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
2020 abitur__bayern_geometrie

7 maths questions

Q1 3 marks Circles Sphere and 3D Circle Problems View
The line segment $[ \mathrm { PQ } ]$ with endpoints $P ( 8 | - 5 | 1 )$ and $Q$ is a diameter of a sphere with center $M ( 5 | - 1 | 1 )$.
Calculate the coordinates of $Q$ and show that the point $R ( 9 | - 1 | 4 )$ lies on the sphere.
Q2 2 marks Circles Sphere and 3D Circle Problems View
Justify without further calculation that the triangle $P Q R$ is right-angled at $R$.
Q3 4 marks Vectors 3D & Lines Normal Vector and Plane Equation View
The points $A _ { 1 } ( 0 | 0 | 0 ) , A _ { 2 } ( 20 | 0 | 0 ) , A _ { 3 }$ and $A _ { 4 } ( 0 | 10 | 0 )$ represent the vertices of the base of the multipurpose hall in the model, and the points $B _ { 1 } , B _ { 2 } , B _ { 3 }$ and $B _ { 4 }$ represent the vertices of the roof surface. The side wall that lies in the $x _ { 1 } x _ { 3 }$-plane in the model is 6 m high, and the opposite wall is only 4 m high.
Give the coordinates of the points $B _ { 2 } , B _ { 3 }$ and $B _ { 4 }$ and confirm that these points lie in the plane $E : x _ { 2 } + 5 x _ { 3 } - 30 = 0$.
Q4 3 marks Vectors 3D & Lines Dihedral Angle Computation View
Calculate the angle of inclination of the roof surface with respect to the horizontal.
Q5 6 marks Vectors 3D & Lines MCQ: Distance or Length Optimization on a Line View
The point $T ( 7 | 10 | 0 )$ lies on the edge $\left[ \mathrm { A } _ { 3 } \mathrm {~A} _ { 4 } \right]$. Investigate computationally whether there are points on the edge $\left[ \mathrm { B } _ { 3 } \mathrm {~B} _ { 4 } \right]$ for which the following holds: The line segments connecting the point to the points $B _ { 1 }$ and $T$ are perpendicular to each other. If applicable, give the coordinates of these points.
Q6 5 marks Vectors: Lines & Planes Find Cartesian Equation of a Plane View
The point $L$, which lies vertically above the midpoint of the edge $\left[ \mathrm { A } _ { 1 } \mathrm {~A} _ { 2 } \right]$, represents the position of a floodlight in the model, which is installed 12 m above the base. The points $L , B _ { 2 }$ and $B _ { 3 }$ determine a plane $F$. Find an equation of $F$ in normal form.
(for verification: $F : 3 x _ { 1 } + x _ { 2 } + 5 x _ { 3 } - 90 = 0$ )
Q7 3 marks Vectors: Lines & Planes Find Parametric Representation of a Line View
The plane $F$ intersects the $x _ { 1 } x _ { 2 }$-plane in the line $g$. Determine an equation of $g$.
(for verification: $g : \vec { X } = \left( \begin{array} { c } 30 \\ 0 \\ 0 \end{array} \right) + \lambda \cdot \left( \begin{array} { c } 1 \\ - 3 \\ 0 \end{array} \right) , \lambda \in \mathbb { R }$ )