Electrician Math Algebra & Fractions for the IBEW Test
A step-by-step how-to for the math section of the NJATC/IBEW electrical apprenticeship aptitude test. Linear equations, functions, number series and fractions — with worked examples and the speed drills that actually move your score.
Roughly a third of IBEW math questions come down to solving one-variable linear equations under time pressure. The rules are simple; the speed isn't.
**How to solve a linear equation:**
1. **Distribute** — clear any parentheses (e.g. 3(x + 2) → 3x + 6).
2. **Combine** like terms on each side.
3. **Move variables** to one side and constants to the other (add/subtract both sides).
4. **Isolate x** by dividing both sides by its coefficient.
**Worked example:** Solve 4(x − 3) + 2x = 18
• Distribute: 4x − 12 + 2x = 18
• Combine: 6x − 12 = 18
• Add 12: 6x = 30
• Divide: **x = 5**
**Speed drill:** aim for solving 10 equations in 6 minutes. If you're slower than 40 seconds per equation, the culprit is usually arithmetic — not algebra.
Fractions & Decimals — Without a Calculator
Fractions eat the clock. The exam mixes fractions and decimals inside algebra problems, so you must be fluent in both.
**Core fraction moves:**
• **Add / subtract** — get a common denominator first. 2/3 + 1/4 → 8/12 + 3/12 = 11/12.
• **Multiply** — straight across. 2/3 × 3/5 = 6/15 = 2/5.
• **Divide** — flip the second fraction and multiply. 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
• **Simplify** — always reduce before you finish; the answer choices are always in lowest terms.
**Decimal ↔ fraction shortcuts to memorise:**
1/2 = 0.5 · 1/3 ≈ 0.333 · 1/4 = 0.25 · 1/5 = 0.2 · 1/8 = 0.125 · 3/8 = 0.375 · 5/8 = 0.625
**Worked example:** Solve x/3 + 1/4 = 5/6
• Common denominator 12: 4x/12 + 3/12 = 10/12
• Combine: 4x + 3 = 10
• Solve: 4x = 7 → **x = 7/4** (or 1.75)
Functions & Composite Functions
Function notation trips up most people who've been out of school for a while. The test uses f(x), g(x) and asks you to evaluate, combine, or compose them.
**How to evaluate f(x):**
• f(x) means "the value of function f when the input is x." Just substitute the number for x.
• If f(x) = 2x² − 3, then f(4) = 2(16) − 3 = **29**.
**How to compose functions f(g(x)):**
1. Compute g(x) first — inside out.
2. Feed that answer into f.
**Worked example:** f(x) = 3x + 1 and g(x) = x² − 2. Find f(g(3)).
• g(3) = 9 − 2 = 7
• f(7) = 3(7) + 1 = **22**
**Speed tip:** always write down the substitution step before doing arithmetic. Skipping steps is where careless errors sneak in on the paper test.
Number Series — Spot the Pattern
Number series questions give you 4–6 numbers and ask for the next one. The pattern is one of a small set — learn to test them in order.
**Test the patterns in this order:**
1. **Constant difference (arithmetic):** 3, 7, 11, 15, __ → each term +4 → **19**
2. **Constant ratio (geometric):** 2, 6, 18, 54, __ → each term ×3 → **162**
3. **Alternating operations:** 1, 4, 2, 8, 4, __ → +3, ÷2, ×4, ÷2, ×4 → **16**
4. **Second differences (quadratic):** 1, 4, 9, 16, __ → 3, 5, 7, next +9 → **25** (perfect squares)
5. **Fibonacci-style (sum of previous two):** 1, 1, 2, 3, 5, 8, __ → **13**
**Speed rule:** if you can't identify the pattern in 15 seconds, mark and skip. The test rewards moving on and coming back with fresh eyes.
Polynomials, Factoring & Inequalities
Expect 5–8 questions on factoring quadratics and manipulating polynomial expressions, plus 2–3 on linear inequalities.
**Factoring a quadratic (x² + bx + c):**
Find two numbers that **multiply to c** and **add to b**.
• x² + 7x + 12 → 3 and 4 (3×4=12, 3+4=7) → **(x + 3)(x + 4)**
• x² − 5x + 6 → −2 and −3 → **(x − 2)(x − 3)**
• x² − x − 12 → −4 and 3 → **(x − 4)(x + 3)**
**Solving quadratics by factoring:**
Set each factor to zero. x² − 5x + 6 = 0 → (x−2)(x−3) = 0 → x = 2 or x = 3.
**Inequalities work like equations, with one twist:**
Multiplying or dividing both sides by a **negative** number **flips the inequality sign**.
• −2x > 10 → divide by −2 → **x < −5**
Speed Tips That Actually Move Your Score
Drill mental arithmetic daily — the test is calculator-free, so speed with times tables, fraction adds and decimal conversions is worth more than clever algebra tricks.
Memorise the decimal equivalents of eighths and thirds. You'll save 10+ seconds per problem that mixes fractions and decimals.
For every algebra problem, write the substitution step out. Skipped steps are where most under-1-minute mistakes come from.
Practice mixed-topic sets, not single-topic drills. The real test alternates between equations, functions and series with no warning.
Time every practice set. If a topic consistently takes over 60 seconds per question, drill that topic specifically for a week.
Sleep well the night before. Fatigue destroys arithmetic accuracy far more than any other single factor.
Frequently Asked Questions
What math is on the IBEW aptitude test?
The NJATC/IBEW aptitude test's algebra & functions section (33 questions, ~46 minutes) covers linear equations, polynomials, factoring, functions (including composite functions), number series, inequalities, and basic operations with fractions and decimals. There is no geometry, trigonometry, or calculus.
Can I use a calculator on the IBEW aptitude test?
No. The test is closed-book and calculator-free. You get scratch paper and a pencil. That's why speed with mental arithmetic and fraction manipulation matters as much as knowing the algebra rules.
How much math do I need to pass?
IBEW locals typically look for a scaled score of 4 or higher on the 1–9 result scale. The math section is the make-or-break section for most applicants — hitting 70%+ on math practice tests puts you in a strong position overall.
How long should I study electrician math before the test?
If you haven't touched algebra since high school, plan 4–8 weeks of consistent practice (20–30 minutes a day). If your algebra is fresh, 2–3 weeks of targeted drilling on functions, number series and fractions is usually enough.
What's the best way to practice electrician math?
Do timed, mixed-topic sets under the ~1-minute-per-question pressure of the real test. Adaptive quiz apps like Voltly identify which math topics you're weakest on and re-serve those question types until you consistently get them right.
Drill math the way the real test hits you.
Timed. Mixed. Calculator-free.
A PDF gives you the same 20 problems in the same order. Voltly's adaptive engine mixes equations, fractions, functions and series at the exact ~60-second-per-question pace of the NJATC/IBEW test, and re-serves the topics you keep missing until they're instinct.
