KYOTE Algebraic Reasoning 3 — Questions and Answers
Question 1: Solve the system: 2x + y = 7 and x − y = 2.
- x = 3, y = 1 (Correct answer)
- x = 2, y = 3
- x = 4, y = −1
- x = 1, y = 5
Correct answer: x = 3, y = 1
Adding the equations: 3x = 9, so x = 3; substituting gives y = 1.
Question 2: Which expression is equivalent to (x + 5)²?
- x² + 10x + 25 (Correct answer)
- x² + 25
- x² + 5x + 25
- x² + 10x + 10
Correct answer: x² + 10x + 25
(x + 5)² = x² + 2(5)x + 5² = x² + 10x + 25.
Question 3: A car travels at a constant speed of 60 mph. Which equation gives distance d after t hours?
- d = 60t (Correct answer)
- t = 60d
- d = 60 + t
- d = t/60
Correct answer: d = 60t
Distance equals rate times time, so d = 60t.
Question 4: What are the x-intercepts of y = x² − x − 6?
- x = 3 and x = −2 (Correct answer)
- x = −3 and x = 2
- x = 6 and x = −1
- x = 3 and x = 2
Correct answer: x = 3 and x = −2
Factor as (x − 3)(x + 2) = 0, so x = 3 or x = −2.
Question 5: Simplify: (4x³ − 2x² + x) ÷ (2x)
- 2x² − x + 1/2 (Correct answer)
- 2x² − x + 1
- 4x² − 2x + 1
- 2x³ − x²
Correct answer: 2x² − x + 1/2
Divide each term by 2x: 4x³/2x = 2x², −2x²/2x = −x, x/2x = 1/2.
Question 6: The number of tickets sold t is 50 more than twice the number of volunteers v. Which equation models this?
- t = 2v + 50 (Correct answer)
- v = 2t + 50
- t = 50v + 2
- t = 2v − 50
Correct answer: t = 2v + 50
Fifty more than twice v translates directly to t = 2v + 50.
Question 7: Which graph feature does the vertex of a parabola y = ax² + bx + c represent when a < 0?
- The maximum point (Correct answer)
- The minimum point
- The y-intercept
- An x-intercept
Correct answer: The maximum point
When a < 0 the parabola opens downward, making the vertex the maximum point.
KYOTE Algebraic Reasoning 3
Solve the system: 2x + y = 7 and x − y = 2.