Praxis Core key terms

The central point a passage is built to communicate. It is broader than any single detail and is usually stated or strongly implied in the introduction or conclusion.

A specific fact, example, statistic, or reason that explains or backs up a passage's main idea. Details answer who, what, when, or why and should connect logically to the point they support.

A conclusion a reader draws by combining stated information with reasonable assumptions. A valid inference must be supported by the text, not merely by personal opinion or outside knowledge.

The attitude an author expresses toward the subject, such as critical, amused, or respectful. Tone is revealed through word choice, sentence structure, and the kinds of details the author chooses to include.

The reason an author writes a text, commonly to inform, persuade, entertain, or explain. Identifying purpose helps a reader judge which details matter and how evidence is being used.

The feelings or associations a word carries beyond its literal meaning, such as the difference between 'thrifty' and 'stingy.' Connotation shapes tone and can reveal an author's bias.

The literal, dictionary meaning of a word, separate from the emotions or associations it may trigger. Distinguishing denotation from connotation helps readers avoid misreading an author's intent.

A fact is a statement that can be verified with evidence; an opinion expresses a belief, judgment, or feeling. Passages often blend both, so readers must separate verifiable claims from evaluative ones.

A text structure that examines similarities and differences between two or more subjects. Signal words like 'similarly,' 'however,' and 'unlike' often mark this organization.

The way information in a passage is organized, such as chronological order, cause and effect, problem and solution, or comparison. Recognizing structure helps a reader locate key information quickly.

A sentence, usually near the start of a paragraph, that states the paragraph's main point. The remaining sentences typically develop or support that point with evidence or explanation.

A word or phrase such as 'therefore,' 'meanwhile,' or 'in contrast' that signals the relationship between ideas. Transitions guide readers through shifts in time, logic, or emphasis.

The rule that a verb must match its subject in number and person. Singular subjects take singular verbs, and intervening phrases do not change the subject's number.

The requirement that a pronoun match its antecedent in number and gender. A singular antecedent needs a singular pronoun, and unclear antecedents create ambiguity for readers.

A group of words punctuated as a sentence but lacking a subject, a verb, or a complete thought. Fragments are repaired by adding the missing element or joining them to a nearby sentence.

Two or more independent clauses joined without correct punctuation or a conjunction. Run-ons are fixed with a period, semicolon, or coordinating conjunction plus comma.

A specific run-on error in which two independent clauses are joined by only a comma. Correcting it requires a semicolon, a period, or a comma plus a coordinating conjunction.

A group of words containing a subject and a verb. An independent clause expresses a complete thought, while a dependent clause cannot stand alone as a sentence.

A word, phrase, or clause that describes another element in a sentence. A misplaced or dangling modifier attaches to the wrong word and produces confusing or illogical meaning.

Using matching grammatical forms for items in a list or comparison, such as 'hiking, swimming, and biking.' Parallelism makes writing clearer and easier to read.

The quality of writing in which ideas connect logically and flow smoothly from one to the next. Coherence depends on clear organization, transitions, and consistent focus.

A sentence that states the central claim of an essay and previews how the argument will be developed. It usually appears at the end of the introduction and governs the body paragraphs.

A punctuation mark used to show possession or to form contractions. Its placement relative to a plural or singular noun determines whether one or more owners are indicated.

A comparison of two quantities by division, often written as a fraction or with a colon. Ratios express relative size rather than absolute amounts.

An equation stating that two ratios are equal. Proportions are solved by cross-multiplying and are used to scale quantities up or down.

A rate expressed per one unit of a given quantity, such as miles per hour or cost per item. Unit rates allow direct comparison between different offers or speeds.

A ratio comparing a number to 100, meaning 'per hundred.' Percents are converted to decimals by dividing by 100 and are used to compute discounts, taxes, and interest.

The arithmetic average of a data set, found by adding all values and dividing by the number of values. The mean is affected strongly by unusually large or small values.

The middle value of a data set when values are arranged in order. With an even number of values, the median is the average of the two middle numbers.

The difference between the largest and smallest values in a data set. Range measures how spread out the data are but ignores values in between.

A number from 0 to 1 expressing how likely an event is, calculated as favorable outcomes divided by total possible outcomes when outcomes are equally likely.

The amount of surface a two-dimensional figure covers, measured in square units. Common formulas include length times width for rectangles and half base times height for triangles.

The total distance around the outside of a two-dimensional figure, measured in linear units. For a rectangle it equals twice the sum of length and width.

The amount of space a three-dimensional solid occupies, measured in cubic units. For a rectangular prism it equals length times width times height.

A symbol, usually a letter, that represents an unknown or changing quantity in an expression or equation. Variables allow general relationships to be written compactly.

An equation in which every variable appears to the first power, producing a straight line when graphed. Solving it means isolating the variable using inverse operations.

A mathematical phrase combining numbers, variables, and operations without an equals sign. An expression can be evaluated or simplified but not solved.

The agreed sequence for evaluating expressions: parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right. Following it ensures consistent results.

The largest number that divides evenly into two or more given numbers. It is used to simplify fractions and factor algebraic expressions.

The smallest number that is a multiple of two or more given numbers. It is used to find a common denominator when adding or subtracting fractions.