Curriculum Modules

{
  "id": "algerian-bac-math-2026",
  "subject": "math",
  "level": "11-12",
  "version": "1.0",
  "locale": "ar-DZ",

  "concepts": [
    {
      "id": "complex-numbers",
      "title": "Complex Numbers",
      "title_localized": "الأعداد المركبة",
      "explanation": "A complex number z = a + bi where a is the real part and b is the imaginary part...",
      "misconceptions": [
        {
          "description": "Students confuse i^2 = -1 with i = -1",
          "detection_pattern": "i equals negative one",
          "correction_strategy": "Clarify that i is the square root of -1, so i^2 = -1, but i itself is not -1."
        }
      ]
    }
  ],

  "problems": [
    {
      "id": "complex-add-1",
      "concept_id": "complex-numbers",
      "statement": "Calculate (3 + 2i) + (1 - 4i)",
      "hints": ["Add real parts together, then imaginary parts together"],
      "solution": "4 - 2i",
      "difficulty": "easy"
    }
  ],

  "worked_examples": [
    {
      "id": "complex-multiply-example",
      "concept_id": "complex-numbers",
      "title": "Multiplying complex numbers",
      "steps": [
        { "description": "Apply distributive property (FOIL)", "expression": "(2+3i)(1-i) = 2(1) + 2(-i) + 3i(1) + 3i(-i)" },
        { "description": "Simplify each term", "expression": "= 2 - 2i + 3i - 3i^2" },
        { "description": "Replace i^2 with -1", "expression": "= 2 + i - 3(-1) = 5 + i" }
      ]
    }
  ],

  "system_prompt_additions": "You are tutoring for the Algerian BAC exam. Use formal Arabic mathematical terminology on the whiteboard. When the student speaks in Darja, respond verbally in Darja but write all notation in standard form."
}