Overall objectives:

1 - Know and apply the rules of matrix calculation;
2 - Classify systems of linear equations regarding the existence of a solution and solve these systems using the Gaussian elimination method and Cramer's rule;
3 - Recognize and interpret geometric properties of function graphs;
4 - Characterize the function derived from a function. Relate the sign and zeros of the derived function to the monotony and extremes of the function. Solve simple optimization problems involving differentiable functions;
5 - Determine immediate primitives and apply the technique of part primitivation;
6 - Use defined integrals when calculating areas of regions in the plan;
7 - Use trigonometric ratios (sine, cosine and tangent) and their relationships in solving elementary problems.

Syllabus:

1 - Matrix:
1.1 - Generalities;
1.2 - Matrix operations (addition, multiplication and transposition);
1.3 - Determinants;
1.4 - Systems of linear equations:
1.4.1 - Representation of a system of linear equations in matrix form;
1.4.2 - Gauss method;
1.4.3 - Cramer's rule.
2 - Real functions of real variable:
2.1 - Generalities;
2.2 - Polynomial (linear and quadratic), rational, exponential and logarithmic functions;
2.3 - Limit of a function at one point;
2.4 - Continuity;
2.5 - Derived from a function at a point;
2.6 - Derived function;
2.7 - Derivation rules;
2.8 - Second order derivative.
3 - Primitives and integral calculus:
3.1 - Generalities;
3.2 - Primitivation techniques;
3.3 - Defined integral;
3.4 - Application of the integrals defined in the calculation of areas of plan regions.
4 - Trigonometry:
4.1 - Trigonometric ratios;
4.2 - Fundamental formula of trigonometry;
4.3 - Trigonometric circumference;
4.4 - Trigonometry application to solve elementary problems.

Literature/Sources:

Agudo, F. R. Dias , 1989 , Introdução à álgebra linear e geometria analítica , Escolar Editora
Stewart, J. , 2012 , Cálculo - Volume I , Editora Thomson
Neves, M. A. F., Guerreiro, L. & Silva, A. P. , 2020 , Máximo - Matemática A - 10.º ano , Porto Editora
Neves, M. A. F., Guerreiro, L. & Silva, A. P. , 2020 , Máximo - Matemática A - 11.º ano , Porto Editora
Neves, M. A. F., Guerreiro, L. & Silva, A. P. , 2020 , Máximo - Matemática A - 12.º ano , Porto Editora

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
In accordance with the expected for the Professional Higher Technical Courses.