Math ClubMath Club

Term 1 · Year 1

Term 1 — Functions, Sets, Intuition of Change

Rigorous mathematical language + introduction to the rate of change as the concept that precedes calculus.

10 lessons  ·  10 published ·  ~32h of study

(Year 1 — Foundations)

Classes (didactic grouping)

Each Class groups 2–5 Lessons by topic. Click on a Lesson to study the content.

Class A — Foundations of mathematical language

~6h · 2 lessons
  1. Lesson 1
    Number sets, intervals, notation
    ℕ, ℤ, ℚ, ℝ, intervals, ∩, ∪, complement
    published →
  2. Lesson 2
    Functions: definition, domain, image
    f: A→B, Cartesian graph, surjective/injective
    published →

Class B — Families of elementary functions

~9h · 3 lessons
  1. Lesson 3
    Linear functions (first degree)
    Slope as constant rate of change
    published →
  2. Lesson 4
    Quadratic functions
    Vertex, roots, axis of symmetry, quadratic formula
    published →
  3. Lesson 5
    Function composition and inverse function
    f∘g, f⁻¹, condition for invertibility
    published →

Class C — Exponential, logarithm and growth models

~9h · 3 lessons
  1. Lesson 6
    Exponential functions
    a^x, the number e via compound interest
    published →
  2. Lesson 7
    Logarithmic functions
    log_a x as the inverse of a^x; ln, log base 10
    published →
  3. Lesson 8
    Exponential growth and decay
    Population, radioactive decay, compound interest
    published →

Class D — Average rate of change (bridge to Calculus)

~6h · 2 lessons
  1. Lesson 9
    Average rate of change — gateway to calculus
    Δy/Δx, geometric and physical interpretation — gateway to calculus
    published →
  2. Lesson 10
    Consolidation Term 1: integrative workshop
    Integrating workshop, ENEM/EJU/Abitur-style problems
    published →

Test yourself this term

There are 10 exam versions covering this term, each with answer key + step-by-step solutions. Take one after each group of lessons.

Open exams for Term 1 →