Algebra
What this section tests
The algebra portion of the IBEW aptitude test checks whether you can manipulate expressions and solve equations quickly and without a calculator. Expect linear equations and inequalities in one variable, ratios and proportions, systems of two equations, exponent rules, radicals, polynomial multiplication and factoring, and quadratics solvable by factoring or the quadratic formula. Many items are worded as job-site problems - conduit lengths, load totals, resistance - so translate the words into an equation first, then solve.
Rules to have automatic
- Combine like terms and apply the distributive law in both directions; factoring is distribution run backwards.
- Exponent rules: x^a · x^b = x^(a+b), x^a ÷ x^b = x^(a−b), (x^a)^b = x^(ab), x^0 = 1, x^(−a) = 1/x^a.
- Multiplying or dividing an inequality by a negative number flips the sign; adding or subtracting never does.
- For a system, substitution is fastest when one variable is already isolated; elimination is fastest when coefficients line up.
- For ax² + bx + c = 0, factor when the numbers are friendly, otherwise use x = [−b ± √(b² − 4ac)] ÷ 2a.
Worked example
Three conduit lengths total 47 feet. The second is 5 feet longer than the first, and the third is twice the first. Find the first length. Let the first be x. Then the second is x + 5 and the third is 2x. x + (x + 5) + 2x = 47 → 4x + 5 = 47 → 4x = 42 → x = 10.5 feet. Check: 10.5 + 15.5 + 21 = 47. Checking is not optional; it catches sign and translation errors in seconds.
Traps that cost marks
- Dropping a negative when distributing a minus sign across parentheses.
- Solving for x but answering the wrong quantity - the question asked for the third length, not the first.
- Mixing units, feet with inches, before the equation is written.
- Squaring both sides of a radical equation and keeping the extraneous root instead of substituting back.