Portuguese Curriculum

Math learned before the university Distribution of subjects in each year

10th grade(15-16 years old)

11th grade(16-17 years old)

12th grade(17-18 years old)

Plane and Space Geometry I Solving problems of Geometry in

the plane and in the space. Analytic Geometry. The method Cartesian for

studying geometry in the plane and space.

Plane and Space Geometry II Problems involving triangles

(Trigonometry). Trigonometric Circle and

trigonometric functions sine, cosine and tangent.

Scalar product of two vectors and applications.

Intersection, parallelism and perpendicularity of lines and planes.

Linear programming (introduction).

Plane and Space Geometry IIICombinatorics and Probability Introduction to the calculation of

probabilitiesFrequency distribution and

probability distributionCombinatorics.

Functions and Graphs. Polynomial functions. Absolute value function. Function, graphic and graphing

representation. Intuitive study of the Properties

of:- Quadratic functions;- Absolute value function. Polynomial functions (grades 3

and 4). Decomposition of polynomials in

factors.

Rational functions and functions with radicals. Rate of change and derivative.

Problems involving functions or rate of change.

Properties of the functions like f (x) = a + b / (cx + d)

Experimental approach of the concept of limit.

Rate of change and derivatives in simple cases.

Operations with functions. Composition and inverse of

functions.

Exponential and logarithmic functions. Limits and Continuity. Concept of Derivative and Derivative Applications. Theory of limits Differential calculus Optimization problems.

Statistics Statistics - Generalities Organization and interpretation

of statistical variables (qualitative and quantitative).

Reference to bi-dimensional distributions (graphical and intuitive approach).

Real Successions. Definition and properties. Examples (the case of

progressions) Sequence (1 + 1 / n) n and the first

definition of e (Neper number). Limits: infinitely large and infinitely

small. Real limits and convergence.

Trigonometry and complex numbers. Functions sine, cosine and

calculation of derivatives Historical introduction of

complex numbers. Complexes as algebraic and

trigonometric form; operations and geometric interpretation.