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Final

All You Need for German Math Olympiad

 ​​Curriculum Topics – Grades 7-8

  1. Number Systems and Properties
    - Rational and irrational numbers
    - Absolute value and opposites
    - Prime factorization, LCM/GCD, exponents and roots
    - Scientific notation and estimation
  2. Fractions, Decimals, and Percent Applications
    - Conversions between forms
    - Percent increase/decrease, discounts, profit/loss, tax
    - Multi-step word problems with percentages
    - Comparing ratios and proportional quantities
  3. Expressions, Equations, and Inequalities
    - Simplifying algebraic expressions
    - Solving multi-step linear equations and inequalities
    - Equations with parentheses and variables on both sides
    - Representing and interpreting solutions on number lines
  4. Functions and Sequences
    - Understanding input-output rules and function tables
    - Linear and simple non-linear patterns
    - Arithmetic and geometric sequences
    - Using function notation and interpreting graphs
  5. Geometry and Coordinate Reasoning
    - Angles, triangles, and polygons: properties and angle sums
    - Parallel lines cut by a transversal
    - Perimeter, area, and volume of 2D and 3D figures
    - Coordinate geometry: distance, midpoint, gradient
  6. Transformations and Symmetry
    - Translations, reflections, rotations, and dilations
    - Identifying symmetry and congruence
    - Describing transformations algebraically and graphically
    - Tessellations and geometric pattern investigations
  7. Data Analysis and Visual Representation
    - Reading and creating histograms, box plots, and double bar graphs
    - Measures of central tendency and spread
    - Interpreting misleading graphs
    - Using data to make decisions and predictions
  8. Probability and Combinatorics
    - Theoretical vs. experimental probability
    - Tree diagrams and outcome tables
    - Simple permutations and combinations
    - Using probability in games and simulations
  9. Logical Reasoning and Problem Solving
    - Multi-step logic puzzles, constraints, and grid problems
    - Deductive and inductive reasoning
    - Error analysis and correcting flawed reasoning
    - Justifying conclusions with evidence
  10. Modelling and Real-World Applications
    - Graphing and interpreting real-world data (e.g. population growth, speed-time)
    - Budgeting, scaling, and conversion problems
    - Modelling using equations, inequalities, or graphs
    - Investigations (e.g., “Design a fair game”, “Estimate school water use”)