KH0021 Mathematics for Technical Preparatory Year I 12.0 credits

Matematik för basår I

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Course information

Content and learning outcomes

Course contents *


Vectors; Arithmetical operations. Components of vectors. Coordinates. Vector length.

Algebraic expression and algebraic methods; Implication and equivalence. Polynomial. Powers. Square roots. Absolute value. Equations. Factorial polynoms Rational expressions. Linear equation systems. Linear inequalities.

Functions; Linear functions. Direct proportionality. Quadratic functions. Power functions.

Right-angle trigonometry.

Uniformity; Triangle theorems Area and volume scale factors.


Exponential functions.

Logarithms; Logarithm laws. Natural logarithms.

Derivatives; Change rates. Limits. The definition of the derivative. Derivation rules.

Derivatives and graphs; Extreme points and extreme values. Increasing and decreasing. Maximum and minimum values. Second derivative.

The equation of the circle.

Area theorem. Sine law. Cosine law.

Intended learning outcomes *

The overall goal of the course is to give new students enough skills and understanding to be able to follow the mathematics courses of the 3- and 5-year engineering programs.

The courses should also contribute to a good introduction to higher education.

The student should be able to formulate, analyse and solve mathematical problems in the area and to explain the mathematical reasoning in writing. The problems can be based on realistic situations and/or include handling of mathematical procedures of standard character.

Course Disposition

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Literature and preparations

Specific prerequisites *

Completed upper secondary education including documented proficiency in Swedish corresponding to Swedish B, and English corresponding to English A. For students who received/will receive their final school grades after 31 December 2009, there is an additional entry for mathematics as follows:
documented proficiency in mathematics corresponding to Mathematics 2a,2b,2c, or Mathematics B with at least the grade Pass

Recommended prerequisites

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Matematik 5000, Kurs 3c Basår.  ISBN 978-91-27-43010-5 (Förlag: Natur och Kultur)

Formler och tabeller. ISBN 978-91-27-42245-2 (Förlag: Natur och Kultur)

Examination and completion

Grading scale *

A, B, C, D, E, FX, F

Examination *

  • TENA - Written examination, 6.0 credits, Grading scale: A, B, C, D, E, FX, F
  • TENB - Written examination, 6.0 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

TENA - Examination, 6.0 credits. Grade scale A-F

TENB - Examination, 6.0 credits. Grade scale A-F

Other requirements for final grade *

Final grades are based on the total number of points from both written examinations.

For final grade, it is required that all examination parts are approved

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Hanna Magnholt Ohlman

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web KH0021

Offered by

CBH/Engineering Pedagogics

Main field of study *

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Education cycle *

Pre-university level

Add-on studies

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Hanna Magnholt Ohlman (

Ethical approach *

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.