KYOTE College Placement 3 — Questions and Answers
Question 1: What is the slope of the line passing through (−2, 1) and (4, 7)?
- 1 (Correct answer)
- 2
- −1
- 3
Correct answer: 1
Slope = (7 − 1) / (4 − (−2)) = 6 / 6 = 1.
Question 2: Which of the following is a solution to x² − 5x + 6 = 0?
- x = 3 (Correct answer)
- x = −3
- x = 6
- x = 1
Correct answer: x = 3
Factor: (x − 2)(x − 3) = 0, giving x = 2 or x = 3; x = 3 is listed.
Question 3: Convert 0.35 to a fraction in lowest terms.
- 7/20 (Correct answer)
- 35/100
- 7/10
- 1/3
Correct answer: 7/20
0.35 = 35/100; dividing numerator and denominator by 5 gives 7/20.
Question 4: If f(x) = 2x² − 3, what is f(−2)?
- 5 (Correct answer)
- −11
- 1
- 13
Correct answer: 5
f(−2) = 2(−2)² − 3 = 2(4) − 3 = 8 − 3 = 5.
Question 5: Which inequality represents 'three less than twice a number is at most 11'?
- 2n − 3 ≤ 11 (Correct answer)
- 2n + 3 ≤ 11
- 3 − 2n ≤ 11
- 2n − 3 ≥ 11
Correct answer: 2n − 3 ≤ 11
'Twice a number' is 2n, 'three less than' means subtract 3, and 'at most 11' means ≤ 11.
Question 6: What is 25% of 360?
- 90 (Correct answer)
- 72
- 45
- 120
Correct answer: 90
25% = 0.25; 0.25 × 360 = 90.
Question 7: Which of the following sets of side lengths forms a right triangle?
- 6, 8, 10 (Correct answer)
- 5, 6, 8
- 3, 4, 6
- 7, 8, 11
Correct answer: 6, 8, 10
Check 6² + 8² = 36 + 64 = 100 = 10², satisfying the Pythagorean theorem.
KYOTE College Placement 3
What is the slope of the line passing through (−2, 1) and (4, 7)?