germany-abitur

2019 abitur__bayern_geometrie

9 maths questions

QB a 2 marks Vectors 3D & Lines Distance from a Point to a Line (Show/Compute) View
On the basis of the model, calculate the total length of the borehole rounded to the nearest metre.
QB b 3 marks Vectors 3D & Lines MCQ: Angle Between Skew Lines View
At the transition between the two sections of the borehole, the drilling direction must be changed by the angle that is described in the model by the angle of intersection of the two lines $A P$ and $P Q$. Determine the size of this angle.
QB c 2 marks Vectors 3D & Lines Normal Vector and Plane Equation View
Determine an equation of the plane $E$ in normal form. (for verification: $E : 4 x _ { 1 } + 4 x _ { 2 } - 10 x _ { 3 } - 43 = 0$ )
QB d 6 marks Vectors 3D & Lines Line-Plane Intersection View
The borehole is extended in a straight line and leaves the water-bearing rock layer at a depth of 3600 m below the Earth's surface. The exit point is described in the model as a point $R$ on the line $P Q$. Determine the coordinates of $R$ and calculate the thickness of the water-bearing rock layer rounded to the nearest metre. (for verification: $x _ { 1 }$ and $x _ { 2 }$ coordinate of $R : 1.04$ )
QB e 3 marks Vectors 3D & Lines Line-Plane Intersection View
Show by calculation that the second borehole reaches the water-bearing rock layer in the model at the point $T ( t | - t | - 4,3 )$, and explain how the length of the second borehole to the water-bearing rock layer is influenced by the location of the associated drilling site.
Q1a 3 marks Straight Lines & Coordinate Geometry Section Ratio and Division of Segments View
Determine the coordinates of $D$ and give the coordinates of the midpoint $M$ of the line segment $[ A C ]$.
Justify that the triangles $B C M$ and $A B M$ have the same area without calculating it.
Q2a 2 marks Vectors: Lines & Planes Find Intersection of a Line and a Plane View
The plane $E : 3 x _ { 1 } + 2 x _ { 2 } + 2 x _ { 3 } = 6$ contains a point whose three coordinates are equal. Determine these coordinates.
Q2b 3 marks Proof Existence Proof View
Justify that the following statement is correct: There are infinitely many planes that do not contain a point whose three coordinates are equal.