Regents Ultimate Regents Algebra 4

Question 1

A ball is thrown upward. Its height h (feet) after t seconds is h = -16t² + 64t + 5. What is the maximum height?

Accepted Answer

69 feet

Answer

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)?

Accepted Answer

x ≥ 4

Answer

The radicand must be non-negative: x - 4 ≥ 0, so x ≥ 4.

Question 3

Which value of x satisfies 2^(x+1) = 32?

Accepted Answer

4

Answer

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?

Accepted Answer

60

Answer

Two standard deviations above the mean: 50 + 2(5) = 60.

Question 5

Solve for x: (x + 3)/(x - 2) = 4

Accepted Answer

x = 11/3

Answer

Cross-multiply: x + 3 = 4(x - 2) → x + 3 = 4x - 8 → 11 = 3x → x = 11/3.

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