Study Guide

Objectives

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

Student:
• you recognize the mathematical notations related to the subject areas and can use the most central ones
• you know how to solve an oblique triangle and you know how to calculate the parts and areas of different plane patterns
• you know the calculations of plane and space vectors
• you can solve basic problems of plane vectors and space vectors
• you know the basic concepts of functions and recognize the typical properties of different functions
• you recognize graphs of different types of functions
• you know the meaning of the sine curve parameters
• you know how to use and apply the topics in technical problems
• you know how to create a mathematical model of technology problems and you know how to apply it in the solution of the problem
• you are able to present and justify logically chosen solutions
• you 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
• diagonal triangle (sine and cosine theorem)
• sum of vectors, difference, multiplication by a number
• plane vector coordinate and polar coordinate representation
• vectors in space
• dot product and cross product of vectors (3D)
• function and related concepts
• 1st-degree polynomial function, straight line (creating an equation from the graph), linear dependence
• 2nd degree polynomial function, parabola
• direct and inverse proportionality, 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 and space vectors
• can solve vector problems like the examples presented
• recognize 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 calculations of plane and space vectors
• can solve basic problems of plane vectors and space vectors
• knows the basic concepts of functions and recognizes the typical properties of different functions
• recognize graphs of different types of functions
• 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 made

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.