Step-Wise Marking Scheme for One Question

ROLE: Act as a senior mathematics examiner and head of the marking panel.

CONTEXT: I teach Class [CLASS/GRADE] for [BOARD or EXAM e.g. CBSE / ICSE / State Board / JEE / NEET]. I need a fair, defensible step-wise marking scheme for ONE question so that every teacher marking it awards the same marks.

YOUR TASK:
1. Read the question and its total marks carefully.
2. Solve the question fully on your own, internally, before writing anything.
3. Break the full solution into logical steps.
4. Assign a clear mark or part-mark to each step, matching the official marking style for [BOARD or EXAM].
5. List the common mistakes students make at each step and whether they should lose marks.
6. State exactly how much credit a correct method earns even if the final answer is wrong.

INPUT: Here is the question: [PASTE THE QUESTION HERE]. Total marks for this question: [TOTAL MARKS].

HOW TO WORK IT OUT: Solve the problem internally first. Then VERIFY the final answer using at least two independent checks (for example re-substitution, an alternate method, or a units and sign sanity check). Never invent formulas, theorems or values. Keep all mathematics fully legible using clean LaTeX or clear plain text. The sum of all step marks must equal the total marks exactly; if it does not, fix the scheme before showing it to me.

OUTPUT FORMAT, in this exact order:
1. QUESTION (restated cleanly).
2. MODEL SOLUTION (the full correct working, step by step).
3. MARKING TABLE with three columns: Step | What the student must show | Marks. Include a TOTAL row that equals [TOTAL MARKS].
4. CORRECT FINAL ANSWER (boxed or clearly labelled).
5. COMMON ERRORS AND DEDUCTIONS (bullet list: the error, and marks lost).
6. PARTIAL CREDIT RULE (one line: how much for correct method but wrong answer).
7. VERIFICATION NOTE (one or two lines stating the two checks you used and that they agree).

RULES: Be strict and consistent. Do not award marks for steps the student did not need to show. Do not pad the scheme with extra steps that do not exist in the real solution. If the question is ambiguous, state the one assumption you made in a single line at the top, then continue.

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)).

FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return the complete material as a clean, print-ready A4 handout that can be pasted into Word or Google Docs and saved as PDF. Use a clear title, logical sections, readable mathematics and page-break markers where needed. Keep student material separate from the answer key or teacher notes.


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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