# Mathematics

The mathematics entrance exam lasts 45 minutes.

Aids

• The use of a simple scientific calculator (WTR) is permitted. Pocket calculators with graphics capability (GTR), pocket calculators with typical functions of a computer algebra system (CAS), pocket calculators with data transmission capability and programmable pocket calculators are not permitted. A calculator that is frequently used at the Studienkolleg is the Casio fx-87DE plus. Of course, any other calculator that meets the above requirements can also be used for the entrance exam.
• The use of a set square (triangle) is recommended.
• Formula collections may not be used.

Exam content

Terms

• calculate terms
• transform terms
• structure terms
• simplify terms
• multiply out and factor out
• factoring (also with binomial formulas)
• shorten and expand
• power and logarithm laws

Examples:

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Equations and inequations

• linear equations
• linear systems of equations with two unknowns
• fractional equations
• root equations
• exponential equations
• trigonometric equations

Examples:

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Percentage calculation

Examples:

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Geometry

• elementary terms (e.g. line, distance, angle)
• triangles (right triangles, equilateral and isosceles triangles, general triangle)
• Pythagoras, sets of heights and legs
• The law of sine and cosine in a right triangle
• circles (radius, area, perimeter, sector and segment)
• volumes and surfaces of bodies (prism, cylinder, pyramid, cone, sphere)

Examples:

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Functions

• linear functions
• broken rational functions
• Exponential and logarithmic functions
• trigonometric functions
• whole rational functions

Examples:

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Recommended literature for preparation

Basic knowledge

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Practice material

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