Doubt-Clearing Class Plan

ROLE: Act as a mathematics teacher who runs calm, well-organised doubt-clearing classes.

CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM]. A doubt class can become chaotic. I want a plan that anticipates the most common doubts on the topic below, answers them clearly, and gives me a fair system to take live questions. Lesson length is [DURATION].

YOUR TASK:
1. Predict the 6 to 8 most common doubts students have on this topic.
2. For each predicted doubt, give a short, clear explanation and one worked example.
3. Give me a simple system to collect and prioritise live doubts (for example a quick written-doubt slip method).
4. Prepare 3 'tricky but common' questions to use if the class goes quiet.
5. End with a 2-question check to confirm the main doubts are cleared.

INPUT: Here is the topic, and any specific doubts I already know about: [PASTE THE TOPIC AND KNOWN DOUBTS HERE].

HOW TO WORK IT OUT: Solve all examples internally first. VERIFY each final answer two independent ways and never invent values or formulas. Keep maths legible in clean plain text or simple LaTeX. Keep each explanation short enough to deliver quickly.

OUTPUT FORMAT (exact headings, in order):

OUTPUT FILE FORMAT: present the complete result as a clean, ready-to-use document I can paste straight into Microsoft Word or Google Docs - a clear bold title, section headings, neatly numbered items, comfortable spacing, and simple tables only where helpful (avoid heavy formatting that breaks on paste). It must also print cleanly to PDF on A4 (File > Print > Save as PDF). Keep all mathematics fully readable (fractions as a/b, powers as x^2, roots as sqrt(x)).

MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.
1. TITLE BLOCK - topic, class, board, duration, 'Compiled by [YOUR NAME]'.
2. PREDICTED COMMON DOUBTS - each with a clear explanation and one worked example with two checks.
3. LIVE-DOUBT SYSTEM - how to collect and prioritise questions fairly.
4. BACKUP TRICKY QUESTIONS - 3 with full solutions.
5. DOUBT-CLEARED CHECK - 2 questions with answers.

RULES: Explanations must be short and clear. Keep the class orderly. Every answer verified.

At the very end add a footer line: 'Prepared by [YOUR NAME]', and put 'Compiled by [YOUR NAME]' in the title block.

CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.

GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.

SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
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Questions, feedback or appreciation are always welcome.
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