IBEW Aptitude Test Algebra and Functions Questions and Answers

Question 1

An electrical contractor purchases a spool of wire that is 1,250 feet long. If they use 3/5 of the spool for one job and then 1/4 of the remaining wire for a second job, how many feet of wire are left on the spool?

Accepted Answer

375 feet

Answer

First, calculate the amount of wire used in the first job: 1,250 feet * (3/5) = 750 feet. The remaining wire is 1,250 - 750 = 500 feet. For the second job, they use 1/4 of the remaining wire: 500 feet * (1/4) = 125 feet. The final amount of wire left is 500 - 125 = 375 feet.

Question 2

Solve the following equation for x: 4(x + 2) - 2x = 14

Accepted Answer

x = 3

Answer

First, distribute the 4 into the parentheses: 4x + 8 - 2x = 14. Then, combine the x terms: 2x + 8 = 14. Subtract 8 from both sides of the equation: 2x = 6. Finally, divide by 2 to solve for x: x = 3.

Question 3

Which of the following expressions is the result of factoring the polynomial x² - 5x - 14?

Accepted Answer

(x + 2)(x - 7)

Answer

To factor the quadratic polynomial x² - 5x - 14, we need to find two numbers that multiply to -14 and add up to -5. These two numbers are +2 and -7. Therefore, the factored form is (x + 2)(x - 7).

Question 4

If f(x) = 3x² + 2x - 5, what is the value of f(-3)?

Accepted Answer

16

Answer

To find f(-3), substitute -3 for every x in the function: f(-3) = 3(-3)² + 2(-3) - 5. Following the order of operations, first calculate the exponent: 3(9) + 2(-3) - 5. Then, perform the multiplication: 27 - 6 - 5. Finally, perform the subtraction from left to right: 21 - 5 = 16.

Question 5

A circuit requires two resistors, R1 and R2. The resistance of R1 is 5 ohms more than twice the resistance of R2. The total resistance of the circuit is 32 ohms. What is the resistance of R2?

Accepted Answer

9 ohms

Answer

Let R2 be 'x'. Then R1 can be expressed as '2x + 5'. Since the total resistance is the sum of the individual resistances, the equation is (2x + 5) + x = 32. Combine the like terms: 3x + 5 = 32. Subtract 5 from both sides: 3x = 27. Divide by 3 to find x: x = 9. So, the resistance of R2 is 9 ohms.

IBEW - Aptitude Test Practice Test

IBEW - Aptitude Test Practice Test

IBEW Aptitude Test Algebra and Functions Questions and Answers