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IBEW aptitude test practice: 18 free questions with worked answers

Here are 18 practice questions in the style of the aptitude test that IBEW/NECA apprenticeship programs give: 6 number series, 8 algebra and functions items, and a short reading passage with 4 questions. They are unofficial: this site wrote them, and none comes from the real test. Work without a calculator, at about 84 seconds a math item, then open each worked answer.

Written November 13, 2026. Format facts are from the electrical training ALLIANCE's own application and sample-test pages.

Unofficial practice. The only official practice is the free sample on the electrical training ALLIANCE's Preparing for the Test page: 5 algebra items and 1 short passage with 3 questions. Take that first. The questions below copy its item types, not its items.

How to use this set

The real test has 33 Algebra and Functions items in 46 minutes and 36 Reading Comprehension items in 51 minutes, with no calculator: about 84 seconds an item. Give yourself 20 minutes for questions 1 to 14 and 6 for 15 to 18, with pencil and scratch paper. Guess rather than leave a blank: the ALLIANCE says there is no penalty for guessing.

Part 1: Number series (questions 1 to 6)

Find the next number. Look at the gaps between the terms before you look at the terms.

1. 4, 7, 13, 25, 49, ?

  1. 73
  2. 96
  3. 97
  4. 98
Answer: C, 97

The gaps are 3, 6, 12, 24: each one doubles, so the next gap is 48, and 49 + 48 = 97. Another way to see it: each term is the one before times 2, minus 1.

2. 81, 27, 9, 3, ?

  1. 0
  2. 1
  3. 1/3
  4. −3
Answer: B, 1

Each term is the one before divided by 3, so 3 ÷ 3 = 1. Gaps that shrink by a factor of 3 (54, 18, 6) tell you to divide.

3. 2, 9, 5, 12, 8, ?

  1. 4
  2. 11
  3. 15
  4. 16
Answer: C, 15

Two steps take turns: +7, −4, +7, −4. Next comes +7: 8 + 7 = 15. The official sample has a series of this kind.

4. 3, −6, 12, −24, ?

  1. −48
  2. 48
  3. −27
  4. 36
Answer: B, 48

Multiply by −2 each time: −24 × −2 = 48. When the signs alternate, look for a negative multiplier.

5. 5, 6, 8, 11, 15, ?

  1. 19
  2. 20
  3. 21
  4. 22
Answer: B, 20

The gaps grow by one: 1, 2, 3, 4, so the next gap is 5, and 15 + 5 = 20.

6. 10, 1, 12, 3, 14, 5, ?

  1. 7
  2. 15
  3. 16
  4. 18
Answer: C, 16

Two series are woven together: 10, 12, 14 in the odd places and 1, 3, 5 in the even ones. The 7th term belongs to the first series: 14 + 2 = 16. Answer A, 7, continues the wrong one.

Part 2: Algebra and functions (questions 7 to 14)

7. P = 2(L + W) − 3. If L = 7 and W = 4, what is P?

  1. 19
  2. 15
  3. 22
  4. 25
Answer: A, 19

Parentheses first: 7 + 4 = 11. Then 2 × 11 = 22, and 22 − 3 = 19. B, 15, comes from doubling only L.

8. Which formula is equivalent to y = 2(x − 3)(x + 4)?

  1. y = 2x² + 2x − 24
  2. y = 2x² − 2x − 24
  3. y = x² + x − 12
  4. y = 2x² + 14x − 24
Answer: A

FOIL the two brackets: First x · x = x², Outer 4x, Inner −3x, Last −12, so x² + x − 12. Then multiply every term by 2: 2x² + 2x − 24. C forgets the 2; B gets the sign of the middle term wrong.

9. Solve 5x − 7 = 3x + 9.

  1. 1
  2. 2
  3. 8
  4. 16
Answer: C, 8
5x − 3x = 9 + 7 2x = 16 x = 8

Check: 5(8) − 7 = 33 and 3(8) + 9 = 33.

10. For the formula y = 3 − 2x, which statement is true?

  1. When x is greater than 1.5, y is negative.
  2. When x is less than 1.5, y is negative.
  3. When x is greater than 3, y is positive.
  4. When x is 0, y is negative.
Answer: A

y is negative when 3 − 2x < 0, that is when 2x > 3, so x > 1.5. Test it: x = 2 gives y = −1. When x is 0, y is 3, so D is false.

11. Which rule fits this table?

x01234
y357911
  1. y = x + 3
  2. y = 2x + 3
  3. y = 3x + 2
  4. y = 2x − 3
Answer: B

When x goes up by 1, y goes up by 2, so the rule is 2x plus something. At x = 0, y = 3, so it is 2x + 3. Check the last column: 2(4) + 3 = 11.

12. Simplify (x³ · x⁴) ÷ x².

  1. x⁵
  2. x¹⁰
  3. x⁶
  4. x¹⁴
Answer: A, x⁵

Multiplying like bases adds exponents (3 + 4 = 7); dividing subtracts them (7 − 2 = 5).

13. If f(x) = x² − 3x, what is f(−2)?

  1. −2
  2. 2
  3. 10
  4. −10
Answer: C, 10

Put −2 everywhere you see x: (−2)² − 3(−2) = 4 + 6 = 10. f(x) means "f of x", not f times x.

14. Solve −3x + 4 ≥ 19.

  1. x ≥ −5
  2. x ≤ −5
  3. x ≥ 5
  4. x ≤ 5
Answer: B, x ≤ −5

Subtract 4: −3x ≥ 15. Divide by −3, and because you divided by a negative number the sign flips: x ≤ −5.

Part 3: Reading comprehension (questions 15 to 18)

The passage is fictional and shorter than a real one; the official sample notes that test passages are longer.

Lending tools, not just books

When the Harlow Public Library opened its tool collection in 2019, the staff expected to lend a few ladders and drills. Within a year the collection held more than 400 items, and the waiting list for the carpet cleaner ran six weeks. The idea was simple. Most households use a power tool for a few hours a year, yet each one buys its own. Sharing, the library argued, saves money and storage space.

Not every borrower returned tools in working order, however. In the first year, about one tool in twelve came back needing repair, usually because a blade had dulled or a battery had been left to drain. Rather than charge fines, the library began a short orientation: before a first loan, each borrower spends twenty minutes with a volunteer learning to check, clean and store the tools. Repairs fell by half the following year.

The orientation had a second effect the staff had not planned. Borrowers began staying after their sessions to ask the volunteers about projects, and the library now hosts a monthly repair night where neighbors fix lamps, chairs and bicycles together.

15. According to the passage, how many tools came back needing repair in the first year?

  1. About one in six
  2. About one in eight
  3. About one in twelve
  4. About one in twenty
Answer: C

"According to the passage" means the answer is stated: "about one tool in twelve came back needing repair."

16. In the second paragraph, "orientation" most nearly means:

  1. a direction on a map
  2. a short training session for newcomers
  3. a personal preference
  4. a waiting list
Answer: B

The sentence defines it: twenty minutes with a volunteer "learning to check, clean and store the tools." The other meanings are real but don't fit here.

17. Which conclusion does the passage best support?

  1. The library stopped lending power tools after the first year.
  2. Teaching borrowers to care for tools reduced damage.
  3. Fines are the best way to protect shared tools.
  4. Most Harlow residents no longer own tools.
Answer: B

This is an inference: repairs "fell by half" after the orientation began. C isn't supported: the library chose not to charge fines ("Rather than charge fines"), so the passage says nothing about how well they work. A and D go beyond anything stated.

18. What is the main idea of the passage?

  1. Tool libraries cost more than they save.
  2. A library's tool collection grew fast, met a problem, and solved it in a way that also brought neighbors together.
  3. Volunteers should repair all borrowed tools.
  4. Carpet cleaners are the most popular tools to borrow.
Answer: B

The main idea covers the whole passage. D is one detail; A and C are never said.

What your result means

No one can turn a score on 18 questions into the test's 1 to 9 scale. Use the set to find your weak item type instead:

For more free practice: the official sample, Ultimate Electrician's Guide's free timed exam (math and reading), JobTestPrep's free questions (timed or untimed) and Khan Academy for the algebra. Paid packs and courses add hundreds of timed questions; the home page compares them with prices read today. One of them is ClassMetric's Union Aptitude Prep ($39 once), which has 403 practice questions, each with its answer explained, and lets you try 10 timed questions free.

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