Curricula

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

September 2, 2024 - November 17, 2024

Learning materials and recommended literature

Written material and video material in the course Moodle workspace.

Teaching methods

Face-to-face teaching, independent study

Active participation in solving exercise tasks is necessary to achieve the learning objectives.

Practical training and working life connections

-

Exam dates and retake possibilities

The timetable for exams is announced in the beginning of the course.

International connections

-

Alternative completion methods

Any implementation of course TZLM1300.

Student workload

Estimated workload: 3 cr * 27 h/cr = 81 h. This means approximately six hours of weekly workload + exams.

Content scheduling

The content is covered roughly in the following order:
- Exponent laws
- Fractional exponents and roots
- Polynomials
- Rational expressions
- Linear equations
- Word problems
- Lines
- Quadratic equations and parabolas
- Percentage calculations and proportions
- Systems of equations
- Geometry
- Geometry
- Exams

Further information for students

If a student does not show activity within three weeks from the start of the course, their course registration will be rejected.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Course is implemented between 2.9 - 18.11.

Learning materials and recommended literature

Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1

Teaching methods

Lectures face-to-face or recordings, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Läpäisykoe Exam-studiossa aikavälillä 1.10. - 9.12.
Arvosanakoe viikolla 46, sen uusintakoe 1 viikolla 48 ja uusintakoe 2 viikolla 50.

Alternative completion methods

Web-based course in Spring 2025 or in Summer 2025

Student workload

Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h

Content scheduling

Schedule will be agreed on the first contact lesson of the course.

Further information for students

Jatkuva palaute: automaattitestit
Lainalaskelma-ryhmätehtävä
Läpäisykoe
Arvosanakoe
Bonustehtävä

Avoin AMK 5

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

September 2, 2024 - November 17, 2024

Learning materials and recommended literature

Written material and video material in the course Moodle workspace.

Teaching methods

Face-to-face teaching, independent study

Active participation in solving exercise tasks is necessary to achieve the learning objectives.

Practical training and working life connections

-

Exam dates and retake possibilities

The timetable for exams is announced in the beginning of the course.

International connections

-

Alternative completion methods

Any implementation of course TZLM1300.

Student workload

Estimated workload: 3 cr * 27 h/cr = 81 h. This means approximately six hours of weekly workload + exams.

Content scheduling

The content is covered roughly in the following order:
- Exponent laws
- Fractional exponents and roots
- Polynomials
- Rational expressions
- Linear equations
- Word problems
- Lines
- Quadratic equations and parabolas
- Percentage calculations and proportions
- Systems of equations
- Geometry
- Geometry
- Exams

Further information for students

If a student does not show activity within three weeks from the start of the course, their course registration will be rejected.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Opintojakso toteutetaan viikoilla 10 - 17 (4.3.-26.4.)

Learning materials and recommended literature

Course material is described during the implementation.

Teaching methods

Itsenäinen opiskelu videoluentojen avulla, viikottainen verkko-ohjaus

Exam dates and retake possibilities

Kokeen ajankohta julkaistaan oppimisympäristössä opintojakson alussa. Kokeen voi tehdä paikan päällä tai etänä.

Student workload

verkko-ohjaukset 9 h
Itsenäiset harjoitukset 32 h
Itsenäinen opiskelu, kokeeseen valmistautuminen sekä koe 40 h

Further information for students

Opintoijakso arvioidaan kurssin lopulla pidettävällä kokeella. Viikottaisista kotitehtävistä saa kokeeseen lisäpisteitä.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

The course is implemented 2.2.2024 - 30.4.2024 at Jamk Rajakatu campus.

Learning materials and recommended literature

Written material and videos by teacher.

Literature:
Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.

Teaching methods

Contact teaching, independent work

Exam dates and retake possibilities

Will be agreed at the begining of the course

Student workload

3 credits corresponds to 81 hours of work

Content scheduling

Topics will be discussed in the following order:

Basics: Calculations, fractions
Algebra: Power rules, algebra with polynomials
Introduction to functions: The concept of a function, 1st degree polynomial functions
First degree equations: The basic idea of solving equations algebraically
Second degree polynomial functions and equations: Parabolas, solving second degree polynomial equations
Systems of equations: Methods for solving systems of equations, applications
Geometry: Angle measurement, trigonometry of right triangles, some fundamentals of planar and 3D geometry

Further information for students

Final exam in two parts

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

The course is implemented 8.1.2024 - 30.4.2024.

Learning materials and recommended literature

Written material and videos by teacher.

Literature:
Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.

Teaching methods

Face-to-face learning, e-learning, independent work.

Exam dates and retake possibilities

Exam dates will be published in the first meeting.

Alternative completion methods

In spring 2024 the course is available as face-to-face and e-learning implementations.

Student workload

3op * 27h/op = 81op

Approximate use of time:
- Face-to-face lessons 16 h
- Exams 4h
- E-lessons approximately 10h
- Independent work 51 h

Content scheduling

Topics will be discussed in the following order:

Basics: Calculations, fractions
Algebra: Power rules, algebra with polynomials
Introduction to functions: The concept of a function, 1st degree polynomial functions
First degree equations: The basic idea of solving equations algebraically
Second degree polynomial functions and equations: Parabolas, solving second degree polynomial equations
Systems of equations: Methods for solving systems of equations, applications
Geometry: Angle measurement, trigonometry of right triangles, some fundamentals of planar and 3D geometry

Further information for students

Exam in two parts:
- Exam to pass
- Exam for grade

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

The course is implemented 22.1.2024 - 3.5.2024.

Learning materials and recommended literature

Learning material will be announced at the first meeting of the course.

Appropriate textbooks in Finnish:
- Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
- Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.

Teaching methods

Face-to-face and online, guided exercises and independent work.

Exam dates and retake possibilities

Will be announced at the first meeting of the course.

Alternative completion methods

Face-to-face and online implementations are available in autumn and in spring. It is also possible to attend the course online during summer 2024.

Student workload

3cr = 3 * 27 h = 81h

Content scheduling

Course schedule will presented at the first meeting.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Weeks 43-51

Learning materials and recommended literature

Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.

Teaching methods

Weekly contact teaching and weekly homework exercises, independent studying from theory material, exams.

Exam dates and retake possibilities

Schedule of the exams and resits will be given in the beginning of the course.

Student workload

approx. 30h for lessons
approx. 48h of independent studying and exercises
approx. 3h for exams

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Toteutus on viikoilla 43 - 50 (23.10.-15.12.2023) Lutakon kampuksen Dynamolla

Learning materials and recommended literature

Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -oppikirjaa.

Teaching methods

Kontaktiopetus 3+2 h/viikko (luentoja ja laskuharjoituksia)
Itsenäisiä laskuharjoituksia
Automaattitestejä

Exam dates and retake possibilities

Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.

Alternative completion methods

Mahdollisuus tenttiä kurssikokeella opintojakson alussa.

Student workload

Kontaktiopetus noin 30h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25h

Further information for students

Arviointimenetelmä:
Opintojaksoon liittyy pakollisia kotitehtäviä ja välitestejä. Arviointi tehdään opintojakson päätteeksi olevalla läpäisytestillä ja arvosanakokeella. Läpäisytestiin ja arvosanakokeeseen voi osallistua, jos opintojakson pakolliset suoritteet on hyväksytysti tehty. Läpäisytesteillä saa arvosanan 1. Korkeampi arvosana edellytttää arvosanakokeeseen osallistumista.


Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Avoin AMK 5 paikkaa

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Weeks 43-50

Learning materials and recommended literature

Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.

Teaching methods

Weekly contact teaching and weekly homework exercises, independent studying from theory material, exams.

Exam dates and retake possibilities

Times of the exams will be given in the first lesson of the course.

Student workload

approx. 30h for lessons and exams
approx. 50h independent studying

Further information for students

Open University of Applied Sciences 5

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Toteutus on viikoilla 43 - 50 (23.10.-15.12.2023) Lutakon kampuksen Dynamolla

Learning materials and recommended literature

Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -oppikirjaa.

Teaching methods

Kontaktiopetus 3+2 h/viikko (luentoja ja laskuharjoituksia)
Itsenäisiä laskuharjoituksia
Automaattitestejä

Exam dates and retake possibilities

Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.

Alternative completion methods

Mahdollisuus tenttiä kurssikokeella opintojakson alussa.

Student workload

Kontaktiopetus noin 30h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25h

Further information for students

Arviointimenetelmä:
Opintojaksoon liittyy pakollisia kotitehtäviä ja välitestejä. Arviointi tehdään opintojakson päätteeksi olevalla läpäisytestillä ja arvosanakokeella. Läpäisytestiin ja arvosanakokeeseen voi osallistua, jos opintojakson pakolliset suoritteet on hyväksytysti tehty. Läpäisytesteillä saa arvosanan 1. Korkeampi arvosana edellytttää arvosanakokeeseen osallistumista.


Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Avoin AMK 5 paikkaa

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Toteutus on viikoilla 43 - 50 (23.10.-15.12.2023) Lutakon kampuksen Dynamolla

Learning materials and recommended literature

Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -oppikirjaa.

Teaching methods

Kontaktiopetus 3+2 h/viikko (luentoja ja laskuharjoituksia)
Itsenäisiä laskuharjoituksia
Automaattitestejä

Exam dates and retake possibilities

Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.

Alternative completion methods

Mahdollisuus tenttiä kurssikokeella opintojakson alussa.

Student workload

Kontaktiopetus noin 30h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25h

Further information for students

Arviointimenetelmä:
Opintojaksoon liittyy pakollisia kotitehtäviä ja välitestejä. Arviointi tehdään opintojakson päätteeksi olevalla läpäisytestillä ja arvosanakokeella. Läpäisytestiin ja arvosanakokeeseen voi osallistua, jos opintojakson pakolliset suoritteet on hyväksytysti tehty. Läpäisytesteillä saa arvosanan 1. Korkeampi arvosana edellytttää arvosanakokeeseen osallistumista.


Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Avoin AMK 5 paikkaa

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Toteutus on viikoilla 43 - 51 (23.10.-19.12.2023) Lutakon kampuksen Dynamolla

Learning materials and recommended literature

Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -oppikirjaa.

Teaching methods

Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Itsenäisiä laskuharjoituksia
Automaattitestejä

Exam dates and retake possibilities

Opintojaksosta on kurssikoe ja kaksi uusintamahdollisuutta.
Tenttien ja uusintamahdollisuuksien ajankohdat julkaistaan opintojakson alussa oppimisympäristössä.

Kurssi päättyy uusintakoe-2:een. Tämän jälkeen kurssipalautuksia ei voi enää palauttaa ja vaillinaisesti suoritettu kurssi tulee käydä kokonaan uudelleen seuraavan kurssitoteutuksen yhteydessä.

Alternative completion methods

Mahdollisuus tenttiä kurssikokeella opintojakson alussa.

Student workload

Opintojakson laskennallinen kuormitus on 3 op * 27 h/op = 81 h.
Kontaktiopetus ja -ohjaus noin 30 h
Viikottaiset laskuharjoitukset ja testit 6 x 6 h = 36 h
Itsenäinen materiaalin opiskelu ja kokeisiin valmistautuminen 12 h
Loppukokeet 3 h

Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.

Further information for students

Arviointimenetelmä:
Opintojaksoon liittyy pakollisia kotitehtäviä ja välitestejä. Arviointi tehdään opintojakson päätteeksi olevalla läpäisy- ja arvosanakokeella. Läpäisy- ja arvosanakokeeseen voi osallistua, kun opintojakson pakolliset suoritteet (kotitehtävät ja välitestit) on hyväksytysti tehty. Läpäisykokeella saa arvosanan 1. Korkeampi arvosana edellyttää arvosanakokeeseen osallistumista.

Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Toteutus on viikoilla 43 - 51 (23.10.-19.12.2023) verkko-opetuksena ja monimuotoryhmän lähipäivänä.

Tarkemmat aikataulut sovitaan ja ilmoitetaan opintojakson alussa.

Learning materials and recommended literature

Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -oppikirjaa.

Teaching methods

Kontaktiopetus etäopetuksena 2+2 h/viikko (luentoja ja laskuharjoituksia)
Itsenäisiä laskuharjoituksia
Automaattitestejä

Exam dates and retake possibilities

Opintojaksosta on kurssikoe ja kaksi uusintamahdollisuutta.
Tenttien ja uusintamahdollisuuksien ajankohdat julkaistaan opintojakson alussa oppimisympäristössä.

Kurssi päättyy uusintakoe-2:een. Tämän jälkeen kurssipalautuksia ei voi enää palauttaa ja vaillinaisesti suoritettu kurssi tulee käydä kokonaan uudelleen seuraavan kurssitoteutuksen yhteydessä.

Alternative completion methods

Mahdollisuus tenttiä kurssikokeella opintojakson alussa.

Student workload

Opintojakson laskennallinen kuormitus on 3 op * 27 h/op = 81 h.
Kontaktiopetus ja -ohjaus noin 30 h
Viikottaiset laskuharjoitukset ja testit 6 x 6 h = 36 h
Itsenäinen materiaalin opiskelu ja kokeisiin valmistautuminen 12 h
Loppukokeet 3 h

Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.

Further information for students

Arviointimenetelmä:
Opintojaksoon liittyy pakollisia kotitehtäviä ja välitestejä. Arviointi tehdään opintojakson päätteeksi olevalla läpäisy- ja arvosanakokeella. Läpäisy- ja arvosanakokeeseen voi osallistua, kun opintojakson pakolliset suoritteet (kotitehtävät ja välitestit) on hyväksytysti tehty. Läpäisykokeella saa arvosanan 1. Korkeampi arvosana edellyttää arvosanakokeeseen osallistumista.

Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

viikot 43-50 1,5h sessio 2 kertaa viikossa

Learning materials and recommended literature

Kurssin työtilasta liittyvä kirjallinen sekä videoina oleva materiaali. Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -oppikirjaa.

Teaching methods

Kontaktiopetus, joka sisältää sekä luennointia että laskuharjoituksien laskemista. Osa laskuharjoituksista tehdään kotitehtävinä. Lisäksi kontaktituntien ulkopuolella opiskelija perehtyy kirjalliseen teoriamateriaaliin ja opetusvideoihin.

Exam dates and retake possibilities

Ainakin joitakin osasuorituksia tehdään Exam-tenttistudiossa.

Student workload

Kontaktiopetus noin 30h
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25h

Further information for students

Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Course is implemented between 4.9. - 12.11.

Learning materials and recommended literature

Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1

Teaching methods

Lectures face-to-face or recordings, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Läpäisykoe Exam-studiossa aikavälillä 23.10. - 30.11.
Arvosanakoe viikolla 45, sen uusintakoe 1 viikolla 47 ja uusintakoe 2 viikolla 2/2024.

Alternative completion methods

Web-based course in Spring 2024 or in Summer 2024

Student workload

Lectures, quided exercises and exam 40 h
Independent work and automatic tests 41 h

Content scheduling

Schedule will be agreed on the first contact lesson of the course.

Further information for students

Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe

Avoin AMK 5

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Course is implemented between 4.9. - 17.11.

Learning materials and recommended literature

Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1

Teaching methods

Lectures face-to-face or recordings, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Läpäisykoe Exam-studiossa aikavälillä 23.10. - 30.11.
Arvosanakoe viikolla 46, sen uusintakoe 1 viikolla 48 ja uusintakoe 2 viikolla 2/2024.

Alternative completion methods

Web-based course in Spring 2024 or in Summer 2024

Student workload

Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h

Content scheduling

Schedule will be agreed on the first contact lesson of the course.

Further information for students

Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Bonustehtävä

Avoin AMK 5

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Course is implemented between 4.9. - 17.11.

Learning materials and recommended literature

Videos in the learning environment, text files, automatic tests
Extra material in Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1

Teaching methods

Lectures face-to-face or recordings, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Läpäisykoe Exam-studiossa aikavälillä 23.10. -30.11.
Arvosanakoe viikolla 46, sen uusintakoe 1 viikolla 48 ja uusintakoe 2 viikolla 2/2024.

Alternative completion methods

Web-based course in Spring 2024 or in Summer 2024

Student workload

Lectures, quided exercises and exam 40 h
Independent work and automatic tests 40 h

Content scheduling

Schedule will be agreed on the first contact lesson of the course.

Further information for students

Jatkuva palaute: automaattitestit
Läpäisykoe
Arvosanakoe
Bonustehtävä

Avoin AMK 5

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Course is implemented between 30.8.2023 - 31.7.2024.

Learning materials and recommended literature

Videos in the learning environment, text files, automatic tests
Extra material: Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1

Teaching methods

Distance learning, booklet tasks, automatic tests, independent work, learning diary, self assessment, application, exam. Guiding methods: Question column, Zoom-address and Whats'app-group for students.

Exam dates and retake possibilities

Three timetables:
- timetable 1: 30.8.2022 - 10.12.2022 (registration 1.8. - 30.9.; exam online 13.11., re-exam1 27.11., re-exam 2 8.12.)
- timetable 2: 1.10.2022 - 31.5.2023 (registration 1.10. - 28.2.; exam online 6.5., re-exam1 20.5., re-exam 2 27.5.)
- timetable 3: 1.3.2023 - 31.7.2023 (registration 1.3. - 31.7.; exam in Exam Studio 3.7. - 31.7.,arvosanakoe elokuussa myöhemmin ilmoitettavana ajankohtana)

Passing exam in Exam Studio, open according to the time table of the course.

Student workload

This is a nonstop course. Student may enroll to the course during 1.8.-31.5. There are three (3) different time periods inside the nonstop course:

- Course studied by 10.12.
- Course studied by 31.5.
- Course studied by 31.7.

Student chooses the time period in the virtual study environment. Time period should be selected based on students enrollment and study right time. Student can create own time schedule for the assignments and tasks within the selected time period.

The workspace for the first implementation will open on August 30, the second on October 1. and the third 1.3. Registrations are accepted once a week on Mondays. If the virtual study environment has not opened for you within 2 weeks after enrollment, please contact the course teacher.

The calculated workload is the number of credits times 27 hours, so in this course it is 81 hours.

Independent work 77 h
Own application (voluntary, 5 h)
Controlled exam 4 h

Further information for students

Continous feedback: automatic tests
Passing exam
Grading exam
Own application

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

The course is implemented 21.8.2023 - 12.11.2023.

Learning materials and recommended literature

Written material and videos

Literature:
Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.

Teaching methods

Face-to-face learning, e-learning, independent work.

Exam dates and retake possibilities

Exam to pass the course and derermine grade During week 45 (online).
First resit: Week 47 at campus.
Second resit: Week 2/2014 (online)

Exam to pass the course also available in Exam-studio

Alternative completion methods

In spring 2024 the course is available as face-to-face and e-learning implementations.

Student workload

3op * 27h/op = 81op

Face-to-face lessons 16 h
Exams 4h
E-lessons approximately 10h
Independent work 51 h

Content scheduling

Topics will be discussed in the following order:

Basics: Calculations, fractions
Algebra: Power rules, algebra with polynomials
Lines and linear interpolation
Second degree polynomial functions and equations and root equations
Percentage calculations and proportionality
Groups of equations: a pair of equations

Further information for students

Exam in two parts:
- Exam to pass
- Exam for grade

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Course is implemented between 30.10. - 17.12.

Learning materials and recommended literature

Videos in the learning environment, text files, automatic tests
College Algebra 2e (https://openstax.org/details/books/college-algebra-2e)

Teaching methods

Lectures face-to-face or recordings, guided exercises, booklet tasks, independent work, automatic tests, exam.

Exam dates and retake possibilities

Exam Part 1: Core questions in the Exam studio between 20.11.2023 - 7.1.2024 (obligatory)
Exam Part 2: Grading questions in week 50, resit 1 in week 51 and resit 2 in week 2/2024. (optional)

Student workload

Lectures, quided exercises and exam 30 h
Independent work and automatic tests 51 h

Content scheduling

Schedule will be agreed on the first contact lesson of the course.

Further information for students

automatic tests
Exam Part 1: Core questions (obligatory)
Exam Part 2: Grading questions (grades 2-5)

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Opintojakso toteutetaan 29.8.2022 - 16.10.2022.

Luennot toteutetaan lähiopetuksena sekä live-streamina verkossa.

Laskuharjoitukset lähiopetuksena päivätoteutuksen opiskelijoille ja verkossa monimuotototeutuksen opiskelijoille.

Learning materials and recommended literature

Oppimateriaalina toimivat opettajan valmistelema kirjallinen- ja videomateriaali sekä harjoitustehtävät.

Kurssille sopivia oppikirjoja suomeksi:
- Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
- Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.

Teaching methods

Opintojakso koostuu luennoista, ohjatuista laskuharjoituksista, itsenäisestä harjoittelusta ja kokeista.

Exam dates and retake possibilities

Tenttien aikataulut ilmoitetaan ensimmäisellä luennolla.

Student workload

36 h kontaktiopetusta
5 h kokeita
40 h itsenäistä työskentelyä

Content scheduling

Opintojakson aihepiirit käsitellään seuraavassa järjestyksessä:
1. Potenssien laskusäännöt
2. Polynomit ja rationaalilausekkeet
3. Johdatus funktioihin
4. Ensimmäisen asteen yhtälöt
5. Toisen asteen yhtälöt
6. Yhtälöryhmät

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Course is implemented between 30.8.2022 - 31.7.2023.

Learning materials and recommended literature

Videos in the learning environment, text files, automatic tests
Extra material: Alestalo - Lehtola - Nieminen - Rantakaulio: Tekninen matematiikka 1

Teaching methods

Distance learning, booklet tasks, automatic tests, independent work, learning diary, self assessment, application, exam. Guiding methods: Question column, Zoom-address and Whats'app-group for students.

Exam dates and retake possibilities

Three timetables:
- timetable 1: 30.8. - 10.12.2022 (registration 1.8. - 30.9.; exam online 14.11., re-exam1 28.11., re-exam 2 8.12.)
- timetable 2: 1.10.2022 - 31.5.2023 (registration 1.10. - 28.2.; exam online 2.5., re-exam1 16.5., re-exam 2 30.5.)
- timetable 3: 1.3. - 31.7.2023 (registration 1.3. - 31.7.; exam in Exam Studio 3.7. - 31.7.)

Passing exam in Exam Studio, open according to the time table of the course.

Student workload

This is a nonstop course. Student may enroll to the course during 1.8.-31.5. There are three (3) different time periods inside the nonstop course:

- Course studied by 10.12.
- Course studied by 31.5.
- Course studied by 31.7.

Student chooses the time period in the virtual study environment. Time period should be selected based on students enrollment and study right time. Student can create own time schedule for the assignments and tasks within the selected time period.

The workspace for the first implementation will open on August 30, the second on October 1. and the third 1.3. Registrations are accepted once a week on Mondays. If the virtual study environment has not opened for you within 2 weeks after enrollment, please contact the course teacher.

The calculated workload is the number of credits times 27 hours, so in this course it is 81 hours.

Independent work 77 h
Own application (voluntary, 5 h)
Controlled exam 4 h

Further information for students

Continous feedback: automatic tests
Self-assessment
Passing exam
Grading exam
Own application

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

The course is implemented 30.1.2023 - 7.5.2023 at Gradia's Viitaniemi campus

Learning materials and recommended literature

Material prepared by teacher

Teaching methods

Contact teaching, independent work

Exam dates and retake possibilities

Will be agreed at the begining of the course

Student workload

3 credits corresponds to 81 hours of work

Content scheduling

Preliminary schedule will presented at the beginning of the course

Further information for students

Final exam in two parts

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

The course is implemented 9.1.2022 - 14.5.2022.

Learning materials and recommended literature

Written material and videos by teacher.

Literature:
Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.

Teaching methods

Face-to-face learning, e-learning, independent work.

Exam dates and retake possibilities

Exam to pass the course: During week 19.
Exam to determine grade: During week 19 (10.5.2023) at 17.00 online.
First resit: 29.5.2023 at 8.00 at campus.
Second resit: 16.8.2023

Alternative completion methods

In spring 2023 the course is available as face-to-face and e-learning implementations.

Student workload

3op * 27h/op = 81op

Face-to-face lessons 16 h
Exams 4h
E-lessons approximately 10h
Independent work 51 h

Content scheduling

Topics will be discussed in the following order:

Basics: Calculations, fractions
Algebra: Power rules, algebra with polynomials
Introduction to functions: The concept of a function, 1st degree polynomial functions
First degree equations: The basic idea of solving equations algebraically
Second degree polynomial functions and equations: Parabolas, solving second degree polynomial equations
Systems of equations: Methods for solving systems of equations, applications
Geometry: Angle measurement, trigonometry of right triangles, some fundamentals of planar and 3D geometry

Further information for students

Exam in two parts:
- Exam to pass
- Exam for grade

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

The course is implemented 9.1.2022 - 14.5.2022.

Learning materials and recommended literature

Written material and videos by teacher.

Literature:
Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.

Teaching methods

Face-to-face learning, e-learning, independent work.

Exam dates and retake possibilities

Exam to pass the course: During week 18.
Exam to determine grade: During week 18 (3.5.2023) at 17.00 online.
First resit: 29.5.2023 at 8.00 at campus.
Second resit: 16.8.2023

Alternative completion methods

In spring 2023 the course is available as face-to-face and e-learning implementations.

Student workload

3op * 27h/op = 81op

Face-to-face lessons 10 h
Exams 4h
E-lessons approximately 10h
Independent work approximately 57 h

Content scheduling

Topics will be discussed in the following order:

Basics: Calculations, fractions
Algebra: Power rules, algebra with polynomials
Introduction to functions: The concept of a function, 1st degree polynomial functions
First degree equations: The basic idea of solving equations algebraically
Second degree polynomial functions and equations: Parabolas, solving second degree polynomial equations
Systems of equations: Methods for solving systems of equations, applications
Geometry: Angle measurement, trigonometry of right triangles, some fundamentals of planar and 3D geometry

Further information for students

Exam in two parts:
- Exam to pass
- Exam for grade

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

The course is implemented 23.1.2023 - 12.5.2023.

Learning materials and recommended literature

Learning material will be announced at the first meeting of the course.

Appropriate textbooks in Finnish:
- Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
- Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.

Teaching methods

Online and face-to-face learning, guided exercises and independent work.

Exam dates and retake possibilities

Will be announced at the first meeting of the course.

Alternative completion methods

Face-to-face, hybrid and online implementations are available in autumn and in spring. It is also possible to attend the course online during summer 2023.

Student workload

3cr = 3 * 27 h = 81h

Content scheduling

Course schedule will presented at the first meeting.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Teaching methods

Avoin AMK erillisryhmä

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Toteutus on viikoilla 43 - 50 (24.10.-16.12.) Lutakon kampuksen Dynamolla.

Learning materials and recommended literature

Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -oppikirjaa.

Teaching methods

Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia

Exam dates and retake possibilities

Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.

Alternative completion methods

Mahdollisuus tenttiä kurssikokeella opintojakson alussa.

Student workload

Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h

Further information for students

Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.

Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Weeks 43-50

Learning materials and recommended literature

Free openly licensed textbooks will be used. Links will be shared in the learning environment Moodle.

Teaching methods

Weekly contact teaching and weekly homework exercises, independent studying from theory material, exams.

Exam dates and retake possibilities

Times of the exams will be given in the first lesson of the course.

Student workload

approx. 30h for lessons and exams
approx. 50h independent studying

Further information for students

Open University of Applied Sciences 5

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Toteutus on viikoilla 43 - 50 (24.10.-16.12.) Lutakon kampuksen Dynamolla.

Learning materials and recommended literature

Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -oppikirjaa.

Teaching methods

Kontaktiopetus 2+2 h/viikko (luentoja ja laskuharjoituksia)
Videoluentoja
Itsenäisiä laskuharjoituksia

Exam dates and retake possibilities

Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.

Alternative completion methods

Mahdollisuus tenttiä kurssikokeella opintojakson alussa.

Student workload

Kontaktiopetus noin 25 h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25 h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25 h

Further information for students

Arviointimenetelmä:
Kurssin lopussa pidetään koe. Viikoittaisista kotitehtävistä saa kokeeseen lisäpisteitä.

Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Toteutus on viikoilla 43 - 50 (24.10.-16.12.2022) Lutakon kampuksen Dynamolla

Learning materials and recommended literature

Opettajan oppimisympäristössä julkaisema kirjallinen materiaali.
Lisämateriaaliksi suositellaan esimerkiksi Alestalo, Lehtola, Nieminen, Rantakaulio: Tekninen Matematiikka 1 -oppikirjaa.

Teaching methods

Kontaktiopetus 3+2 h/viikko (luentoja ja laskuharjoituksia)
Itsenäisiä laskuharjoituksia
Automaattitestejä

Exam dates and retake possibilities

Tentin ajankohdat ja uusintapäivät julkaistaan opintojakson ensimmäisellä kerralla opintojakson oppimisympäristössä.

Alternative completion methods

Mahdollisuus tenttiä kurssikokeella opintojakson alussa.

Student workload

Kontaktiopetus noin 30h. Joillakin viikoilla voi olla etäopetusta Dynamon tilojen käytettävyydestä riippuen.
Harjoitukset kontaktituntien ulkopuolella noin 25h
Teoriamateriaalin opiskelu, kokeisiin valmistautuminen ja kokeiden suorittaminen noin 25h

Further information for students

Arviointimenetelmä:
Opintojaksoon liittyy pakollisia kotitehtäviä ja välitestejä. Arviointi tehdään opintojakson päätteeksi olevalla läpäisytestillä ja arvosanakokeella. Läpäisytestiin ja arvosanakokeeseen voi osallistua, jos opintojakson pakolliset suoritteet on hyväksytysti tehty. Läpäisytesteillä saa arvosanan 1. Korkeampi arvosana edellytttää arvosanakokeeseen osallistumista.


Suositellaan valitsemaan myös opintojakso Mat1 Tukiopinnot, jos lukion pitkän matematiikan opintoja ei ole pohjalla.
Avoin AMK 5 paikkaa

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.

Objectives

Course purpose

During this course you will learn mathematical equation solving skills that are necessary during your studies in the field of technology.

Course competences

EUR-ACE: Knowledge and understanding
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

Learning outcomes

After completing this course you are able to simplify expressions. You are able to solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of a calculator or a computer. You are able to solve mathematical problems by using given models. You also get to know mathematical content related to your own field of study.

Content

In this course, you will learn the mathematical equation solving skills you need to study engineering. You will master the sieving of expressions and be able to solve polynomial and root equations and groups of equations manually, graphically and using computer technology. You will learn how to solve mathematical problems using ready-made models and become familiar with the mathematical content of the degree programme. This course will give you a strong foundation in solving technical problems and applying mathematical skills in practice.

Most important contents are:

- Simplifying expressions (fractional exponents, polynomials, rational expressions, binomial formulas)
- Drawing and interpreting graphs of functions
- Linear equations and lines
- Quadratic equations and parabolas
- Equations involving roots
- Systems of equations
- Percentages and proportions
- Trigonometry of right triangles
- Basics of solid geometry
- Degree-program-related content

Time and location

Avoin AMK polkuopiskelijat: 5 paikkaa

Evaluation scale

0-5

Evaluation criteria, satisfactory (1-2)

Grade 1

You are able to simplify expressions. You recognise different types of equations and are able to solve simple polynomial equations, equations involving roots and pairs of equations. You can solve verbal and geometric problems when the mathematical model is given.

Grade 2

You understand the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Evaluation criteria, good (3-4)

Grade 3

You master the notion and notation of polynomial equations. You can solve polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve simple verbal and geometric problems.

Grade 4

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then solve such verbal and geometric problems that coincide with previously treated problems.

Evaluation criteria, excellent (5)

Grade 5

You master the notion and notation of polynomial equations. You can solve challenging polynomial equations, equations involving roots and systems of equations by hand, graphically and with the help of information technology. You are able to mathematically model and then creatively solve new verbal and geometric problems.

Prerequisites

You know the fundamental rules of arithmetic and can perform basic mathematical operations both numerically and symbolically. You know the difference between an expression and an equation. You can solve simple equations of first and second degree. You are familiar with basic calculations involving percentage. You know what a function is.

Further information

The course is well suited to be taken before the beginning of studies in technology. The course also offers good mathematical competencies for studies in other fields than technology. The course is offered also in the open university of applied sciences.