Study Guide

Objective

After completing the course the student can:
- solve equations, including radical, exponential and logarithmic equations
- use determinants and matrices
- apply dot and cross products
- perform basic operations on complex numbers
- use relevant mathematical terms and notation correctly

Content

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Materials

Itslearning-sivulta löytyvät:
Luentomuistiinpanot
Kurssilla on käytössä kirja, josta on valtaosa tehtävistä: Insinöörin Matematiikka, Tuomenlehto, Holmlund, Huuskonen, Makkonen, Surakka.

Teaching methods

Luennot
Laskuharjoitukset
Kokeet

Exam schedules

Kaksi osakoetta. Aikataulu ilmoitetaan kursin Itslearning sivustolla

Completion alternatives

Osakokeet
Tehdyistä tehtävistä saa hyvitystä kurssi arvosanaan.

Student workload

26*2h luennot
13*2h laskuharjoitukset
2*2h kokeet
loppu opiskelijan itsenäistä opiskelua

Content scheduling

1. osa:
- trigonometria
- vektorit
- matriisit

2. osa:
- Lukujärjestelmät
- Kompleksiluvut
- Funktiot: polynomi, rationaali-, eksponentti- ja logaritmifunktiot
- 1. asteen yhtälö
- 2. asteen yhtälö
- yhtälöryhmät
- Epäyhtälö

Evaluation scale

H-5

Assessment methods and criteria

Osakokeista täytyy saada tietty määrä pisteitä päästäkseen läpi.
Laskuharjoituksista saatavat lisäpisteet parantavat arvosanaa.
Arvosanataulukko löytyy Itslearning-sivulta.

Assessment criteria, fail (0)

Ei tarpeeksi pisteitä kokeista.

Assessment criteria, satisfactory (1-2)

Arvosanataulukko löytyy Itslearning sivulta

Assessment criteria, good (3-4)

Arvosanataulukko löytyy Itslearning sivulta

Assessment criteria, excellent (5)

Arvosanataulukko löytyy Itslearning sivulta

Qualifications

High school mathematics courses (higher or subsidiary level)
OR
Primary+secondary school and vocational school maths curriculum AND course: Introduction to Mathematics and Physics
OR
equivalent skills

Objective

After completing the course the student can:
- solve equations, including radical, exponential and logarithmic equations
- use determinants and matrices
- apply dot and cross products
- perform basic operations on complex numbers
- use relevant mathematical terms and notation correctly

Content

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Materials

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

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding of the basic mathematics and help students to solve equations, including radical, exponential and logarithmic equations and use determinants and matrices (e.g. for solving linear simultaneous equations), apply dot and cross products (e.g. in games, physics and electrical engineering applications), moreover the students can use relevant mathematical denotation correctly
The students will team up for a project work and writing reports on some current and relevant aspect of basic math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration

Student workload

Classroom activities: Classroom activities participation 50 h
Homework: Working on homework sets 1-6 30 h
Project work: Research, presentation material, presentation 20h
Final exam: Preparing for the final exam 25 h

Content scheduling

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations;
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in ITS Learning

Evaluation scale

H-5

Assessment methods and criteria

Assessment Method
1. 30% of the homework is MANDATORY and students can get points if they do more than 50%.

2. Points distributed as follow:
i. First Exam = 20 points
ii. Second Exam = 20 points
iii. Homework =10 points
Total = 50 points

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.
Collect (0--20) points and doing less than 30% of the assignments.

Assessment criteria, satisfactory (1-2)

Collect (20--32) points in the exams and doing more 50% of the assignments.

Assessment criteria, good (3-4)

Collect (32--44) points in the exams and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (44--50) points in the exam and doing at least 85% of the assignments.

Qualifications

High school mathematics courses (higher or subsidiary level)
OR
Primary+secondary school and vocational school maths curriculum AND course: Introduction to Mathematics and Physics
OR
equivalent skills

Objective

After completing the course the student can:
- solve equations, including radical, exponential and logarithmic equations
- use determinants and matrices
- apply dot and cross products
- perform basic operations on complex numbers
- use relevant mathematical terms and notation correctly

Content

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Materials

Available on the ITSL page
Lecture notes
Exercise assignments and solutions

Formula Book
Function Calculator (Casio fx-82EX or equivalent)

Teaching methods

Lectures
Exercise sessions
Exams

Exam schedules

PART 1:
Midterm exam 1 and its retake in November
PART 2:
Midterm exam 2 and its retake in December

Final retake in January of the following year:
You can choose to retake either one or both of the midterm exams.

Student workload

Classroom instruction 52 hours
Independent study approximately 68 hours
Exams and exam preparation approximately 15 hours

Content scheduling

September, REVIEW PART:
- basic arithmetic operations, fractions
- exponent, root, logarithm
- polynomials
- 1st and 2nd degree equations, systems of equations

September-November, PART 1:
- functions and equations, power equation, root equation, exponential equation, logarithmic equation, inequality
- trigonometry
- complex numbers

November-December, PART 2:
- matrices, determinants
- vectors
- number systems

Further information

Email.

Evaluation scale

H-5

Assessment methods and criteria

A passing grade of 8/20 must be obtained from each of the midterm exams. The scores from the midterm exams are added together, and additional points from exercise assignments are added to this sum. Exercise assignments can provide a maximum of 10 extra points, which can improve the overall grade.

Grade table based on points:
0-15: 0
16-22: 1
23-29: 2
30-35: 3
36-42: 4
43-50: 5

Assessment criteria, fail (0)

Not enough points from the exams.

Assessment criteria, satisfactory (1-2)

According to the grade table.

Assessment criteria, good (3-4)

According to the grade table.

Assessment criteria, excellent (5)

According to the grade table.

Qualifications

High school mathematics courses (higher or subsidiary level)
OR
Primary+secondary school and vocational school maths curriculum AND course: Introduction to Mathematics and Physics
OR
equivalent skills

Objective

After completing the course the student can:
- solve equations, including radical, exponential and logarithmic equations
- use determinants and matrices
- apply dot and cross products
- perform basic operations on complex numbers
- use relevant mathematical terms and notation correctly

Content

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Materials

ITSL-sivulta löytyvät:
Luentomuistiinpanot
Laskuharjoitusten tehtävät ja vastaukset

Teaching methods

Luennot
Laskuharjoitukset
Kokeet

Exam schedules

OSA1:
Osakoe1 ja sen uusinta marraskuussa
OSA2:
Osakoe2 ja sen uusinta joulukuussa

Lopullinen uusinta seuraavan vuoden tammikuussa:
voi tehdä jomman kumman tai kummatkin osakokeista

Student workload

6*2h kertausosan luennot
6*1h kertausosan laskuharjoitukset
20*2h luennot
20*1h laskuharjoitukset, joissa yhteensä noin 150 kpl tehtäviä
2*2h kokeet
loppu opiskelijan itsenäistä opiskelua

Content scheduling

Syyskuu, KERTAUSOSA:
- peruslaskutoimitukset, murtoluvut
- potenssi, juuri, logaritmi
- polynomit
- 1. ja 2. asteen yhtälöt, yhtälöpari

Syyskuu-marraskuu, OSA1:
- funktiot ja yhtälöt, potenssiyhtälö, juuriyhtälö, eksponenttiyhtälö, logaritmiyhtälö, epäyhtälö
- trigonometria
- kompleksiluvut

Marraskuu-joulukuu, OSA2:
- matriisit, determinantit
- vektorit
- lukujärjestelmät

Further information

Sähköposti.

Evaluation scale

H-5

Assessment methods and criteria

Osakokeista täytyy saada 16/40 pistettä yhteensä päästäkseen läpi.
Laskuharjoituksista saatavat lisäpisteet parantavat arvosanaa, niitä voi saada max 10 pistettä.
Arvosanataulukko pisteiden mukaan:
0-15: 0
16-22: 1
23-29: 2
30-35: 3
36-42: 4
43-50: 5

Assessment criteria, fail (0)

Ei tarpeeksi pisteitä kokeista.

Assessment criteria, satisfactory (1-2)

Arvosanataulukon mukaan.

Assessment criteria, good (3-4)

Arvosanataulukon mukaan.

Assessment criteria, excellent (5)

Arvosanataulukon mukaan.

Qualifications

High school mathematics courses (higher or subsidiary level)
OR
Primary+secondary school and vocational school maths curriculum AND course: Introduction to Mathematics and Physics
OR
equivalent skills

Objective

After completing the course the student can:
- solve equations, including radical, exponential and logarithmic equations
- use determinants and matrices
- apply dot and cross products
- perform basic operations on complex numbers
- use relevant mathematical terms and notation correctly

Content

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Evaluation scale

H-5

Qualifications

High school mathematics courses (higher or subsidiary level)
OR
Primary+secondary school and vocational school maths curriculum AND course: Introduction to Mathematics and Physics
OR
equivalent skills

Objective

After completing the course the student can:
- solve equations, including radical, exponential and logarithmic equations
- use determinants and matrices
- apply dot and cross products
- perform basic operations on complex numbers
- use relevant mathematical terms and notation correctly

Content

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Materials

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

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding of the basic mathematics and help students to solve equations, including radical, exponential and logarithmic equations and use determinants and matrices (e.g. for solving linear simultaneous equations), apply dot and cross products (e.g. in games, physics and electrical engineering applications), moreover the students can use relevant mathematical denotation correctly
The students will team up for a project work and writing reports on some current and relevant aspect of basic math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration

Student workload

Classroom activities: Classroom activities participation 50 h
Homework: Working on homework sets 1-6 30 h
Project work: Research, presentation material, presentation 20h
Final exam: Preparing for the final exam 25 h

Content scheduling

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations;
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in Optima

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6 , 30 %
-Total of thirty homework exercises based on reading material and classroom notes
-diagnostic/formative self / teacher evaluation in connection with each homework set return session
Project work, reports, presentations, 40 %
-Each outcome of the project work is assessed independently (assessment criteria is specified in Optima)
-peer feedback summative teacher feedback at the end of the course
Final exam, 30 %
-A written exam (1,5 hrs) on specified material
-Summativeteacher evaluationat the end of the course

Qualifications

High school mathematics courses (higher or subsidiary level)
OR
Primary+secondary school and vocational school maths curriculum AND course: Introduction to Mathematics and Physics
OR
equivalent skills

Objective

After completing the course the student can:
- solve equations, including radical, exponential and logarithmic equations
- use determinants and matrices
- apply dot and cross products
- perform basic operations on complex numbers
- use relevant mathematical terms and notation correctly

Content

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Materials

ITSL-sivulta löytyvät:
Luentomuistiinpanot
Laskuharjoitusten tehtävät ja vastaukset

Teaching methods

Luennot
Laskuharjoitukset
Kokeet

Exam schedules

OSA1:
Osakoe1 ja sen uusinta marraskuussa
OSA2:
Osakoe2 ja sen uusinta joulukuussa

Lopullinen uusinta seuraavan vuoden tammikuussa:
voi tehdä jomman kumman tai kummatkin osakokeista

Completion alternatives

Pelkät osakokeet ilman pisteitä laskuharjoituksista

Student workload

4*1h kertausosan luennot
4*2h kertausosan laskuharjoitukset
22*1h luennot
22*2h laskuharjoitukset, joissa yhteensä noin 150 kpl tehtäviä
2*2h kokeet
loppu opiskelijan itsenäistä opiskelua

Content scheduling

Elokuu-syyskuu, KERTAUSOSA:
- peruslaskutoimitukset, murtoluvut
- potenssi, juuri
- polynomit
- 1. ja 2. asteen yhtälöt, yhtälöpari

Syyskuu-marraskuu, OSA1:
- lukujärjestelmät
- funktiot ja yhtälöt, juuriyhtälö, eksponenttiyhtälö, logaritmiyhtälö
- trigonometria

Marraskuu-joulukuu, OSA2:
- kompleksiluvut
- matriisit, determinantit
- vektorit

Evaluation scale

H-5

Assessment methods and criteria

Osakokeista täytyy saada tietty määrä pisteitä päästäkseen läpi.
Laskuharjoituksista saatavat lisäpisteet parantavat arvosanaa.
Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, fail (0)

Ei tarpeeksi pisteitä kokeista.

Assessment criteria, satisfactory (1-2)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, good (3-4)

Arvosanataulukko löytyy ITSL-sivulta.

Assessment criteria, excellent (5)

Arvosanataulukko löytyy ITSL-sivulta.

Qualifications

High school mathematics courses (higher or subsidiary level)
OR
Primary+secondary school and vocational school maths curriculum AND course: Introduction to Mathematics and Physics
OR
equivalent skills

Objective

After completing the course the student can:
- solve equations, including radical, exponential and logarithmic equations
- use determinants and matrices
- apply dot and cross products
- perform basic operations on complex numbers
- use relevant mathematical terms and notation correctly

Content

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Materials

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

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding of the basic mathematics and help students to solve equations, including radical, exponential and logarithmic equations and use determinants and matrices (e.g. for solving linear simultaneous equations), apply dot and cross products (e.g. in games, physics and electrical engineering applications), moreover the students can use relevant mathematical denotation correctly
The students will team up for a project work and writing reports on some current and relevant aspect of basic math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration

Student workload

Classroom activities: Classroom activities participation 50 h
Homework: Working on homework sets 1-6 30 h
Project work: Research, presentation material, presentation 20h
Final exam: Preparing for the final exam 25 h

Content scheduling

- Sets of numbers and number systems
- Real functions
- Polynomials equations and inequalities, exponential and logarithmic equations;
- Trigonometry for right triangles
- Complex numbers
- Vectors and matrices

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in Optima

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6 , 30 %
-Total of thirty homework exercises based on reading material and classroom notes
-diagnostic/formative self / teacher evaluation in connection with each homework set return session
Project work, reports, presentations, 40 %
-Each outcome of the project work is assessed independently (assessment criteria is specified in Optima)
-peer feedback summative teacher feedback at the end of the course
Final exam, 30 %
-A written exam (1,5 hrs) on specified material
-Summativeteacher evaluationat the end of the course

Qualifications

High school mathematics courses (higher or subsidiary level)
OR
Primary+secondary school and vocational school maths curriculum AND course: Introduction to Mathematics and Physics
OR
equivalent skills