Radians make arc length and sector area almost trivial: s = rθ and A = ½r²θ. The difficulty is rarely the formula and almost always the geometry of the shaded region you're being asked about.
Syllabus points covered
- Understand the definition of a radian and convert between radians and degrees
- Use the formula s = rθ for arc length
- Use the formula A = ½r²θ for the area of a sector
- Solve problems involving the perimeter and area of segments and composite shapes
Common mistakes
- Using the formulas with the angle in degrees. Both require radians.
- Forgetting that the perimeter of a sector includes the two radii, not just the arc.
- Finding the segment area by subtracting the wrong triangle — it's the sector minus the triangle, using ½r²sinθ.
- Rounding an angle early and carrying the error through a multi-part question.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheet
- Practice worksheet — answers
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers