Study Guide

Objectives

In this course you will learn the basics of the mathematics behind technology, with the subject area Geometry, vectors, functions and matrices

As a student, you
• recognize the mathematical notations related to the subject areas and know how to use the most important of them
• master solving a diagonal triangle
• can calculate the parts and areas of different plane patterns and the volumes and areas of different objects
• know how to solve basic tasks in vector calculus

• know the basic concepts of functions and recognize the typical properties of different functions
• recognize graphs of different types of functions
• will learn how to calculate the base ten logarithm of a number
• 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)
• space geometry (volumes and surfaces of 3D objects)
• sum of vectors, difference, multiplication by a number
• plane vector coordinate and polar coordinate representation
• space vectors (brief mention)
• function and related concepts
• 1st degree polynomial function, straight line (creating an equation from the graph), linear dependence
• 2nd degree polynomial function, parabola
• learns how to calculate logarithms to the base of ten from a number
• directly and inversely proportional, a piecewise defined function

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 right-angled and diagonal triangles
• can calculate the surface areas of different plane patterns and the volumes of pieces
• knows the calculations of plane 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
• master solving the diagonal triangle
• can calculate the parts and areas of different plane patterns as well as the volumes and areas of different objects
• can solve basic tasks in vector calculus
• knows the basic concepts of functions and recognizes the typical properties of different functions
• recognize graphs of different types of functions
• learns how to calculate logarithms to the base of ten from a number
• 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.