The IBEW aptitude test's first section, Algebra and Functions, has 33 questions in 46 minutes, with no calculator. Below is one practice question of each of the eight types in our bank, in the test's format: four options, one best answer. Work each one on paper before you open the answer; every explanation shows the working and the exact slip behind each wrong option.
01How to use these
- Pace. About 84 seconds a question on the real test. Time yourself: eight questions in about 11 minutes.
- By hand. No calculator, as on test day. Write every step; most misses are a dropped negative sign.
- Read the wrong answers too. Each one is a mistake someone really makes. If you picked it, the explanation tells you which.
02The eight questions
1. Evaluate a formula
Evaluate a formula or expression for given values. Put every negative in parentheses before you square it: (-3)² = 9, but -3² = -9.
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Evaluate 2y³ - y when y = -2.
- -62
- -14
- -10
- 18
Show the answer
B. Correct. (-2)³ = -8, so 2y³ = -16. Subtracting y = -2 adds 2: -16 + 2 = -14.
Why not the others
A. This cubes 2y instead of y alone: (-4)³ = -64, then -64 + 2 = -62.
C. This multiplies y by 3 instead of cubing it (3 × -2 = -6), giving 2(-6) + 2 = -10.
D. This treats (-2)³ as +8. An odd power of a negative number stays negative.
ID IBEW-A-016 · Task IBEW-A-1 (Evaluate a formula)
2. Equivalent expressions
Pick the expression equivalent to a product or sum: expand, simplify or factor. Multiply every term by every term, then combine like terms. Check one option by putting x = 1 into both forms.
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Which expression is equivalent to 4(2x - 3)(x + 1)?
- 2x² - x - 3
- 8x² - 4x - 3
- 8x² - 4x - 12
- 8x² + 20x - 12
Show the answer
C. Correct. (2x - 3)(x + 1) = 2x² + 2x - 3x - 3 = 2x² - x - 3, and 4 times that is 8x² - 4x - 12.
Why not the others
A. This is (2x - 3)(x + 1) multiplied out correctly, but the 4 in front was never multiplied in.
B. Multiplies the 4 into the x² and x terms but forgets to multiply it into the constant -3.
D. Treats -3 × x as +3x, so the middle term becomes 2x + 3x = 5x instead of -x; times 4 gives 20x.
ID IBEW-A-046 · Task IBEW-A-2 (Equivalent expressions)
3. Number series
Find the next or missing number in a series. Write the differences under the numbers. If they are not constant, look for alternating steps, ratios or squares.
-
What number comes next in this series? 2, 5, 10, 17, 26, ...
- 35
- 36
- 37
- 50
Show the answer
C. Correct. The terms are 1² + 1, 2² + 1, 3² + 1, ... so next is 6² + 1 = 37 (gaps 3, 5, 7, 9, 11 agree).
Why not the others
A. Adds 9 again; the gaps are 3, 5, 7, 9, so the next gap is 11.
B. Gives 6² but forgets the + 1; every term is one more than a square (26 = 5² + 1).
D. Uses 7² + 1, which skips 6² + 1; 50 is the term after next.
ID IBEW-A-101 · Task IBEW-A-3 (Number series)
4. Linear functions and inequalities
Linear functions and inequalities: for which inputs is the output positive or negative. Solve it like an equation, and flip the inequality sign when you multiply or divide by a negative number.
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For which values of x is y = 15 - 5x negative?
- x < -3
- x > -3
- x < 3
- x > 3
Show the answer
D. Correct. 15 - 5x < 0 gives -5x < -15; dividing by -5 reverses the sign, so x > 3.
Why not the others
A. Moves the 15 with the wrong sign (-5x < 15) and then also forgets to reverse when dividing by -5.
B. Moves the 15 with the wrong sign. From 15 - 5x < 0, subtracting 15 gives -5x < -15, not -5x < 15.
C. Forgets to reverse the inequality when dividing -5x < -15 by -5. Check x = 0: y = 15, which is not negative.
ID IBEW-A-132 · Task IBEW-A-4 (Linear functions and inequalities)
5. Table to rule
Find the rule that fits an input/output table. Find the change in y per step of x, then the starting value. Test the rule on two rows, not one.
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Which equation fits every pair in the table? x: 2, 3, 4, 5 → y: 13, 19, 25, 31
- y = x + 11
- y = 7x - 1
- y = 5x + 3
- y = 6x + 1
Show the answer
D. Correct. y rises by 6 each time x rises by 1, so the slope is 6; 6 × 2 + 1 = 13, and 6 × 5 + 1 = 31.
Why not the others
A. Fits x = 2 only. For x = 3 it gives 14, but the table shows 19.
B. Fits x = 2 (13), but x = 3 gives 20. The y-values rise by 6, not 7.
C. Fits x = 2 (13), but x = 3 gives 18. The y-values rise by 6, not 5.
ID IBEW-A-156 · Task IBEW-A-5 (Table to rule)
6. Equations and formulas
Solve a linear equation, or rearrange a formula for one letter. Do the same thing to both sides, one step at a time, and undo operations in reverse order.
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The perimeter of a rectangle is P = 2(l + w). Which equation is solved for w?
- w = P - 2l
- w = P/2 + l
- w = (P - 2l)/2
- w = (P - l)/2
Show the answer
C. Correct. P = 2l + 2w, so 2w = P - 2l and w = (P - 2l)/2.
Why not the others
A. Gets 2w = P - 2l but forgets to divide both sides by 2.
B. Divides by 2 correctly but adds l instead of subtracting it.
D. Subtracts l instead of 2l; the 2 multiplies l as well as w.
ID IBEW-A-079 · Task IBEW-A-6 (Equations and formulas)
7. Exponents and arithmetic
Exponents, roots, scientific notation, fractions, decimals and percents by hand. Add exponents when multiplying, subtract when dividing, multiply for a power of a power.
-
What is the value of 2⁻³ + 5⁰?
- -7
- 1/8
- 9/8
- 41/8
Show the answer
C. Correct. 2⁻³ = 1/2³ = 1/8 and 5⁰ = 1, so the sum is 1/8 + 8/8 = 9/8.
Why not the others
A. This treats 2⁻³ as -8. A negative exponent gives a reciprocal, 1/8, not a negative number.
B. This treats 5⁰ as 0. Any nonzero number to the zero power is 1.
D. This treats 5⁰ as 5. Any nonzero number to the zero power is 1.
ID IBEW-A-032 · Task IBEW-A-7 (Exponents and arithmetic)
8. Word problems
Word problems: turn a sentence into an expression or equation; ratios and rates. Name the unknown, write the equation, then check the answer against the words.
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On a job, the ratio of 15-amp circuits to 20-amp circuits is 3 : 4. There are 36 twenty-amp circuits. How many 15-amp circuits are there?
- 27
- 35
- 48
- 63
Show the answer
A. Correct. 36 ÷ 4 = 9 circuits per part, and the 15-amp circuits are 3 parts: 3 × 9 = 27.
Why not the others
B. Subtracts the difference in the ratio (4 - 3 = 1) from 36; a ratio compares by multiplying, not by subtracting.
C. Inverts the ratio and works out 36 × 4/3; the 15-amp count is the smaller part, 3/4 of 36.
D. Adds 27 and 36, giving the total number of circuits instead of the 15-amp count.
ID IBEW-A-122 · Task IBEW-A-8 (Word problems)
03Answer key
| Question | Answer | Type |
|---|---|---|
| Q1 | B | Evaluate a formula |
| Q2 | C | Equivalent expressions |
| Q3 | C | Number series |
| Q4 | D | Linear functions and inequalities |
| Q5 | D | Table to rule |
| Q6 | C | Equations and formulas |
| Q7 | C | Exponents and arithmetic |
| Q8 | A | Word problems |
04More practice
The IBEW aptitude test study guide explains each type with a worked example and a timing plan.
How these questions are written and checked: how our questions are made. Found a mistake? Tell us and we will fix it.
ToolboxPrep is an independent study site, not affiliated with or endorsed by the IBEW (International Brotherhood of Electrical Workers), NECA (National Electrical Contractors Association), the Electrical Training ALLIANCE (formerly NJATC) or any JATC. Our IBEW aptitude test questions and reading passages are original practice material written to the published format of the test. They are not actual test questions, not recalled or “brain dump” questions, and not the official sample questions. IBEW, NECA and Electrical Training ALLIANCE are names and trademarks of their owners.