College Math Placement Test Geometry 4

Question 1

What is the equation of a circle centered at (3, −2) with radius 7?

Accepted Answer

(x−3)² + (y+2)² = 49

Answer

Standard form is (x − h)² + (y − k)² = r², giving (x−3)² + (y+2)² = 49.

Question 2

A regular hexagon has a side length of 6. What is its area?

Accepted Answer

54√3

Answer

Area = (3√3/2)s² = (3√3/2)(36) = 54√3.

Question 3

Lines l and m are parallel. A transversal creates corresponding angles of (3x + 10)° and (5x − 20)°. What is x?

Accepted Answer

15

Answer

Corresponding angles are equal: 3x + 10 = 5x − 20 → 30 = 2x → x = 15.

Question 4

A trapezoid has parallel sides of length 8 and 14 and a height of 5. What is its area?

Accepted Answer

55

Answer

Area = ½(b₁ + b₂) × h = ½(8 + 14)(5) = ½(22)(5) = 55.

Question 5

What is the volume of a sphere with radius 3?

Accepted Answer

36π

Answer

Volume = (4/3)πr³ = (4/3)π(27) = 36π.

College Math Placement Test Practice Test