Matemaattisten aineiden perustaidot (5 op)

Arviointiasteikko

H-5

Sisällön jaksotus

Part A:
1 Basic arithmetic operations
2 Fractions
3 Powers
4 Roots
5 Polynomials, simplifying rational expressions
6 Polynomial equations of 1. and 2. degree
7 Simultaneous linear equations
Part B:
8 Percentages
9 Concepts of variable and function, graphs of functions
10 Lines and parabolas
11 Basics of geometry
12 Basics of trigonometry
13 International system of units, unit conversions
14 Field-specific content: speed/acceleration, volume/mass/density

Tavoitteet

Opiskelija saavuttaa ammattikorkeakoulun matemaattis-luonnontieteellisissä opinnoissa tarvittavat lähtötiedot ja -taidot.

Sisältö

• Lukujen esitystavat ja lukujoukot
• Peruslaskutoimitukset ja laskujärjestys
• Murtoluvuilla laskeminen ja murtolausekkeiden käsittely
• Potenssien ja juurten laskusäännöt
• Murtopotenssit ja negatiiviset potenssit
• Polynomien laskusäännöt
• Rationaalilausekkeiden sieventäminen
• Prosenttilaskenta
• Ensimmäisen ja toisen asteen polynomiyhtälöt
• Lineaarinen yhtälöpari
• Suora ja paraabeli
• Funktion ja muuttujan peruskäsitteet
• Funktion kuvaajan piirtäminen ja tulkinta
• Geometrian ja trigonometrian perusasioita
• Suureet ja SI-järjestelmä
• Yksiköiden käsittely laskuissa ja yksikkömuunnokset
• Koulutuskohtaisia sisältöjä

Oppimateriaalit

1. Precalculus (3rd edition), Fred Safier, SCHAUM’S outlines.
2. Engineering Mathematics (6th edition), K.A. Stroud [MACMILLAN PRESS LTD]
3. Formula book: Technical formulas
And:
Lecture notes.
Exercises.
Can be found from ITSL-website.

Opetusmenetelmät

The course combines a variety of learning methods to support student engagement and understanding. These include:
Teacher-directed classroom activities: Lectures and guided discussions to introduce and explain key concepts.
Group work: Collaborative problem-solving and peer learning through small-group tasks and discussions.
Independent work: Self-paced study and individual assignments to reinforce learning outside the classroom.
Project work: Larger, structured assignments requiring research, planning, implementation, and reporting.
Reports: Written reflections or analyses that document understanding and project outcomes.
Task-based learning (homework): Regular assignments designed to build skills and apply theoretical knowledge.
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Tenttien ajankohdat ja uusintamahdollisuudet

Exam Schedule:
First Exam: after lectures of Part A is on October 2025
First Retake: 5 November 2025
Second Exam: after lectures of Part B is on December 2025
First Retake: (Date to be confirmed in 2026)
Final Retake for Both Parts: 13 January 2026
Exact times for all exams will be published in the official schedule.

mportant:
Homework and exercises must be submitted on time. Late submissions will not be accepted, and there are no opportunities for retakes or make-ups.

Pedagogiset toimintatavat ja kestävä kehitys

The contents of the course give understanding of the basic mathematics and help students to:
-Perform calculations with integers, decimals, and fractions.
-Simplify, compare, and perform operations with fractions.
- Apply exponent laws and simplify square roots.
- Simplify and factor polynomials; simplify rational expressions.
-Solve linear and quadratic equations.
-Solve systems of linear equations using substitution and elimination.
- Solve problems involving percentage changes and applications.
-Understand variables, functions, and graphing.
- Graph and analyze linear equations and parabolas.
-Understand geometric concepts like angles, area, and perimeter.
- Apply basic trigonometric ratios in right-angled triangles.
- Apply mathematical concepts to real-world problems (e.g., speed, acceleration, volume).

Opiskelijan ajankäyttö ja kuormitus

Estimated Student Workload

Classroom Activities:
Participation in lectures, discussions, and in-class exercises – 50 hours

Homework:
Completion of homework sets 1–6 – 30 hours

Project Work:
Research, preparation of presentation materials, and delivery of the presentation – 20 hours

Final Exam Preparation:
Independent study and review for the final exam – 25 hours

Total Estimated Workload: 125 hours

Arviointimenetelmät ja arvioinnin perusteet

1. Homework Policy
* Completing at least 30% of the homework is mandatory.
* Students can earn homework points only if they complete more than 50% of the total homework assignments.

2. Distribution of Points
- First Exam: 20 points
- Second Exam: 20 points
- Homework: 10 points

Total: 50 points

Hylätty (0)

The student did not pass the final examination and failed to engage with the assigned coursework

Arviointikriteerit, tyydyttävä (1-2)

Scoring between 25 and 35 points in the exams and completing 30% to 50% of the assignments

Arviointikriteerit, hyvä (3-4)

"Scoring between 35 and 45 points in the exams and completing at least 50% to 75% of the assignments."

Arviointikriteerit, kiitettävä (5)

Scoring between 45 and 50 points in the exam and completing at least 75% of the assignments.

Lisätiedot

All essential practical details related to the course are available on ITS Learning, including:
Timetables: Dates and times for lectures, tutorials, exams, and other scheduled activities.
Project Work: Descriptions of project topics, deadlines, submission guidelines, and evaluation criteria.
Grading Information: Breakdown of how grades are calculated, including the weight of exams, assignments, and project components.
Web Materials: Access to lecture slides, supplementary readings, assignment instructions, and other digital resources.
Announcements: Updates and important notices related to the course.
Please check ITS Learning regularly to stay informed and up to date.