KYOTE College Placement 2 — Questions and Answers
Question 1: Simplify: (3x²y)(4xy³)
- 12x³y⁴ (Correct answer)
- 7x³y⁴
- 12x²y³
- 7x²y⁴
Correct answer: 12x³y⁴
Multiply coefficients (3×4=12) and add exponents for like bases: x²·x¹=x³ and y¹·y³=y⁴.
Question 2: Which of the following is the equation of a line with slope -2 passing through (1, 3)?
- y = -2x + 5 (Correct answer)
- y = -2x + 1
- y = 2x + 1
- y = -2x - 5
Correct answer: y = -2x + 5
Using point-slope form: y - 3 = -2(x - 1) → y = -2x + 2 + 3 = -2x + 5.
Question 3: What is the value of |−7| + |3|?
- 10 (Correct answer)
- 4
- -4
- -10
Correct answer: 10
Absolute value is always non-negative: |−7| = 7 and |3| = 3, so 7 + 3 = 10.
Question 4: Factor completely: x² − 9
- (x − 3)(x + 3) (Correct answer)
- (x − 9)(x + 1)
- (x − 3)²
- (x + 9)(x − 1)
Correct answer: (x − 3)(x + 3)
x² − 9 is a difference of squares: a² − b² = (a − b)(a + b), where a = x and b = 3.
Question 5: A car travels 180 miles in 3 hours. At the same rate, how far will it travel in 5 hours?
- 300 miles (Correct answer)
- 270 miles
- 360 miles
- 108 miles
Correct answer: 300 miles
The rate is 180 ÷ 3 = 60 mph; at 60 mph for 5 hours, distance = 60 × 5 = 300 miles.
Question 6: Solve for x: 2(x − 4) = 3x + 1
- x = −9 (Correct answer)
- x = 9
- x = −1
- x = 1
Correct answer: x = −9
Expand: 2x − 8 = 3x + 1 → −x = 9 → x = −9.
Question 7: Which expression is equivalent to (x + 2)²?
- x² + 4x + 4 (Correct answer)
- x² + 4
- x² + 2x + 4
- x² − 4x + 4
Correct answer: x² + 4x + 4
(x + 2)² = x² + 2(2)(x) + 4 = x² + 4x + 4 using the perfect square trinomial pattern.
