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
2024 abitur__bayern_geometrie

9 maths questions

QA a 2 marks Vectors 3D & Lines MCQ: Cross-Section or Surface Area of a Solid View
Show that the edge length of the cube is 12.
QA b 3 marks Vectors 3D & Lines Section Division and Coordinate Computation View
Determine the coordinates of one of the two vertices of the octahedron that do not lie in $H$.
QB a 3 marks Vectors 3D & Lines Distance from a Point to a Line (Show/Compute) View
Calculate the length of the line segment [AB] and state the special position of this line segment in the coordinate system. (for verification: $\overline { \mathrm { AB } } = \sqrt { 2 }$ )
QB b 3 marks Vectors: Lines & Planes Find Cartesian Equation of a Plane View
Determine an equation of $E$ in coordinate form. (for verification: $E : x _ { 1 } + x _ { 2 } + 2 x _ { 3 } - 20 = 0$ )
QB c 4 marks Vectors: Lines & Planes Parallelism Between Line and Plane or Constraint on Parameters View
Justify that every line of the family lies in $E$, and determine the value $k$ for which the point $C$ lies on $g _ { k }$. (for verification: $k = 0.8$ )
QB d 5 marks Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines View
Justify that the magnitude of the angle of intersection of $g _ { k }$ and the $x _ { 1 } x _ { 2 }$-plane is less than $30 ^ { \circ }$ if $2 k ^ { 2 } > 1$ holds.
QB e 3 marks Vectors 3D & Lines Dihedral Angle Computation View
Using the result from task $a$, give the width of the gate to the nearest meter. Justify using the statement from task $d$ that the straight line of travel of the skier is inclined at less than $30 ^ { \circ }$ to the horizontal.
QB f 4 marks Vectors 3D & Lines Line-Plane Intersection View
Justify by calculation that the skier actually passes through the gate.
QB g 3 marks Circles Sphere and 3D Circle Problems View
At the point that corresponds to point C in the model, the skier's line of travel is continued without a kink by a circular arc curve. During travel along this curve, the skier reaches a point that corresponds to point $D ( 18 | - 2 | 2 )$. The circular arc that describes this curve is part of a circle with center $M \left( m _ { 1 } \left| m _ { 2 } \right| m _ { 3 } \right)$. The coordinates of $M$ can be determined using the following system of equations. I $\quad m _ { 1 } + m _ { 2 } + 2 m _ { 3 } - 20 = 0$ II $\quad \left( \begin{array} { l } m _ { 1 } - 9 \\ m _ { 2 } - 1 \\ m _ { 3 } - 5 \end{array} \right) \circ \left( \begin{array} { c } 1.8 \\ 0.2 \\ - 1 \end{array} \right) = 0$ III $\sqrt { \left( m _ { 1 } - 9 \right) ^ { 2 } + \left( m _ { 2 } - 1 \right) ^ { 2 } + \left( m _ { 3 } - 5 \right) ^ { 2 } } = \sqrt { \left( m _ { 1 } - 18 \right) ^ { 2 } + \left( m _ { 2 } + 2 \right) ^ { 2 } + \left( m _ { 3 } - 2 \right) ^ { 2 } }$ Explain the geometric considerations that underlie equations I, II and III.