Bluebook SAT Test Circles 12

Question 1

A circle has equation (x + 3)² + (y − 5)² = 49. Which transformation maps this circle to the unit circle x² + y² = 1?

Accepted Answer

Translate (3,−5), then dilate by factor 1/7

Answer

First shift center (−3, 5) to origin by translating (+3, −5), giving x² + y² = 49, then shrink radius 7 to 1 by scaling by 1/7.

Question 2

A wheel of radius 2 feet rolls along a flat road without slipping. How far has the center of the wheel traveled after the wheel makes 5 complete rotations?

Accepted Answer

20π feet

Answer

Each rotation the wheel travels one circumference = 2π(2) = 4π feet. Five rotations = 5 × 4π = 20π feet.

Question 3

In a circle with radius 13, a chord is drawn 5 units from the center. What is the length of the chord?

Accepted Answer

Both B and C

Answer

Half-chord = √(13²−5²) = √(169−25) = √144 = 12. Full chord = 24. Both B and C are equal.

Question 4

Circle O has center (0, 0) and radius 5. Line y = 3 intersects the circle. What are the x-coordinates of the intersection points?

Accepted Answer

±4

Answer

Substituting y = 3: x² + 9 = 25, so x² = 16 and x = ±4.

Question 5

A sector has radius 6 and central angle 150°. What is the area of the sector?

Accepted Answer

15π

Answer

Area = (150/360) × π(6)² = (5/12) × 36π = 15π.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Circles 12