Electrician aptitude test › Electrician math test
Electrician math test: what's on the aptitude test, topic by topic
The math on the electrician aptitude test is algebra, not electrical math. The electrical training ALLIANCE test used by IBEW/NECA apprenticeships gives 33 Algebra and Functions items in 46 minutes, with no calculator. They cover number series, formulas, exponents, equations, inequalities, polynomials and functions. Below is each topic with one worked example.
No electrical math, and no formulas to memorize
The ALLIANCE's pages still call it the "NJATC aptitude test battery," so you will see both names. It describes the math section as "a test of your ability to solve problems using algebra." Its applicant page adds that "there is no need to memorize certain formulas or factual material in order to do well on the tests" and that "Previous knowledge of electrical work is not required." The official sample shows the item types: put numbers into a formula, pick the equivalent form of a formula, find the next number in a pattern, decide when a formula's value is negative, and match a table to a rule.
If you searched "electrician math" for the job itself, such as Ohm's law, conduit fill or voltage drop, that is trade math, and the entrance test doesn't ask for it. This page is about the entrance test.
| Topic | What an item asks | The rule to know |
|---|---|---|
| Number series | The next number in a row | Look at the gaps first |
| Formulas | The value of A when B and C are given | Parentheses, powers, then × and ÷ left to right |
| Exponents and roots | Simplify a power or a root | Add exponents to multiply, subtract to divide |
| Ratios | A missing value in a proportion | Cross products are equal |
| Equations | Solve for x | Get x alone; check by substituting |
| Inequalities | When a value is positive or negative | Dividing by a negative flips the sign |
| Polynomials | The equivalent expanded formula | FOIL gives all four products |
| Factoring | The factored form | Take out the common factor first |
| Functions | f(3), or the rule behind a table | f(x) means "f of x," not f times x |
1. Number series
A series item gives a row of numbers and asks for the next one. The official sample has one, so treat series as one item type among several, not a section of its own. OpenStax's advice is to look for "multiples or powers" and for "a pattern in the signs."
| Kind | Example | Rule | Next |
|---|---|---|---|
| Arithmetic | 7, 11, 15, 19, ? | Add 4 each time | 23 |
| Geometric | 5, 15, 45, 135, ? | Multiply by 3 | 405 |
| Alternating | 20, 23, 19, 22, 18, ? | +3, then −4, taking turns | 21 |
| Powers | 1, 8, 27, 64, ? | Cubes: 1³, 2³, 3³, 4³ | 125 |
Gaps that stay the same mean adding; gaps that grow by a fixed factor mean multiplying; gaps that switch sign usually mean two rules taking turns.
2. Order of operations and formulas
Work the innermost parentheses first, then powers, then multiplication and division "in order from left to right," then addition and subtraction. Multiplication does not always come before division.
And left to right: 24 ÷ 4 × 2 = 6 × 2 = 12, not 24 ÷ 8 = 3.
3. Exponents and roots
To multiply like bases, add the exponents; to raise a power to a power, multiply them. Any nonzero number to the zero power is 1, and a negative exponent means the reciprocal.
The radical sign means the positive root, even though −9 squared is also 81.
4. Ratios and proportions
In a proportion, the cross products are equal: multiply each denominator by the opposite numerator.
5. Linear equations
The goal is to get the variable alone on one side, then check by substituting back into the original equation.
6. Inequalities
Solve them like equations, with one difference: multiplying or dividing by a negative number reverses the sign. The official sample asks this as a statement, such as "when b is less than 8, a is negative," so be ready to read the answer as words.
7. Word problems into equations
Name the unknown with a letter, restate the problem in one sentence, translate the clue words, solve, and check that the answer makes sense.
8. Polynomials and FOIL
FOIL (First, Outer, Inner, Last) finds all four products when you multiply two binomials. It works only for two binomials. Then combine like terms: same variable, same exponent.
If a number sits in front, as in 2(x + 5)(x − 3), multiply every term by it at the end.
9. Factoring
Always take out the greatest common factor first. For x² + bx + c, find two numbers that multiply to c and add to b. A difference of squares factors into conjugates; a sum of squares does not factor.
10. Function notation and tables
A function gives exactly one output for each input. In f(x) the parentheses don't mean multiplication: substitute the number for x. For a table, find how much y changes when x goes up by 1, then fix the starting value.
If your test isn't the ALLIANCE test: fractions, decimals, percent
The GAN battery's numerical computation section covers "basic arithmetic (whole numbers, fractions, decimals)," IEC of Utah's math test lists fractions, decimals, ratios and percentages, and ABC Southern California's TABE has a math computation part. If you face one of those, add arithmetic drills to the topics above. One worked example: a spool holds 250 feet of wire and a job uses 3/5 of it. What's left is 2/5, and 250 × 2/5 = 100 feet. Percent works the same way: 15% of 240 is 0.15 × 240 = 36. See the GAN test and IEC and ABC tests.
Doing it without a calculator
46 minutes for 33 items is about 84 seconds each. None of the examples above needs a calculator, and the official sample's items are built the same way: small whole numbers and simple fractions such as ½. The ALLIANCE's advice is to work steadily, not spend too long on any one question, and answer every item, since there is no penalty for guessing.
To drill these topics under time, start with the free official sample, then 18 free practice questions with worked answers. The home page compares paid prep, from books to question banks. ClassMetric's Union Aptitude Prep, for one, is $39 once and has 403 practice questions (180 number series, 168 algebra and functions, 55 reading), timed like the ALLIANCE test; it has no mechanical reasoning, paper folding or interview prep. See the class.