IBEW Aptitude Test cheat sheet

Order of operations: parentheses, exponents, multiplication/division left to right, then addition/subtraction left to right.

Distribute before combining: a(b + c) = ab + ac; watch for a minus sign flipping every term inside: -(x - 5) = -x + 5.

Linear equation solve order: clear fractions by multiplying by the LCD, distribute, collect variables on one side, isolate the constant, divide.

Slope from two points: m = (y2 - y1)/(x2 - x1); horizontal line m = 0, vertical line slope is undefined.

Slope-intercept form y = mx + b: m is the rate of change, b is the y-value where the line crosses the y-axis.

Systems of two equations: substitution when one variable is already isolated; elimination when coefficients can be matched by multiplying.

Exponent rules: x^a * x^b = x^(a+b); x^a / x^b = x^(a-b); (x^a)^b = x^(ab); x^0 = 1 for x not zero; x^(-a) = 1/x^a.

Quadratic factoring: find two numbers whose product is c and sum is b for x^2 + bx + c; roots are where each factor equals zero.

Inequality rule: multiplying or dividing both sides by a negative number reverses the inequality sign.

Function notation: f(3) means substitute 3 for every x in the rule, then evaluate; f(x) is the output, not multiplication.

Vertical line test: a graph is a function only if no vertical line crosses it more than once.

Domain restrictions: denominators cannot equal zero; even roots require a nonnegative radicand.

Shifts: f(x) + k moves the graph up k; f(x - h) moves it right h; f(-x) reflects over the y-axis; -f(x) reflects over the x-axis.

Line from a graph: read b at the y-intercept, then count rise over run to a second clear point for m.

Parallel lines share the same slope; perpendicular slopes are negative reciprocals, so m1 * m2 = -1.

x-intercept is found by setting y = 0; y-intercept is found by setting x = 0.

Reading a graph: slope is the rate of change and the y-intercept is the starting value in a real-world linear model.

Main idea is the claim the whole passage supports; a detail question answer must be traceable to specific lines.

Contrast signals (however, although, yet, rather) usually mark the author's real point or a shift in argument.

Cause-effect signals: because, therefore, thus, consequently, as a result, hence.

Inference answers must follow necessarily from the text; an answer that needs outside knowledge is wrong.

Tone words: critical, neutral, enthusiastic, cautious, skeptical - match the author's attitude, not the topic's.

Eliminate choices that are too broad, too narrow, or that swap in a word the passage never uses.

Vocabulary in context: substitute each option back into the sentence and keep the one that preserves the surrounding logic.

Sequence questions: locate time markers (first, then, after, finally) and order events by those markers, not by paragraph position.

Mechanical advantage of a lever: MA = effort arm / resistance arm, measured from the fulcrum; class 1 has the fulcrum between load and effort.

Pulley systems: a single fixed pulley changes direction only (MA = 1); movable pulleys supporting the load give MA equal to the number of supporting rope segments.

Inclined plane: less force over a longer distance; steeper ramp means more force required.

Gear trains: meshed gears turn in opposite directions; the smaller gear turns faster, and speed ratio is inversely proportional to tooth count.

Pressure = force / area, so a smaller contact area produces greater pressure for the same force.

Hydraulics: pressure is transmitted equally, so force out = force in * (area out / area in).

Torque = force * perpendicular distance from the pivot; the same force applied farther out produces more turning effect.

Density and buoyancy: an object floats if its density is less than the fluid's; submerged volume displaces fluid equal to the buoyant force.

Electrical basics: series circuits share one current path; parallel circuits share voltage across branches.