SAT Math Flashcards: Circles

What this deck covers

This deck focuses on Circles, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the length of an arc with radius 5 and angle 60°?

Answer: $\text{Arc Length} = \frac{5\pi}{3}$. Use $s = r\theta$ where $\theta = \frac{\pi}{3}$ radians.

Flashcard 2: What is the standard form equation of a circle?

Answer: $(x-h)^2 + (y-k)^2 = r^2$. Where $(h,k)$ is the center and $r$ is the radius.

Flashcard 3: What is the formula for the equation of a circle in standard form?

Answer: $(x - h)^2 + (y - k)^2 = r^2$. Standard form with center $(h,k)$ and radius $r$.

Flashcard 4: What is the formula for the area of a sector with radius $r$ and angle $\theta$?

Answer: $A = \frac{1}{2}r^2\theta$. Formula for sector area with angle in radians.

Flashcard 5: Identify the center of the circle $(x - 3)^2 + (y + 2)^2 = 16$.

Answer: Center is $(3, -2)$. Center coordinates are $(h,k) = (3,-2)$.

Flashcard 6: Find the circumference if the radius of a circle is 7.

Answer: $C = 14\pi$. Apply $C = 2\pi r$ with $r = 7$.

Flashcard 7: Identify the area of a circle with diameter 8.

Answer: $A = 16\pi$. Use $A = \pi r^2$ with $r = 4$.

Flashcard 8: Identify the center of the circle $(x - 3)^2 + (y + 2)^2 = 16$.

Answer: Center is $(3, -2)$. Center coordinates are $(h,k) = (3,-2)$.

Flashcard 9: Identify the center and radius of $x^2 + y^2 = 49$.

Answer: Center is $(0, 0)$, $r = 7$. Origin center with $r = \sqrt{49} = 7$.

Flashcard 10: What is the term for a circle's distance across through the center?

Answer: Diameter. Standard term for longest chord through center.

Flashcard 11: What distinguishes a minor arc from a major arc?

Answer: A minor arc is less than 180°; a major arc is more. Classification based on arc's angular measure.

Flashcard 12: Calculate the radius if the area is $36\pi$.

Answer: $r = 6$. Solve $36\pi = \pi r^2$ to get $r = 6$.

Flashcard 13: Find the radius if the circumference is $20\pi$.

Answer: $r = 10$. Solve $20\pi = 2\pi r$ to get $r = 10$.

Flashcard 14: What is the radius of the circle $(x + 1)^2 + (y - 4)^2 = 25$?

Answer: $r = 5$. Radius equals $\sqrt{25} = 5$.

Flashcard 15: State the definition of a secant line in a circle.

Answer: A line that intersects a circle at two points. Distinguishes secant from tangent lines.

Flashcard 16: Calculate the area of a sector with radius 3 and angle 30°.

Answer: $A = \frac{3\pi}{2}$. Use $A = \frac{1}{2}r^2\theta$ with $\theta = \frac{\pi}{6}$.

Flashcard 17: State the formula for the length of an arc.

Answer: $\text{Arc Length} = r\theta$. Formula with angle $\theta$ in radians.

Flashcard 18: Find the diameter if the circumference is $18\pi$.

Answer: $d = 18$. Solve $18\pi = 2\pi r$ to get $r = 9$, so $d = 18$.

Flashcard 19: What is the formula to find the diameter of a circle given the radius?

Answer: $d = 2r$. Diameter is twice the radius.

Flashcard 20: What is the length of an arc with radius 5 and angle 60°?

Answer: $\text{Arc Length} = \frac{5\pi}{3}$. Use $s = r\theta$ where $\theta = \frac{\pi}{3}$ radians.

Flashcard 21: What is the relationship between a radius and a tangent?

Answer: They are perpendicular at the point of tangency. Radius and tangent form $90°$ angle at contact point.

Flashcard 22: What is the formula for the area of a sector with radius $r$ and angle $\theta$?

Answer: $A = \frac{1}{2}r^2\theta$. Formula for sector area with angle in radians.

Flashcard 23: What is the formula for the area of a circle?

Answer: $A = \pi r^2$. Standard formula for area using radius squared.

Flashcard 24: What is the formula for the circumference of a circle?

Answer: $C = 2\pi r$. Standard formula relating circumference to radius.

Flashcard 25: What is the term for the distance from the center to any point on the circle?

Answer: Radius. Fundamental distance measurement in circles.

Flashcard 26: What is the name for the part of a circle bounded by a chord and the arc?

Answer: Segment. Region between chord and its corresponding arc.

Flashcard 27: Calculate the area when the radius is 4.

Answer: $A = 16\pi$. Apply $A = \pi r^2$ with $r = 4$.

Flashcard 28: Find the circumference of a circle with diameter 14.

Answer: $C = 14\pi$. Apply $C = \pi d$ with $d = 14$.

Flashcard 29: What defines a chord in a circle?

Answer: A line segment with both endpoints on the circle. Distinguishes chord from other circle segments.

Flashcard 30: Identify the area of a circle with diameter 8.

Answer: $A = 16\pi$. Use $A = \pi r^2$ with $r = 4$.