Regents Ultimate Regents Algebra 2 — Questions and Answers
Question 1: A function is defined as f(x) = 3x² - 12x + 9. What are the zeros of this function?
- x = 1 and x = 3 (Correct answer)
- x = -1 and x = -3
- x = 2 and x = 6
- x = 0 and x = 4
Correct answer: x = 1 and x = 3
Factor out 3 to get 3(x² - 4x + 3) = 3(x - 1)(x - 3), so zeros are x = 1 and x = 3.
Question 2: The sequence 5, 8, 11, 14, ... is arithmetic. What is the 20th term?
- 62 (Correct answer)
- 60
- 58
- 65
Correct answer: 62
Using aₙ = a₁ + (n-1)d: a₂₀ = 5 + (19)(3) = 5 + 57 = 62.
Question 3: Which inequality represents the solution to -4x + 7 > 19?
- x < -3 (Correct answer)
- x > -3
- x < 3
- x > 3
Correct answer: x < -3
Subtracting 7 gives -4x > 12; dividing by -4 (flip inequality) gives x < -3.
Question 4: If f(x) = 2x + 5 and g(x) = x², what is f(g(3))?
- 23 (Correct answer)
- 18
- 121
- 41
Correct answer: 23
g(3) = 9, then f(9) = 2(9) + 5 = 23.
Question 5: What is the axis of symmetry of the parabola y = -2x² + 8x - 3?
- x = 2 (Correct answer)
- x = -2
- x = 4
- x = 8
Correct answer: x = 2
The axis of symmetry is x = -b/(2a) = -8/(2·(-2)) = -8/(-4) = 2.
Question 6: A student scores 72, 85, 90, and 67 on four tests. What score is needed on the fifth test to have a mean of 80?
- 86 (Correct answer)
- 80
- 90
- 76
Correct answer: 86
Total needed = 5 × 80 = 400; current sum = 314; so 400 - 314 = 86.
Question 7: Which expression is equivalent to (2x³y²)(3x²y⁴)?
- 6x⁵y⁶ (Correct answer)
- 6x⁶y⁸
- 5x⁵y⁶
- 6x⁵y⁸
Correct answer: 6x⁵y⁶
Multiply coefficients (2·3 = 6) and add exponents: x³⁺² = x⁵ and y²⁺⁴ = y⁶, giving 6x⁵y⁶.
Regents Ultimate Regents Algebra 2
A function is defined as f(x) = 3x² - 12x + 9.
What are the zeros of this function?