Regents Ultimate Regents Algebra 3 — Questions and Answers
Question 1: The graph of a line passes through (0, -4) and (3, 2). What is the equation of the line?
- y = 2x - 4 (Correct answer)
- y = 2x + 4
- y = (1/2)x - 4
- y = -2x - 4
Correct answer: y = 2x - 4
Slope = (2 - (-4))/(3 - 0) = 6/3 = 2; y-intercept is -4, so y = 2x - 4.
Question 2: What is the solution set of |2x - 3| = 7?
- x = 5 or x = -2 (Correct answer)
- x = 5 or x = 2
- x = -5 or x = 2
- x = -5 or x = -2
Correct answer: x = 5 or x = -2
2x - 3 = 7 gives x = 5, and 2x - 3 = -7 gives x = -2.
Question 3: A rectangle has length (x + 5) and width (x - 2). Which expression represents its area?
- x² + 3x - 10 (Correct answer)
- x² - 3x - 10
- x² + 3x + 10
- 2x + 3
Correct answer: x² + 3x - 10
Using FOIL: (x+5)(x-2) = x² - 2x + 5x - 10 = x² + 3x - 10.
Question 4: What is the value of x in the system: 3x + y = 11 and x - y = 1?
- 3 (Correct answer)
- 2
- 4
- 5
Correct answer: 3
Adding the equations: 4x = 12, so x = 3.
Question 5: Which describes an exponential decay function?
- f(x) = 500(0.85)ˣ (Correct answer)
- f(x) = 500(1.15)ˣ
- f(x) = 500x²
- f(x) = 500 - 15x
Correct answer: f(x) = 500(0.85)ˣ
A base between 0 and 1 (0.85) produces exponential decay.
Question 6: Factor completely: x² - 49
- (x + 7)(x - 7) (Correct answer)
- (x - 7)²
- (x + 7)²
- Cannot be factored
Correct answer: (x + 7)(x - 7)
This is a difference of two perfect squares: x² - 49 = (x + 7)(x - 7).
Question 7: The table shows a relation. Which ordered pair would make this relation NOT a function? {(1,3), (2,5), (3,7), (?,9)}
- (2, 9) (Correct answer)
- (4, 9)
- (5, 9)
- (6, 9)
Correct answer: (2, 9)
If x = 2 is repeated with a different y-value, the relation fails the vertical line test and is not a function.
Regents Ultimate Regents Algebra 3
The graph of a line passes through (0, -4) and (3, 2).
What is the equation of the line?