IBEW Aptitude Test flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Order of operations

Evaluate parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. This sequence determines the single correct value of an expression.

Distributive property

Multiplying a sum means multiplying each term: a(b + c) = ab + ac. A minus sign in front changes the sign of every term inside the parentheses.

Slope formula

The slope through two points is the change in y divided by the change in x: m = (y2 - y1)/(x2 - x1). A vertical line has undefined slope.

Slope-intercept form

The equation y = mx + b describes a line where m is the slope, or rate of change, and b is the y-intercept, the output when x equals zero.

Solving linear equations

Clear fractions, distribute, gather variable terms on one side and constants on the other, then divide by the coefficient. Substitute the result back to verify.

Elimination method

Multiply one or both equations so a variable's coefficients become opposites, add the equations to remove that variable, solve, then back-substitute to find the other value.

Exponent product rule

When multiplying powers with the same base, add the exponents: x^a times x^b equals x^(a+b). When dividing, subtract the exponents instead.

Negative exponent

A negative exponent means reciprocal: x^(-a) equals 1 divided by x^a. Any nonzero base raised to the zero power equals one.

Inequality sign reversal

Multiplying or dividing both sides of an inequality by a negative number flips the direction of the inequality symbol. Adding or subtracting never flips it.

Factoring quadratics

For x^2 + bx + c, find two numbers whose product is c and whose sum is b. Setting each factor to zero gives the solutions, called roots.

Function notation

The expression f(3) means replace every x in the function rule with 3 and compute the output. It does not mean f multiplied by 3.

Vertical line test

A graph represents a function only if every vertical line crosses it at most once. Two crossings at the same x mean one input has two outputs.

Domain restrictions

A function's domain excludes any x making a denominator zero. Even roots also require a nonnegative value beneath the radical sign.

Graph transformations

Adding k outside the function shifts the graph up by k; subtracting h inside shifts it right by h; a negative outside reflects across the x-axis.

Parallel and perpendicular slopes

Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals, so their product equals negative one.

Finding intercepts

Set y equal to zero and solve to find the x-intercept; set x equal to zero and solve to find the y-intercept. Intercepts are where the graph crosses the axes.

Rate of change from graph

On a linear graph, slope equals the rate of change: divide the vertical change by the horizontal change between two clear points on the line.

Reading slope meaning

In a real-world linear model, slope is the amount the output changes per one-unit increase in input, and the y-intercept is the starting value.

Main idea

The main idea is the central claim the entire passage supports. Correct answers to main-idea questions cover the whole passage, not one supporting detail.

Contrast signal words

Words such as however, although, yet, and rather signal a shift or qualification. The author's actual position often appears right after such a signal.

Cause and effect signals

Because, therefore, thus, consequently, and as a result mark causal links. Questions about why something happened usually hinge on these words.

Valid inferences

A correct inference follows necessarily from stated evidence. An answer requiring outside knowledge or an unstated assumption is not supported by the passage.

Author's tone

Tone is the author's attitude toward the subject, such as critical, neutral, or cautious. It is inferred from word choice rather than from the topic itself.

Vocabulary in context

To define a word in context, substitute each answer choice into the original sentence and keep the option that preserves the sentence's logic and meaning.

Eliminating wrong choices

Reject options that are too broad, too narrow, or that introduce terms absent from the passage. Remaining answers must be directly supported by the text.

Chronological order questions

Order events by time markers such as first, then, after, and finally, rather than by the order in which the passage happens to mention them.

Lever mechanical advantage

Mechanical advantage equals effort arm length divided by resistance arm length, both measured from the fulcrum. A longer effort arm reduces the force needed.

Pulley mechanical advantage

A single fixed pulley changes force direction only, with advantage of one. Movable pulleys give advantage equal to the number of rope segments supporting the load.

Inclined plane tradeoff

A ramp trades force for distance: a gentler, longer incline requires less force but over a greater distance. A steeper ramp needs more force.

Gear rotation rules

Meshed gears rotate in opposite directions. The gear with fewer teeth turns faster, and speed ratio is inversely proportional to the tooth-count ratio.

Pressure formula

Pressure equals force divided by area. For the same force, a smaller contact area produces greater pressure, which is why sharp edges cut easily.

Hydraulic force multiplication

Pressure transmits equally through a confined fluid, so output force equals input force multiplied by the ratio of output piston area to input piston area.