These are the questions most test-takers get right. They are worth practising anyway: on the digital SAT the easy questions in Module 1 are what route you into the harder, higher-scoring Module 2, so dropping one costs more than it looks.
Every question below is a real item from the SAT Climb bank, tagged easy by the same difficulty model the app uses to build your practice. Pick an answer before you open the explanation.
Math · Geometry and Trigonometry~1 per testEasy tier
None of these repeat the 25 hard Circles questions, so the two pages together are 45 different questions on this one skill.
Question 1Easy
A circle in the xy-plane has equation x2+y2−6x+8y=0. What is the radius of the circle?
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Why A is right
Complete the square: x2 - 6x + y2 + 8y=0 becomes (x−3)2−9+(y+4)2−16=0, which simplifies to (x−3)2+(y+4)2=25. The radius is 25=5.
Why the others are wrong
BThis is the diameter of the circle, not the radius.
CThis is r² from the standard form equation, not the radius itself.
DThis incorrectly takes the square root of the sum of the coefficients of x and y.
Question 2Easy
A circle has a radius of 8. What is the area of a sector of this circle that has a central angle of π/4 radians?
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Why A is right
The area of a sector is (θ/2π)×πr2, which simplifies to (θ/2) × r2. Substituting: (π/4)/2×64=81×64=8π.
Why the others are wrong
BThis incorrectly uses the diameter instead of the radius in the calculation.
CThis omits the necessary factor from the sector formula.
DThis treats π/4 radians as if it were 45 degrees without proper conversion to the sector area formula.
Question 3Easy
A circle has a central angle measuring 60°. If the radius of the circle is 12, what is the length of the arc intercepted by this central angle?
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Why B is right
Arc length equals (θ/360∘)×2πr. Substituting θ=60∘ and r=12 gives 36060×2π(12)=61×24π=4π.
Why the others are wrong
AThis incorrectly uses the diameter 24 in place of radius, then makes an additional calculation error.
CThis omits π from the arc length formula, giving only the coefficient.
DThis omits π and also makes a calculation error in the fraction.
Question 4Easy
A circle in the xy-plane has equation x2+y2+10x−4y+4=0. What are the coordinates of the center of the circle?
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Why C is right
Complete the square: ([MATH]x2+10x+25)[/MATH] + ([MATH]y2−4y+4) = -4 + 25 + 4 = 25[/MATH], giving (x+5)2+(y−2)2=25. The center is (-5, 2).
Why the others are wrong
AThis incorrectly uses positive values and divides the coefficients by 2 without applying the sign change.
BThis uses the coefficients directly from the original equation without completing the square.
DThis uses the coefficients with incorrect signs without completing the square.
Question 5Easy
In a circle with radius 6, a central angle measures 60°. What is the length of the arc intercepted by this central angle?
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Why A is right
Arc length equals (θ/360∘)×2πr. With θ=60∘ and r=6, arc length = 36060×2π(6)=61×12π=2π.
Why the others are wrong
BThis omits π from the arc length calculation.
CThis uses diameter (12) instead of radius (6) in the formula.
DThis converts 60° to radians (π/3) but doesn't multiply by the radius.
Question 6Easy
In the xy-plane, a circle has center (2, -3) and passes through the point (6, 0). What is the length of the diameter of the circle?
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Why C is right
The radius is the distance from the center to the point: √[(6−2)2 + (0−(−3))2] = 16+9=25=5. The diameter is twice the radius, so 2×5=10.
Why the others are wrong
AThis is the radius of the circle, not the diameter.
BThis results from an arithmetic error in computing the distance.
DThis is the square of the radius rather than the diameter.
Question 7Easy
In a circle, a central angle measures 90°. If the radius of the circle is 8, what is the area of the sector formed by this central angle?
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Why D is right
Sector area equals (θ/360°) × πr2. With θ = 90° and r=8, sector area = 36090×π(82) = 41×64π=16π.
Why the others are wrong
AThis incorrectly uses r instead of r² in the area formula.
BThis uses the arc length formula instead of the sector area formula.
CThis correctly calculates (1/4) × 64 but omits π from the result.
Question 8Easy
A circle has a central angle measuring 90° and a radius of 8. What is the area of the sector formed by this central angle?
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Why C is right
Sector area equals (θ/360°) × πr2. Substituting θ = 90° and r=8 gives 36090×π(64)=41×64π=16π.
Why the others are wrong
AThis makes a calculation error when simplifying (1/4) × 64π.
BThis omits π from the sector area formula.
DThis incorrectly uses diameter 16 in place of radius 8, inflating the result.
Question 9Easy
A circle has a radius of 8. What is the length of an arc of the circle that has a central angle of 45°?
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Why C is right
Arc length is (θ/360∘)×2πr, where θ is the central angle in degrees. Substituting θ=45∘ and r=8 gives 36045×2π(8)=81×16π=2π.
Why the others are wrong
AThis incorrectly calculates the arc length by using an incorrect fraction of the circumference.
BThis incorrectly uses a calculation that would correspond to a 90° angle, not 45°.
DThis correctly computes the numerical coefficient but omits π from the final answer.
Question 10Easy
A circle has a radius of 6. What is the area of a sector of the circle that has a central angle of 60°?
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Why A is right
The area of a sector is (θ/360°) × πr2, where θ is the central angle in degrees. Substituting θ = 60° and r=6 gives 36060×π(6)2=61×36π=6π.
Why the others are wrong
BThis incorrectly uses diameter 12 instead of radius 6 in the calculation.
CThis correctly computes the numerical coefficient but omits π from the final answer.
DThis incorrectly treats the degree measure as if it were already in the formula without proper conversion.
Question 11Easy
A circle has a radius of 8. What is the length of an arc that subtends a central angle of π/4 radians?
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Why B is right
Arc length is calculated using the formula s=rθ, where r is the radius and θ is the central angle in radians. Substituting r=8 and θ = π/4 gives s=8(π/4)=2π.
Why the others are wrong
AThis results from incorrectly using half the radius in the arc length formula.
CThis results from using the diameter instead of the radius in the arc length formula.
DThis results from omitting π from the calculation, treating the angle as if it were dimensionless.
Question 12Easy
In a circle with radius 10, a sector has a central angle of 2π/5 radians. What is the area of the sector?
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Why B is right
The area of a sector is (1/2)r2θ, where r is the radius and θ is the central angle in radians. Substituting r=10 and θ = 2π/5 gives (1/2)(100)(2π/5)=20π.
Why the others are wrong
AThis results from an arithmetic error when multiplying the terms.
CThis results from using the diameter instead of the radius, giving (1/2)(400)(2π/5).
DThis results from omitting π from the final calculation.
Question 13Easy
A circle has a radius of 15. What is the length of an arc of this circle that is intercepted by a central angle measuring 120°?
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Why B is right
Arc length equals (θ/360∘)×2πr. Substituting θ=120∘ and r=15 gives 360120×2π(15)=31×30π=10π.
Why the others are wrong
AThis makes a calculation error when simplifying (1/3) × 30π.
CThis incorrectly uses diameter 30 in place of radius 15, doubling the correct answer.
DThis omits π from the arc length formula.
Question 14Easy
In a circle, a central angle of measure 120∘ forms a sector with area 12π. What is the radius of the circle?
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Why B is right
Sector area = (θ/360∘)×πr2. With θ=120∘ and area = 12π: 12π=360120×πr2, so 12π=31πr2. Solving gives r2 = 36, so r=6.
Why the others are wrong
AThis uses an incorrect calculation, possibly confusing radius with a fraction of the area.
CThis is the diameter (2r) instead of the radius.
DThis is r² = 36 without taking the square root.
Question 15Easy
The equation of a circle in the xy-plane is x2+y2−6x+4y−12=0. What is the radius of the circle?
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Why C is right
Completing the square: ([MATH]x2−6x+9)[/MATH] + ([MATH]y2+4y+4) = 12 + 9 + 4[/MATH], which gives (x−3)2+(y+2)2=25. Therefore the radius is 25=5.
Why the others are wrong
AThis incorrectly uses half the coefficient of x as the radius without completing the square.
BThis incorrectly uses half the coefficient of y or confuses intermediate values from the completion process.
DThis incorrectly identifies the diameter (2r = 10) instead of the radius.
Question 16Easy
In the xy-plane, a circle has center (4, -3) and radius 6. Which equation represents this circle?
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Why C is right
The standard form of a circle with center (h, k) and radius r is (x−h)2+(y−k)2 = r2. Substituting h=4, k=−3, and r=6 gives (x−4)2+(y+3)2=36.
Why the others are wrong
AThis uses the radius instead of the radius squared on the right side.
BThis incorrectly places the signs in the equation, reversing the center coordinates.
DThis uses the diameter instead of the radius squared on the right side.
Question 17Easy
A circle in the xy-plane has center (3, -2) and radius 5. Which equation represents this circle?
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Why B is right
The standard form of a circle with center (h, k) and radius r is (x−h)2+(y−k)2 = r2. Substituting (3, -2) and r=5 gives (x−3)2+(y+2)2=25.
Why the others are wrong
AThis incorrectly uses r = 5 instead of r² = 25 on the right side of the equation.
CThis incorrectly flips the signs in the center coordinates, giving center (-3, 2) instead of (3, -2).
DThis incorrectly uses the diameter 10 instead of squaring the radius to get 25.
Question 18Easy
The equation of a circle is x2+y2+10x−4y+4=0. What are the coordinates of the center of this circle?
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Why A is right
Completing the square: ([MATH]x2+10x+25)[/MATH] + ([MATH]y2−4y+4) + 4 = 25 + 4[/MATH], which simplifies to (x+5)2+(y−2)2=25. The center is (-5, 2).
Why the others are wrong
BThis incorrectly reverses the signs when converting from the completed square form.
CThis incorrectly uses the coefficients directly without completing the square or adjusting signs.
DThis uses the coefficients directly and also fails to adjust the signs correctly.
Question 19Easy
A circle in the xy-plane has its center at (3, -2) and has a radius of 5. Which equation represents this circle?
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Why B is right
The standard form of a circle with center (h, k) and radius r is (x−h)2+(y−k)2 = r2. Substituting the center (3, -2) and radius 5 gives (x−3)2+(y+2)2=25.
Why the others are wrong
AThis incorrectly uses the radius itself instead of r², which should be 25.
CThis reverses the signs of the center coordinates, giving center (-3, 2) instead of (3, -2).
DThis uses the diameter 10 instead of squaring the radius to get 25.
Question 20Easy
The equation of a circle is x2+y2−6x−8y=0. What is the radius of this circle?
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Why C is right
Completing the square: ([MATH]x2−6x+9)[/MATH] + ([MATH]y2−8y+16) = 0 + 9 + 16[/MATH], giving (x−3)2+(y−4)2=25. Since r2 = 25, the radius r=5.
Why the others are wrong
AThis is half the x-coefficient, not accounting for completing the square.
BThis is half the y-coefficient, not accounting for completing the square.
DThis is the diameter (2r) instead of the radius.
What to do after easy
Getting these right quickly is the point: speed on the easy questions is what buys time for the hard ones. When they stop costing you effort, move up.
Questions are written by SAT Climb and drawn from its own item bank. SAT® is a registered trademark of College Board, which is not affiliated with and does not endorse SAT Climb.