Course syllabus

# Tekniskt basår: Matematik 4 Pre-University Course in Technical Sciences: Mathematics 4

## TBAA10, 9 credits, G1 (First Cycle)

Valid for: 2020/21
Decided by: PLED TB
Date of Decision: 2020-04-03

## General Information

Compulsory for: TB1, TNB1-NABA
Language of instruction: The course will be given in Swedish

## Aim

The purpose of the course is to complete an upper secondary school education in Mathematics 4.

## Learning outcomes

Knowledge and understanding
For a passing grade the student must

Does not exist in this form.

Competences and skills
For a passing grade the student must

Does not exist in this form.

Judgement and approach
For a passing grade the student must

Does not exist in this form.

## Contents

Mathematics 4, Part a

•    Handling trigonometric expressions, and proof and use of trigonometric formulae including the Pythagorean trigonometric identity and the addition formulae.
•    Algebraic and graphical methods for solving trigonometric equations.
•    Different methods of proof in mathematics, with examples from the areas of arithmetic, algebra or geometry.
•    Properties of trigonometric functions, logarithmic functions, compound functions and absolute amounts as functions.
•    Drawing graphs and their related asymptotes.
•    Derivation and use of the rules of derivation for trigonometric, logarithmic, exponential and compound functions, and also the product and quotients of functions.
•    Strategies for mathematical problem solving including the use of digital tools and programming.
•    Mathematical problems of importance in societal life and applications in other subjects.
•    Mathematical problems related to the history of mathematics.

Mathematics 4, Part b

•    Methods of calculating complex numbers written in different forms including rectangular and polar forms.
•    The complex number plane, representation of complex numbers as points and vectors.
•    Conjugates and absolute amounts of a complex number.
•    Use and proof of de Moivre's formula.
•    Algebraic and graphical methods for solving simple polynomial equations with complex roots and real polynomial equations of higher degrees, also by means of the factor theorem.
•    Properties of trigonometric functions, logarithmic functions, compound functions and absolute amounts as functions.
•    Drawing graphs and their related asymptotes.
•    Algebraic and graphical methods for determining integrals with and without digital tools, including estimates of magnitudes.
•    The concept of differential equations and their properties in simple applications that are relevant to subjects typical of programmes.
•    Strategies for mathematical problem solving including the use of digital tools and programming.
•    Mathematical problems of importance in societal life and applications in other subjects.
•    Mathematical problems related to the history of mathematics.

## Examination details

Grading scale: UG - (U,G) - (Fail, Pass)
Assessment: Written examinations

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Parts
Code: 0120. Name: Written Exam, Part a.
Credits: 4,5. Grading scale: UG. Assessment: Written examination.
Code: 0220. Name: Written Exam, Part b.
Credits: 4,5. Grading scale: UG. Assessment: Written examination.