College Math Placement Test Intermediate Algebra 5 — Questions and Answers
Question 1: What is the solution to the compound inequality −1 ≤ 2x + 3 ≤ 7?
- −2 ≤ x ≤ 2 (Correct answer)
- −2 ≤ x ≤ 5
- 1 ≤ x ≤ 5
- −4 ≤ x ≤ 2
Correct answer: −2 ≤ x ≤ 2
Subtract 3 from all parts: −4 ≤ 2x ≤ 4, then divide by 2: −2 ≤ x ≤ 2.
Question 2: Which of the following lines is perpendicular to y = (2/3)x + 1?
- y = −(3/2)x + 4 (Correct answer)
- y = (2/3)x − 5
- y = (3/2)x + 1
- y = −(2/3)x − 1
Correct answer: y = −(3/2)x + 4
Perpendicular slopes are negative reciprocals; the negative reciprocal of 2/3 is −3/2.
Question 3: Simplify: (x² − 4x + 4)/(x − 2)
- x − 2 (Correct answer)
- x + 2
- x² − 2
- 1/(x−2)
Correct answer: x − 2
x²−4x+4 = (x−2)², so (x−2)²/(x−2) = x−2 for x ≠ 2.
Question 4: A ball is thrown upward with height h(t) = −16t² + 64t + 5 (feet). What is the maximum height?
- 69 ft (Correct answer)
- 64 ft
- 5 ft
- 85 ft
Correct answer: 69 ft
Vertex at t = −64/(2·−16) = 2; h(2) = −16(4)+64(2)+5 = −64+128+5 = 69 ft.
Question 5: Which of the following is the equation of a circle with center (−2, 3) and radius 5?
- (x+2)² + (y−3)² = 25 (Correct answer)
- (x−2)² + (y+3)² = 25
- (x+2)² + (y−3)² = 5
- (x−2)² + (y+3)² = 5
Correct answer: (x+2)² + (y−3)² = 25
Standard form (x−h)²+(y−k)²=r²; with h=−2, k=3, r=5: (x+2)²+(y−3)²=25.
Question 6: Solve for x: (x/3) + (x/4) = 7
- 12 (Correct answer)
- 21
- 84
- 3
Correct answer: 12
LCD is 12: (4x+3x)/12 = 7 → 7x = 84 → x = 12.
Question 7: If the graph of y = f(x) is shifted 3 units left and 2 units down, the new equation is:
- y = f(x + 3) − 2 (Correct answer)
- y = f(x − 3) + 2
- y = f(x + 3) + 2
- y = f(x − 3) − 2
Correct answer: y = f(x + 3) − 2
Left h units: replace x with (x+h); down k units: subtract k from f(x); gives f(x+3)−2.
College Math Placement Test Intermediate Algebra 5
What is the solution to the compound inequality −1 ≤ 2x + 3 ≤ 7?