Mathematics

High school mathematics knowledge.

Expository and collaborative method with resolution of exercises by students with the coordination and guidance of the teacher. Classes presented in Portuguese.

With this training unit it is intended that the trainee develops reasoning, methodologies, and good practices of scientific thinking. The skills to be acquired include: understanding of elementary mathematical concepts, operations with real numbers, solving equations, etc.; interpret phenomena and solve problems using functions and their graphs; solve trigonometry problems, including the use of angles and trigonometric relations; apply mathematical knowledge in the scope of information and communication technologies.

Theme 1. Elements of trigonometry (trigonometric relations in the right triangle, trigonometric circle, trigonometric formulas).

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

Theme 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, equations of the line and plane, scalar product, geometric interpretation, parallelism and perpendicularity, intersection of planes and geometric interpretation, resolution of linear systems, classification, and geometric interpretation).

Theme 4. Real functions of real variable (notion of function, domain, range and image, injective, surjective, and bijective function, real function of real variable and graph, odd and even function, monotony, composite function, inverse function, relation between the graphs of a function and its inverse, polynomial functions (highlights n = 0, n = 1, n = 2), absolute value function, trigonometric functions, exponential function of base a, logarithm function of base a, particular case a = e, representation of regions in the plane, , limit and continuity).

Theme 5. Differential calculus (definition of the derivative and geometric interpretation, algebra of derivatives, derivative of the composite function, derivative of the inverse function, monotony and concavity, calculation of limits by the Cauchy rule, optimization problems without restrictions, applications).

Theme 6. Introduction to linear programming (formulation of the problem, linear programming model, admissible region and graphic resolution, particular cases: impossible problem and unlimited problem).

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

In order to carry out continuous assessment, the student must attend at least 75% of all classes, that is, he must be present for at least 42 hours of the 56 hours of contact provided. To be able to submit to the evaluation by exam, the student must have at least 50% of attendance in all classes, that is, he must be present in at least 28 hours of the 56 hours of contact foreseen. Cases identified in the legislation in force are excluded.

Continuous assessment consists of two tests (to be taken in person) with equal weighting, and coursework completed throughout the semester.

The tests account for 60% (12 points) of the final grade (out of 20 points).

The first test will take place in the second week of November, with a duration of 2 hours, and will cover Topics 1, 2, and 3.

The second test will take place during the period allocated for the recovery of lost classes and exam preparation, with a duration of 2 hours, and will cover Topics 4 and 5.

Coursework accounts for 40% (8 points) of the final grade (out of 20 points).

Topic 6 is assessed through an individual assignment completed during class, worth 2 points out of 20. The remaining assignments are also completed during class and have a total value of 6 points out of 20.

In all tests, students must obtain a minimum score of 5 out of 20.

If n1 is the grade obtained in the first test and n2 the grade in the second test (both on a scale of 0 to 20), the contribution of the tests to the final grade is calculated as (n1 + n2) /2*0.6. A student passes the course if the sum of the results from the tests and coursework is greater than or equal to 10 points.

In the first season exam, a student who has chosen Continuous Assessment may retake the result of one, and only one, of the two tests taken, or may take an examination (worth 20 points), or may take an examination (worth 12 points) to which the grades from coursework completed during the semester will be added. In the second season exam, a student who has chosen Continuous Assessment may take an examination (worth 20 points), or may take an examination (worth 12 points) to which the grades from coursework completed during the semester will be added. At special season exam, a student who has chosen Continuous Assessment may only take an examination (worth 20 points), with no grades from coursework completed during the semester being considered.

The Assessment by Exam consists of taking a test (20 points) in any of the seasons, provided for in the school calendar. The student is approved if the exam result is equal to or higher than 10 points.

The student cannot use a calculating machine in the tests and exams of the course.

NAO