Opetussuunnitelmat

Objective

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

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

Location and time

Opintojakso toteutetaan 10.1.2022 - 30.3.2022.

Oppimateriaali ja suositeltava kirjallisuus

Opettajan laatima kirjallinen materiaali ja videomateriaali.

Teaching methods

Kontaktiopetus, verkko-opetus, itsenäinen opiskelu

Exam schedules

Loppukoe maaliskuun lähipäivien yhteydessä
Uusintakokeet huhtikuun jo toukokuun lähipäivien yhteydessä.

Student workload

3op * 27h/op = 81h

Content scheduling

Opintojaksolla sisältö käsitellään seuraavassa järjestyksessä:

Perusteet: Luvuilla laskemisen ja laskujärjestyssääntöjen kertaus, geometrian perusteita
Algebraa: Potenssien laskusännöt, polynomit, lausekkeiden sieventäminen
Johdatus funktioihin: Suoran yhtälö, lineaariset mallit, trigonometriset funktiot
Ensimmäisen asteen yhtälöt: Algebrallisen yhtälönratkaisun perusajatus
Toisen asteen polynomifunktiot ja -yhtälöt: Paraabelin yhtälö, toisen asteen yhtälön ratkaiseminen
Yhtälöryhmät: Yhtälöryhmien ratkaisumenetelmiä ja sovelluksia

Further information

Osaamisen arviointiin käytetään kaksiosaista loppukoetta.

Evaluation scale

0-5

Arviointikriteerit, tyydyttävä (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.

Arviointikriteerit, hyvä (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.

Assessment 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.

Qualifications

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.