IBEW Aptitude Test Math: The 33 Algebra and Functions Questions, 46 Minutes, No Calculator (2026)

Not affiliated with the IBEW, NECA, the electrical training ALLIANCE or any JATC. Program names belong to their owners. The format facts below come from the electrical training ALLIANCE applicant pages and JATC pages we opened in October 2026. All example questions on this page are our own.

The math section at a glance

Item	Algebra and Functions
Questions	33
Time	46 minutes
Average time per question	About 84 seconds on average across the section
Calculator	Not allowed
Guessing penalty	None. Your score is the number you answer correctly
Electrical knowledge needed	None
What comes next	A short break, then the 36 question Reading Comprehension test

The question count and time come from the electrical training ALLIANCE application page, which also says the whole battery takes about two and a half hours and that you will not be able to use a calculator. The NECA-IBEW Electrical Training Center in Portland and the Austin Electrical Training Alliance publish the same 33 questions in 46 minutes.

Your JATC may also ask for one year of high school algebra with a passing grade, or one post high school algebra course, before you can test. The ALLIANCE lists this among the minimum requirements a local JATC may set and says minimums can be waived for documented electrical construction work hours (ALLIANCE application page). Check your JATC’s own rules.

The five question types

The ALLIANCE sample test page shows a handful of sample algebra items. We will not copy them here. They illustrate the five patterns below, each with our own small example. This is a study guide, not a complete list of what the test can ask.

Type	What you do	Our example
Evaluate a formula	Put numbers in for letters and work it out in order	If R = 4(m – 3) + n, m = 7 and n = 5, then R = 21
Equivalent expressions	Multiply out brackets or collect like terms	(x – 4)(x + 6) = x² + 2x – 24
Number patterns	Find the rule and the next number	3, 7, 6, 10, 9, 13 follows +4 then -1
When is it positive or negative	Turn a formula into an inequality	y = 3x – 12 is negative when x is less than 4
Tables and rules	Match a table of x and y values to a formula, a sentence or a graph	x = 0, 1, 2, 3 gives y = 7, 5, 3, 1, so y = 7 – 2x

The ALLIANCE says you do not need to memorize formulas or facts to do well. What you need is speed with the basic moves: order of operations, negative numbers, fractions and distributing.

Worked examples, step by step

Example 1: evaluate a formula. R = 4(m – 3) + n with m = 7 and n = 5.

1. Brackets first: 7 – 3 = 4.
2. Multiply: 4 × 4 = 16.
3. Add n: 16 + 5 = 21.

Check: work backward. 21 – 5 = 16, 16 ÷ 4 = 4, 4 + 3 = 7, which is m.

Example 2: multiply two brackets. Find an expression equal to 2(x – 4)(x + 6).

1. Multiply the brackets: x × x = x², x × 6 = 6x, -4 × x = -4x, -4 × 6 = -24.
2. Collect: x² + 6x – 4x – 24 = x² + 2x – 24.
3. Multiply by 2: 2x² + 4x – 48.

Check: put x = 1 into both forms. 2(1 – 4)(1 + 6) = 2 × (-3) × 7 = -42. And 2 + 4 – 48 = -42. They match.

Example 3: number pattern. 3, 7, 6, 10, 9, ?

1. Differences: +4, -1, +4, -1.
2. The next step is +4, so 9 + 4 = 13.

Check: positions 1, 3 and 5 are 3, 6, 9, and positions 2, 4 and 6 are 7, 10, 13; each rises by 3.

Example 4: when is it negative? y = 3x – 12.

1. Negative means y < 0, so 3x – 12 < 0.
2. Add 12: 3x < 12.
3. Divide by 3: x < 4.

Check: x = 3 gives 9 – 12 = -3, negative. x = 5 gives 15 – 12 = 3, positive. x = 4 gives 0, neither.

Example 5: table to rule. x = 0, 1, 2, 3 and y = 7, 5, 3, 1.

1. When x goes up by 1, y goes down by 2, so the slope is -2.
2. When x = 0, y = 7, so the starting value is 7.
3. The rule is y = 7 – 2x.

Check: x = 3 gives 7 – 6 = 1, which matches the table.

Check yourself: five algebra questions

Set a timer for 7 minutes, about 84 seconds per question, and use no calculator. These are our own questions in the five patterns above.

Question 1 (formula). If A = 3(x + 2) – 5, what is A when x = 4?

A. 9. B. 11. C. 13. D. 15.

Question 2 (multiplying). Multiply (x + 3)(x – 5).

A. x² – 2x – 15. B. x² + 2x – 15. C. x² – 8x + 15. D. x² – 2x + 15.

Question 3 (pattern). What comes next: 5, 9, 7, 11, 9, ?

A. 7. B. 11. C. 13. D. 15.

Question 4 (inequality). For y = 2x – 10, which values of x make y positive?

A. x < 5. B. x > -5. C. x > 5. D. x < -5.

Question 5 (table to rule). x = 0, 1, 2, 3 and y = 6, 4, 2, 0. Which rule fits?

A. y = 6 + 2x. B. y = 6 – 2x. C. y = 2x – 6. D. y = 3 – x.

Check yourself: answers

1. C. 3(4 + 2) – 5 = 3 × 6 – 5 = 18 – 5 = 13.
2. A. x × x = x², x × (-5) = -5x, 3 × x = 3x and 3 × (-5) = -15. Then -5x + 3x = -2x, so the product is x² – 2x – 15.
3. C. The steps are +4, -2, +4, -2, so the next step is +4: 9 + 4 = 13.
4. C. Positive means 2x – 10 > 0. Add 10: 2x > 10. Divide by 2: x > 5.
5. B. When x goes up by 1, y goes down by 2, and y = 6 when x = 0, so y = 6 – 2x.

Check: in question 5, x = 3 gives 6 – 6 = 0, which matches the table, and x = 1 gives 6 – 2 = 4.

A timing plan for 46 minutes

With 33 questions you have 46 × 60 ÷ 33 = 83.6 seconds each. Because there is no guessing penalty, never leave a question blank.

1. First pass, about 33 minutes. Give each question up to one minute. If you cannot see the path in that time, mark a guess and circle the number.
2. Second pass, about 10 minutes. Go back to the circled questions.
3. Last 3 minutes. Make sure every question has an answer.

Check: 33 + 10 + 3 = 46 minutes.

How to practice without a calculator

• Put your calculator away from day one. Do every practice set with pencil and scrap paper, the same tools the test gives you.
• Drill the small skills daily. Ten minutes of times tables to 12, fraction to decimal swaps (1/4 = 0.25, 3/8 = 0.375) and signed numbers.
• Sort your mistakes by type. Use the five types in the table above. If most misses are in one type, spend the next three days there.
• Time yourself in blocks of 11. Eleven questions in about 15 minutes matches the real pace, and three blocks make one full section.
• Do at least two full timed sections of 33 questions before test day.

If you have been out of school for years, start with the order of operations and negative numbers before you try timed sets. Our guide to getting into an electrical apprenticeship with no experience covers the steps before and after the test.

Separate algebra eligibility from test preparation

An aptitude score and proof of algebra study are different requirements. The electrical training ALLIANCE describes possible local algebra and transcript requirements; individual programs set their own application procedures. West Texas JATC, for example, lists specified algebra study or the Tech Math Course. The Electrical Trades Center publishes its own application and document-upload process.

Before buying a replacement course, ask your target program whether it accepts that exact course and what completion document it needs. Save the program’s reply privately. Use a record with the course title, provider, grade or completion requirement, accepted evidence, and application deadline.

For practice, work the following original exercises without a calculator first. These are teaching examples, not questions from an actual admission exam.

Algebra evidence and problem-solving practice

1. TX-053: You passed a practice aptitude test. Does that by itself prove completion of the target program’s algebra prerequisite?
   Answer: No. Check and supply the separate evidence that program accepts.
2. TX-053: Does one JATC accepting Tech Math establish acceptance by every program?
   Answer: No. Obtain confirmation from your own target program before paying.
3. TX-053: What should an alternative-course record include?
   Answer: The exact course, provider, completion standard, accepted evidence, and deadline.
4. TX-062: Solve 3(x + 2) = 21.
   Answer: x = 5. Divide both sides by 3 to get x + 2 = 7, then subtract 2.
5. TX-062: If f(x) = 2x squared – 3, find f(-2).
   Answer: 5. Square -2 first to get 4, multiply by 2, then subtract 3.
6. TX-062: Expand (x + 4)(x – 2).
   Answer: x squared + 2x – 8. Multiply all four pairs and combine the middle terms.

Official references checked October 16, 2026

• Electrical training ALLIANCE: apprenticeship application
• Electrical training ALLIANCE: Online Tech Math
• West Texas JATC: applicant qualifications
• Electrical Trades Center: application process

Is this the right test for your JATC?

Not every JATC uses this test. Some, such as JATC Local 26 in the Washington, D.C. area and the Phoenix Electrical JATC, now use the GAN aptitude test. Its math is numerical computation and numerical reasoning, not an Algebra and Functions section. Look for the words “Algebra and Functions”, “NJATC” or “electrical training ALLIANCE” on your JATC’s application page. If you see “GAN” or “Personal Experience Form”, you are taking the GAN test.

In Texas? The Texas Electrical Apprenticeship Entry Kit covers 13 Texas programs.

FAQ

Sources checked October 2026

• electrical training ALLIANCE, The Application Process: https://www.electricaltrainingalliance.org/SamplePage/ApplyingforApprenticeship
• electrical training ALLIANCE, Preparing for the Test: https://www.electricaltrainingalliance.org/SamplePage/PreparingfortheTest
• electrical training ALLIANCE, Apprenticeship Training: https://www.electricaltrainingalliance.org/training/apprenticeshipTraining
• NECA-IBEW Electrical Training Center, Preparing for the Aptitude Test: https://nietc.org/applicants/preparing-to-apply/preparing-for-the-aptitude-test-and-the-interview/
• Austin Electrical Training Alliance, Apprentice Program: https://austineta.org/apprentice-program-2/
• JATC Local 26, GAN Bullet Points: https://www.jatc26.org/wp-content/uploads/2026/02/GAN-Bullet-Points-1.pdf
• Phoenix Electrical JATC, FAQ: https://pejatc.org/faq/