IBEW Aptitude Test key terms

A letter or symbol that stands for an unknown or changing number in an expression or equation. For example, in 3x + 5 = 20, the letter x is the variable whose value you must find.

The number multiplied by a variable in a term. In 7y, the coefficient is 7; in -4ab, it is -4. A variable written alone has an implied coefficient of 1.

A fixed number in an expression or equation that does not change value. In 2x + 9, the 9 is a constant, while x can vary.

A mathematical phrase combining numbers, variables, and operations but with no equals sign. Examples include 4x - 7 and (a + b)/2. Expressions are simplified or evaluated, not solved.

A statement that two mathematical expressions are equal, joined by an equals sign. Solving an equation means finding the value of the variable that makes the statement true, such as x = 4 in 2x = 8.

Terms that have exactly the same variable parts, so they can be combined by adding or subtracting their coefficients. 5x and -2x are like terms; 5x and 5x squared are not.

To rewrite an expression in a shorter, equivalent form by combining like terms, reducing fractions, or applying operations. Simplifying 3x + 2x - x gives 4x without changing its value.

A rule stating that a number outside parentheses multiplies each term inside: a(b + c) = ab + ac. It is the main tool for removing parentheses before solving equations.

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

A small raised number showing how many times a base is multiplied by itself. In 5 cubed, the exponent 3 means 5 times 5 times 5, which equals 125.

A number that, when multiplied by itself, produces the given value. The square root of 49 is 7 because 7 times 7 equals 49. Every positive number has a positive and a negative square root.

A comparison of two quantities by division, often written with a colon or as a fraction. A 3:2 ratio of wire to conduit means for every 3 lengths of wire there are 2 lengths of conduit.

An equation stating that two ratios are equal, such as 4/6 = 8/12. Proportions are solved by cross-multiplying to find an unknown quantity in a scaling problem.

A shortcut for solving a proportion: multiply the numerator of one fraction by the denominator of the other. From a/b = c/d you get ad = bc, which isolates the unknown.

A ratio comparing quantities with different units, such as miles per hour or dollars per hour. Rates are often used in work problems where time and output are related.

A statement comparing two expressions that are not necessarily equal, using symbols such as less than, greater than, or at most. Solving an inequality works like an equation, but multiplying by a negative flips the sign.

An equation whose graph is a straight line because the variable appears only to the first power. The standard form is y = mx + b, where m is the slope and b is the y-intercept.

A measure of how steep a line is, equal to rise over run, or the change in y divided by the change in x. A positive slope rises left to right; a negative slope falls.

The point where a graph crosses the vertical y-axis, occurring where x equals zero. In y = 3x + 7, the y-intercept is 7.

The point where a graph crosses the horizontal x-axis, occurring where y equals zero. Finding it means setting y to zero and solving for x.

A rule that assigns exactly one output value to each input value. In a function, no input may produce two different outputs, which can be checked with the vertical line test.

The complete set of allowable input values for a function. For example, a function dividing by x has a domain of all real numbers except zero.

The set of all possible output values a function can produce from its domain. On a graph, the range is the spread of values along the vertical axis.

A grid formed by a horizontal x-axis and a vertical y-axis crossing at the origin. Points are located by ordered pairs written as (x, y).

Two numbers written in the form (x, y) that locate a single point on a coordinate plane. The first number gives horizontal position; the second gives vertical position.

The point (0, 0) where the x-axis and y-axis intersect on a coordinate plane. It serves as the reference point from which all other points are measured.

A visual picture of the relationship between variables, usually plotted on a coordinate plane. Reading a graph means identifying points, trends, and where a line crosses the axes.

The central point a passage is built to communicate, stated or implied. Every supporting detail in the text relates back to this controlling idea, so identifying it guides all other questions.

A fact, example, or reason in a passage that explains or backs up the main idea. Detail questions ask you to locate specific information stated directly in the text.

A conclusion drawn from evidence in the passage plus reasonable reasoning, though not stated directly. A valid inference must be supported by the text, not by personal opinion.

The writer's attitude toward the subject, revealed through word choice and phrasing. Tone may be neutral, critical, cautious, or enthusiastic, and it shapes how a passage should be read.

Information in surrounding sentences that helps you work out the meaning of an unfamiliar word. Contrast clues, examples, and definitions nearby often reveal what a term means.

The order in which events or steps are presented in a passage. Words such as first, then, next, and finally signal the sequence and help you follow a process or narrative.

A push or pull acting on an object, measured in newtons or pounds. Force can change an object's speed, direction, or shape, and unbalanced forces cause acceleration.

A twisting or turning effect produced by a force applied at a distance from a pivot. Torque equals force times lever-arm distance, so a longer wrench increases turning power.

A rigid bar that pivots at a fulcrum to multiply force or distance. The effort applied on one side balances the load on the other according to their distances from the fulcrum.

The factor by which a machine multiplies the effort force you apply. An advantage greater than one means the machine lets you move a larger load with less effort.

A grooved wheel with a rope or cable that changes the direction of a force or reduces the effort needed to lift a load. Multiple rope segments supporting a load increase mechanical advantage.

A resisting force that opposes motion when two surfaces touch and slide or roll against each other. Friction converts motion into heat and must be overcome to keep an object moving.