Portuguese curriculum
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The document outlines the mathematics curriculum in Portugal across 3 years of secondary school (grades 10-12). In 10th grade, students study plane and space geometry, analytic geometry, functions and graphs including polynomial functions, and introductory statistics. 11th grade covers additional geometry topics, trigonometry, rational functions, rates of change and derivatives. 12th grade introduces exponential, logarithmic and complex functions, limits, calculus including optimization problems, and trigonometry. The curriculum provides a progressive introduction to more advanced mathematical concepts each year leading up to university entrance.
Portuguese curriculum
- 1. Portuguese Curriculum Math learned before the university Distribution of subjects in each year 10th grade 11th grade 12th grade (15-16 years old) (16-17 years old) (17-18 years old) Plane and Space Geometry I Plane and Space Geometry II Plane and Space Geometry III Solving problems of Geometry in Problems involving triangles Combinatorics and Probability the plane and in the space. (Trigonometry). Introduction to the calculation of Analytic Geometry. Trigonometric Circle and probabilities The method Cartesian for studying trigonometric functions sine, cosine Frequency distribution and geometry in the plane and space. and tangent. probability distribution Scalar product of two vectors and Combinatorics. applications. Intersection, parallelism and perpendicularity of lines and planes. Linear programming (introduction). Functions and Graphs. Polynomial Rational functions and functions Exponential and logarithmic functions. Absolute value function. with radicals. Rate of change and functions. Limits and Continuity. Function, graphic and graphing derivative. Concept of Derivative and representation. Problems involving functions or Derivative Applications. Intuitive study of the Properties rate of change. Theory of limits of: Properties of the functions like Differential calculus - Quadratic functions; f (x) = a + b / (cx + d) Optimization problems. - Absolute value function. Experimental approach of the Polynomial functions (grades 3 concept of limit. and 4). Rate of change and derivatives in Decomposition of polynomials in simple cases. factors. Operations with functions. Composition and inverse of functions. Statistics Real Successions. Trigonometry and complex Statistics - Generalities Definition and properties. numbers. Organization and interpretation of Examples (the case of progressions) Functions sine, cosine and statistical variables (qualitative Sequence (1 + 1 / n) n and the first calculation of derivatives and quantitative). definition of e (Neper number). Historical introduction of complex Reference to bi-dimensional Limits: infinitely large and infinitely numbers. distributions (graphical and small. Complexes as algebraic and intuitive approach). Real limits and convergence. trigonometric form; operations and geometric interpretation.