word.

Expressing ideas clearly in the fewest necessary words; the clearest, shortest correct option usually wins.

Selecting precise, appropriate words that fit the sentence's meaning and tone.

Mixing short and long, simple and complex sentences to keep writing engaging.

Joining short, choppy sentences with conjunctions or clauses to improve flow.

The standard rules of grammar, usage, punctuation, capitalization, and spelling.

An error that wrongly switches person (e.g. 'one … you'); keep the point of view consistent.

Using two negatives in one clause (e.g. 'don't have no'); standard English uses only one.

Used to compare two things, usually with '-er' or 'more' (taller, more careful).

Used to compare three or more things, usually with '-est' or 'most' (tallest, most careful).

'Good' is an adjective (a good meal); 'well' is an adverb (she sings well).

Use 'fewer' for countable items (fewer cars); use 'less' for uncountable amounts (less water).

The noun or pronoun that performs the action or is described.

The part of a sentence containing the verb that tells what the subject does or is.

The noun a pronoun refers back to.

Standard, conventional phrasing (e.g. 'interested in', not 'interested on').

Whether a sentence supports the paragraph's point; cut sentences that do not.

Arranging sentences so ideas build logically within a paragraph.

A word like 'however', 'therefore', or 'moreover' that links clauses; often follows a semicolon.

An introduction or topic sentence that clearly previews what the paragraph or essay is about.

A closing that restates the main point and gives the reader a sense of completion.

The formal, edited English the PERT Writing subtest expects — correct grammar, usage, and mechanics.

Stating a clear central claim or position early so the rest of the writing supports it — a PERT Writing skill.

Keeping every sentence on the chosen topic or argument without drifting — a PERT Writing skill.

Backing a claim with reasons, examples, and evidence rather than mere assertion.

Combining information from multiple texts into a coherent, well-supported point.

Accurately representing and attributing the data, conclusions, and views of others.

Recognizing competing arguments or information while still establishing your own claim.

The three layers PERT Writing tests: grammar conventions, correct usage, and mechanics (punctuation, spelling, capitalization).

Word pairs the PERT tests, such as affect/effect, then/than, accept/except, and lie/lay.

'Affect' is usually a verb meaning to influence; 'effect' is usually a noun meaning a result.

'Then' refers to time or sequence; 'than' is used in comparisons.

'Accept' means to receive; 'except' means to leave out or exclude.

Joining equal ideas with a coordinating conjunction (and, but, or) — a PERT sentence-structure skill.

Making one idea dependent on another using a subordinating conjunction (because, although) to show emphasis.

Keeping verb tense and pronouns consistent within a passage, a tested PERT grammar skill.

Using the correct subjective, objective, or possessive form of a pronoun for its role in the sentence.

Adjectives modify nouns; adverbs (often ending in -ly) modify verbs, adjectives, or other adverbs.

Words and phrases that connect ideas and signal logical relationships within a passage.

The voice and attitude of a piece; effective writing maintains an appropriate, consistent style and tone.

Presenting complex information so it is organized, coherent, and easy to follow.

Editing a draft to remove confusion, wordiness, and errors so the meaning is clear.

On the PERT, you choose revisions that improve a draft passage, not isolated grammar trivia.

Using standard spelling; the PERT Writing subtest tests recognition of correct spelling in context.

Keeping subject-verb and pronoun-antecedent agreement throughout a passage.

Sequencing sentences and ideas so the passage develops in a logical, connected way.