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Mathematics (T-Course)

The university entrance exam in mathematics consists of three exercises.
The exam requirements refer to the subject-related areas mentioned below.
The time provided for the exercises is 180 minutes.
Assistive equipment: pocket calculator (without chart function)

   1. Sequences and Series

  • Monotonous and finite series
  • Arithmetic and geometric sequences
  • Arithmetic and geometric series
  • Convergent sequences

   2. Boundary Values

  • Boundary value of a numerical sequence
  • Euler´s number e
  • Application examples of constant and inconstant growth

   3. Functions

  • Continuity and Differentiability
  • Boundary Values, rational functions with and without parameters
  • fractional rational function with and without parametres
  • Irrational functions with and without parametres
  • Expotential functions with and without parametres
  • Logarithmic funkcions with and without parametres
  • Curve sketching:
    Domain, roots, poles, gaps, symmetry, margins, asymptotes, extremes, turning points, sketching of graphs
  • Exercises on extreme values

   4. Integral Calculus

  • Specific and unspecific integrals
  • Integral processes
  • Area calculations

   5. Matrix

  • Calculations
  • Systems of equations and matrix

   6. Vector Algebra

  • Vectors in two-and three dimensional space
  • Addition and subtrakction of vectors
  • Vector products:
    scalar product, vector prodct and scalar triple product (and applications)
  • Straight lines in space and their relative position
  • Planes in the space and their geometric relation
  • Cuboid, parallelepiped, pyramid und tetrahedron
  • Characterization of circles and balls using methods of vector algebra
  • Tangents and tangent planes to circles and balls
  • Polars and polar planes

 

Comments: exam drafts as pdf-file

 

 

Mathematics (M-Course)

The university entrance exam in mathematics consists of three exercises.
The exam requirements refer to the subject-related areas mentioned below.
The time provided for the exercises is 180 minutes.
Assistive equipment: pocket calculator (without chart function)

   1. Sequences and Series

  • Monotonous and finite series
  • Arithmetic and geometric sequences
  • Arithmetic and geometric series
  • Convergent sequences

   2. Boundary Values

  • Boundry value of a numerical sequence
  • Euler's number e
  • Application examples of constant and inconstant growth

   3. Functions

  • Continuity and Differentiability
  • Boundry values, rational functions with & without parameters
  • Fractional rational function with & without parameters
  • Irrational function with & without parameters
  • Expotential function with & without parameters
  • Logarithmic function with & without parameters
  • Curve sketching:
    Domain, roots, poles, gaps, symmetry, margins, asymptotes, extremes, turning points, sketching of graphs
  • Exercises on extreme values

   4. Integral Calculus

  •       Specific and unspecific integrals
  •       Integral processes
  •       Area calculations

 


Comments: exam drafts as  pdf-file

 

 

Mathematics (W-Course)

The university entrance exam in mathematics consists of three exercises.
The exam requirements refer to the subject-related areas mentioned below.
The time provided for the exercises is 180 minutes.
Assistive equipment: pocket calculator (without chart function)

   1. Sequences and Series

  • Monotonous and finite series
  • Arithmetic and geometric sequences
  • Arithmetic and geometric series
  • Convergent sequences

   2. Boundary Values

  • Boundry value of a numerical sequence
  • Euler's number e
  • Application examples of constant and inconstant growth

   3. Functions

  • Continuity and Differentiability
  • Boundry values, rational functions with & without parameters
  • Fractional rational function with & without parameters
  • Irrational function with & without parameters
  • Expotential function with & without parameters
  • Logarithmic function with & without parameters
  • Curve sketching:
    Domain, roots, poles, gaps, symmetry, margins, asymptotes, extremes, turning points, sketching of graphs
  • Exercises on extreme values

   4. Integral Calculus

  • Specific and unspecific integrals
  • Integral processes
  •  Area calculations 

   5. Linear Programming

  • Graphical solution methods, Simplex algorithm

   6. Basis of Descriptive statistics

  • Ascertainment of data
  • Data representation in tabular and graphical form
  • Frequency distribution
  • Positional dimensions and statistical dispersion
  • Regression Analysis and correlation

   7. Combinatorics

  • Permutation
  • Combination
  • Variation

   8. Basis of Probability Theory

  • Random Experiment
  • Laplace-probability
  • Conditional probability
  • Probability distribution




Comments: exam drafts as  pdf-file