Math ClubMath Club

Teaching Program

Optimized High School

120 / 120 published lessons·~384h (128h/year · 32h/term)

Year 1 · 15 anos

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.

40 of 40 lessons published (100%)JP Math I + Math A · DE Klasse 10 · SG Sec 4 (E-Math)

Term 1 — Functions, Sets, Intuition of Change10/10 · ~32h
  1. L1Number sets, intervals, notation
  2. L2Functions: definition, domain, image
  3. L3Linear functions (first degree)
  4. L4Quadratic functions
  5. L5Function composition and inverse function
  6. L6Exponential functions
  7. L7Logarithmic functions
  8. L8Exponential growth and decay
  9. L9Average rate of change — gateway to calculus
  10. L10Consolidation Term 1: integrative workshop
Term 2 — Trigonometry and Sequences10/10 · ~32h
  1. L11Trigonometric ratios in the right triangle
  2. L12Trigonometric circle and radians
  3. L13Trigonometric functions
  4. L14Trigonometric equations and inequalities
  5. L15Law of sines and law of cosines
  6. L16Numerical sequences
  7. L17Arithmetic progressions (PA)
  8. L18Geometric progressions (GP)
  9. L19Intuitive limit of sequences
  10. L20Trim 2 Consolidation: trigonometry + sequences workshop
Term 3 — Analytic Geometry and 2D Vectors10/10 · ~32h
  1. L21Cartesian Plane: Distance, Midpoint
  2. L22Equation of a Line
  3. L23Relative Position of Lines
  4. L24Equation of the Circle
  5. L25Conics: ellipse, parabola, hyperbola
  6. L26Vectors in the Plane
  7. L27Dot Product
  8. L28Applications of Vectors in Physics
  9. L292x2 and 3x3 Linear Systems
  10. L30Term 3 Consolidation: Analytic Geometry + Vectors
Term 4 — Matrices, Determinants, Combinatorics10/10 · ~32h
  1. L31Introduction to Matrices
  2. L32Matrix Operations
  3. L33Transpose, Identity, Inverse Matrix
  4. L342x2 and 3x3 Determinants
  5. L35Solving Systems via Matrices
  6. L36Fundamental Counting Principle
  7. L37Permutations and Arrangements
  8. L38Combinations and Newton's Binomial
  9. L39Basic Discrete Probability
  10. L40Year 1 Consolidation: Integration Workshop
Open teaching plan for Year 1 →
Year 2 · 16 anos

Year 2 — Differential Calculus and Probability

Here the student formally meets the derivative. Alongside, they gain descriptive statistics and probability — the foundations for everything that follows in a Master's in Engineering, Economics, or Finance.

40 of 40 lessons published (100%)JP Math II + Math B · DE Klasse 11 LK · SG JC 1 (H2 Math início)

Term 5 — Limits and Continuity10/10 · ~32h
  1. L41Formal Limit: ε-δ Definition
  2. L42Algebraic Properties of Limits
  3. L43Continuity of Functions
  4. L44One-Sided and Infinite Limits
  5. L45Fundamental Limits and Indeterminate Forms
  6. L46Intermediate Value Theorem (IVT) and Applications
  7. L47Asymptotes and Asymptotic Behavior
  8. L48Limits with Trigonometric Functions
  9. L49Limit of Sequences (Formalized)
  10. L50Term 5 Consolidation: Limits and Continuity
Term 6 — Derivatives: Concept and Rules10/10 · ~32h
  1. L51Derivative: definition via limit
  2. L52Differentiation Rules
  3. L53The Chain Rule
  4. L54Implicit Differentiation
  5. L55Higher-Order Derivatives
  6. L56Derivatives of Inverse Functions
  7. L57Linear Approximation and Differentials
  8. L58Related Rates
  9. L59Differentiability and Smoothness
  10. L60Term 6 Consolidation: Derivatives
Term 7 — Applications of the Derivative10/10 · ~32h
  1. L61Maxima and Minima
  2. L62Applied Optimization
  3. L63Curve Sketching
  4. L64L'Hôpital's Rule
  5. L65Taylor Polynomials
  6. L66Concavity and Inflection Points
  7. L67Marginal Analysis in Economics
  8. L68Kinematics: Position, Velocity, and Acceleration
  9. L69Newton-Raphson Method
  10. L70Consolidation Term 7: Maxima, L'Hôpital, Taylor, Newton
Term 8 — Descriptive Statistics and Probability10/10 · ~32h
  1. L71Measures of central tendency: mean, median, mode
  2. L72Variance and standard deviation
  3. L73Quartiles, percentiles, and boxplots
  4. L74Discrete random variable
  5. L75Binomial distribution
  6. L76Normal distribution
  7. L77Central Limit Theorem
  8. L78Correlation and simple linear regression
  9. L79Deep Dive into Bayes' Theorem
  10. L80Consolidation Term 8 — Applied Statistics and Probability
Open teaching plan for Year 2 →
Year 3 · 17 anos

Year 3 — Integral, ODEs, Inference, Linear Algebra

The synthesis: integral calculus, ODEs (with the bridge to the Black-Scholes PDE), statistical inference, and introductory linear algebra. Whoever finishes Year 3 is ready for Calculus I in any federal-university engineering program.

40 of 40 lessons published (100%)JP Math III + Math C · DE Klasse 12 LK · SG JC 2 (H2 Math final)

Term 9 — Integral Calculus10/10 · ~32h
  1. L81Antiderivative and indefinite integral
  2. L82Definite integral and oriented area
  3. L83Fundamental Theorem of Calculus
  4. L84Technique: u-substitution
  5. L85Integration by Parts
  6. L86Integrals of rational functions (partial fractions)
  7. L87Trigonometric integrals and trigonometric substitution
  8. L88Area between curves
  9. L89Volume by slicing: disks, washers, and cylindrical shells
  10. L90Term 9 Consolidation (integral calculus)
Term 10 — Differential Equations10/10 · ~32h
  1. L91Introduction to Ordinary Differential Equations
  2. L92Separable ODEs
  3. L931st-order linear ODEs
  4. L94Population models: Malthus and Verhulst
  5. L952nd-order linear ODEs with constant coefficients
  6. L96Mechanical vibrations: mass-spring-damper
  7. L97RLC Circuits
  8. L98Euler's Method (Numerical)
  9. L99Newton's Law of Cooling
  10. L100Consolidation Quarter 10 (ODEs)
Term 11 — Inferential Statistics and Regression10/10 · ~32h
  1. L101Sampling: types, biases, and sampling distribution
  2. L102Confidence interval for the mean
  3. L103Hypothesis testing: structure and logic
  4. L104z-test and Student's t-test
  5. L105Simple linear regression
  6. L106Multiple regression
  7. L107One-way ANOVA
  8. L108Chi-squared test: goodness of fit and independence
  9. L109Introductory Bayesian Statistics
  10. L110Consolidation Term 11: Statistical Inference
Term 12 — Advanced Linear Algebra and Synthesis10/10 · ~32h
  1. L111Vector spaces: axioms, subspaces, basis, dimension
  2. L112Linear transformations
  3. L113Kernel and Image
  4. L114Eigenvalues and eigenvectors
  5. L115Diagonalization
  6. L116Special matrices: symmetric, orthogonal, and Hermitian
  7. L117Singular Value Decomposition (SVD)
  8. L118Principal Component Analysis (PCA)
  9. L119Synthesis: Black-Scholes revisited
  10. L120Final Workshop
Open teaching plan for Year 3 →

Compared workload: JP Math I ~140h/year · DE Klasse 10 LK ~120h/year · SG E-Math ~135h/year. Our program 128h/year is within the compatible window. Each lesson equates to ~3h of study + exercises; each class groups 3-5 didactic lessons. See official references in the Manifesto.

Pedagogical philosophy

  • Bruner — spiral: each concept revisited at increasing levels (rate of change at 15, derivative at 16, linear operator at 17).
  • Vygotsky — ZPD: scaffolding declared in each class. Hard task + calibrated support.
  • Singapore — CPA: concrete → pictorial → abstract for every new concept.
  • Japan — fewer concepts, greater detail: topics exhausted before moving on.
  • Germany LK: at least one formal proof per term, age-calibrated.
  • Brazil — explicit door 15: Brazilian vocabulary and examples (BNCC, ENEM, real). Not a translation of a foreign textbook.

How to contribute

Lessons are MDX files at content/aulas/ano-N/trim-T/aula-NN.mdx. Each lesson follows the canonical template (6+1 doors: formal/5/10/15/25/40/practical) with an exercise list using <ListaExercicios seed="aula-NN"> for deterministic 25% answer keys. Pull requests welcome.