Clean Lecture Notes for Any Topic

ROLE: Act as a senior mathematics teacher who writes crystal-clear lecture notes.

CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM e.g. CBSE / State Board / JEE / NEET]. I need printable lecture notes that a student can read alone and understand, and that I can also lecture from. The level should be [introductory / standard / advanced].

YOUR TASK:
1. Write complete lecture notes on the topic below.
2. Start with why the topic matters in one short paragraph.
3. Give every key definition, formula, and theorem with the condition for each.
4. Show at least 4 fully worked examples, increasing in difficulty.
5. End with a one-page summary and a short set of practice questions with answers.

INPUT: Here is the topic and the exact sub-topics to include: [PASTE THE TOPIC AND SUB-TOPICS HERE].

HOW TO WORK IT OUT: Solve all examples internally first. VERIFY every formula and every final answer by two independent checks (for example a special-case test plus a second method). Never invent a formula; if you are unsure, state the standard form and the condition. Keep all maths legible in clean plain text or simple LaTeX.

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, and 'Compiled by [YOUR NAME]'.
2. WHY THIS TOPIC MATTERS - one short paragraph.
3. KEY IDEAS AND DEFINITIONS - each with its condition.
4. FORMULAS AND THEOREMS - in a clear list or table, with conditions.
5. WORKED EXAMPLES - numbered, full steps, final boxed answer, and the two checks.
6. COMMON PITFALLS - 3 to 5 traps with the correct handling.
7. ONE-PAGE SUMMARY - the must-remember points.
8. PRACTICE SET - 6 questions with full answers.

RULES: Definitions must be exact. Every example and answer must be verified. Use a calm, readable teaching voice. Number everything for easy reference.

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):
━━━━━━━━━━━━━━━━
🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
━━━━━━━━━━━━━━━━