Polytechnic Mathematics 1 — Questions and Answers
Question 1: What is the derivative of f(x) = 3x² + 5x - 2?
- 6x + 5 (Correct answer)
- 3x + 5
- 6x - 2
- 5x + 3
Correct answer: 6x + 5
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°)?
- 0
- 1 (Correct answer)
- -1
- 0.5
Correct answer: 1
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?
- x = (-b ± √(b²-4ac)) / 2a (Correct answer)
- x = (-b ± √(b²+4ac)) / 2a
- x = (b ± √(b²-4ac)) / 2a
- x = (-b ± √(b²-4ac)) / a
Correct answer: x = (-b ± √(b²-4ac)) / 2a
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?
- x² + C (Correct answer)
- 2x² + C
- x + C
- 2 + C
Correct answer: x² + C
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?
- -1/2 (Correct answer)
- 2
- -2
- 1/2
Correct answer: -1/2
Perpendicular lines have slopes that are negative reciprocals of each other, so the slope is -1/2.
Question 6: What is the determinant of a 2×2 matrix [[a,b],[c,d]]?
- ad - bc (Correct answer)
- ac - bd
- ad + bc
- ab - cd
Correct answer: ad - bc
The determinant of a 2×2 matrix is calculated as ad - bc, the product of the main diagonal minus the product of the off-diagonal.
Polytechnic Mathematics 1
What is the derivative of f(x) = 3x² + 5x - 2?