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Pathways and courses

A pathway is an ordered route through lessons. Lessons are shared, so progress made in one pathway counts in any other pathway that uses the same lesson.

Mathematics pathways

  • British mathematics pilot

    16 lessons across Years 10–13, with practice and teacher copies. England and international qualification routes remain separate and planned.

    Open British pathway

  • Middle school · Grades 6–8

    Three grade programmes, 30 units and 90 guided lessons, with Common Core standards and England KS3 connections.

    Explore middle school

  • Trigonometry foundations to calculus readiness

    18 lessons

    Core first, enrichment by interest; 2–6 sessions per week, no fixed deadline.

    Starts with: Angles as rotation: degrees, radians and arcs; Right triangles, exact values and similarity; Heights, distances and model assumptions

  • Coordinate geometry and conics

    12 lessons

    Work from coordinate foundations to conics; optional proof extensions do not block progress.

    Starts with: Distance, midpoint and section ratios; Signed area, collinearity and coordinate proof; Locus: necessity, sufficiency and restrictions

  • Loney analytical and proof enrichment

    18 lessons

    Follow prerequisites. T22 is deliberately deferred until the BC series lessons.

    Starts with: Logarithms, historical tables and interpolation; Complex numbers and De Moivre’s theorem; Finite cosine sums and cancellation

  • Calculus AB, BC and the AB → BC bridge

    Calculus pathways live on their own site and use the same account.

    Open Calculus

Trigonometry

Review editionNot yet human-reviewed

Angles as rotation through identities, inverse functions and analytical enrichment, with Loney-referenced practice.

Unit T1Angle and triangle foundations

  1. T01Angles as rotation: degrees, radians and arcs
    45 min
  2. T02Right triangles, exact values and similarity
    45 min
  3. T03Heights, distances and model assumptions
    45 min

Unit T2Circular functions and equations

  1. T04Unit circle, signs and reduction formulas
    45 min
  2. T05Graphs, amplitude, phase and periodic models
    45 min
  3. T06General solutions of trigonometric equations
    45 min

Unit T3Identities and transformations

  1. T07Deriving and using addition formulas
    45 min
  2. T08Double, triple and half angles
    45 min
  3. T09Products, sums and finite trigonometric series
    45 min
  4. T10Identity proofs and preserving domains
    45 min

Unit T4Inverse functions and equation strategy

  1. T11Inverse functions and principal branches
    45 min
  2. T12Quadratic equations in ratios and amplitude methods
    45 min

Unit T5Triangles and geometric applications

  1. T13Sine rule, cosine rule and triangle area
    45 min
  2. T14The ambiguous SSA case
    45 min
  3. T15Triangle centres, radii and area identities
    45 min
  4. T16Cyclic quadrilaterals and regular polygons
    45 min

Unit T6Approximation and coordinate bridges

  1. T17Small angles and a bridge to limits
    45 min
  2. T18Logarithms, historical tables and interpolation
    Enrichment45 min
  3. T19Eliminating an angle: from trigonometry to a locus
    45 min

Unit T7Analytical enrichment and proof

  1. T20Complex numbers and De Moivre’s theorem
    Enrichment45 min
  2. T21Finite cosine sums and cancellation
    Enrichment45 min
  3. T22Power series as a later calculus connection
    Enrichment45 min
  4. T23Projection and resolving vectors
    Enrichment45 min
  5. T24Trigonometric proof studio: bounds and equality
    Enrichment45 min

Coordinate geometry

Review editionNot yet human-reviewed

Coordinates and loci, lines, circles, conics and polar forms, building toward proof.

Unit G1Coordinates and loci

  1. G01Distance, midpoint and section ratios
    45 min
  2. G02Signed area, collinearity and coordinate proof
    45 min
  3. G03Locus: necessity, sufficiency and restrictions
    45 min

Unit G2Straight lines and distance

  1. G04Straight-line equations and intersections
    45 min
  2. G05Angles, parallelism and perpendicularity
    45 min
  3. G06Distances, feet and reflections
    45 min

Unit G3Line families and coordinate systems

  1. G07Families of lines and angle bisectors
    Enrichment45 min
  2. G08Pairs of lines and second-degree equations
    Enrichment45 min
  3. G09Translation, rotation and oblique axes
    Enrichment45 min

Unit G4Circles and their systems

  1. G10Circles from conditions
    45 min
  2. G11Tangents, chords and contact
    45 min
  3. G12Power, radical axis and circle systems
    Enrichment45 min

Unit G5Parabolas

  1. G13Parabola from focus and directrix
    45 min
  2. G14Parabola tangents and normals
    Enrichment45 min

Unit G6Ellipses and hyperbolas

  1. G15Ellipse: foci, axes and eccentricity
    45 min
  2. G16Ellipse parametrization and tangency
    Enrichment45 min
  3. G17Hyperbola, foci and asymptotes
    45 min
  4. G18Hyperbola tangents and the rectangular case
    Enrichment45 min

Unit G7Polar and general conics

  1. G19Polar coordinates and line equations
    45 min
  2. G20Polar conics and eccentricity
    Enrichment45 min
  3. G21Classifying and tracing a general conic
    Enrichment45 min

Unit G8Advanced geometry and proof

  1. G22Pole, polar and chords of contact
    Enrichment45 min
  2. G23Diameter directions and conjugacy
    Enrichment45 min
  3. G24Geometry proof studio and calculus connection
    Enrichment45 min