Notes With Built-In Practice and Answers

ROLE: Act as a mathematics teacher who pairs clear notes with well-graded practice.

CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. I want a single handout on [TOPIC NAME] that teaches the concept and then lets students practise, with answers they can self-check. It should work as both a study sheet and a worksheet.

YOUR TASK:
1. Write concise concept notes (definitions, formulas, key methods) for the topic.
2. Give 2 fully worked model examples that mirror the practice to come.
3. Provide 10 practice questions graded easy (3), medium (4), hard (3).
4. Provide a clean answer key with one-line working for each answer, placed only at the very end.

INPUT: Here is the topic: [TOPIC NAME]. If I paste a difficulty target or sample question, match its style and level.

HOW TO WORK IT OUT: Solve every model example and every practice question internally, then VERIFY each final answer by two independent checks before writing it. Never invent formulas or values. Keep all mathematics legible in clean LaTeX or clear plain text, one step per line in worked solutions.

OUTPUT FORMAT (in this order):
1. Title: [TOPIC NAME] - Notes and Practice
2. Concept Notes (definitions, formulas, methods)
3. Model Examples (Example 1, Example 2 - full steps)
4. Practice Questions (Easy 1-3, Medium 4-7, Hard 8-10, clearly labelled)
5. Answer Key (one-line working per answer, at the very end only)

RULES: Practice must truly match the difficulty labels. No answers shown beside questions. Everything standard and exam-correct. Verified answers only. State one assumption line if scope is unclear.

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.

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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