Year 1 · 15 years old
Year 1 — Foundations
Establishes rigorous language: sets, functions, trigonometry, analytic geometry, vectors, matrices, combinatorics. The last lesson of each term is an integrative workshop. Lesson 9 ("average rate of change") already plants the seed of Calculus.
JP Math I + Math A · DE Klasse 10 · SG Sec 4 (E-Math)
Schedule by term
Click a term to see Classes and Lessons (each Lesson opens the content). Lessons grouped into Classes didactic groups (3-5 lessons per Class). Or use the tabs below to browse by subject.
Term 1 — Functions, Sets, Intuition of Change
open →Rigorous mathematical language + introduction to the rate of change as the concept that precedes calculus.
10 lessons · ~32h of study
- ~6hClass A — Foundations of mathematical language(2 lessons)
- ~9hClass B — Families of elementary functions(3 lessons)
- ~9hClass C — Exponential, logarithm and growth models(3 lessons)
- ~6hClass D — Average rate of change (bridge to Calculus)(2 lessons)
Term 2 — Trigonometry and Sequences
open →Trigonometric tools + introduction to the idea of limit via sequences.
10 lessons · ~32h of study
- ~6hClass A — Triangle trigonometry(2 lessons)
- ~9hClass B — Trigonometric functions and equations(3 lessons)
- ~9hClass C — Sequences, arithmetic and geometric progressions(3 lessons)
- ~6hClass D — Intuitive limit of a sequence(2 lessons)
Term 3 — Analytic Geometry and 2D Vectors
open →Geometric language of functions + vectors as new objects.
10 lessons · ~32h of study
- ~9hClass A — Cartesian plane and lines(3 lessons)
- ~6hClass B — Circle and conics(2 lessons)
- ~9hClass C — Vectors in the plane and the dot product(3 lessons)
- ~6hClass D — Linear systems + synthesis(2 lessons)
Term 4 — Matrices, Determinants, Combinatorics
open →Algebraic structures + bridge to probability.
10 lessons · ~32h of study
- ~6hClass A — Matrices: definition and operations(2 lessons)
- ~9hClass B — Inverse, determinants, systems(3 lessons)
- ~9hClass C — Combinatorics: fundamental counting principle, permutations, combinations(3 lessons)
- ~6hClass D — Probability + yearly synthesis(2 lessons)
Lessons organized by subject
Functions
The language of functions — domain, range, composition, inverse, main classes.
- Lesson 1publishedℕ, ℤ, ℚ, ℝ, intervals, ∩, ∪, complement
- Lesson 2publishedf: A→B, Cartesian graph, surjective/injective
- Lesson 3publishedSlope as constant rate of change
- Lesson 4publishedVertex, roots, axis of symmetry, quadratic formula
- Lesson 5publishedf∘g, f⁻¹, condition for invertibility
- Lesson 6publisheda^x, the number e via compound interest
- Lesson 7publishedlog_a x as the inverse of a^x; ln, log base 10
- Lesson 8publishedPopulation, radioactive decay, compound interest
Pre-Calculus
Average rate of change as the gateway to calculus, no ε-δ yet.
- Lesson 9publishedΔy/Δx, geometric and physical interpretation — gateway to calculus
- Lesson 10publishedIntegrating workshop, ENEM/EJU/Abitur-style problems
Trigonometry
Trigonometric ratios and functions, identities, applications in measurement and periodic modeling.
- Lesson 11publishedsin, cos, tan, measurement applications
- Lesson 12publishedRadians, fundamental identities
- Lesson 13publishedPeriodicity, graphs of sin x, cos x, tan x
- Lesson 14publishedsin x = 1/2, etc.
- Lesson 15publishedNon-right triangles, area via 1/2 ab sin C
Sequences
Arithmetic and geometric progressions, recurrences, and the first intuition of limit (1/n → 0).
- Lesson 16published(aₙ), recurrence, monotonicity, boundedness
- Lesson 17publishedaₙ = a₁ + (n-1)d, sum formula
- Lesson 18publishedaₙ = a₁q^(n-1), geometric sum, infinite series
- Lesson 19publishedlim aₙ via inspection, divergence, oscillation
- Lesson 20publishedTrig + sequences synthesis
Analytic Geometry
Points, lines, circles and conics in the Cartesian plane.
- Lesson 21publishedCoordinates, quadrants, distance between points
- Lesson 22publishedy = mx + n, Ax + By + C = 0, slope
- Lesson 23publishedParallel, perpendicular, point-line distance
- Lesson 24published(x-a)² + (y-b)² = r², tangents
- Lesson 25publishedEllipse, parabola, hyperbola — canonical equations
Vectors
Vectors in the plane and the dot product — first geometric algebra.
- Lesson 26publishedComponents, magnitude, addition, scalar multiplication
- Lesson 27publishedu·v = u₁v₁ + u₂v₂ = |u||v|cos θ
- Lesson 28publishedWork, resultant force, free-body diagrams
- Lesson 29publishedSubstitution, addition, geometric interpretation
- Lesson 30publishedIntegrating workshop with vectors + lines + conics
Matrices
Matrix operations, determinants, linear systems — antechamber of linear algebra.
- Lesson 31publishedNotation, types of matrices (square, identity, diagonal)
- Lesson 32publishedAddition, scalar multiplication, matrix product
- Lesson 33publishedAᵀ, A⁻¹, existence conditions
- Lesson 34published2×2, 3×3, Sarrus rule, geometric properties
- Lesson 35publishedAx = b, Cramer's rule for n = 2, 3
Combinatorics
Counting principle, permutations, arrangements, combinations.
- Lesson 36publishedFCP, applications to telephones, passwords
- Lesson 37publishedn!, P(n,r), order matters
- Lesson 38publishedC(n,r), Pascal's triangle, applications
Probability
Discrete probability, events, conditional independence.
- Lesson 39publishedClassical, frequentist, conditional probability
- Lesson 40publishedYear 1 synthesis, ENEM/SAT mixed problems