Mathematics A — Grade 11

Mathematics A — Grade 11

A complete English-language course translated and expanded from the Portuguese Domínio — Matemática A, 11.º Ano (Edições ASA). It follows the national Aprendizagens Essenciais for the advanced mathematics track.

How to use this course

Each unit mirrors the textbook's structure: a Recall of prior knowledge, numbered lessons with definitions and formulas, step-by-step worked examples, practice problems with hidden solutions (click to reveal), a summary, and a short final test. Mathematics is typeset with MathJax.

Units

Unit 1

Trigonometry

Solving triangles, the trigonometric circle, radians, and periodic functions.

Volume 1
Unit 2

Scalar Product

Line slope, dot product in plane and space, perpendicularity, planes.

Volume 1
Unit 3

Counting

Addition and multiplication principles, arrangements, permutations, combinations.

Volume 2
Unit 4

Sequences

General term, recurrence, and arithmetic & geometric progressions.

Volume 2
Unit 5

Functions

Polynomials, Ruffini's rule, factorization, inequalities, rational functions.

Volume 3
Unit 6

Differential Calculus

Rates of change, the derivative, differentiation rules, monotonicity, optimization.

Volume 3

Full syllabus at a glance

  1. Trigonometry — triangle problems; exact ratios of 30°, 45°, 60°; generalized angles and the trigonometric circle; radians and first-quadrant reduction; sine, cosine, tangent functions and periodic phenomena.
  2. Scalar (dot) product — slope and inclination of a line; dot product in the plane and in space; properties; coordinate form and perpendicularity; Cartesian equations of planes; relative positions of lines and planes.
  3. Counting — general addition and multiplication principles; arrangements (with and without repetition), permutations, combinations.
  4. Sequences — general term, graphical representation, recurrence; arithmetic and geometric progressions and their sums.
  5. Functions — cubic and quartic functions; polynomial division, Ruffini's rule, the remainder theorem, root multiplicity; factorization; polynomial equations and inequalities; operations on functions; rational functions.
  6. Differential calculus — average and instantaneous rate of change; the derivative function; differentiation rules; sign of the derivative and monotonicity; optimization in modeling.

Content adapted for study purposes from the topic structure of Domínio — Matemática A, 11.º Ano by Daniela Raposo and Luzia Gomes (Edições ASA). This is an independent English study resource, not an official translation.