Regents Ultimate Regents Algebra 4 — Questions and Answers
Question 1: A ball is thrown upward. Its height h (feet) after t seconds is h = -16t² + 64t + 5. What is the maximum height?
- 69 feet (Correct answer)
- 64 feet
- 85 feet
- 70 feet
Correct answer: 69 feet
Vertex at t = -64/(2·(-16)) = 2; h(2) = -16(4) + 64(2) + 5 = -64 + 128 + 5 = 69 feet.
Question 2: What is the domain of f(x) = √(x - 4)?
- x ≥ 4 (Correct answer)
- x > 4
- x ≤ 4
- All real numbers
Correct answer: x ≥ 4
The radicand must be non-negative: x - 4 ≥ 0, so x ≥ 4.
Question 3: Which value of x satisfies 2^(x+1) = 32?
- 4 (Correct answer)
- 3
- 5
- 6
Correct answer: 4
Since 32 = 2⁵, we have 2^(x+1) = 2⁵, so x + 1 = 5 and x = 4.
Question 4: A data set has a mean of 50 and standard deviation of 5. Which score is 2 standard deviations above the mean?
- 60 (Correct answer)
- 55
- 65
- 70
Correct answer: 60
Two standard deviations above the mean: 50 + 2(5) = 60.
Question 5: Solve for x: (x + 3)/(x - 2) = 4
- x = 11/3 (Correct answer)
- x = 5/3
- x = 11
- x = -5
Correct answer: x = 11/3
Cross-multiply: x + 3 = 4(x - 2) → x + 3 = 4x - 8 → 11 = 3x → x = 11/3.
Question 6: The scatter plot of a data set shows a strong negative correlation. Which correlation coefficient best represents this?
- r = -0.92 (Correct answer)
- r = 0.92
- r = -0.12
- r = 0.12
Correct answer: r = -0.92
A strong negative correlation is represented by a value of r close to -1, such as -0.92.
Question 7: What is the product of (3 + 2i)(3 - 2i)?
- 13 (Correct answer)
- 9
- 5
- 1
Correct answer: 13
Using difference of squares: (3)² - (2i)² = 9 - 4i² = 9 - 4(-1) = 9 + 4 = 13.
Regents Ultimate Regents Algebra 4
A ball is thrown upward.
Its height h (feet) after t seconds is h = -16t² + 64t + 5.
What is the maximum height?