Sachsen-Anhalt Abitur Mathematics study plan
Sachsen-Anhalt Abitur Mathematics · Give each week a clear focus.
8 weeks · About 6 hours per week
Analysis
Set up a formula sheet covering Ableitungsregeln (Produkt-, Quotienten-, Kettenregel), Stammfunktionen and the Hauptsatz, then rewrite it from memory at the end of the week.
Differentiate 20 mixed functions (e^x, ln x, sin/cos, Wurzel-, gebrochenrationale Terme) and justify each rule choice in one sentence.
Sketch graphs of 6 functions using Nullstellen, Extremstellen and Wendestellen, and mark monotonicity intervals on each sketch.
Solve 5 realitätsnahe Extremwertaufgaben (Zielfunktion aufstellen, Nebenbedingung einsetzen, Definitionsbereich prüfen).
Your checkpoint
A one-page handwritten Ableitungs-/Stammfunktionen reference sheet plus 6 annotated Kurvendiskussion sketches, all self-corrected against the official Lösungen.
Analysis
Compute 12 bestimmte Integrale, including substitution and partielle Integration, and state the used rule above each line.
Calculate Flächen zwischen Graphen and Rotationsvolumen for 5 given function pairs, including splitting regions at Schnittstellen.
Interpret Integral als Bilanz/rekonstruierte Größe in 4 Anwendungsaufgaben (Zuflussrate, Geschwindigkeit, mittlere Änderungsrate).
Write out the full Beweisidee of the Hauptsatz and one Begründung why Stetigkeit für die Existenz der Stammfunktion genügt.
Your checkpoint
A timed 90-minute Klausurteil consisting of 3 complete Analysis tasks (Kurvendiskussion, Flächenberechnung, Anwendung) scored with the official Erwartungshorizont, with a written error log.
Analysis
Model 4 Sachkontexte with e-Funktionen (Wachstum, Abkühlung, Medikamentenabbau) and interpret every parameter in the context.
Analyse 5 e-Funktionenscharen f_t(x) = t·x·e^(−tx) or similar: determine Nullstellen, Extrema and Grenzverhalten in terms of t.
Solve 6 Gleichungen involving ln and e (also substitutions like z = e^x) and check Lösungen for Gültigkeit im Definitionsbereich.
Explain in writing how Parameteränderungen the graph (Streckung, Verschiebung, Asymptote) affect, using two examples.
Your checkpoint
A Scharanalyse of one function family on a single A4 sheet: general results in t, one fully worked special case, and the graph family sketch.
Analysis & Lineare Algebra / Analytische Geometrie
Re-solve all Analysis tasks missed in weeks 1–3 without notes and reach at least 80% of the official points.
Compute 10 Geraden- und Ebenengleichungen in Parameterform from three given points or two directions, and convert 5 into Koordinatenform.
Determine Lagebeziehungen (identisch, parallel, schneidend, windschief) for 8 Geraden-/Ebenenpaare and give the Schnittpunkt or Schnittgerade where it exists.
Start a personal Fehlerkatalog that names each error type (Rechenfehler, Ansatzfehler, Begründungsfehler).
Your checkpoint
A 60-minute closed-book Analysis mini-test at 80% or better plus a Lagebeziehungen decision tree drawn from memory.
Lineare Algebra / Analytische Geometrie
Compute 10 Abstandsprobleme: Punkt–Ebene via Hesse-Normalform, Punkt–Gerade, windschiefe Geraden via Hilfsebene.
Determine 8 Winkel (Gerade–Ebene, Ebene–Ebene, Gerade–Gerade) with the correct cos/sin formula and interpret the result geometrically.
Calculate 6 Flächeninhalte von Dreiecken and Volumina von Pyramiden/Prismen using Kreuzprodukt and Spatprodukt.
Apply 4 Anwendungsaufgaben (Dachkonstruktion, Pyramide, Schatten, Spiegelung) and justify each modelling choice.
Your checkpoint
A one-page Methodenübersicht (Abstand, Winkel, Volumen) with a fully worked example for each method and the formula derivation for Punkt–Ebene.
Lineare Algebra / Analytische Geometrie & Stochastik
Solve 6 Aufgaben zu Geraden-/Ebenenscharen, including orthogonalen Ebenen and parameterabhängigen Lagebeziehungen.
Compute 12 Wahrscheinlichkeiten with Binomialverteilung (exact, at least, at most, between) and use Gegenereignis efficiently.
Handle 6 Aufgaben with Erwartungswert, Standardabweichung and Sigma-Regeln, and interpret the results in the Sachkontext.
Set up 5 Hypothesentests (einseitig, zweiseitig): H0/H1, Signifikanzniveau, Annahme-/Ablehnungsbereich, Fehler 1. und 2. Art.
Your checkpoint
A 90-minute mixed Klausurteil (Lineare Algebra + Stochastik) scored with the official Erwartungshorizont, plus a completed Binomialverteilung formula card.
Stochastik
Solve 8 Aufgaben zu Baumdiagrammen, bedingter Wahrscheinlichkeit, Unabhängigkeit and Vierfeldertafeln, including Vertauschung von P(A|B) und P(B|A).
Analyse 5 Aufgaben zu Bernoulli-Ketten and to the difference between Binomial- and Normalverteilung as approximation.
Interpret 4 Aufgaben critically: which model fits, which assumptions are questionable, what the p-value does and does not mean.
Re-work every Stochastik error from week 6 and write a corrected Lösung in full sentences.
Your checkpoint
A written Stochastik-Portfolio: 4 fully worked, self-explained Aufgaben with correct interpretations, checked against official solutions.
Analysis & Lineare Algebra / Analytische Geometrie & Stochastik
Complete 3 full timed mock exams (Wahlteil-style, 5 hours each or split into 90-minute blocks) under exam conditions.
Score each mock with the official Erwartungshorizont and record the point loss per domain in a table.
Close the three largest remaining gaps by targeted re-practice and re-testing those task types.
Memorize the final Formelsammlung content you are allowed to bring and rehearse the Wahlteil task-selection strategy in 10 minutes.
Your checkpoint
A final score table across the 3 mock exams showing domain-wise percentages and evidence that every domain is at or above 70%.
Milestones
Week 2: Can compute a definite integral with substitution or partielle Integration and a Fläche zwischen zwei Graphen in under 15 minutes each, with correct notation and units.
Week 4: Scores at least 80% on a closed-book Analysis mini-test and can classify the Lagebeziehung of any two Geraden/Ebenen without notes.
Week 6: Solves a binomial probability 'at least k' task and a full Hypothesentest in under 20 minutes each, with correct interpretation of the result.
Week 8: All three domains at or above 70% on the final mock exams, with a written Fehlerkatalog showing each remaining gap has been re-tested.