Additional Topics in Math

Circles, Arcs, and Sectors

Apply circle theorems, arc length, and sector area. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on circles, arcs, and sectors is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 A circle has radius 3. What is the length of an arc subtended by a central angle of 30 degrees? Use … easy 400-500 Open
2 A circle has radius 11. What is the area of a sector with central angle 45 degrees? Use π ≈ 3.14. easy 400-500 Open
3 A circle has radius 4. What is the length of an arc subtended by a central angle of 60 degrees? Use … easy 400-500 Open
4 A circle has radius 2. What is the area of a sector with central angle 90 degrees? Use π ≈ 3.14. easy 400-500 Open
5 A circle has radius 2. What is the length of an arc subtended by a central angle of 120 degrees? Use… easy 400-500 Open
6 A circle has radius 4. What is the area of a sector with central angle 135 degrees? Use π ≈ 3.14. easy 400-500 Open
7 A circle has radius 2. What is the length of an arc subtended by a central angle of 180 degrees? Use… easy 500-600 Open
8 A circle has radius 6. What is the area of a sector with central angle 30 degrees? Use π ≈ 3.14. easy 500-600 Open
9 A circle has radius 8. What is the length of an arc subtended by a central angle of 45 degrees? Use … medium 500-600 Open
10 A circle has radius 9. What is the area of a sector with central angle 60 degrees? Use π ≈ 3.14. medium 500-600 Open
11 A circle has radius 2. What is the length of an arc subtended by a central angle of 90 degrees? Use … medium 500-600 Open
12 A circle has radius 9. What is the area of a sector with central angle 120 degrees? Use π ≈ 3.14. medium 500-600 Open
13 A circle has radius 4. What is the length of an arc subtended by a central angle of 135 degrees? Use… medium 600-700 Open
14 A circle has radius 12. What is the area of a sector with central angle 180 degrees? Use π ≈ 3.14… medium 600-700 Open
15 A circle has radius 11. What is the length of an arc subtended by a central angle of 30 degrees? Use… medium 600-700 Open
16 A circle has radius 11. What is the area of a sector with central angle 45 degrees? Use π ≈ 3.14. medium 600-700 Open
17 A circle has radius 4. What is the length of an arc subtended by a central angle of 60 degrees? Use … medium 600-700 Open
18 A circle has radius 3. What is the area of a sector with central angle 90 degrees? Use π ≈ 3.14. medium 600-700 Open
19 A circle has radius 12. What is the length of an arc subtended by a central angle of 120 degrees? Us… hard 600-700 Open
20 A circle has radius 4. What is the area of a sector with central angle 135 degrees? Use π ≈ 3.14. hard 700-800 Open
21 A circle has radius 6. What is the length of an arc subtended by a central angle of 180 degrees? Use… hard 700-800 Open
22 A circle has radius 6. What is the area of a sector with central angle 30 degrees? Use π ≈ 3.14. hard 700-800 Open
23 A circle has radius 4. What is the length of an arc subtended by a central angle of 45 degrees? Use … hard 700-800 Open
24 A circle has radius 11. What is the area of a sector with central angle 60 degrees? Use π ≈ 3.14. hard 700-800 Open
25 A circle has radius 6. What is the length of an arc subtended by a central angle of 90 degrees? Use … hard 700-800 Open