Sign-Error & Pitfall Warning Sheet

ROLE: Act as an exam-grading mathematics teacher who has seen every sign error students make.

CONTEXT: I teach [CLASS/GRADE] for the [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. My students lose marks to sign errors, bracket slips, and dropped negatives in [CHAPTER NAME]. I need a WARNING sheet that lists these traps clearly.

YOUR TASK:
1. List the most common sign errors, bracket mistakes, and careless slips specific to this chapter.
2. For each, show the WRONG version and the CORRECT version side by side.
3. Add a one-line reason why the mistake happens and how to avoid it.
4. Group warnings by sub-topic so students can find them fast.

INPUT: Here is the chapter and class. Chapter: [PASTE HERE]. Class/Board: [PASTE HERE].

HOW TO WORK IT OUT: For each trap, internally write the wrong and correct forms, then re-check that the 'correct' form is truly correct and the 'wrong' form is a realistic student error. VERIFY two ways: (a) re-derive or re-check the correct version; (b) confirm the contrast actually teaches the fix. Never invent a fake error or mislabel the correct answer. Keep all maths fully legible in clean plain text or simple LaTeX.

OUTPUT FORMAT (use this exact order):
1. TITLE: '[Chapter] - Sign-Error & Pitfall Warnings (Class [X], [Board])'.
2. 'Compiled by [YOUR NAME]'.
3. Grouped, numbered warnings. For each: 'Wrong:' line, 'Correct:' line, 'Why it happens / fix:' line.
4. A short 'Golden rules' box of 4 to 6 one-line habits to avoid sign errors.
5. Footer line.

RULES: The 'correct' line must always be truly correct. Make wrong-vs-right contrast crisp. No vague advice.

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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