Core Academic Skills Assessment Mathematics: Algebra and Functions 4 — Questions and Answers
Question 1: Simplify: (x² − 9)/(x + 3) for x ≠ −3.
- x − 3 (Correct answer)
- x + 3
- x² − 3
- (x − 3)(x + 3)
Correct answer: x − 3
Factor the numerator: (x − 3)(x + 3)/(x + 3) = x − 3.
Question 2: Which of the following tables of values represents a linear function?
- x: 0,1,2,3 → y: 4,7,10,13 (Correct answer)
- x: 0,1,2,3 → y: 1,2,4,8
- x: 0,1,2,3 → y: 0,1,4,9
- x: 0,1,2,3 → y: 5,4,2,−1
Correct answer: x: 0,1,2,3 → y: 4,7,10,13
The differences between consecutive y-values are constant (3), confirming a linear function.
Question 3: If 2^x = 32, what is x?
- 5 (Correct answer)
- 4
- 6
- 16
Correct answer: 5
32 = 2⁵, so x = 5.
Question 4: Which system of equations has no solution?
- y = 2x + 1 and y = 2x − 3 (Correct answer)
- y = x + 2 and y = −x + 2
- y = 3x and y = x + 4
- y = −x + 1 and y = x − 1
Correct answer: y = 2x + 1 and y = 2x − 3
Two lines with the same slope (2) but different y-intercepts are parallel and never intersect.
Question 5: What is the range of f(x) = x² + 3?
- y ≥ 3 (Correct answer)
- All real numbers
- y ≤ 3
- y > 0
Correct answer: y ≥ 3
Since x² ≥ 0 for all real x, the minimum value of f(x) is 3, so y ≥ 3.
Question 6: Solve for x: (x/4) + 3 = (x/2) − 1.
- 16 (Correct answer)
- 8
- −16
- 4
Correct answer: 16
Multiply through by 4: x + 12 = 2x − 4 → x = 16.
Question 7: The function y = 2(x − 1)² + 3 is in vertex form. What is its vertex?
- (1, 3) (Correct answer)
- (−1, 3)
- (1, −3)
- (2, 3)
Correct answer: (1, 3)
Vertex form y = a(x − h)² + k has vertex (h, k); here h = 1 and k = 3.
Core Academic Skills Assessment Mathematics: Algebra and Functions 4
Simplify: (x² − 9)/(x + 3) for x ≠ −3.