Polytechnic Mathematics

Question 1

What is the derivative of f(x) = 3x² + 5x - 2?

Accepted Answer

6x + 5

Answer

Using the power rule, the derivative of 3x² is 6x, the derivative of 5x is 5, and the constant -2 disappears.

Question 2

What is the value of sin(90°)?

Accepted Answer

1

Answer

Sin(90°) equals 1, which corresponds to the maximum value of the sine function.

Question 3

Which of the following is the correct formula for the quadratic formula?

Accepted Answer

x = (-b ± √(b²-4ac)) / 2a

Answer

The quadratic formula is x = (-b ± √(b²-4ac)) / 2a, used to solve ax² + bx + c = 0.

Question 4

What is the integral of f(x) = 2x?

Accepted Answer

x² + C

Answer

Integrating 2x using the power rule gives x²/1 · 2/2 = x², plus the constant of integration C.

Question 5

What is the slope of a line perpendicular to y = 2x + 3?

Accepted Answer

-1/2

Answer

Perpendicular lines have slopes that are negative reciprocals of each other, so the slope is -1/2.

Polytechnic Practice Test