# 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

• 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. Vector Algebra

• Vectors in two-and three dimensional space
• Addition and subtraction 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

Sample test 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

• 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

Sample test 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

• Monotonous and finite sequences
• Arithmetic and geometric sequences
• 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. Basis of Descriptive statistics

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

## 7. Combinatorics

• Faculty, binomial coefficient
• Permutations, combinations, variations with and without repetition

## 8. Basis of Probability Theory

• Random experiments
• Multistage random experiments
• Kolmogoroff's axioms
• Laplace experiments
• Tree diagram
• Conditional probability, independent events
• Random variables and their probability distributions:
• Expected value, variance, standard deviation
• Binomial distribution, hypergeometric distribution
• "Fair" games

Sample test as pdf file