Mathematics

High school mathematics knowledge.

Essentially expository method in theoretical classes and collaborative in practical classes, with students solving exercises with the coordination and guidance of the teacher.

This training unit is intended for the trainee to develop reasoning, attitudes, behaviors, methodologies and good practices of scientific thinking. The skills to be acquired include: understanding and using elementary mathematics concepts, operating with real numbers, solving equations, etc.; interpret phenomena and solve problems using functions and their graphs; solve trigonometry problems, including the use of generalizations of the notions of angles and trigonometric ratios; apply mathematical knowledge within the scope of information and communication technologies.

Topic 1. Elements of trigonometry (trigonometric ratios in the right triangle, trigonometric circle, trigonometric formulas).

Topic 2. Complex numbers (algebraic form, geometric representation in the Argand plane, conjugate, module and argument, operations with complex numbers in algebraic form, trigonometric form, operations with complex numbers in trigonometric form).

Topic 3. Elements of analytical geometry (points and vectors in R^2 and R^3, operations with points and vectors, distance between points, norm of a vector, straight line and plane equations, scalar product, geometric interpretation, parallelism and perpendicularity, intersection of planes and geometric interpretation, resolution of linear systems, classification and geometric interpretation).

Topic 4. Real functions of a real variable (notion of function, domain, arrival set and codomain, injective, surjective and bijective functions, real function of a real variable and graph, even and odd function, monotony, compound function, inverse function, relation between the graphs of a function and its inverse, polynomial functions (highlights n=0, n=1, n=2), module function, trigonometric functions, exponential function with base a, logarithm function with base a, particular case a= and, representation of flat regions, limit and continuity).

Topic 5. Differential calculus (definition of derivative and geometric interpretation, derivation rules, derivative of the composite function, derivative of the inverse function, monotony and concavity, calculation of limits using Cauchy’s rule, unrestricted optimization problems, applications).

Topic 6. Introduction to linear programming (problem formulation, linear programming model, admissible region and graphical resolution, particular cases: impossible problem and unlimited problem).

The student can choose a Continuous Assessment or an Assessment by Exam.

To be able to undergo continuous assessment, the student must have at least 75% attendance in all classes, that is, they must be present in at least 42 hours of the 56 contact hours planned. To be able to undergo assessment by exam, the student must have at least 50% attendance in all classes, that is, they must be present in at least 28 hours of the 56 hours of contact scheduled. Cases identified in current legislation are excluded.

Continuous assessment consists of three tests (which are assumed to be carried out in person) with equal marks and assignments throughout the semester. Tests have a weight of 70% (14 points) and assignments have a weight of 30% (6 points) in the final grade (20 points).

The first test will be on October 25th from 2:30 pm to 4 pm and themes 1 and 2 will be evaluated.

The second test will be on December 6th from 2:30 pm to 4 pm and themes 3 and 4 will be evaluated.

The third test will be on January 5th from 9:30 to 11am and themes 5 and 6 will be evaluated.

In all tests, the student must obtain a minimum rating of 5 out of 20. If n1 is the grade obtained in the first test, n2 the grade in the second test and n3 the grade in the third test (grades on a scale of 0 to 20 values), then the contribution of the tests to the final grade is given by the expression (n1+ n2+n3)/3*0.7. The student is approved if the sum of the test results and assignments is greater than or equal to 10 points.

Student results are posted on the attendance agenda; successful students are exempt from the Mathematics exam during the normal exam period; Failed students are admitted to the Mathematics exam during the normal exam period.

During the normal exam period, the student who opted for Continuous Assessment can retrieve the result of one and only one of the three tests carried out or can take an exam (for 20 points) or can take an exam (for 14 points) to which the grade of work carried out during the semester. At the time of exam appeals, the student who opted for Continuous Assessment can take an exam (for 20 points) or can take an exam (for 14 points) to which the grade of the work carried out during the semester is added.

During the special exam period, the student who opted for Continuous Assessment can only take one exam (for 20 points) and the work carried out during the semester will not be counted. Assessment by Exam consists of carrying out an exam (20 points) in any of the periods, normal, recourse and special, provided for in the school calendar.

The student is approved if the exam result is greater than or equal to 10 points. The student cannot use a calculating machine in the tests and exams of the curricular unit.

NAO