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IBEW Aptitude Test practice questions

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Question 1Algebra

Simplify the expression 5(2x - 3) - 4x + 7.

  1. 6x + 22
  2. 6x - 22
  3. 14x - 8
  4. 6x - 8 Correct answer.

Explanation

Distribute the 5 to get 10x - 15, then combine like terms: 10x - 4x = 6x and -15 + 7 = -8. The simplified result is 6x - 8.

Question 2Algebra

Solve for x: 3x + 12 = 45.

  1. x = 9
  2. x = 15
  3. x = 11 Correct answer.
  4. x = 19

Explanation

Subtract 12 from both sides to get 3x = 33, then divide both sides by 3 to isolate x. This gives x = 11, which checks out because 3(11) + 12 = 45.

Question 3Algebra

A jobsite crew calculates labor cost with the formula C = 42h + 250, where h is hours worked. What is the labor cost when h = 8?

  1. $586 Correct answer.
  2. $336
  3. $530
  4. $636

Explanation

Substitute h = 8 into the formula: 42 times 8 equals 336, then add the fixed 250 to get 586. The total labor cost is therefore $586.

Question 4Algebra

What is the slope of the line that passes through the points (2, 5) and (6, 13)?

  1. 4
  2. 1/2
  3. 2 Correct answer.
  4. 8

Explanation

Slope equals the change in y divided by the change in x, so (13 - 5) / (6 - 2) = 8 / 4 = 2. The line rises 2 units for every 1 unit it moves to the right.

Question 5Algebra

Simplify the expression (x^3)(x^5).

  1. 2x^8
  2. x^2
  3. x^8 Correct answer.
  4. x^15

Explanation

When multiplying powers that share the same base, add the exponents: 3 + 5 = 8. The result is x to the eighth power, not a product of the exponents.

Question 6Algebra

Solve the inequality 4x - 7 < 21.

  1. x < 7 Correct answer.
  2. x < 3.5
  3. x > 7
  4. x > 3.5

Explanation

Add 7 to both sides to get 4x < 28, then divide both sides by 4 to get x < 7. Dividing by a positive number does not reverse the inequality symbol.

Question 7Algebra

Evaluate the expression 2a^2 - 3b when a = 3 and b = 4.

  1. 30
  2. 42
  3. 24
  4. 6 Correct answer.

Explanation

Square a first: 3 squared is 9, and 2 times 9 is 18. Then subtract 3 times 4, which is 12, so 18 - 12 = 6.

Question 8Algebra

Which equation represents a line parallel to y = 3x - 5?

  1. y = 3x + 2 Correct answer.
  2. y = -1/3x + 5
  3. y = -3x + 2
  4. y = (1/3)x - 5

Explanation

Parallel lines share the same slope but have different y-intercepts. The given line has slope 3, so y = 3x + 2 is parallel because it also has slope 3.

Question 9Algebra

Solve the system: x + y = 10 and x - y = 4.

  1. x = 6, y = 4
  2. x = 5, y = 5
  3. x = 3, y = 7
  4. x = 7, y = 3 Correct answer.

Explanation

Adding the two equations eliminates y and gives 2x = 14, so x = 7. Substituting back into x + y = 10 gives y = 3, and both equations check.

Question 10Algebra

Factor the quadratic x^2 - 7x + 12.

  1. (x - 3)(x - 4) Correct answer.
  2. (x - 2)(x - 6)
  3. (x + 3)(x + 4)
  4. (x - 1)(x - 12)

Explanation

Two numbers that multiply to 12 and add to -7 are -3 and -4. Therefore the quadratic factors as (x - 3)(x - 4), which expands back to the original expression.

Question 11Algebra

Using the quadratic formula, solve x^2 - 4x - 5 = 0.

  1. x = 5 or x = 1
  2. x = -5 or x = -1
  3. x = -5 or x = 1
  4. x = 5 or x = -1 Correct answer.

Explanation

Here a = 1, b = -4, and c = -5, so the discriminant is 16 + 20 = 36 and its square root is 6. Applying the formula gives (4 + 6)/2 = 5 and (4 - 6)/2 = -1.

Question 12Algebra

A conduit run's total length L in feet after t hours of work is modeled by L = 18t + 6. After how many hours will the run reach 96 feet?

  1. 6
  2. 4
  3. 5 Correct answer.
  4. 5.5

Explanation

Set 18t + 6 equal to 96, then subtract 6 to get 18t = 90. Dividing both sides by 18 gives t = 5 hours.

Question 13Algebra

Simplify (2x^2 y)(3x y^3).

  1. 6x^3 y^4 Correct answer.
  2. 5x^3 y^4
  3. 6x^2 y^3
  4. 6x^3 y^3

Explanation

Multiply the coefficients: 2 times 3 is 6. Add exponents for each base: x has 2 + 1 = 3 and y has 1 + 3 = 4, giving 6x^3 y^4.

Question 14Algebra

The line 2x + 3y = 12 crosses the y-axis at which point?

  1. (0, 4) Correct answer.
  2. (0, 12)
  3. (0, 6)
  4. (6, 0)

Explanation

A y-intercept occurs where x = 0, so substitute zero to get 3y = 12 and y = 4. The point is (0, 4).

Question 15Algebra

Solve for x: 5(x - 2) = 3x + 8.

  1. x = 3
  2. x = -9
  3. x = 1
  4. x = 9 Correct answer.

Explanation

Distribute to get 5x - 10 = 3x + 8, then subtract 3x from both sides to get 2x - 10 = 8. Adding 10 gives 2x = 18, so x = 9.

Question 16Algebra

What is the slope of a line perpendicular to y = -2x + 7?

  1. -2
  2. 2
  3. 1/2 Correct answer.
  4. -1/2

Explanation

Perpendicular slopes are negative reciprocals of each other. The negative reciprocal of -2 is 1/2, so the perpendicular line rises half a unit per unit right.

Question 17Algebra

Combine into a single fraction: 3/x + 2/(x + 1).

  1. (5x + 3)/(x(x + 1)) Correct answer.
  2. 5/(2x + 1)
  3. (5x + 1)/(x(x + 1))
  4. (6)/(x(x + 1))

Explanation

Use the common denominator x(x + 1): the first term becomes 3(x + 1) and the second becomes 2x. Adding numerators gives 3x + 3 + 2x = 5x + 3 over x(x + 1).

Question 18Algebra

If f(x) = 2x^2 - x + 1, what is f(-2)?

  1. 7
  2. 11 Correct answer.
  3. 9
  4. -5

Explanation

Substitute -2: 2 times 4 equals 8, then -(-2) becomes +2, and adding 1 gives 8 + 2 + 1 = 11. Careful sign handling is essential when squaring a negative.

Question 19Algebra

Solve for x: 2^(x + 1) = 32.

  1. x = 5
  2. x = 6
  3. x = 16
  4. x = 4 Correct answer.

Explanation

Rewrite 32 as 2^5 so the equation becomes 2^(x + 1) = 2^5. Equal bases mean equal exponents, so x + 1 = 5 and x = 4.

Question 20Algebra

A crew's material cost C in dollars is modeled by C = 3n + 40, where n is the number of fixtures. If the budget is $250, what is the greatest number of fixtures the crew can install?

  1. 60
  2. 80
  3. 83
  4. 70 Correct answer.

Explanation

Set 3n + 40 less than or equal to 250, so 3n is at most 210 and n is at most 70. Since 70 fixtures cost exactly $250, that is the maximum whole number allowed.

Question 21Algebra

Simplify the expression (x^2 - 9)/(x - 3) for x not equal to 3.

  1. x + 3 Correct answer.
  2. x^2 - 3
  3. x - 3
  4. 1/(x + 3)

Explanation

The numerator is a difference of squares and factors as (x - 3)(x + 3). Canceling the common factor (x - 3) leaves x + 3, valid wherever x is not 3.

Question 22Algebra

For what values of k does x^2 + kx + 9 = 0 have exactly one real solution?

  1. k = 0 only
  2. k = 6 or k = -6 Correct answer.
  3. k = 9 only
  4. k = 3 or k = -3

Explanation

A quadratic has exactly one real solution when its discriminant b^2 - 4ac equals zero. Here that means k^2 - 36 = 0, so k = 6 or k = -6.

Question 23Algebra

The system y = 2x + 1 and y = 2x - 4 has which type of solution set?

  1. Infinitely many solutions along the line
  2. Two solutions where the lines cross
  3. Exactly one solution at the y-intercept
  4. No solution, because the lines are parallel Correct answer.

Explanation

Both equations have slope 2 but different y-intercepts, 1 and -4. Parallel lines never intersect, so the system is inconsistent and has no solution.

Question 24Algebra

If 3^(2x) = 27^(x - 1), what is x?

  1. x = 3 Correct answer.
  2. x = 1
  3. x = 0
  4. x = -3

Explanation

Rewrite 27 as 3^3 so the right side becomes 3^(3x - 3). Equating exponents gives 2x = 3x - 3, and solving yields x = 3.

Question 25Algebra

A rectangular panel has a length 4 feet longer than its width, and its area is 96 square feet. What is its width?

  1. 10 feet
  2. 6 feet
  3. 12 feet
  4. 8 feet Correct answer.

Explanation

Let the width be w, so the length is w + 4 and w(w + 4) = 96. This gives w^2 + 4w - 96 = 0, which factors as (w + 12)(w - 8) = 0, so the positive width is 8 feet.

Question 26Algebra

An apprentice's pay is modeled by P = 16h + 40, where h is hours worked in a week and 40 is a fixed weekly tool allowance. What does the 16 represent in this model?

  1. The number of hours worked
  2. The fixed weekly allowance
  3. The hourly pay rate in dollars Correct answer.
  4. The total weekly pay

Explanation

In a linear model of the form y = mx + b, the coefficient m multiplying the variable gives the constant rate of change. Here h is hours, so 16 dollars per hour is the rate at which pay grows. The 40 is the constant added regardless of hours.

Question 27Algebra

Evaluate the expression 3x - 2y when x = -4 and y = 5.

  1. -2
  2. 2
  3. -22 Correct answer.
  4. 22

Explanation

Substitute carefully, keeping the signs: 3(-4) - 2(5) = -12 - 10 = -22. A common slip is losing the negative sign on x before multiplying.

Question 28Algebra

Which value of x satisfies the inequality -3x + 5 > 20?

  1. x > 5
  2. x > -5
  3. x < 5
  4. x < -5 Correct answer.

Explanation

Subtract 5 from both sides to get -3x > 15, then divide by -3. Dividing an inequality by a negative number reverses the direction, giving x < -5.

Question 29Algebra

Simplify the expression 4x + 7 - 2x + 3 - x.

  1. x + 4
  2. 3x + 10
  3. 5x + 10
  4. x + 10 Correct answer.

Explanation

Combine like terms separately: the x-terms are 4x - 2x - x = x, and the constants are 7 + 3 = 10. The simplified result is x + 10.

Question 30Algebra

A jobsite supply model gives the cost of wire in dollars as C = 0.85f, where f is the number of feet purchased. If a crew spends $136 on wire, how many feet did they buy?

  1. 136
  2. 115.6
  3. 160 Correct answer.
  4. 186

Explanation

Set 0.85f = 136 and divide both sides by 0.85, giving f = 160. Dividing by a decimal less than one increases the value, so the answer should exceed 136.

Question 31Algebra

What is the slope of the line passing through the points (2, 3) and (6, 11)?

  1. 4
  2. 1/2
  3. 8
  4. 2 Correct answer.

Explanation

Slope equals the change in y divided by the change in x: (11 - 3)/(6 - 2) = 8/4 = 2. Keeping the subtraction in the same order for both coordinates is essential.

Question 32Algebra

Solve for x: 7 - 2(x - 3) = 1.

  1. x = 9
  2. x = 3
  3. x = 6 Correct answer.
  4. x = 4

Explanation

Distribute to get 7 - 2x + 6 = 1, then combine to 13 - 2x = 1. Subtracting 13 gives -2x = -12, so x = 6.

Question 33Algebra

Which expression is equivalent to (x^5)(x^-2)?

  1. x^-10
  2. x^-3
  3. x^7
  4. x^3 Correct answer.

Explanation

When multiplying powers with the same base, add the exponents: 5 + (-2) = 3, so the product is x^3. The base stays the same throughout.

Question 34Algebra

A crew leader graphs a budget line where B is the remaining balance in dollars and d is days on the job. Which statement describes a line with a slope of -75 in this context?

  1. The balance drops $75 for each additional day worked Correct answer.
  2. The crew works 75 days before spending anything
  3. The balance grows $75 for each additional day worked
  4. The balance starts at $75 on day zero

Explanation

Slope is the change in the vertical quantity per one-unit change in the horizontal quantity. A slope of -75 means the balance decreases by 75 dollars for each additional day. The starting balance would be the y-intercept, not the slope.

Question 35Algebra

Solve the equation 3/(x - 2) = 5/(x + 4) for x, noting any restriction on x.

  1. x = 2
  2. x = 1
  3. x = -11
  4. x = 11 Correct answer.

Explanation

Cross-multiply to get 3(x + 4) = 5(x - 2), which expands to 3x + 12 = 5x - 10. Solving gives 22 = 2x, so x = 11, which is valid because it is neither 2 nor -4.

Question 36Algebra

A rectangular junction box lid has a perimeter of 46 inches, and its length is 5 inches more than twice its width. What is the width?

  1. 8 inches
  2. 12 inches
  3. 6 inches Correct answer.
  4. 10 inches

Explanation

Let w be the width; then the length is 2w + 5. Perimeter gives 2w + 2(2w + 5) = 46, so 6w + 10 = 46 and w = 6. Checking: length 17 and width 6 give perimeter 46.

Question 37Algebra

The function f(x) = 4x - 9 gives the number of fittings needed for x panels. What is the value of f^-1(15)?

  1. 51
  2. 4
  3. 15
  4. 6 Correct answer.

Explanation

To find the inverse value, set 4x - 9 = 15 and solve: 4x = 24, so x = 6. This means 6 panels require 15 fittings under the model.

Question 38Algebra

Simplify (6x^3 - 9x^2)/(3x) for x not equal to 0.

  1. 2x^2 - 3x Correct answer.
  2. 2x^3 - 3x^2
  3. 2x^2 - 9x
  4. 3x - 2x^2

Explanation

Divide each term in the numerator by 3x: 6x^3/(3x) = 2x^2 and -9x^2/(3x) = -3x. The result is 2x^2 - 3x.

Question 39Algebra

For the quadratic y = x^2 - 6x + 5, what are the coordinates of the vertex?

  1. (3, -4) Correct answer.
  2. (-3, -4)
  3. (3, 4)
  4. (6, 5)

Explanation

The x-coordinate of the vertex is -b/(2a) = 6/2 = 3. Substituting gives 9 - 18 + 5 = -4, so the vertex is (3, -4).

Question 40Algebra

If a line has an x-intercept at (4, 0) and a y-intercept at (0, -8), which equation represents it?

  1. y = -2x + 4
  2. y = -2x - 8
  3. y = 2x + 4
  4. y = 2x - 8 Correct answer.

Explanation

Slope is (0 - (-8))/(4 - 0) = 8/4 = 2, and the y-intercept is -8, so y = 2x - 8. Substituting x = 4 confirms y = 0.

Question 41Algebra

A crew's output is modeled by N = 12t + 5, where N is the number of units installed and t is hours after the shift begins. What does N = 41 mean?

  1. 41 units are installed after 3 hours Correct answer.
  2. 41 hours are needed to install 3 units
  3. 41 units are installed after 4 hours
  4. 41 units are installed at the start of the shift

Explanation

Set 12t + 5 = 41, giving 12t = 36 and t = 3. So the model reaches 41 installed units at 3 hours into the shift.

Question 42Algebra

Solve the system: 3x + 2y = 16 and x - y = 2.

  1. x = 4, y = 2 Correct answer.
  2. x = 2, y = 4
  3. x = 4, y = -2
  4. x = 6, y = 4

Explanation

From the second equation x = y + 2. Substituting gives 3(y + 2) + 2y = 16, so 5y = 10 and y = 2, then x = 4. Both original equations are satisfied.

Question 43Algebra

Which expression is the complete factorization of 2x^2 - 8?

  1. 2(x^2 - 4)
  2. (x - 2)(x + 4)
  3. (2x - 4)(x + 2)
  4. 2(x - 2)(x + 2) Correct answer.

Explanation

Factor out the common 2 to get 2(x^2 - 4), then apply the difference of squares to obtain 2(x - 2)(x + 2). Complete factorization requires factoring until no further factors remain.

Question 44Algebra

The expression (x + 3)/(x^2 - x - 12) can be simplified for which domain restriction?

  1. x cannot equal -3 only
  2. x cannot equal 0
  3. x cannot equal 4 or -3 Correct answer.
  4. x cannot equal 3 or -4

Explanation

Factor the denominator as (x - 4)(x + 3), so the fraction simplifies to 1/(x - 4) when x is not -3. The simplified denominator also excludes x = 4, so both values must be excluded from the original domain.

Question 45Algebra

A crew's daily production P after t hours follows P = 25t - t^2. During which time interval is production increasing?

  1. 0 < t < 25
  2. 0 < t < 12.5 Correct answer.
  3. t > 25
  4. t > 12.5

Explanation

This is a downward-opening parabola with vertex at t = -b/(2a) = 25/2 = 12.5. Production rises from t = 0 up to the vertex and falls afterward, so it increases on 0 < t < 12.5.

Question 46Algebra

Solve for x: 9^(x) = 27^(x - 2).

  1. x = 3
  2. x = -6
  3. x = 2
  4. x = 6 Correct answer.

Explanation

Rewrite both sides with base 3: 3^(2x) = 3^(3x - 6). Equating exponents gives 2x = 3x - 6, so x = 6. Checking gives 9^6 = 27^4, which holds.

Question 47Algebra

The quadratic 2x^2 + bx + 8 = 0 has no real solutions. Which condition on b must hold?

  1. b > 0
  2. b = 8 or b = -8
  3. b > 8 or b < -8
  4. -8 < b < 8 Correct answer.

Explanation

No real solutions require a negative discriminant: b^2 - 4(2)(8) < 0, so b^2 < 64. That gives -8 < b < 8.

Question 48Algebra

A crew's cost function is C(n) = 2n^2 - 16n + 50 dollars for n fixtures. What is the minimum cost, and at how many fixtures does it occur?

  1. $2 at 4 fixtures
  2. $18 at 4 fixtures Correct answer.
  3. $50 at 0 fixtures
  4. $18 at 8 fixtures

Explanation

The vertex occurs at n = -b/(2a) = 16/4 = 4. Evaluating gives 2(16) - 64 + 50 = 18, so the minimum cost is $18 at 4 fixtures.

Question 49Algebra

Simplify the complex fraction (1/x + 1/y) / (1/x - 1/y) for x and y nonzero and x not equal to y.

  1. (y - x)/(x + y)
  2. (y + x)/(x - y)
  3. (x - y)/(x + y)
  4. (x + y)/(y - x) Correct answer.

Explanation

Multiply numerator and denominator by xy to clear the minor fractions. The numerator becomes y + x and the denominator becomes y - x, giving (x + y)/(y - x).

Question 50Algebra

If a line passes through (2, 5) and is perpendicular to the line 4x - 3y = 12, what is the slope of that line?

  1. 4/3
  2. -3/4 Correct answer.
  3. -4/3
  4. 3/4

Explanation

Rewrite 4x - 3y = 12 as y = (4/3)x - 4, so the given slope is 4/3. A perpendicular line has the negative reciprocal, which is -3/4.