College Math Placement Test Geometry 4 — Questions and Answers
Question 1: What is the equation of a circle centered at (3, −2) with radius 7?
- (x−3)² + (y+2)² = 49 (Correct answer)
- (x+3)² + (y−2)² = 49
- (x−3)² + (y+2)² = 7
- (x−3)² + (y−2)² = 49
Correct answer: (x−3)² + (y+2)² = 49
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?
- 54√3 (Correct answer)
- 36√3
- 72√3
- 108
Correct answer: 54√3
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?
- 15 (Correct answer)
- 10
- 20
- 5
Correct answer: 15
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?
- 55 (Correct answer)
- 110
- 56
- 70
Correct answer: 55
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?
- 36π (Correct answer)
- 12π
- 108π
- 27π
Correct answer: 36π
Volume = (4/3)πr³ = (4/3)π(27) = 36π.
Question 6: In a right triangle, one acute angle is 30°. If the hypotenuse is 20, what is the side opposite the 30° angle?
- 10 (Correct answer)
- 10√3
- 20√3
- 20/√3
Correct answer: 10
In a 30-60-90 triangle, the side opposite 30° is half the hypotenuse: 20/2 = 10.
Question 7: A chord is 8 cm long and is 3 cm from the center of a circle. What is the radius of the circle?
- 5 cm (Correct answer)
- 4 cm
- √55 cm
- √73 cm
Correct answer: 5 cm
The perpendicular from center bisects the chord; r² = 4² + 3² = 16 + 9 = 25, so r = 5.
College Math Placement Test Geometry 4
What is the equation of a circle centered at (3, −2) with radius 7?