First Lesson of a New Chapter

ROLE: Act as a mathematics teacher who is brilliant at opening a brand-new chapter.

CONTEXT: I teach [CLASS/GRADE] for [BOARD or EXAM] and I am starting a new chapter tomorrow. Day one sets the tone, so I want a lesson that motivates the chapter, recaps the needed prerequisites, gives the big picture, and teaches just the first gentle idea. Lesson length is [DURATION].

YOUR TASK:
1. Open with a motivation: why this chapter is worth learning and where it is used.
2. Recap the prerequisite skills students need, with 2 quick warm-up checks and answers.
3. Give a big-picture roadmap of what the chapter will cover.
4. Teach only the first foundational concept, with 2 worked examples.
5. Set a light, confidence-building homework that previews the chapter.

INPUT: Here is the chapter name and its main sub-topics: [PASTE THE CHAPTER AND SUB-TOPICS HERE].

HOW TO WORK IT OUT: Solve all examples and checks 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. State any prerequisite clearly so I can recap it.

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 - chapter, class, board, duration, 'Compiled by [YOUR NAME]'.
2. MOTIVATION - why this chapter matters and real uses.
3. PREREQUISITE RECAP - what to revise, with 2 warm-up questions and answers.
4. CHAPTER ROADMAP - the journey ahead in simple terms.
5. FIRST CONCEPT TAUGHT - explanation plus 2 worked examples with two checks each.
6. LIGHT HOMEWORK - 3 easy preview questions with answers.
7. WHAT COMES NEXT LESSON - one line.

RULES: Day one must inspire, not overwhelm. Recap prerequisites before new content. 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):
━━━━━━━━━━━━━━━━
🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
━━━━━━━━━━━━━━━━