Free IBEW Aptitude Test Number Sequences and Functions Questions and Answers 1 — Questions and Answers
Question 1: An electrical signal's voltage is modeled by the function V(t) = 2t² - 8. At what positive value of t does the voltage equal 42?
- t = 25
- t = 4
- t = 5 (Correct answer)
- t = 17
Correct answer: t = 5
To solve for t, set the function equal to 42: 2t² - 8 = 42. First, add 8 to both sides to get 2t² = 50. Then, divide both sides by 2 to get t² = 25. Finally, take the square root of both sides. Since the question asks for a positive value, t = 5.
Question 2: What is the next number in the following sequence: 3, 7, 16, 32, 57, ...?
- 81
- 91
- 78
- 93 (Correct answer)
Correct answer: 93
The pattern is based on adding the square of consecutive integers. The difference between 3 and 7 is 4 (2²). The difference between 7 and 16 is 9 (3²). The difference between 16 and 32 is 16 (4²). The difference between 32 and 57 is 25 (5²). The next step is to add 6², which is 36. So, 57 + 36 = 93.
Question 3: The function f(x) represents the number of feet of wire an apprentice can install in 'x' hours. If f(x) = 50x - 5, which of the following statements is true?
- The apprentice installs wire at a rate of 45 feet per hour.
- In 3 hours, the apprentice will have installed exactly 150 feet of wire.
- The function has a starting value of -5, which represents a setup time.
- After 4 hours, the apprentice will have installed 195 feet of wire. (Correct answer)
Correct answer: After 4 hours, the apprentice will have installed 195 feet of wire.
To find the amount of wire installed after 4 hours, substitute x=4 into the function: f(4) = 50(4) - 5. This calculates to 200 - 5 = 195. Therefore, the apprentice will have installed 195 feet of wire.
Question 4: A wiring project's progress can be tracked by the sequence: 5, 12, 19, 26, 33. This represents the number of circuits completed each day. Which function, C(d), correctly models the number of circuits completed on day 'd'?
- C(d) = 5d + 7
- C(d) = 7d - 2 (Correct answer)
- C(d) = d + 7
- C(d) = 5d
Correct answer: C(d) = 7d - 2
This is an arithmetic sequence with a common difference of 7. The formula for the nth term of an arithmetic sequence is a_n = a_1 + (n-1)d. Here, a_1 = 5, n=d, and d=7. So, C(d) = 5 + (d-1)7 = 5 + 7d - 7 = 7d - 2. We can check this: C(1)=7(1)-2=5, C(2)=7(2)-2=12, C(3)=7(3)-2=19.
Question 5: Identify the pattern and find the missing number in the sequence: 81, 27, __, 3, 1.
- 18
- 9 (Correct answer)
- 12
- 6
Correct answer: 9
This is a geometric sequence where each term is found by dividing the previous term by 3. 81 / 3 = 27. 27 / 3 = 9. 9 / 3 = 3. 3 / 3 = 1. The missing number is 9.
Question 6: Given the function g(x) = (x + 4) / (x - 2), what is the value of g(8)?
- 1
- Undefined
- 2 (Correct answer)
- 12
Correct answer: 2
To evaluate g(8), substitute 8 for every 'x' in the function's definition. This gives: g(8) = (8 + 4) / (8 - 2). Simplifying the numerator and denominator gives 12 / 6. The final result is 2.
Free IBEW Aptitude Test Number Sequences and Functions Questions and Answers 1
An electrical signal's voltage is modeled by the function V(t) = 2t² - 8.
At what positive value of t does the voltage equal 42?