PARCC - Partnership for Assessment of Readiness for College and Careers Algebra 1 — Questions and Answers
Question 1: Solve for x: 2(x + 3) = 5x - 9
- x = 5 (Correct answer)
- x = 3
- x = -1
- x = 7
Correct answer: x = 5
Distribute to get 2x + 6 = 5x - 9. Subtract 2x from both sides: 6 = 3x - 9. Add 9: 15 = 3x, so x = 5.
Question 2: What is the y-intercept of the line 4x − 2y = 8?
- 4
- −4 (Correct answer)
- 2
- −2
Correct answer: −4
Solve for y: −2y = −4x + 8, so y = 2x − 4. The y-intercept is the constant term, −4.
Question 3: Which expression is equivalent to (x + 3)²?
- x² + 9
- x² + 3x + 9
- x² + 6x + 9 (Correct answer)
- x² + 6x + 6
Correct answer: x² + 6x + 9
Using FOIL: (x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9. The middle term is 2(x)(3) = 6x.
Question 4: If g(x) = x² − 3x + 2, what is g(4)?
- 2
- 4
- 6 (Correct answer)
- 10
Correct answer: 6
Substitute x = 4: g(4) = (4)² − 3(4) + 2 = 16 − 12 + 2 = 6.
Question 5: Solve the system of equations: x + y = 7 and x − y = 3
- x = 4, y = 3
- x = 5, y = 2 (Correct answer)
- x = 3, y = 4
- x = 6, y = 1
Correct answer: x = 5, y = 2
Add the two equations to eliminate y: 2x = 10, so x = 5. Substitute back: 5 + y = 7, giving y = 2.
Question 6: What are the solutions to x² − 5x + 6 = 0?
- x = 1 and x = 6
- x = −2 and x = −3
- x = 2 and x = 3 (Correct answer)
- x = 3 and x = 6
Correct answer: x = 2 and x = 3
Factor the quadratic: (x − 2)(x − 3) = 0. Setting each factor to zero gives x = 2 or x = 3.
PARCC - Partnership for Assessment of Readiness for College and Careers Algebra 1
Solve for x: 2(x + 3) = 5x - 9