Syllabus
This year’s course structure
The course consists of approximately 60 sessions preparing students for the Feststellungsprüfung. It is divided into 9 sections, each with 5–7 sessions. The last session of each section is always reserved for review, reinforcement, or a mock exam.
Section 1: Mathematical Foundations (Foundation)
- Number systems and set theory
- Mathematical language and notation
- Exponent laws, radicals, and scientific notation
- Factorization and binomial theorem
- Absolute value and logarithm properties
- Problem-solving strategies (IDEA method)
Section 2: Equations & Problem-Solving (Foundation)
- Linear equations and inequalities
- Systems of linear equations (substitution, elimination, graphical)
- Quadratic and biquadratic equations
- Fractional and radical equations
- Exponential and cubic equations
- Complex word problems in business contexts
- Mini-Mock Exam 1
Section 3: Functions as Business Models (Foundation)
- Concept of functions, domain, and range
- Cost, revenue, and profit functions
- Linear and quadratic models
- Function transformations and graphical analysis
- Composition and inverse functions
- Mini-Mock Exam 2
Section 4: Advanced Functions & Analysis (Exam Focus)
- Polynomial and rational functions
- Exponential and logarithmic functions
- Transformation patterns across function families
- Quick recognition of exam-style function problems
- Functions Mastery Check
Section 5: Differential Calculus (Exam Focus)
- Limits and continuity
- Derivatives as rates of change (marginal cost, revenue, profit)
- Rules of differentiation: power, product, quotient, chain
- Graphical calculus: f, f’, f’’ relationships
- Optimization and curve sketching
- Function determination (critical exam skill)
- Related rates in business contexts
- Full Mock Exam 1
Section 6: Integral Calculus (Exam Focus)
- Antiderivatives and indefinite integrals
- Definite integrals and the fundamental theorem of calculus
- Substitution method
- Area between curves (consumer/producer surplus, Gini coefficient)
- Applications in economics (profit, cost, accumulation)
- Integration in finance (present value, surplus problems)
- Mini-Mock Exam 3
Section 7: Probability & Statistics (Exam Focus)
- Descriptive statistics (mean, median, standard deviation)
- Basic probability rules and sample spaces
- Combinatorics and counting principles
- Conditional probability and independence
- Bayes’ theorem with applications
- Contingency tables and probability extraction
- Binomial and normal distributions
- Full Mock Exam 2
Section 8: Financial Mathematics (Applied Topics)
- Sequences and series (geometric progressions)
- Compound and simple interest
- Present and future value
- Loan amortization and annuities
- Growth and decay models in business contexts
Section 9: Synthesis & Exam Preparation (Exam Focus)
- Multi-topic business problem solving
- Intensive practice in function determination
- Graphical methods and exam shortcuts
- Comprehensive review and exam strategies
- Full exam simulation (3 problems, 180 minutes)
- Final Q&A, formula sheet preparation, and exam-day coaching