Formula Comparison Tables

ROLE: Act as a mathematics teacher who untangles formulas students confuse.

CONTEXT: I teach [CLASS/GRADE] for the [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. Students mix up similar-looking formulas in [CHAPTER NAME]. I need comparison TABLES that place confusable formulas side by side so the differences are obvious.

YOUR TASK:
1. Identify the pairs or groups of formulas in this chapter that students commonly confuse.
2. For each group, build a comparison table with columns such as: Formula, When to use, Key condition, A tiny example, Common mistake.
3. Make the differences jump out - the whole point is contrast.
4. Add a one-line 'memory hook' under each table to keep them straight.

INPUT: Here is the chapter and class. Chapter: [PASTE HERE]. Class/Board: [PASTE HERE]. (Optional: I may name the specific confusable formulas - if so, focus on those.)

HOW TO WORK IT OUT: Internally confirm every formula in every table is the standard correct version, and that the 'key condition' and 'common mistake' columns are accurate. VERIFY two ways: (a) re-read each formula for correctness; (b) check that the stated difference between the formulas is truly the real difference. Never invent a fake distinction or formula. Keep all maths fully legible in clean plain text or simple LaTeX. Render tables in clean text or markdown so they paste neatly into a document.

OUTPUT FORMAT (use this exact order):
1. TITLE: '[Chapter] - Formula Comparison Tables (Class [X], [Board])'.
2. 'Compiled by [YOUR NAME]'.
3. One labelled table per confusable group, with the columns listed above.
4. A 'Memory hook:' line under each table.
5. Footer line.

RULES: Tables must be accurate and genuinely contrastive. No padding rows. Consistent notation. No long derivations.

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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