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
2021 abitur__bayern_stochastik

9 maths questions

QA b 3 marks Discrete Probability Distributions Binomial Distribution Identification and Application View
Justify that $X$ is not binomially distributed.
QB 1 3 marks Probability Definitions Event Expression and Partition View
On a Saturday morning, four families arrive one after another at the entrance area of an amusement park. Each of the four families pays at one of six cashiers, whereby it is assumed that each cashier is chosen with equal probability. Describe in the context of the problem two events $A$ and $B$ whose probabilities can be calculated using the following terms: $P ( A ) = \frac { 6 \cdot 5 \cdot 4 \cdot 3 } { 6 ^ { 4 } } ; P ( B ) = \frac { 6 } { 6 ^ { 4 } }$
QB 2a 2 marks Normal Distribution Direct Probability Calculation from Given Normal Distribution View
Determine the probability that at least 25 hand carts are rented.
QB 2b 2 marks Geometric Distribution View
Determine the probability that the fifth family is the first to rent a hand cart.
QB 2c 5 marks Measures of Location and Spread View
Using the table of values, determine the smallest interval symmetric about the expected value in which the values of the random variable $X$ lie with a probability of at least $75 \%$.
QB 3 6 marks Probability Definitions Probability Distribution and Sampling View
The amusement park holds a game of chance in which entrance tickets to the amusement park can be won. At the beginning of the game, one rolls a die whose faces are numbered with the numbers 1 to 6. If one obtains the number 6, one may then spin a wheel of fortune with three sectors once (see schematic diagram). If sector $K$ is obtained, one wins a child ticket worth 28 euros; for sector $E$, an adult ticket worth 36 euros. For sector $N$, one wins nothing. The central angle of sector $N$ is $160 ^ { \circ }$. The sizes of sectors $K$ and $E$ are chosen such that the average winnings per game amount to three euros. Determine the size of the central angles of sectors $K$ and $E$.
QB 4a 2 marks Discrete Probability Distributions Probability Computation for Compound or Multi-Stage Random Experiments View
Determine for the case $n = 5$ the probability that not all three badges have the same motif.
QB 4b 2 marks Proof Computation of a Limit, Value, or Explicit Formula View
Justify that the probability that three different motifs appear on the badges has the value $\frac { ( n - 1 ) \cdot ( n - 2 ) } { n ^ { 2 } }$.
QB 4c 3 marks Sign Change & Interval Methods View
Determine how large $n$ must be at minimum so that the probability that three different motifs appear on the badges is greater than $90 \%$.