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Term 4 · Year 1

Term 4 — Matrices, Determinants, Combinatorics

Algebraic structures + bridge to probability.

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 — Matrices: definition and operations

~6h · 2 lessons
  1. Lesson 31
    Introduction to Matrices
    Notation, types of matrices (square, identity, diagonal)
    published →
  2. Lesson 32
    Matrix Operations
    Addition, scalar multiplication, matrix product
    published →

Class B — Inverse, determinants, systems

~9h · 3 lessons
  1. Lesson 33
    Transpose, Identity, Inverse Matrix
    Aᵀ, A⁻¹, existence conditions
    published →
  2. Lesson 34
    2x2 and 3x3 Determinants
    2×2, 3×3, Sarrus rule, geometric properties
    published →
  3. Lesson 35
    Solving Systems via Matrices
    Ax = b, Cramer's rule for n = 2, 3
    published →

Class C — Combinatorics: fundamental counting principle, permutations, combinations

~9h · 3 lessons
  1. Lesson 36
    Fundamental Counting Principle
    FCP, applications to telephones, passwords
    published →
  2. Lesson 37
    Permutations and Arrangements
    n!, P(n,r), order matters
    published →
  3. Lesson 38
    Combinations and Newton's Binomial
    C(n,r), Pascal's triangle, applications
    published →

Class D — Probability + yearly synthesis

~6h · 2 lessons
  1. Lesson 39
    Basic Discrete Probability
    Classical, frequentist, conditional probability
    published →
  2. Lesson 40
    Year 1 Consolidation: Integration Workshop
    Year 1 synthesis, ENEM/SAT mixed 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 4 →