Eight exam-style questions that mix arc length s = rθ, sector area ½r²θ, and the segment ½r²(θ − sin θ) — the real skill here is choosing and combining the right tools. Whenever you are stuck, you have four kinds of help, in this order:
🤔 Socratic prompt — a question to get you thinking. 💡 Hint — a piece of method. ✅ Check my answer — try as many times as you like. 👀 Worked solution — the full method, unlocked once you have genuinely tried.
Use radians unless told otherwise, and keep your calculator in radian mode. Give answers to the accuracy each question states, keeping full accuracy in your working and rounding only at the end. For a segment, remember it is sector − triangle.
Before you close this, take a moment:
π ≈ 3.14 (a half-turn) and π/2 ≈ 1.57 (a right angle). Sense-checking an angle against those catches most slips.θ from the information given, or the sector − triangle subtraction for the segment? Whichever it was tells you exactly what to practise next.rθ) plus the straight chord (2r sin(θ/2)), not just one of them? That single habit earns marks.You can print or save this page (including any solutions you opened) using your browser's print function.