germany-abitur

Papers (25)
2025
abitur__nrw_analysis-gk 3 abitur_nrw__typ_analysis_lk 4 abitur_nrw__typ_stochastik_gk 3 abitur_nrw__typ_stochastik_lk 3
2024
abitur__bayern_geometrie 9 abitur__bayern_infinitesimalrechnung 2 abitur__bayern_stochastik 9
2023
abitur__bayern_geometrie 9 abitur__bayern_infinitesimalrechnung 2 abitur__bayern_stochastik 10
2022
abitur__bayern_geometrie 9 abitur__bayern_infinitesimalrechnung 1 abitur__bayern_stochastik 8
2021
abitur__bayern_geometrie 10 abitur__bayern_infinitesimalrechnung 2 abitur__bayern_stochastik 9
2020
abitur__bayern_geometrie 7 abitur__bayern_infinitesimalrechnung 2 abitur__bayern_stochastik 9
2019
abitur__bayern_geometrie 9 abitur__bayern_infinitesimalrechnung 2 abitur__bayern_stochastik 2
2018
abitur__bayern_geometrie 1 abitur__bayern_infinitesimalrechnung 2 abitur__bayern_stochastik 2
2022 abitur__bayern_stochastik

8 maths questions

QA a 2 marks Discrete Probability Distributions Proof of Distributional Properties or Symmetry View
Justify that the probability $P ( X = 4 )$ agrees with the probability $P ( X = 10 )$.
QA b 3 marks Discrete Probability Distributions Proof of Distributional Properties or Symmetry View
The probability distributions of $X$ and $Y$ are each represented by one of the following diagrams I, II and III. Assign $X$ and $Y$ to the appropriate diagram and justify your assignment.\n[Figure]\n[Figure]\n[Figure]
QB 1a 6 marks Binomial Distribution Compute Cumulative or Complement Binomial Probability View
15 plants are treated with the plant protection product and then sprayed with fungal spores. Determine the probability of each of the following events:\n$E _ { 1 }$ : ``None of the plants become infested with fungi.''\n$E _ { 2 }$ : ``At most two plants become infested with fungi.''\n$E _ { 3 }$ : ``12 or 13 plants remain free of fungal infestation.''
QB 1b 4 marks Binomial Distribution Find Minimum n for a Probability Threshold View
Determine the smallest value of $n$ for which the probability that at least one plant becomes infested with fungi is at least $99 \%$.
QB 1c 4 marks Normal Distribution Symmetric Interval / Confidence-Style Bound View
Given that in an experiment with 400 plants the value of the random variable $X _ { 400 }$ deviates from the expected value by at most one standard deviation, determine the smallest and largest possible relative frequency of plants that become infested with fungi.
QB 1d 3 marks Normal Distribution Multiple-Choice Conceptual Question on Normal Distribution Properties View
In general, the following inequality holds for a random variable $X$ with expected value $\mu$ and standard deviation $\sigma$ for $k > 0$ :
$$P ( \mu - k \cdot \sigma < X < \mu + k \cdot \sigma ) \geq 1 - \frac { 1 } { k ^ { 2 } }$$
Explain the statement of this inequality for $k = 2$.
QB 2a 4 marks Probability Definitions Probability Using Set/Event Algebra View
Determine $x$ using a four-field table.\n(for verification: $x = 13$ )
QB 2b 4 marks Conditional Probability Direct Conditional Probability Computation from Definitions View
Calculate $P _ { S } ( T )$ and $P _ { \bar { S } } ( T )$ and justify that the results of the experiment do not allow conclusions to be drawn about the effectiveness of the plant protection product against the tropical fungus.