Abitur Mathematics study plan
Abitur Mathematics · Give each week a clear focus.
8 weeks · About 6 hours per week
Analysis: functions, derivatives, integrals, curve sketching
Review and apply differentiation rules (power, product, quotient, chain) to polynomial, exponential, logarithmic, and trigonometric functions
Compute derivatives of composite functions and implicit functions
Determine tangent lines and normal lines to curves at given points
Solve basic optimization problems (e.g., maximize area, minimize cost) using derivatives
Your checkpoint
A one-page summary sheet of differentiation rules with three worked examples for each rule, plus solutions to five optimization problems from past Abitur exams.
Analysis: functions, derivatives, integrals, curve sketching
Analyze functions for domain, symmetry, zeros, extrema, and inflection points using derivatives
Sketch graphs of rational, exponential, and trigonometric functions using curve-sketching techniques
Determine limits at infinity and near vertical asymptotes
Solve problems involving families of functions (e.g., f_k(x) = x^2 + kx) and their properties
Your checkpoint
A complete curve sketch for two different families of functions, including all intercepts, asymptotes, extrema, and inflection points, with justifications.
Analysis: functions, derivatives, integrals, curve sketching
Compute definite and indefinite integrals using substitution and integration by parts
Calculate areas between curves and volumes of solids of revolution
Apply the fundamental theorem of calculus to evaluate definite integrals
Solve applied problems involving accumulation functions and rates of change
Your checkpoint
A set of ten integration problems (including area and volume applications) solved step-by-step, with a self-graded rubric.
Analysis: functions, derivatives, integrals, curve sketching & Mathematical modelling and problem solving in applied contexts
Interpret and model real-world scenarios (e.g., population growth, decay, motion) using exponential and trigonometric functions
Formulate differential equations for simple models and solve them analytically
Use calculus to solve optimization problems in context (e.g., maximizing profit, minimizing material)
Critically evaluate assumptions and limitations of mathematical models
Your checkpoint
A written solution to a multi-part modeling problem (e.g., spread of a disease, cooling of a body) that includes function construction, derivative analysis, and interpretation of results.
Analytic Geometry / Linear Algebra: vectors, lines, planes, distances, matrices
Perform vector operations (addition, scalar multiplication, dot product, cross product) and interpret geometrically
Determine equations of lines and planes in vector and parametric form
Calculate distances between points, lines, and planes
Solve systems of linear equations using Gaussian elimination and matrix methods
Your checkpoint
A summary table of vector formulas (dot product, cross product, line/plane equations) with three worked examples each, plus solutions to five distance problems.
Analytic Geometry / Linear Algebra: vectors, lines, planes, distances, matrices & Mathematical modelling and problem solving in applied contexts
Apply matrices to solve geometric transformations and systems of equations
Use vectors to model real-world situations (e.g., forces, velocities, intersections of planes)
Determine intersections of lines and planes and classify the solution set
Solve problems involving angles between vectors, lines, and planes
Your checkpoint
A set of five applied problems (e.g., determining whether a plane intersects a line, finding the angle between two planes) solved with full working and diagrams.
Stochastics: probability, binomial and normal distributions, hypothesis testing
Calculate probabilities using combinatorial methods and probability distributions
Apply the binomial distribution to solve problems involving fixed number of trials and constant probability
Use the normal distribution (including standardization and z-scores) to approximate binomial probabilities and solve real-world problems
Conduct hypothesis tests for a population proportion using binomial and normal approximations, including stating null and alternative hypotheses, significance level, and conclusion
Your checkpoint
A two-page cheat sheet summarizing probability rules, binomial and normal formulas, and the steps of hypothesis testing, accompanied by solutions to three past exam problems.
Analysis: functions, derivatives, integrals, curve sketching & Analytic Geometry / Linear Algebra: vectors, lines, planes, distances, matrices & Stochastics: probability, binomial and normal distributions, hypothesis testing & Mathematical modelling and problem solving in applied contexts
Synthesize knowledge from all domains by solving full-length Abitur-style practice exams under timed conditions
Identify and review weak areas through error analysis
Practice presenting solutions clearly and concisely, as required in the exam
Review key formulas and concepts from all domains
Your checkpoint
A completed mock exam (three hours) with self-assessment and a personalized review list of topics to revisit before the exam.
Milestones
Week 2: Can sketch a curve for a given function (including a family of functions) without prompts, correctly identifying all key features (zeros, extrema, inflection points, asymptotes) and justifying with derivatives.
Week 4: Can solve a multi-part modeling problem that combines differentiation, integration, and interpretation, scoring at least 80% on a self-graded rubric.
Week 6: Can solve vector and matrix problems involving lines, planes, and distances with at least 90% accuracy on a set of ten problems.
Week 7: Can conduct a full hypothesis test for a proportion, including checking conditions, computing the test statistic, and interpreting the p-value in context, with at least 80% accuracy on three problems.
Week 8: Complete a full mock exam under timed conditions, achieving a score of at least 70% overall and identifying at least three specific areas for final review.