PARCC Advanced Mathematics 3 — Questions and Answers
Question 1: Solve for x: 3(x - 2) = 2x + 5.
- 11 (Correct answer)
- 1
- -11
- 7
Correct answer: 11
3x-6=2x+5, so x=11.
Question 2: What is the discriminant of x² + 4x + 5 = 0?
- -4 (Correct answer)
- 4
- 36
- -36
Correct answer: -4
b²-4ac = 16-20 = -4.
Question 3: A negative discriminant means a quadratic has what kind of roots?
- Two complex roots (Correct answer)
- Two real roots
- One real root
- No roots at all
Correct answer: Two complex roots
A negative discriminant yields two complex conjugate roots.
Question 4: What is (3 + 2i) + (1 - 5i)?
- 4 - 3i (Correct answer)
- 4 + 7i
- 2 - 3i
- 4 - 7i
Correct answer: 4 - 3i
Add real and imaginary parts: (3+1)+(2-5)i = 4-3i.
Question 5: Factor completely: x² - 16.
- (x - 4)(x + 4) (Correct answer)
- (x - 4)²
- (x - 16)(x + 1)
- (x + 4)²
Correct answer: (x - 4)(x + 4)
Difference of squares: x²-16 = (x-4)(x+4).
Question 6: What is the domain of f(x) = 1/(x - 3)?
- All real numbers except 3 (Correct answer)
- All real numbers
- x ≥ 3
- x > 0
Correct answer: All real numbers except 3
The denominator cannot be zero, so x ≠ 3.
Question 7: If a function is increasing on an interval, its slope on that interval is:
- Positive (Correct answer)
- Negative
- Zero
- Undefined
Correct answer: Positive
An increasing function has a positive rate of change.
PARCC Advanced Mathematics 3
Solve for x: 3(x - 2) = 2x + 5.