openfreebooks-bookgenerator/data/math-curriculum.json

{
  "title": "Mathematics",
  "subtitle": "HKDSE Compulsory Part (S4–S6)",
  "intro": "Topic units across three strands. The map shows required prerequisites; the list follows a readable teaching order.",
  "graph": {
    "edges": [
      { "from": "directed-numbers-rates", "to": "polynomials-expansion-factorisation" },
      { "from": "polynomials-expansion-factorisation", "to": "algebraic-fractions-formulas" },
      { "from": "polynomials-expansion-factorisation", "to": "linear-equations-two-unknowns" },
      { "from": "linear-equations-two-unknowns", "to": "linear-inequalities-one-unknown" },
      { "from": "polynomials-expansion-factorisation", "to": "laws-of-indices" },
      { "from": "laws-of-indices", "to": "quadratic-equations" },
      { "from": "polynomials-expansion-factorisation", "to": "factor-remainder-theorems" },
      { "from": "quadratic-equations", "to": "factor-remainder-theorems" },
      { "from": "quadratic-equations", "to": "complex-numbers" },
      { "from": "quadratic-equations", "to": "functions-graphs" },
      { "from": "quadratic-equations", "to": "sequences-series" },
      { "from": "functions-graphs", "to": "exponential-logarithmic" },
      { "from": "functions-graphs", "to": "variations" },
      { "from": "functions-graphs", "to": "sequences-series" },
      { "from": "functions-graphs", "to": "linear-programming" },
      { "from": "sequences-series", "to": "linear-programming" },
      { "from": "polynomials-expansion-factorisation", "to": "coordinate-geometry-foundations" },
      { "from": "quadratic-equations", "to": "coordinate-circles" },
      { "from": "functions-graphs", "to": "advanced-trigonometry" },
      { "from": "coordinate-geometry-foundations", "to": "deductive-geometry" },
      { "from": "coordinate-geometry-foundations", "to": "coordinate-circles" },
      { "from": "deductive-geometry", "to": "congruence-similarity" },
      { "from": "congruence-similarity", "to": "pythagoras-theorem" },
      { "from": "pythagoras-theorem", "to": "introduction-trigonometry" },
      { "from": "introduction-trigonometry", "to": "mensuration-3d" },
      { "from": "introduction-trigonometry", "to": "advanced-trigonometry" },
      { "from": "coordinate-circles", "to": "circle-properties" },
      { "from": "deductive-geometry", "to": "circle-properties" },
      { "from": "coordinate-circles", "to": "loci" },
      { "from": "circle-properties", "to": "loci" },
      { "from": "directed-numbers-rates", "to": "statistical-charts-averages" },
      { "from": "statistical-charts-averages", "to": "measures-dispersion" },
      { "from": "statistical-charts-averages", "to": "basic-probability" },
      { "from": "basic-probability", "to": "permutations-combinations-probability" },
      { "from": "measures-dispersion", "to": "normal-distribution-z-scores" },
      { "from": "measures-dispersion", "to": "statistical-literacy" },
      { "from": "basic-probability", "to": "statistical-literacy" },
      { "from": "permutations-combinations-probability", "to": "statistical-literacy" }
    ]
  },
  "strands": [
    {
      "id": "number-algebra",
      "title": "Number & Algebra",
      "chapters": [
        {
          "slug": "directed-numbers-rates",
          "title": "Directed numbers, rates & ratios",
          "description": "Operate with negative numbers and solve ratio, rate, and proportion problems in context.",
          "status": "live",
          "curriculums": ["DSE"]
        },
        {
          "slug": "polynomials-expansion-factorisation",
          "title": "Polynomials: expansion & factorisation",
          "description": "Expand products, collect like terms, and factorise expressions using common factors and identities.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "algebraic-fractions-formulas",
          "title": "Algebraic fractions & formulas",
          "description": "Simplify algebraic fractions and change the subject of formulas in applied contexts.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "linear-equations-two-unknowns",
          "title": "Linear equations in two unknowns",
          "description": "Solve simultaneous linear equations by substitution, elimination, and graphical interpretation.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "linear-inequalities-one-unknown",
          "title": "Linear inequalities in one unknown",
          "description": "Solve and represent linear inequalities on the number line and in word problems.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "laws-of-indices",
          "title": "Laws of indices",
          "description": "Apply index laws to simplify expressions with integer and rational exponents.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "quadratic-equations",
          "title": "Quadratic equations",
          "description": "Solve quadratics by factorising, completing the square, and the formula. Model real problems with parabolas and roots.",
          "status": "live",
          "curriculums": ["DSE"]
        },
        {
          "slug": "factor-remainder-theorems",
          "title": "Factor & remainder theorems",
          "description": "Use the factor and remainder theorems to factorise higher-degree polynomials and solve related equations.",
          "status": "planned",
          "curriculums": ["DSE"],
          "tier": "non-foundation"
        },
        {
          "slug": "complex-numbers",
          "title": "Complex numbers",
          "description": "Represent complex numbers in Cartesian form and perform operations including conjugates and division.",
          "status": "planned",
          "curriculums": ["DSE"],
          "tier": "non-foundation"
        },
        {
          "slug": "functions-graphs",
          "title": "Functions & graphs",
          "description": "Study domains, ranges, transformations, and graphs of common functions including quadratics and rationals.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "exponential-logarithmic",
          "title": "Exponential & logarithmic functions",
          "description": "Explore laws of logarithms, exponential growth and decay, and sketch related graphs.",
          "status": "planned",
          "curriculums": ["DSE"],
          "tier": "non-foundation"
        },
        {
          "slug": "sequences-series",
          "title": "Sequences & series",
          "description": "Work with arithmetic and geometric sequences, sigma notation, and finite summation formulas.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "variations",
          "title": "Variations",
          "description": "Model direct, inverse, joint, and partial variation and solve combined variation problems.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "linear-programming",
          "title": "Linear programming",
          "description": "Graph linear inequalities, identify feasible regions, and optimise objective functions in two variables.",
          "status": "planned",
          "curriculums": ["DSE"],
          "tier": "non-foundation"
        }
      ]
    },
    {
      "id": "measures-shape-space",
      "title": "Measures, Shape & Space",
      "chapters": [
        {
          "slug": "coordinate-geometry-foundations",
          "title": "Coordinate geometry foundations",
          "description": "Plot points, find distances and midpoints, and work with slopes of lines in the Cartesian plane.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "deductive-geometry",
          "title": "Deductive geometry",
          "description": "Prove angle and side relationships for intersecting lines, triangles, and polygons.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "congruence-similarity",
          "title": "Congruence & similarity",
          "description": "Apply congruence and similarity criteria to justify properties of triangles and scale figures.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "pythagoras-theorem",
          "title": "Pythagoras' theorem",
          "description": "Use Pythagoras' theorem and its converse in 2D problems and coordinate settings.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "introduction-trigonometry",
          "title": "Introduction to trigonometry",
          "description": "Define sine, cosine, and tangent ratios and solve right-angled triangle problems.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "mensuration-3d",
          "title": "Mensuration in 3D",
          "description": "Find volumes and surface areas of prisms, cylinders, pyramids, cones, and spheres.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "coordinate-circles",
          "title": "Coordinate geometry of circles",
          "description": "Find equations of circles, tangents, and intersections using coordinate methods and distance.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "advanced-trigonometry",
          "title": "Advanced trigonometry",
          "description": "Use sine and cosine rules, radians, and trigonometric graphs in 2D and 3D applications.",
          "status": "planned",
          "curriculums": ["DSE"],
          "tier": "non-foundation"
        },
        {
          "slug": "circle-properties",
          "title": "Properties of circles",
          "description": "Apply chord, tangent, and angle theorems in circles to prove results and solve geometry problems.",
          "status": "planned",
          "curriculums": ["DSE"],
          "tier": "non-foundation"
        },
        {
          "slug": "loci",
          "title": "Loci",
          "description": "Describe and construct loci in the plane, linking geometric constraints to algebraic equations.",
          "status": "planned",
          "curriculums": ["DSE"],
          "tier": "non-foundation"
        }
      ]
    },
    {
      "id": "data-handling",
      "title": "Data Handling",
      "chapters": [
        {
          "slug": "statistical-charts-averages",
          "title": "Charts & averages",
          "description": "Organise data with tables and charts and calculate mean, median, and mode.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "measures-dispersion",
          "title": "Measures of dispersion",
          "description": "Interpret range, interquartile range, variance, and standard deviation for comparing data sets.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "basic-probability",
          "title": "Basic probability",
          "description": "Calculate theoretical and experimental probabilities for simple events and complements.",
          "status": "planned",
          "curriculums": ["DSE"]
        },
        {
          "slug": "permutations-combinations-probability",
          "title": "Permutations, combinations & probability",
          "description": "Count outcomes with permutations and combinations, then compute probabilities in finite sample spaces.",
          "status": "planned",
          "curriculums": ["DSE"],
          "tier": "non-foundation"
        },
        {
          "slug": "normal-distribution-z-scores",
          "title": "Normal distribution & z-scores",
          "description": "Model continuous data with the normal curve, standardise with z-scores, and read probabilities from tables.",
          "status": "planned",
          "curriculums": ["DSE"],
          "tier": "non-foundation"
        },
        {
          "slug": "statistical-literacy",
          "title": "Statistical literacy",
          "description": "Evaluate claims in media and research: sampling bias, correlation versus causation, and misleading charts.",
          "status": "planned",
          "curriculums": ["DSE"]
        }
      ]
    }
  ]
}