Bluebook SAT Test Circles 3 — Questions and Answers
Question 1: The equation (x − 1)² + (y + 7)² = 25 represents a circle. What are the center and radius?
- Center (1, −7), radius 5 (Correct answer)
- Center (−1, 7), radius 5
- Center (1, −7), radius 25
- Center (1, 7), radius 5
Correct answer: Center (1, −7), radius 5
Standard form (x−h)²+(y−k)²=r²: h=1, k=−7, r=√25=5.
Question 2: A circle has area 100Ï€. What is the diameter?
- 20 (Correct answer)
- 10
- 50
- 100
Correct answer: 20
A = πr² = 100π → r² = 100 → r = 10 → diameter = 20.
Question 3: An arc length of 6Ï€ is cut from a circle of radius 9. What is the central angle in radians?
- 2Ï€/3 (Correct answer)
- π/3
- 3Ï€/2
- π
Correct answer: 2Ï€/3
Arc = rθ → 6π = 9θ → θ = 6π/9 = 2π/3.
Question 4: What is the area of a sector with radius 5 and central angle π/2 radians?
- 25Ï€/4 (Correct answer)
- 5Ï€/2
- 25Ï€/2
- 5Ï€/4
Correct answer: 25Ï€/4
Sector area = (1/2)r²θ = (1/2)(25)(π/2) = 25π/4.
Question 5: An inscribed angle intercepts a semicircle (arc of 180°). What is the measure of the inscribed angle?
- 90° (Correct answer)
- 180°
- 45°
- 60°
Correct answer: 90°
An inscribed angle is half the intercepted arc: 180°/2 = 90° (Thales' theorem).
Question 6: Rewrite x² + y² − 4x + 8y + 4 = 0 in standard form and identify the center.
- Center (2, −4) (Correct answer)
- Center (−2, 4)
- Center (4, −8)
- Center (2, 4)
Correct answer: Center (2, −4)
Complete the square: (x²−4x+4)+(y²+8y+16) = −4+4+16 = 16; center is (2, −4).
Question 7: A wheel has radius 3 feet. How far does the wheel travel in one full rotation?
- 6Ï€ feet (Correct answer)
- 3Ï€ feet
- 9Ï€ feet
- 12Ï€ feet
Correct answer: 6Ï€ feet
One full rotation = circumference = 2Ï€r = 2Ï€(3) = 6Ï€ feet.
Bluebook SAT Test Circles 3
The equation (x − 1)² + (y + 7)² = 25 represents a circle.
What are the center and radius?