NSAA NSAA Mathematics - Algebra and Functions 2 — Questions and Answers
Question 1: What is the range of the function f(x) = x² + 1 for all real x?
- All real numbers
- x ≥ 0
- f(x) ≥ 1 (Correct answer)
- f(x) > 0
Correct answer: f(x) ≥ 1
Since x² ≥ 0 for all real x, f(x) = x² + 1 ≥ 1.
Question 2: Simplify: (3x²y)(2xy³)
- 5x³y⁴
- 6x³y⁴ (Correct answer)
- 6x²y³
- 5x²y⁴
Correct answer: 6x³y⁴
Multiply coefficients: 3×2=6; add exponents: x^(2+1)=x³, y^(1+3)=y⁴. Result: 6x³y⁴.
Question 3: The graph of y = (x-2)² + 3 has its vertex at:
- (-2, 3)
- (2, 3) (Correct answer)
- (2, -3)
- (-2, -3)
Correct answer: (2, 3)
In the form y = (x-h)² + k, the vertex is at (h, k) = (2, 3).
Question 4: If log₂(x) = 5, what is x?
- 10
- 16
- 25
- 32 (Correct answer)
Correct answer: 32
log₂(x) = 5 means x = 2⁵ = 32.
Question 5: Expand and simplify: (x + 3)(x - 5)
- x² - 2x - 15 (Correct answer)
- x² + 2x - 15
- x² - 8x + 15
- x² + 8x - 15
Correct answer: x² - 2x - 15
Using FOIL: x² - 5x + 3x - 15 = x² - 2x - 15.
Question 6: What is the sum of the roots of 3x² - 6x + 2 = 0?
- −2
- 2 (Correct answer)
- 2/3
- 6
Correct answer: 2
Sum of roots = -b/a = -(-6)/3 = 2.
NSAA NSAA Mathematics - Algebra and Functions 2
What is the range of the function f(x) = x² + 1 for all real x?