IBEW Aptitude Test Algebra and Functions Questions and Answers 1 — 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?
- 500 feet
- 375 feet (Correct answer)
- 250 feet
- 125 feet
Correct answer: 375 feet
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
- x = 5
- x = 11
- x = 3 (Correct answer)
- x = -3
Correct answer: x = 3
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?
- (x - 2)(x + 7)
- (x + 2)(x - 7) (Correct answer)
- (x - 14)(x + 1)
- (x + 5)(x - 2)
Correct answer: (x + 2)(x - 7)
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)?
- 16 (Correct answer)
- 28
- -26
- 38
Correct answer: 16
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?
- 13 ohms
- 19 ohms
- 27 ohms
- 9 ohms (Correct answer)
Correct answer: 9 ohms
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.
Question 6: Simplify the following algebraic expression: (4x²y³)(3xy⁴)
- 7x³y⁷
- 12x²y¹²
- 7x²y¹²
- 12x³y⁷ (Correct answer)
Correct answer: 12x³y⁷
To simplify this expression, multiply the coefficients (4 * 3 = 12). Then, for the variables, add the exponents of the like bases. For x, the exponents are 2 and 1, so x^(2+1) = x³. For y, the exponents are 3 and 4, so y^(3+4) = y⁷. The simplified expression is 12x³y⁷.
IBEW Aptitude Test Algebra and Functions Questions and Answers 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?