PARCC - Partnership for Assessment of Readiness for College and Careers Algebra Practice Test 1 — Questions and Answers
Question 1: Simplify the expression: 4(2x + 3) - 2(x - 5).
- 6x + 22 (Correct answer)
- 6x + 2
- 10x + 22
- 8x + 22
Correct answer: 6x + 22
Distribute: 4(2x + 3) = 8x + 12 and 2(x - 5) = 2x - 10. Subtracting gives 8x + 12 - 2x + 10 = 6x + 22.
Question 2: Which equation represents a line with slope -3 and y-intercept 7?
- y = 7x - 3
- y = -3x + 7 (Correct answer)
- y = 3x + 7
- y = -3x - 7
Correct answer: y = -3x + 7
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. With m = -3 and b = 7, the equation is y = -3x + 7.
Question 3: What are the solutions to x² - 5x + 6 = 0?
- x = 2 and x = 3 (Correct answer)
- x = -2 and x = -3
- x = 1 and x = 6
- x = -1 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 and x = 3.
Question 4: If y varies directly with x and y = 15 when x = 5, what is y when x = 8?
- 18
- 24 (Correct answer)
- 40
- 12
Correct answer: 24
Direct variation means y = kx. Solving for k: k = 15/5 = 3. Then y = 3(8) = 24.
Question 5: Which inequality represents 'twice a number decreased by 4 is at most 10'?
- 2n - 4 ≥ 10
- 2n + 4 ≤ 10
- 2n - 4 ≤ 10 (Correct answer)
- 2(n - 4) ≤ 10
Correct answer: 2n - 4 ≤ 10
'Twice a number' is 2n, 'decreased by 4' gives 2n - 4, and 'at most 10' means ≤ 10, yielding 2n - 4 ≤ 10.
Question 6: What is the value of x in the system of equations: x + y = 9 and x - y = 3?
- x = 3
- x = 6 (Correct answer)
- x = 9
- x = 12
Correct answer: x = 6
Adding the two equations eliminates y: (x + y) + (x - y) = 9 + 3 → 2x = 12 → x = 6.
PARCC - Partnership for Assessment of Readiness for College and Careers Algebra Practice Test 1
Simplify the expression: 4(2x + 3) - 2(x - 5).