TSI - Texas Success Initiative Algebraic Reasoning and Functions Questions and Answers 2 — Questions and Answers
Question 1: Solve for x: 3x - 7 = 2x + 5
- x = 12 (Correct answer)
- x = -2
- x = 2
- x = -12
Correct answer: x = 12
Subtract 2x from both sides: x - 7 = 5. Add 7 to both sides: x = 12.
Question 2: Which of the following is the solution set of the inequality 2x + 3 > 11?
- x > 4 (Correct answer)
- x < 4
- x > 7
- x < 7
Correct answer: x > 4
Subtract 3 from both sides: 2x > 8. Divide both sides by 2: x > 4.
Question 3: What is the vertex of the parabola y = x² - 6x + 8?
- (3, -1) (Correct answer)
- (3, 1)
- (-3, -1)
- (6, 8)
Correct answer: (3, -1)
Complete the square or use h = -b/(2a) = 6/2 = 3. Then y = 9 - 18 + 8 = -1. Vertex is (3, -1).
Question 4: A function f(x) = 2x + 1. What is f(f(3))?
- 15 (Correct answer)
- 7
- 13
- 14
Correct answer: 15
First evaluate f(3) = 2(3) + 1 = 7. Then f(7) = 2(7) + 1 = 15.
Question 5: Solve the system: x + y = 6 and x - y = 2.
- x = 4, y = 2 (Correct answer)
- x = 2, y = 4
- x = 3, y = 3
- x = 5, y = 1
Correct answer: x = 4, y = 2
Add the two equations: 2x = 8, so x = 4. Substitute back: 4 + y = 6, so y = 2.
Question 6: Which expression is equivalent to (x + 3)(x - 5)?
- x² - 2x - 15 (Correct answer)
- x² + 2x - 15
- x² - 2x + 15
- x² - 8x - 15
Correct answer: x² - 2x - 15
Use FOIL: x·x = x², x·(-5) = -5x, 3·x = 3x, 3·(-5) = -15. Combine: x² - 2x - 15.
TSI - Texas Success Initiative Algebraic Reasoning and Functions Questions and Answers 2
Solve for x: 3x - 7 = 2x + 5