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IBEW aptitude test

IBEW aptitude test math: the algebra, step by step

By the nodiexam teamUpdated

The math on the IBEW aptitude test is the Algebra and Functions part: 33 questions in 46 minutes, and calculators are not allowed. The official sample pages show evaluating formulas, equivalent expressions, number patterns, and function tables. Also, one applicant wrote that equations, number sequences and graphs made up most of the math, and another wrote that the test had parabolas.

Below is every topic we practice, each with one worked example and a short drill. Work each drill on paper, then open its answers. If a topic feels shaky, the free full-length practice test shows how it comes up under the clock.

The first five topics are the question types the electrical training ALLIANCE shows on its sample pages. The last four are the rest of the school algebra we practice. Posts from applicants who took the test mention equations, graphs and parabolas, and word problems use the same skills.

1. Evaluating formulas

You get a formula and some values. Put the values in and work it out by hand. Do powers first, then times and divide, then plus and minus. Put negative numbers in parentheses so the signs stay right.

Worked example. y = 3x² − 2x + 5. What is y when x = −2?

  1. Square first: (−2)² = 4.
  2. Times 3: 3 × 4 = 12.
  3. The middle term: −2x = −2 × (−2) = +4.
  4. Add it up: 12 + 4 + 5 = 21.

y = 21. The common slip is squaring −2 as −4. That gives 3 × (−4) + 4 + 5 = −3.

Try it

  1. P = V² ÷ R. Find P when V = 10 and R = 4.
  2. F = 9C ÷ 5 + 32. Find F when C = 25.
  3. y = 2x² − x. Find y when x = −3.
Show answers
  1. P = 100 ÷ 4 = 25.
  2. 9 × 25 = 225, 225 ÷ 5 = 45, 45 + 32 = 77.
  3. 2 × 9 = 18, then 18 − (−3) = 21.

2. Equivalent expressions

Pick the expression that means the same as the one given. Remove the parentheses, then collect the x terms and the plain numbers. Watch the sign in front of each set of parentheses. A minus changes every sign inside.

Worked example. Which expression equals 4(x − 3) − 2(x + 5)?

  • A. 2x − 22
  • B. 2x − 2
  • C. 2x + 2
  • D. 6x − 22
  1. Multiply out the first part: 4x − 12.
  2. Multiply out the second part, minus sign included: −2x − 10.
  3. Collect the x terms: 4x − 2x = 2x.
  4. Collect the numbers: −12 − 10 = −22.

The answer is A, 2x − 22. B comes from writing −2x + 10, forgetting that the minus applies to the 5 as well.

Try it

  1. Simplify 5(2x + 1) − 3x.
  2. Expand (x + 4)(x − 2).
  3. Factor x² + 7x + 12.
Show answers
  1. 10x + 5 − 3x = 7x + 5.
  2. x² − 2x + 4x − 8 = x² + 2x − 8.
  3. Find two numbers that multiply to 12 and add to 7: 3 and 4. So (x + 3)(x + 4).

3. Number patterns

Find the rule in a row of numbers and give the next one. Look at the gaps between numbers first. If the gaps don't stay the same, try times or divide, then look for two rules taking turns.

Worked example. What comes next? 3, 7, 15, 31, ?

  1. The gaps are 4, 8, 16. Each gap doubles.
  2. The next gap is 32, so the next number is 31 + 32 = 63.
  3. Check with a second rule: each number is double the one before, plus 1. 31 × 2 + 1 = 63. Both rules agree.

The next number is 63.

Try it

  1. 81, 27, 9, 3, ?
  2. 2, 5, 4, 7, 6, 9, ?
  3. 1, 4, 9, 16, 25, ?
Show answers
  1. Divide by 3 each time: 1.
  2. Plus 3, then minus 1, taking turns: 9 − 1 = 8.
  3. These are the squares 1², 2², 3² and so on: 6² = 36.

4. Sign of a formula's output

You are told whether some values are positive or negative, and you decide the sign of the result without exact numbers. Two rules do most of the work. A negative times a negative is positive. A negative times a positive is negative.

Worked example. x is negative and y is positive. Which expression is always negative?

  • A. x × y
  • B. x²
  • C. y − x
  • D. x² × y
  1. A: negative times positive is negative. Always negative.
  2. B: a square is never negative.
  3. C: y − x means positive minus a negative, which is positive plus a positive. Always positive.
  4. D: x² is positive and y is positive, so the result is positive.

The answer is A. If you're unsure, test with numbers: x = −2 and y = 3 give A = −6, B = 4, C = 5, D = 12.

Try it

  1. If x = −4, is x³ positive or negative?
  2. a and b are both negative. What is the sign of a × b? Of a + b?
  3. n is negative. Is n² − n positive or negative?
Show answers
  1. Negative: (−4)³ = −64. An odd power keeps the minus.
  2. a × b is positive, and a + b is negative.
  3. Positive. n² is positive, and minus a negative adds. Test n = −2: 4 + 2 = 6.

5. Matching tables to relationships

You get a table of x and y values and pick the rule that made it. Check how much y changes each time x goes up by 1. That change is the number in front of x. Then test every pair, not only the first one.

Worked example. Which rule fits every pair?

x0123
y41−2−5
  • A. y = 3x + 4
  • B. y = −3x + 4
  • C. y = 4 − x
  • D. y = −3x − 4
  1. Each time x goes up by 1, y goes down by 3. So the rule starts with −3x.
  2. When x = 0, y = 4. So the rule ends with + 4.
  3. Check the last pair: −3 × 3 + 4 = −9 + 4 = −5. It works.

The answer is B, y = −3x + 4. A, C and D all fail at x = 1: they give 7, 3 and −7, but the table says 1.

Try it

  1. x = 1, 2, 3, 4 gives y = 7, 9, 11, 13. Find the rule.
  2. x = 1, 2, 3, 4 gives y = 2, 5, 10, 17. Find the rule.
  3. f(x) = 5 − 2x. Find f(3).
Show answers
  1. y goes up by 2, so 2x. At x = 1, 2 × 1 = 2, and 7 − 2 = 5. y = 2x + 5.
  2. The gaps are 3, 5, 7, so it isn't a straight line. Each y is one more than x squared: y = x² + 1.
  3. 5 − 2 × 3 = 5 − 6 = −1.

6. Solving equations and inequalities

Find the value of x that makes an equation true. With an inequality, the answer is a range of values, such as x < −4. Do the same thing to both sides until x is alone. When you multiply or divide an inequality by a negative number, flip the sign.

Worked example 1. Solve 5x − 7 = 2x + 8.

  1. Take 2x from both sides: 3x − 7 = 8.
  2. Add 7 to both sides: 3x = 15.
  3. Divide by 3: x = 5.
  4. Check: 5 × 5 − 7 = 18, and 2 × 5 + 8 = 18. It works.

Worked example 2. Solve −2x + 3 > 11.

  1. Take 3 from both sides: −2x > 8.
  2. Divide by −2 and flip the sign: x < −4.
  3. Check a value in the range: x = −5 gives 10 + 3 = 13, which is more than 11. It works.

x < −4. Any number less than −4 makes it true. Forgetting to flip gives x > −4, a common wrong choice.

Try it

  1. Solve 3(x + 2) = 21.
  2. Solve x ÷ 4 − 3 = 2.
  3. Solve 4 − 3x ≤ 19.
Show answers
  1. Divide by 3: x + 2 = 7, so x = 5.
  2. Add 3: x ÷ 4 = 5, so x = 20.
  3. Take 4: −3x ≤ 15. Divide by −3 and flip: x ≥ −5.

7. Reading graphs

You read values, slopes and crossing points from a straight line on a grid. The slope is how much y changes when x goes up by 1: take the change in y and divide it by the change in x. The y-intercept is where the line crosses the up-and-down axis.

Worked example. A straight line crosses the y-axis at −2 and passes through the point (3, 4). What is y when x = 5?

  1. Two points on the line: (0, −2) and (3, 4).
  2. Slope: change in y ÷ change in x = (4 − (−2)) ÷ (3 − 0) = 6 ÷ 3 = 2.
  3. The line is y = 2x − 2.
  4. At x = 5: y = 2 × 5 − 2 = 8.

y = 8.

Line graph of y against xPoints: (0, −2); (3, 4); (5, 8)−1012345−4−20246810xy

Try it

  1. A line passes through (0, 5) and (2, 1). What is its slope?
  2. Where does the line y = 3x − 6 cross the x-axis?
  3. A line passes through (1, 3) and (4, 9). What is its slope?
Show answers
  1. (1 − 5) ÷ (2 − 0) = −4 ÷ 2 = −2. The line goes down.
  2. y = 0 there, so 3x = 6 and x = 2. The point is (2, 0).
  3. (9 − 3) ÷ (4 − 1) = 6 ÷ 3 = 2.

8. Quadratics and parabolas

A formula with x² in it makes a curve called a parabola. If the number in front of x² is positive, the curve opens up like a U and the turning point is its lowest point. If it is negative, the curve opens down like an upside-down U and the turning point is its highest point. The roots are where the curve crosses the x-axis.

Worked example. y = x² − 6x + 5. Find the roots and the turning point.

  1. Factor: two numbers that multiply to 5 and add to −6 are −1 and −5. So y = (x − 1)(x − 5).
  2. Roots: y = 0 when x = 1 or x = 5.
  3. The turning point sits halfway between the roots, at x = 3.
  4. Put x = 3 in: 9 − 18 + 5 = −4. The turning point is (3, −4).
  5. The number in front of x² is +1, so the curve opens up and (3, −4) is its lowest point.

Now one that opens down. y = −x² + 4. The minus in front of x² turns the curve upside down. The highest point is (0, 4), and the roots are x = 2 and x = −2, because −(2²) + 4 = 0.

ParabolaParabola opening upward. Turning point (3, −4). Points on the curve: (−1, 12); (0, 5); (1, 0); (2, −3); (3, −4); (4, −3); (5, 0); (6, 5); (7, 12).−101234567−404812xy
ParabolaParabola opening downward. Turning point (0, 4). Points on the curve: (−3, −5); (−2, 0); (−1, 3); (0, 4); (1, 3); (2, 0); (3, −5).−3−2−10123−4−2024xy

Try it

  1. Find the roots of y = x² − 9.
  2. Does y = −2x² + 8x − 3 open up or down? Find its turning point.
  3. Find the turning point of y = (x − 4)² + 1. Is it the highest or lowest point?
Show answers
  1. x² = 9, so x = 3 or x = −3.
  2. Down, because of the −2 in front of x². The turning point is at x = −b ÷ 2a, here −8 ÷ (2 × −2) = 2, and y = −8 + 16 − 3 = 5. So (2, 5), the highest point.
  3. (4, 1). (x − 4)² is never negative, so y is smallest when x = 4. It is the lowest point.

9. Word problems

Short stories about rates, ratios and percentages. Write down what you know, decide what you are looking for, and turn the words into one line of math.

Worked example. A spool holds 250 feet of wire. A job uses 40% of it. How many feet are left?

  1. 10% of 250 is 25, so 40% is 4 × 25 = 100 feet used.
  2. Left over: 250 − 100 = 150 feet.

150 feet. The trap answer is 100, which is the amount used, not the amount left.

Try it

  1. Copper and aluminum scrap are in the ratio 3 to 2. The total is 40 pounds. How many pounds are copper?
  2. A crew pulls wire at 120 feet per hour. How long does 300 feet take?
  3. A $80 tool goes up in price by 15%. What is the new price?
Show answers
  1. 3 + 2 = 5 parts, so each part is 40 ÷ 5 = 8 pounds. Copper is 3 × 8 = 24 pounds.
  2. 300 ÷ 120 = 2.5 hours, which is 2 hours 30 minutes.
  3. 15% of 80 is 12, so the new price is $92.

Working fast without a calculator

  • Know your times tables to 12 and the squares from 1 to 15.
  • Write each step on paper. Sign slips hide in steps done in your head.
  • Use the answer choices. Put each one back into the question when solving gets slow.
  • Estimate first. If you expect about 50 and get 500, look for a slipped zero.

Practice these topics under the clock

The free full-length practice test mixes all nine topics with the official timing and shows your score by topic. Full prep lets you drill any one topic on its own with step-by-step explanations. For the reading part and 2- and 4-week plans, see the study guide. The format and scoring rules are on the IBEW aptitude test overview.

Questions people ask

What kind of math is on the IBEW aptitude test?

High school algebra. The electrical training ALLIANCE's sample pages show evaluating formulas, equivalent expressions, number patterns, and function tables, plus questions on whether a formula gives a positive or negative result. Posts by applicants who took the test add graphs and parabolas, so this page covers those too.

Is there geometry or trigonometry on the IBEW aptitude test?

The math part is called Algebra and Functions, and the question types on the official sample pages are all algebra: evaluating formulas, equivalent expressions, number patterns, and function tables. Spend your study time on the topics on this page.

How fast do I need to work on the math part?

You have 46 minutes for 33 questions, a little under a minute and a half each, and calculators are not allowed. If a question takes more than two minutes, guess, flag it and move on. There is no penalty for guessing.

Sources

Exam facts on this page come from these pages. We checked each one on the date shown.