College Math Placement Test Intermediate Algebra 5

Question 1

What is the solution to the compound inequality −1 ≤ 2x + 3 ≤ 7?

Accepted Answer

−2 ≤ x ≤ 2

Answer

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?

Accepted Answer

y = −(3/2)x + 4

Answer

Perpendicular slopes are negative reciprocals; the negative reciprocal of 2/3 is −3/2.

Question 3

Simplify: (x² − 4x + 4)/(x − 2)

Accepted Answer

x − 2

Answer

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?

Accepted Answer

69 ft

Answer

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?

Accepted Answer

(x+2)² + (y−3)² = 25

Answer

Standard form (x−h)²+(y−k)²=r²; with h=−2, k=3, r=5: (x+2)²+(y−3)²=25.

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