AFQT key terms

A ratio that compares two quantities with different units, such as miles per hour or dollars per pound. In word problems, rates let you scale one quantity to another.

The cost of one item or one unit of measure, found by dividing total cost by the number of items. Comparing unit prices shows which package is the better buy.

An equation stating that two ratios are equal, such as 3/4 = 9/12. You solve for an unknown by cross-multiplying or scaling both sides equally.

A ratio out of 100. To find a percent of a number, convert the percent to a decimal and multiply; to find percent change, divide the change by the original amount.

The sum of a set of values divided by how many values there are. Word problems often give the average and ask you to work backward to a missing total.

Interest computed only on the original principal, using the formula interest = principal × rate × time. The rate is usually written as a decimal per year.

A word problem using distance = rate × time. When two objects move toward or away from each other, add their rates; when one chases another, subtract.

Whole numbers that follow one another in order, such as 7, 8, 9. They are often modeled as n, n+1, n+2 when setting up an equation.

A reduction from the original price, usually given as a percent. Subtract the discount amount from the original price, or multiply by one minus the decimal rate.

A whole number greater than 1 whose only positive divisors are 1 and itself, such as 2, 3, 7, and 11. One is not prime.

A whole number that divides another number evenly with no remainder. For example, 4 is a factor of 12 because 12 ÷ 4 = 3.

The result of multiplying a number by a whole number. Multiples of 6 include 6, 12, 18, and so on, continuing without end.

The largest number that divides evenly into two or more given numbers. It is useful for simplifying fractions and factoring expressions.

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

A small raised number showing how many times the base is used as a factor. In 3 to the fourth power, the exponent 4 means 3 × 3 × 3 × 3.

A number that, when multiplied by itself, gives the original number. The square root of 49 is 7 because 7 × 7 = 49.

The agreed sequence for evaluating expressions: parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

A letter or symbol that stands for an unknown or changing number in an expression or equation, such as x in 2x + 5 = 11.

A mathematical statement that two expressions are equal, connected by an equals sign. Solving it means finding the value of the variable that makes the statement true.

A statement comparing expressions that are not necessarily equal, using symbols such as <, >, ≤, or ≥. Solutions form a range of values rather than a single number.

A word that has the same or nearly the same meaning as another word, such as happy and joyful. Synonym questions test whether you know the closest meaning.

A word with the opposite meaning of another word, such as hot and cold. Antonym questions ask you to pick the choice most nearly opposite in meaning.

Information in the surrounding sentence or paragraph that helps you figure out an unfamiliar word's meaning, such as a definition, example, contrast, or cause-and-effect signal.

A word part attached to the beginning of a root that changes its meaning, such as un- in unhappy or pre- in preview.

A word part attached to the end of a root that changes meaning or part of speech, such as -ness in kindness or -able in readable.

The basic part of a word that carries its core meaning and to which prefixes and suffixes are added, as port in transport and portable.

The emotional or implied association a word carries beyond its literal meaning. For example, thrifty sounds positive while stingy sounds negative, though both involve saving money.

The central point a passage is written to convey. It is often stated in a topic sentence but may need to be inferred from details spread throughout.

A fact, example, or reason that explains or backs up the main idea. Details answer who, what, when, where, or why about the passage's point.

A conclusion drawn from evidence in the passage plus your own reasoning, even though the author does not state it directly.

The reason an author writes a passage, such as to inform, persuade, entertain, or explain. Purpose shapes word choice and how information is organized.

The author's attitude toward the subject, revealed through word choice and details. Tone may be humorous, critical, neutral, or admiring, among many possibilities.

A word or phrase that shows how ideas connect, such as however, therefore, or in addition. Transitions signal contrast, cause, sequence, or emphasis.

A fact can be verified with evidence; an opinion expresses a belief, judgment, or feeling. Recognizing the difference helps you judge how much to trust a statement.