# Equalizer

- Credits: 3
- Ending: Examination
- Range: 0P + 2C
- Semester: summer
- Year: 1
- Faculty of Business Economics with seat in Košice

## Teachers

## Included in study programs

**Teaching results**

The aim of the course is to consolidate and supplement the student's knowledge of high school mathematics. The student will repeat the curriculum, which in terms of content corresponds to the requirements for entrance exams in mathematics and complement his knowledge with the missing knowledge. After completing the course, he will be able to solve simpler and more complex tasks that he will encounter during his further study, both on quantitatively oriented subjects and on other subjects with the economic focus.

Knowledge:

On the given subject the student repeats the curriculum from a high school and completes the missing knowledge from selected areas of mathematics. The student will be able to work with the algebraic expressions, to define different types of equations and inequalities such as quadratic, exponential, logarithmic and trigonometric equations and inequalities and he will know the various types of their solutions, he will master the basic terms and definitions of combinatorics and the principles of solving problems in this area and he will know the important concepts and definitions concerning the real functions.

Skills:

The student will be able to solve basic and advanced problems in arithmetic and elementary algebra, to work with the expressions, polynomials, combination numbers and factorials. The student will be able to solve basic types of equations and inequalities such as quadratic, exponential, logarithmic and trigonometric equations and inequalities. The student will master the basics terms of combinatorics and the principles of solving problems in the field and he will be able to use it in a real situation. He will be able to determine the domain of a function, examine the basic properties of a function and sketch its graph.

Competences:

After completing the course, the student is able to solve simpler and more complex problems in mathematics, he can work with numbers, expressions and functions, to solve the equations with one or more variables and he is ready to apply his knowledge to real quantitative problems that he will encounter in further study. Knowledge acquired in this course represent the basis for successful completion of many subjects of either quantitative and economic focus.

**Indicative content**

Seminars:

1. Arithmetic.

2. Elementary algebra. Expressions with rational exponents.

3. Expressions with factorials and numbers of combination.

4. Polynomials. Operations on polynomials.

5. Partial fraction decomposition.

6. Quadratic equations. Equations with absolute value.

7. Exponential equations.

8. Logarithmic equations.

9. Goniometric equations.

10. Exponential and logarithmic inequalities.

11. Goniometric inequalities.

12. Combinatorics.

13. Basic properties of the function.

**Support literature**

1. BOROŠ, M. 2016. Maturita z matematiky. Ikar, 2016. ISBN: 978-8-055-14889-2

2. CARTER, R. 2018. Algebra 1. Workbook. ISBN: 978-1-790-34009-5

3. FANNON, P. – KADELBURG, V. – WOOLLEY, B. – STEPHEN, W. 2014. Mathematics Higher Level. Cambridge University Press. 2014. ISBN: 978-1-107-67215-4

4. FEŇOVČÍKOVÁ, A. - IŽARÍKOVÁ, G. 2012. Prípravný kurz zo stredoškolskej matematiky. Technická univerzita v Košiciach, 2012. ISBN: 978-80-553-1123-4

5. KOLEKTÍV AUTOROV ČVUT. 2016. Matematika: ČVUT, 2016. ISBN: 978-8-001-05849-7

6. McCUNE, S. L. 2019. Algebra I. Review and Workbook. McGraw-Hill Education, 2019. ISBN: 978-1-260-12894-9

7. MONAHAN, CH. 2019. Algebra II. Review and Workbook. McGraw-Hill Education, 2019. ISBN: 978-1-260-12888-8

8. PELLER, F. – STAREČKOVÁ, A. – PINDA, Ľ. 2012. Matematika (krok za krokom na EU). Ekonóm, 2012. ISBN: 978-80-225-3407-9

9. POLÁK, J. 2015. Přehled stredoškolské matematiky. Prometheus. 2015. ISBN: 9788071964582

10. POLÁK, J. 2018. Středoškolská matematika v úlohách II. Prometheus. 2018. ISBN: 978-80-7196-419-3

11. ŽABKA, J. – KUBÁČEK, Z. 2017. Seminár z matematiky – Matematika pre maturantov, 1. časť. MAPA Slovakia Plus, 2017. ISBN: 978-8-080-67309-3

**Syllabus**

Seminars: 1. Arithmetic. 2. Elementary algebra. Expressions with rational exponents. 3. Expressions with factorials and numbers of combination. 4. Polynomials. Operations on polynomials. 5. Partial fraction decomposition. 6. Quadratic equations. Equations with absolute value. 7. Exponential equations. 8. Logarithmic equations. 9. Goniometric equations. 10. Exponential and logarithmic inequalities. 11. Goniometric inequalities. 12. Combinatorics. 13. Basic properties of the function.

**Requirements to complete the course**

individual work, test

combined exam

• test - 40%

• combined exam - 60%

**Student workload**

• participation in seminars - 26 hours

• preparation for seminars - 26 hours

• preparation for exam - 26 hours

Total: 78 hours

**Language whose command is required to complete the course**

Slovak

Date of approval: 15.02.2023

Date of the latest change: 25.01.2022