Subject: Mathematics VI

Scientific Area:

Mathematics

53 Hours

Number of ECTS:

5 ECTS

Language:

Portuguese

# Overall objectives:

1.1. - To understand the modulus concept of a real number and associate it with the notion of
distance.
1.2. - To distinguish the specificities of the functions defined by monomials namely the quadratic
and cubic functions.
1.3 - Be able to distinguish the situations when the absolute value of the variable is less than one
and when the absolute value of the variable is greater than one and when the absolute value of
the variable is greater than one.
1.4. - Understand the fundamental concepts of mathematics that underlie the mathematical
knowledge that Basic Education students will have to learn.
1.5. - To study trigonometric functions and interpret is as special cases of periodic functions.

# Syllabus:

1 - The modulus concept of a real number and its association with the notion of distance.
Modulus Function and problem-solving related to the concept of Euclidean distance.
2 - Study the monotony and the graphical representation of functions defined by monomials,
namely the quadratic and cubic functions.
3 - Use of ICT in the study of functions.
4 - The trigonometric functions and the importance of periodic functions. Applications.

# Literature/Sources:

Campos Ferreira, J., Introdução à Análise Matemática, Fundação Calouste Gulbenkian. (1985).
Davis, M. & Edwards, C., Elementary Mathematical Modeling, Functions and Graphs., Prentice
Hall (2001).
Palhares, P., Gomes, A., & Amaral E., Complementos de Matemática para professores do Ensino
Básico, Lisboa: LIDEL (2010).
Teixeira, P., Precatado, A., Albuquerque, C., Antunes, C., & Nápoles, S., Funções - 11º ano de
escolaridade, Lisboa: Ministério da Educação, Departamento do Ensino Secundário. (1998).

# Assesssment methods and criteria:

Classes include theoretical and practical moments, dedicated to the introduction or synthesis of
the various topics under study, and others, frequently of a practical nature that involve individual
and group work. We value the attendance work within the activities developed in working groups
and individually. The evaluation will take into consideration all classroom activities and others
performed in distance. Students will be assessed having regard to: Attendance and participation
(10%); A working group that will be subject to presentation to the class (40%); A test (50%).