Berlin Abitur Math 3. PF (GK) study plan

Sketch and analyze polynomial, rational, exponential, and trigonometric functions without aids, determining domain, symmetry, zeros, extrema, and limits at infinity.

Compute derivatives using product, quotient, and chain rules, and verify results by alternative methods (e.g., logarithmic differentiation).

Solve optimization and related-rates problems by setting up the objective function and constraint explicitly.

Explain the relationship between derivative sign, monotonicity, and extrema using the first and second derivative tests.

Determine antiderivatives and evaluate definite integrals using substitution and integration by parts.

Interpret the definite integral as a signed area and compute areas between curves and volumes of solids of revolution.

Apply the fundamental theorem of calculus to solve accumulation and average-value problems.

Model real-world contexts (e.g., growth, motion) with exponential and trigonometric functions and solve using calculus.

Analyze families of functions with parameters (e.g., f(x)=x^3+ax^2) and discuss how the parameter changes the graph.

Perform vector operations (addition, scalar multiplication, dot product, cross product) and interpret them geometrically.

Determine equations of lines and planes in vector and parametric form, including intersections and distances.

Translate between geometric descriptions and algebraic representations of lines and planes.

Set up and solve systems of linear equations using Gaussian elimination and interpret the solution set geometrically.

Compute matrix products, inverses, and determinants, and explain their geometric meaning (e.g., area scaling).

Apply matrix transformations to geometric objects and describe the effect on shapes and orientations.

Solve eigenvalue problems for 2x2 and 3x3 matrices and interpret eigenvectors geometrically.

Solve geometric problems involving spheres, circles, and their intersections with lines and planes.

Compute probabilities using combinatorics (permutations, combinations) and apply the multiplication and addition rules.

Distinguish between discrete and continuous probability distributions and compute expected value and variance.

Model binomial and hypergeometric experiments and calculate probabilities using the respective formulas.

Apply the normal distribution as an approximation to the binomial distribution and use the standard normal table.

Formulate and test hypotheses (one- and two-sided) and interpret errors (Type I and Type II).

Construct confidence intervals for proportions and means and interpret the confidence level.

Analyze stochastically independent events and apply conditional probability and Bayes' theorem.

Solve mixed-topic problems that combine calculus, geometry, and probability within a single context.

Practice structuring full solutions for the Abitur format: given, required, solution, and interpretation.

Identify and avoid common pitfalls (e.g., forgetting units, misinterpreting parameters, misreading the question).

Simulate exam conditions by completing a full past-paper-like set under time constraints.

Review the error logs and formula sheets from weeks 1–7, re-solving every missed problem correctly.

Complete a second full mock exam and compare performance to week 7 to measure improvement.

Memorize key definitions, theorems, and formulas by writing them from memory and checking against notes.

Develop a time-management strategy for the exam (e.g., allocating minutes per problem, order of solving).