{
 "meta": {
  "title": "CBSE Class 10 Board Exam — Repeated Questions & Concepts Analysis",
  "publisher": "ClearSteps (clearsteps.co.in)",
  "license": "CC BY 4.0 — free to reuse with attribution to ClearSteps",
  "board": "CBSE",
  "class": "Class 10",
  "subjects_covered": [
   "Science",
   "Social Science",
   "English",
   "Mathematics (question archetypes only)"
  ],
  "corpus_computed_at": "2026-04-27 06:50:36.404091+00",
  "dataset_published": "2026-08-22",
  "methodology": [
   "Source papers: official CBSE Class 10 board question papers (all available sets/variants per year) from the ClearSteps previous-year-paper corpus.",
   "Every question was mapped to a concept (e.g. \"Ohm’s law and V-I characteristics\"), and concepts were mapped to NCERT chapters.",
   "A concept counts as \"repeated\" in a year if it also appears in at least one earlier year of the corpus. Earliest corpus years therefore show 0% by construction and should be read as baseline years, not low-repeat years.",
   "Rows for 2026 reflect a partial corpus (not all sets ingested at compute time) and are marked partial.",
   "Mathematics concept-level data is excluded: class-purity verification found Class 11/12 concepts mixed into the subject rollup. Mathematics is represented instead by cross-year question archetypes verified as Class 10 content.",
   "Statistics only: no CBSE question text is reproduced in this dataset. Archetype labels are ClearSteps’ own analytical descriptions of question types."
  ],
  "caveats": [
   "Repeat rates are concept-level, not verbatim-question-level: a repeated concept means the same tested idea, not necessarily identical wording or numbers.",
   "Small-sample years (under ~30 questions ingested) are noisier; total_questions is included per row so you can weight accordingly."
  ]
 },
 "repeatability_by_year": [
  {
   "subject": "English",
   "year": 2017,
   "total_questions": 32,
   "unique_concepts": 19,
   "repeated_concepts": 0,
   "repeat_rate_pct": 0,
   "partial": false
  },
  {
   "subject": "English",
   "year": 2018,
   "total_questions": 34,
   "unique_concepts": 22,
   "repeated_concepts": 0,
   "repeat_rate_pct": 0,
   "partial": false
  },
  {
   "subject": "English",
   "year": 2019,
   "total_questions": 160,
   "unique_concepts": 36,
   "repeated_concepts": 22,
   "repeat_rate_pct": 61.11,
   "partial": false
  },
  {
   "subject": "English",
   "year": 2020,
   "total_questions": 43,
   "unique_concepts": 21,
   "repeated_concepts": 5,
   "repeat_rate_pct": 23.81,
   "partial": false
  },
  {
   "subject": "English",
   "year": 2022,
   "total_questions": 32,
   "unique_concepts": 8,
   "repeated_concepts": 8,
   "repeat_rate_pct": 100,
   "partial": false
  },
  {
   "subject": "English",
   "year": 2023,
   "total_questions": 98,
   "unique_concepts": 28,
   "repeated_concepts": 13,
   "repeat_rate_pct": 46.43,
   "partial": false
  },
  {
   "subject": "English",
   "year": 2024,
   "total_questions": 124,
   "unique_concepts": 36,
   "repeated_concepts": 19,
   "repeat_rate_pct": 52.78,
   "partial": false
  },
  {
   "subject": "English",
   "year": 2025,
   "total_questions": 125,
   "unique_concepts": 33,
   "repeated_concepts": 19,
   "repeat_rate_pct": 57.58,
   "partial": false
  },
  {
   "subject": "English",
   "year": 2026,
   "total_questions": 17,
   "unique_concepts": 10,
   "repeated_concepts": 0,
   "repeat_rate_pct": 0,
   "partial": true
  },
  {
   "subject": "Science",
   "year": 2016,
   "total_questions": 69,
   "unique_concepts": 25,
   "repeated_concepts": 16,
   "repeat_rate_pct": 64,
   "partial": false
  },
  {
   "subject": "Science",
   "year": 2017,
   "total_questions": 36,
   "unique_concepts": 20,
   "repeated_concepts": 0,
   "repeat_rate_pct": 0,
   "partial": false
  },
  {
   "subject": "Science",
   "year": 2018,
   "total_questions": 33,
   "unique_concepts": 26,
   "repeated_concepts": 0,
   "repeat_rate_pct": 0,
   "partial": false
  },
  {
   "subject": "Science",
   "year": 2019,
   "total_questions": 173,
   "unique_concepts": 55,
   "repeated_concepts": 31,
   "repeat_rate_pct": 56.36,
   "partial": false
  },
  {
   "subject": "Science",
   "year": 2020,
   "total_questions": 148,
   "unique_concepts": 50,
   "repeated_concepts": 29,
   "repeat_rate_pct": 58,
   "partial": false
  },
  {
   "subject": "Science",
   "year": 2022,
   "total_questions": 76,
   "unique_concepts": 26,
   "repeated_concepts": 0,
   "repeat_rate_pct": 0,
   "partial": false
  },
  {
   "subject": "Science",
   "year": 2023,
   "total_questions": 242,
   "unique_concepts": 57,
   "repeated_concepts": 45,
   "repeat_rate_pct": 78.95,
   "partial": false
  },
  {
   "subject": "Science",
   "year": 2024,
   "total_questions": 232,
   "unique_concepts": 58,
   "repeated_concepts": 46,
   "repeat_rate_pct": 79.31,
   "partial": false
  },
  {
   "subject": "Science",
   "year": 2025,
   "total_questions": 245,
   "unique_concepts": 58,
   "repeated_concepts": 47,
   "repeat_rate_pct": 81.03,
   "partial": false
  },
  {
   "subject": "Science",
   "year": 2026,
   "total_questions": 45,
   "unique_concepts": 32,
   "repeated_concepts": 0,
   "repeat_rate_pct": 0,
   "partial": true
  },
  {
   "subject": "Social Science",
   "year": 2018,
   "total_questions": 70,
   "unique_concepts": 25,
   "repeated_concepts": 21,
   "repeat_rate_pct": 84,
   "partial": false
  },
  {
   "subject": "Social Science",
   "year": 2019,
   "total_questions": 117,
   "unique_concepts": 30,
   "repeated_concepts": 24,
   "repeat_rate_pct": 80,
   "partial": false
  },
  {
   "subject": "Social Science",
   "year": 2020,
   "total_questions": 233,
   "unique_concepts": 50,
   "repeated_concepts": 41,
   "repeat_rate_pct": 82,
   "partial": false
  },
  {
   "subject": "Social Science",
   "year": 2022,
   "total_questions": 64,
   "unique_concepts": 25,
   "repeated_concepts": 14,
   "repeat_rate_pct": 56,
   "partial": false
  },
  {
   "subject": "Social Science",
   "year": 2023,
   "total_questions": 197,
   "unique_concepts": 54,
   "repeated_concepts": 40,
   "repeat_rate_pct": 74.07,
   "partial": false
  },
  {
   "subject": "Social Science",
   "year": 2024,
   "total_questions": 215,
   "unique_concepts": 45,
   "repeated_concepts": 36,
   "repeat_rate_pct": 80,
   "partial": false
  },
  {
   "subject": "Social Science",
   "year": 2025,
   "total_questions": 248,
   "unique_concepts": 56,
   "repeated_concepts": 44,
   "repeat_rate_pct": 78.57,
   "partial": false
  },
  {
   "subject": "Social Science",
   "year": 2026,
   "total_questions": 44,
   "unique_concepts": 30,
   "repeated_concepts": 0,
   "repeat_rate_pct": 0,
   "partial": true
  }
 ],
 "chapter_analysis": [
  {
   "subject": "English",
   "chapter": "Reading Comprehension",
   "concepts_tracked": 8,
   "total_appearances": 123,
   "avg_appearance_pct": 47.1,
   "avg_typical_marks": 8.4
  },
  {
   "subject": "English",
   "chapter": "Writing Skills",
   "concepts_tracked": 4,
   "total_appearances": 117,
   "avg_appearance_pct": 50,
   "avg_typical_marks": 7.8
  },
  {
   "subject": "English",
   "chapter": "Grammar",
   "concepts_tracked": 12,
   "total_appearances": 87,
   "avg_appearance_pct": 33.9,
   "avg_typical_marks": 4.5
  },
  {
   "subject": "English",
   "chapter": "First Flight — Prose",
   "concepts_tracked": 6,
   "total_appearances": 82,
   "avg_appearance_pct": 25.6,
   "avg_typical_marks": 6.8
  },
  {
   "subject": "English",
   "chapter": "First Flight — Poetry",
   "concepts_tracked": 6,
   "total_appearances": 41,
   "avg_appearance_pct": 12.2,
   "avg_typical_marks": 5.2
  },
  {
   "subject": "English",
   "chapter": "Writing Skills — Long Compositions",
   "concepts_tracked": 4,
   "total_appearances": 38,
   "avg_appearance_pct": 31.7,
   "avg_typical_marks": 8.8
  },
  {
   "subject": "English",
   "chapter": "Footprints Without Feet",
   "concepts_tracked": 4,
   "total_appearances": 28,
   "avg_appearance_pct": 16.7,
   "avg_typical_marks": 6.3
  },
  {
   "subject": "English",
   "chapter": "Literature Reader — Prose",
   "concepts_tracked": 3,
   "total_appearances": 22,
   "avg_appearance_pct": 22.2,
   "avg_typical_marks": 7.7
  },
  {
   "subject": "English",
   "chapter": "Writing Skills — Short Compositions",
   "concepts_tracked": 2,
   "total_appearances": 11,
   "avg_appearance_pct": 36.7,
   "avg_typical_marks": 3.5
  },
  {
   "subject": "English",
   "chapter": "Literature Reader — Poetry",
   "concepts_tracked": 3,
   "total_appearances": 10,
   "avg_appearance_pct": 11.1,
   "avg_typical_marks": 6.7
  },
  {
   "subject": "English",
   "chapter": "Literature Reader — Drama",
   "concepts_tracked": 2,
   "total_appearances": 10,
   "avg_appearance_pct": 16.7,
   "avg_typical_marks": 6.5
  },
  {
   "subject": "English",
   "chapter": "Formal Letter Writing",
   "concepts_tracked": 2,
   "total_appearances": 7,
   "avg_appearance_pct": 13.3,
   "avg_typical_marks": 5
  },
  {
   "subject": "English",
   "chapter": "Not Marble, nor the Gilded Monuments",
   "concepts_tracked": 1,
   "total_appearances": 4,
   "avg_appearance_pct": 13.3,
   "avg_typical_marks": 6
  },
  {
   "subject": "English",
   "chapter": "Main Course Book (MCB) — Interact in English",
   "concepts_tracked": 1,
   "total_appearances": 4,
   "avg_appearance_pct": 13.3,
   "avg_typical_marks": 10
  },
  {
   "subject": "Science",
   "chapter": "Metals and Non-metals",
   "concepts_tracked": 6,
   "total_appearances": 131,
   "avg_appearance_pct": 41.2,
   "avg_typical_marks": 2.5
  },
  {
   "subject": "Science",
   "chapter": "Life Processes",
   "concepts_tracked": 6,
   "total_appearances": 130,
   "avg_appearance_pct": 42.6,
   "avg_typical_marks": 2.2
  },
  {
   "subject": "Science",
   "chapter": "Chemical Reactions and Equations",
   "concepts_tracked": 6,
   "total_appearances": 127,
   "avg_appearance_pct": 35.3,
   "avg_typical_marks": 2
  },
  {
   "subject": "Science",
   "chapter": "Light - Reflection and Refraction",
   "concepts_tracked": 5,
   "total_appearances": 126,
   "avg_appearance_pct": 45.9,
   "avg_typical_marks": 2.6
  },
  {
   "subject": "Science",
   "chapter": "Electricity",
   "concepts_tracked": 6,
   "total_appearances": 113,
   "avg_appearance_pct": 34.3,
   "avg_typical_marks": 2.7
  },
  {
   "subject": "Science",
   "chapter": "Our Environment",
   "concepts_tracked": 5,
   "total_appearances": 104,
   "avg_appearance_pct": 42.9,
   "avg_typical_marks": 1.8
  },
  {
   "subject": "Science",
   "chapter": "How do Organisms Reproduce?",
   "concepts_tracked": 5,
   "total_appearances": 103,
   "avg_appearance_pct": 38.2,
   "avg_typical_marks": 2.4
  },
  {
   "subject": "Science",
   "chapter": "Carbon and its Compounds",
   "concepts_tracked": 6,
   "total_appearances": 90,
   "avg_appearance_pct": 29.4,
   "avg_typical_marks": 2.8
  },
  {
   "subject": "Science",
   "chapter": "Heredity",
   "concepts_tracked": 5,
   "total_appearances": 90,
   "avg_appearance_pct": 36.5,
   "avg_typical_marks": 2.2
  },
  {
   "subject": "Science",
   "chapter": "Acids, Bases and Salts",
   "concepts_tracked": 5,
   "total_appearances": 90,
   "avg_appearance_pct": 31.2,
   "avg_typical_marks": 2.2
  },
  {
   "subject": "Science",
   "chapter": "Magnetic Effects of Electric Current",
   "concepts_tracked": 4,
   "total_appearances": 65,
   "avg_appearance_pct": 32.4,
   "avg_typical_marks": 2.5
  },
  {
   "subject": "Science",
   "chapter": "Control and Coordination",
   "concepts_tracked": 5,
   "total_appearances": 63,
   "avg_appearance_pct": 28.8,
   "avg_typical_marks": 2.2
  },
  {
   "subject": "Science",
   "chapter": "The Human Eye and the Colourful World",
   "concepts_tracked": 5,
   "total_appearances": 57,
   "avg_appearance_pct": 24.7,
   "avg_typical_marks": 2.2
  },
  {
   "subject": "Social Science",
   "chapter": "Sectors of the Indian Economy",
   "concepts_tracked": 3,
   "total_appearances": 84,
   "avg_appearance_pct": 49.5,
   "avg_typical_marks": 2
  },
  {
   "subject": "Social Science",
   "chapter": "The Rise of Nationalism in Europe",
   "concepts_tracked": 3,
   "total_appearances": 79,
   "avg_appearance_pct": 47.3,
   "avg_typical_marks": 2.3
  },
  {
   "subject": "Social Science",
   "chapter": "Print Culture and the Modern World",
   "concepts_tracked": 2,
   "total_appearances": 74,
   "avg_appearance_pct": 61.3,
   "avg_typical_marks": 2
  },
  {
   "subject": "Social Science",
   "chapter": "Money and Credit",
   "concepts_tracked": 3,
   "total_appearances": 72,
   "avg_appearance_pct": 53.8,
   "avg_typical_marks": 2
  },
  {
   "subject": "Social Science",
   "chapter": "Political Parties",
   "concepts_tracked": 3,
   "total_appearances": 67,
   "avg_appearance_pct": 53.8,
   "avg_typical_marks": 2.3
  },
  {
   "subject": "Social Science",
   "chapter": "Development",
   "concepts_tracked": 3,
   "total_appearances": 66,
   "avg_appearance_pct": 52.7,
   "avg_typical_marks": 1.3
  },
  {
   "subject": "Social Science",
   "chapter": "Globalisation and the Indian Economy",
   "concepts_tracked": 3,
   "total_appearances": 64,
   "avg_appearance_pct": 45.2,
   "avg_typical_marks": 3
  },
  {
   "subject": "Social Science",
   "chapter": "Gender, Religion and Caste",
   "concepts_tracked": 3,
   "total_appearances": 60,
   "avg_appearance_pct": 45.2,
   "avg_typical_marks": 2
  },
  {
   "subject": "Social Science",
   "chapter": "The Making of a Global World",
   "concepts_tracked": 2,
   "total_appearances": 53,
   "avg_appearance_pct": 46.8,
   "avg_typical_marks": 2
  },
  {
   "subject": "Social Science",
   "chapter": "Outcomes of Democracy",
   "concepts_tracked": 1,
   "total_appearances": 53,
   "avg_appearance_pct": 80.7,
   "avg_typical_marks": 4
  },
  {
   "subject": "Social Science",
   "chapter": "Federalism",
   "concepts_tracked": 2,
   "total_appearances": 52,
   "avg_appearance_pct": 58.1,
   "avg_typical_marks": 2.5
  },
  {
   "subject": "Social Science",
   "chapter": "Agriculture",
   "concepts_tracked": 3,
   "total_appearances": 51,
   "avg_appearance_pct": 44.1,
   "avg_typical_marks": 3
  },
  {
   "subject": "Social Science",
   "chapter": "History",
   "concepts_tracked": 3,
   "total_appearances": 50,
   "avg_appearance_pct": 33.3,
   "avg_typical_marks": 3
  },
  {
   "subject": "Social Science",
   "chapter": "Power Sharing",
   "concepts_tracked": 2,
   "total_appearances": 49,
   "avg_appearance_pct": 53.2,
   "avg_typical_marks": 1.5
  },
  {
   "subject": "Social Science",
   "chapter": "Minerals and Energy Resources",
   "concepts_tracked": 2,
   "total_appearances": 43,
   "avg_appearance_pct": 45.2,
   "avg_typical_marks": 2.5
  },
  {
   "subject": "Social Science",
   "chapter": "Resources and Development",
   "concepts_tracked": 2,
   "total_appearances": 39,
   "avg_appearance_pct": 40.3,
   "avg_typical_marks": 2.5
  },
  {
   "subject": "Social Science",
   "chapter": "Manufacturing Industries",
   "concepts_tracked": 3,
   "total_appearances": 38,
   "avg_appearance_pct": 32.3,
   "avg_typical_marks": 3.7
  },
  {
   "subject": "Social Science",
   "chapter": "Life Lines of National Economy",
   "concepts_tracked": 2,
   "total_appearances": 36,
   "avg_appearance_pct": 40.3,
   "avg_typical_marks": 3
  },
  {
   "subject": "Social Science",
   "chapter": "Geography",
   "concepts_tracked": 3,
   "total_appearances": 34,
   "avg_appearance_pct": 31.2,
   "avg_typical_marks": 2.3
  },
  {
   "subject": "Social Science",
   "chapter": "Nationalism in India",
   "concepts_tracked": 2,
   "total_appearances": 34,
   "avg_appearance_pct": 37.1,
   "avg_typical_marks": 2.5
  },
  {
   "subject": "Social Science",
   "chapter": "Water Resources",
   "concepts_tracked": 3,
   "total_appearances": 31,
   "avg_appearance_pct": 28,
   "avg_typical_marks": 2.7
  },
  {
   "subject": "Social Science",
   "chapter": "Forest and Wildlife Resources",
   "concepts_tracked": 2,
   "total_appearances": 16,
   "avg_appearance_pct": 22.6,
   "avg_typical_marks": 1.5
  },
  {
   "subject": "Social Science",
   "chapter": "The Age of Industrialisation",
   "concepts_tracked": 3,
   "total_appearances": 14,
   "avg_appearance_pct": 10.8,
   "avg_typical_marks": 3.7
  },
  {
   "subject": "Social Science",
   "chapter": "Economics",
   "concepts_tracked": 1,
   "total_appearances": 11,
   "avg_appearance_pct": 22.6,
   "avg_typical_marks": 4
  },
  {
   "subject": "Social Science",
   "chapter": "Political Science",
   "concepts_tracked": 1,
   "total_appearances": 10,
   "avg_appearance_pct": 19.4,
   "avg_typical_marks": 4
  },
  {
   "subject": "Social Science",
   "chapter": "Consumer Rights",
   "concepts_tracked": 2,
   "total_appearances": 8,
   "avg_appearance_pct": 12.9,
   "avg_typical_marks": 2
  }
 ],
 "top_concepts": [
  {
   "subject": "English",
   "concept": "Analytical paragraph (data/process/situation)",
   "chapter": "Writing Skills",
   "total_appearances": 59,
   "papers_analysed": 29,
   "appearance_pct": 96.7,
   "typical_marks": 7,
   "last_appeared_year": null
  },
  {
   "subject": "English",
   "concept": "Formal letter writing",
   "chapter": "Writing Skills",
   "total_appearances": 54,
   "papers_analysed": 27,
   "appearance_pct": 90,
   "typical_marks": 6,
   "last_appeared_year": null
  },
  {
   "subject": "English",
   "concept": "Factual passage MCQ (multiple choice)",
   "chapter": "Reading Comprehension",
   "total_appearances": 41,
   "papers_analysed": 29,
   "appearance_pct": 96.7,
   "typical_marks": 9,
   "last_appeared_year": null
  },
  {
   "subject": "English",
   "concept": "Inference-based short answer questions",
   "chapter": "Reading Comprehension",
   "total_appearances": 30,
   "papers_analysed": 17,
   "appearance_pct": 56.7,
   "typical_marks": 8,
   "last_appeared_year": null
  },
  {
   "subject": "English",
   "concept": "From the Diary of Anne Frank: character analysis",
   "chapter": "First Flight — Prose",
   "total_appearances": 29,
   "papers_analysed": 14,
   "appearance_pct": 46.7,
   "typical_marks": 9,
   "last_appeared_year": null
  },
  {
   "subject": "English",
   "concept": "A Letter to God: theme and character of Lencho",
   "chapter": "First Flight — Prose",
   "total_appearances": 26,
   "papers_analysed": 16,
   "appearance_pct": 53.3,
   "typical_marks": 6,
   "last_appeared_year": null
  },
  {
   "subject": "English",
   "concept": "Editing errors in a passage",
   "chapter": "Grammar",
   "total_appearances": 25,
   "papers_analysed": 25,
   "appearance_pct": 83.3,
   "typical_marks": 7,
   "last_appeared_year": null
  },
  {
   "subject": "English",
   "concept": "Factual/descriptive passage comprehension",
   "chapter": "Reading Comprehension",
   "total_appearances": 22,
   "papers_analysed": 14,
   "appearance_pct": 93.3,
   "typical_marks": 10,
   "last_appeared_year": null
  },
  {
   "subject": "English",
   "concept": "Dust of Snow (Robert Frost): poetic devices and central idea",
   "chapter": "First Flight — Poetry",
   "total_appearances": 21,
   "papers_analysed": 10,
   "appearance_pct": 33.3,
   "typical_marks": 5,
   "last_appeared_year": null
  },
  {
   "subject": "English",
   "concept": "Inference and short answer comprehension",
   "chapter": "Reading Comprehension",
   "total_appearances": 19,
   "papers_analysed": 12,
   "appearance_pct": 80,
   "typical_marks": 9,
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   "subject": "Science",
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   "subject": "Science",
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   "subject": "Science",
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   "subject": "Science",
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   "chapter": "Magnetic Effects of Electric Current",
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   "subject": "Social Science",
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   "subject": "Social Science",
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   "subject": "Social Science",
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   "subject": "Social Science",
   "concept": "Functions and need for political parties",
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   "subject": "Social Science",
   "concept": "Features of federalism in India",
   "chapter": "Federalism",
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   "subject": "Social Science",
   "concept": "Organised and unorganised sectors",
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   "subject": "Social Science",
   "concept": "French Revolution and rise of nationalism",
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   "appearance_pct": 58.1,
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  {
   "subject": "Social Science",
   "concept": "Unification of Germany and Italy",
   "chapter": "The Rise of Nationalism in Europe",
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   "archetype": "Prove: parallelogram circumscribing a circle is a rhombus",
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   "total_corpus_years": 6,
   "cross_year_rate_pct": 66.7,
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    2020,
    2022,
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    2023,
    2024,
    2025
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  {
   "archetype": "Bell/clock tolling together — find time using LCM",
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    2023,
    2024,
    2025
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  {
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   "cross_year_rate_pct": 60,
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    2025
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    2023,
    2024
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  {
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    2024,
    2025,
    2026
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  {
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    2023,
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    2025
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  {
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   "year_count": 2,
   "total_corpus_years": 5,
   "cross_year_rate_pct": 40,
   "years_appeared": [
    2023,
    2024
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  {
   "archetype": "Simplify ratio/expression involving tan²A and cot²A to simplest form",
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   "archetype": "Minimum rooms/groups problem using HCF (equal distribution of different categories)",
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   "total_corpus_years": 5,
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   "total_corpus_years": 5,
   "cross_year_rate_pct": 40,
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    2025
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    2024
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   "year_count": 2,
   "total_corpus_years": 5,
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   "archetype": "Use sec²θ - tan²θ = 1 identity to find reciprocal expression",
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   "year_count": 2,
   "total_corpus_years": 6,
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   "year_count": 2,
   "total_corpus_years": 6,
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   "total_corpus_years": 6,
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    2022
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   "year_count": 2,
   "total_corpus_years": 6,
   "cross_year_rate_pct": 33.3,
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    2020,
    2022
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   "archetype": "Prove: AQ = half perimeter of triangle when circle touches one side and extensions of other two sides",
   "concept": "Two tangents from an external point are equal",
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   "year_count": 2,
   "total_corpus_years": 6,
   "cross_year_rate_pct": 33.3,
   "years_appeared": [
    2020,
    2022
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  {
   "archetype": "Prove: AQ = ½(perimeter of triangle) when circle touches extended sides",
   "concept": "Two tangents from an external point are equal",
   "question_count": 3,
   "year_count": 2,
   "total_corpus_years": 6,
   "cross_year_rate_pct": 33.3,
   "years_appeared": [
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    2023
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  {
   "archetype": "Prove: angle between two tangents = supplementary to angle subtended by chord at centre (∠PTQ + ∠POQ = 180°)",
   "concept": "Two tangents from an external point are equal",
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   "year_count": 2,
   "total_corpus_years": 6,
   "cross_year_rate_pct": 33.3,
   "years_appeared": [
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    2024
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  {
   "archetype": "Find perimeter of triangle circumscribing a circle using equal tangent lengths",
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   "year_count": 2,
   "total_corpus_years": 6,
   "cross_year_rate_pct": 33.3,
   "years_appeared": [
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    2022
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  {
   "archetype": "Prove that tangent between two parallel tangents subtends a right angle at the centre",
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   "year_count": 2,
   "total_corpus_years": 6,
   "cross_year_rate_pct": 33.3,
   "years_appeared": [
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   "total_corpus_years": 6,
   "cross_year_rate_pct": 33.3,
   "years_appeared": [
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    2026
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 ]
}