IMAT Mathematics and Statistics 2 ā Questions and Answers
Question 1: What is the derivative of f(x) = xĀ³ + 4x?
- 3xĀ² + 4 (Correct answer)
- xĀ² + 4
- 3xĀ² + 4x
- 3x + 4
Correct answer: 3xĀ² + 4
Differentiating term by term: d/dx(xĀ³) = 3xĀ² and d/dx(4x) = 4, giving 3xĀ² + 4.
Question 2: A bag contains 3 red, 4 blue, and 5 green balls. What is the probability of drawing a blue ball?
- 1/3 (Correct answer)
- 1/4
- 5/12
- 4/5
Correct answer: 1/3
There are 4 blue balls out of 12 total, so P(blue) = 4/12 = 1/3.
Question 3: What are the solutions to xĀ² ā 5x + 6 = 0?
- x = 1 or x = 6
- x = 2 or x = 3 (Correct answer)
- x = ā2 or x = ā3
- x = ā1 or x = 6
Correct answer: x = 2 or x = 3
Factoring gives (xā2)(xā3) = 0, so x = 2 or x = 3.
Question 4: An arithmetic sequence has first term 3 and common difference 4. What is the 10th term?
- 39 (Correct answer)
- 43
- 40
- 36
Correct answer: 39
aā = aā + (nā1)d = 3 + 9Ć4 = 3 + 36 = 39.
Question 5: What is the slope of the line passing through (2, 3) and (6, 11)?
- 1
- 3
- 2 (Correct answer)
- 4
Correct answer: 2
Slope = (yāāyā)/(xāāxā) = (11ā3)/(6ā2) = 8/4 = 2.
Question 6: Simplify ā48.
- 4ā3 (Correct answer)
- 6ā2
- 8ā3
- 4ā6
Correct answer: 4ā3
ā48 = ā(16Ć3) = ā16 Ć ā3 = 4ā3.
Question 7: If 2^x = 16, what is x?
- 2
- 3
- 4 (Correct answer)
- 8
Correct answer: 4
2ā“ = 16, so x = 4.
IMAT Mathematics and Statistics 2
What is the derivative of f(x) = xĀ³ + 4x?