IMAT Mathematics and Statistics 2

Question 1

What is the derivative of f(x) = x³ + 4x?

Accepted Answer

3x² + 4

Answer

Differentiating term by term: d/dx(x³) = 3x² and d/dx(4x) = 4, giving 3x² + 4.

Question 2

A bag contains 3 red, 4 blue, and 5 green balls. What is the probability of drawing a blue ball?

Accepted Answer

1/3

Answer

There are 4 blue balls out of 12 total, so P(blue) = 4/12 = 1/3.

Question 3

What are the solutions to x² − 5x + 6 = 0?

Accepted Answer

x = 2 or x = 3

Answer

Factoring gives (x−2)(x−3) = 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?

Accepted Answer

39

Answer

aₙ = a₁ + (n−1)d = 3 + 9×4 = 3 + 36 = 39.

Question 5

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

Accepted Answer

2

Answer

Slope = (y₂−y₁)/(x₂−x₁) = (11−3)/(6−2) = 8/4 = 2.

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