KYOTE Algebraic Reasoning 2 â Questions and Answers
Question 1: Which value of x satisfies the equation 3(x â 4) = 2x + 1?
- x = 13 (Correct answer)
- x = 11
- x = 7
- x = 5
Correct answer: x = 13
Distribute: 3x â 12 = 2x + 1, then x = 13.
Question 2: A line passes through (0, â2) and has slope 4. What is its equation?
- y = 4x â 2 (Correct answer)
- y = â2x + 4
- y = 4x + 2
- y = â4x â 2
Correct answer: y = 4x â 2
Using slope-intercept form y = mx + b with m = 4 and b = â2 gives y = 4x â 2.
Question 3: Simplify: (2x²y)(3xy³)
- 6xÂłyâ´ (Correct answer)
- 5xÂłyâ´
- 6x²yâ´
- 6xÂłyÂł
Correct answer: 6xÂłyâ´
Multiply coefficients (2¡3 = 6) and add exponents: x^(2+1) = xÂł and y^(1+3) = yâ´.
Question 4: Which inequality represents all real numbers less than â3 or greater than 5?
- x < â3 or x > 5 (Correct answer)
- â3 < x < 5
- x ⤠â3 or x ⼠5
- x < â3 and x > 5
Correct answer: x < â3 or x > 5
Numbers outside the interval (â3, 5) satisfy x < â3 or x > 5.
Question 5: What is the slope of the line 5x â 2y = 10?
- 5/2 (Correct answer)
- â5/2
- 2/5
- â2/5
Correct answer: 5/2
Solve for y: â2y = â5x + 10, so y = (5/2)x â 5, giving slope 5/2.
Question 6: Factor completely: x² â 9x + 18
- (x â 3)(x â 6) (Correct answer)
- (x + 3)(x â 6)
- (x â 3)(x + 6)
- (x â 9)(x â 2)
Correct answer: (x â 3)(x â 6)
Find two numbers that multiply to 18 and add to â9: â3 and â6, giving (x â 3)(x â 6).
Question 7: If f(x) = x² â 4x + 3, what is f(â1)?
- 8 (Correct answer)
- â2
- 6
- 0
Correct answer: 8
f(â1) = (â1)² â 4(â1) + 3 = 1 + 4 + 3 = 8.
KYOTE Algebraic Reasoning 2
Which value of x satisfies the equation 3(x â 4) = 2x + 1?