Study Guide

Objectives

In this course, you will learn the basics of the mathematics behind technology, with topics such as geometry, vectors and functions


As a student, you
• recognize the mathematical notations related to the subject areas and know how to use the most important of them
• know how to solve an oblique triangle and you know how to calculate the parts and areas of different plane patterns
• know the basic tasks of vector calculation
• know the basic concepts of functions and recognize the typical properties of different functions
• recognize graphs of different types of functions
• know the different representations of complex numbers and master the calculation with them
• know the meaning of the sine curve parameters
• know how to use and apply the topics in technical problems
• know how to create a mathematical model of technical problems and can apply it in the solution of the problem
• are able to present and justify logically chosen solutions
• know how to evaluate the reasonableness and correctness of the solutions you make

Content

• right triangle, angle, angle units
• areas of triangles and polygons
• trigonometric functions in general
• oblique triangle (sine and cosine theorem)
• sum of vectors, difference, multiplication by a number
• plane vector coordinate and polar coordinate representation
• space vectors (brief mention)
• complex numbers
• function and related concepts
• 1st degree polynomial function, straight line (creating an equation from the graph), linear dependence
• 2nd degree polynomial function, parabola
• directly and inversely proportional, a piecewise defined function
• sine curve

Assessment criteria, satisfactory (1-2)

Student:
• recognizes the mathematical notations related to the subject areas and know how to use some of them
• knows how to solve an oblique triangle and can calculate the parts and areas of different plane patterns
• knows the calculations of plane vectors
• can solve vector problems like the examples presented
• knows how to use the representations of complex numbers in calculations
• recognizes the basic concepts of functions and the characteristics of different functions
• the presentations and justifications of the chosen solutions may be incomplete
• there may be shortcomings in evaluating the reasonableness and correctness of the solutions made

Assessment criteria, good (3-4)

Student:
• recognizes the mathematical notations related to the subject areas and know how to use the most important of them
• knows how to solve an oblique triangle and can calculate the parts and areas of different plane patterns
• knows the basic tasks of vector calculation
• knows the basic concepts of functions and recognizes the typical properties of different functions
• recognizes graphs of different types of functions
• knows the different representations of complex numbers and is able to calculate with them
• knows the meaning of the parameters of the sine curve
• knows how to use and apply the topics in technical problems
• can create a mathematical model of technology problems and can apply it in the solution of the problem
• is able to present and justify logically chosen solutions
• knows how to evaluate the reasonableness and correctness of the decisions he makes

Assessment criteria, excellent (5)

In addition to the previous, the student has a comprehensive understanding of the subjects of the course and knows how to apply them to more demanding problems. The student has the ability to present and justify logically chosen solutions. Solutions are presented clearly and mathematical concepts are used precisely. The student is highly motivated and takes full responsibility for his own and the group's performance.