KH0024 Mathematics for Technical Preparatory Year II 12.0 credits

Matematik för basår II

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Course information

Content and learning outcomes

Course contents *


Trigonometry; the Unit circle. Trigonometric identities. Addition and the subtraction theorems Trigonometric equations. Trigonometric graphs. Radians. Derivatives of trigonometric functions.

Proof techniques; Direct proofs. Indirect proofs.

Derivatives; Derivatives of composite functions. Product rule. Quotient rule. Relationships between change rates. Asymptots.


Number sequences; Recursion formulae. Arithmetic number sequence. Geometric number sequence.

Complex numbers; Rectangular form. Complex conjugates. Absolute value. Arithmetic rules. The complex plane. Polar form. Exponential form. De Moivre's formula. Euler's formula.

Polynomial equations; Polynomial long division. The factor theorem.

Advanced studies of derivatives and integrals; Repetition of basic concepts. Linear approximation. Change rates. Extreme values. Integrals and area calculations. Partial integration. Solids of revolution

Differential equations; differential equations of the first order. Inhomogeneous differential equations. Differential equations of the second order. Separable differential equations.

Intended learning outcomes *

The overall goal of the course is to give new students enough skills and understanding that is required to be able to follow the mathematical courses that are included in 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 relevant mathematical problems and communicate in writing the mathematical reasoning. 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 *

Mathematics of the upper secondary school 3b, 3c, Mathematics C or Mathematics I for Technical preparatory education. Minimum requirement is a pass grade.

Recommended prerequisites

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Matematik 5000, Kurs 4 Blå lärobok,  förlag: Natur och Kultur, ISBN 978-91-27-42632-0

Matematik 5000, Kurs 5 Blå lärobok, förlag: Natur och Kultur, ISBN 978-91-27-44169-9

Formler och tabeller, Förlag: Natur och Kultur, ISBN 978-91-27-42245-2

Examination and completion

Grading scale *

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

Examination *

  • TENA - Examination, 6.0 credits, Grading scale: A, B, C, D, E, FX, F
  • TENB - 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 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 KH0024

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.