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Zusammenfassung Notizen der Oberstufe - Gymnasium Mathematik $4.29
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Zusammenfassung Notizen der Oberstufe - Gymnasium Mathematik
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  • Course
  • Mathematik
  • Institution
  • Gymnasium
  • Book
  • Lambacher Schweizer. Qualifikationsphase. Schülerbuch Grundkurs. Nordrhein-Westfalen

Einzelne Notizen aus der Qualifikationsphase. Folgende Themen werden behandelt: Vektorrechnung, Windschief, Addition von Vektoren, Gauß-Verfahren, Lösungsmengen von LGS, Ebenen, Lagebeziehungen von Ebenen und Geraden, Wahrscheinlichkeitsrechnung, Erwartungswert & Standardabweichung, Die Binominia...

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Document information

  • No
  • Einzelne kapitel
  • July 13, 2023
  • 13
  • 2022/2023
  • Summary

Subjects

  • vektorrechnung
  • aufgaben
  • mathematik
  • abitur
  • oberstufe
  • windschief
  • addition von vektoren
  • vektoren
  • gauß verfahren
  • lösungsmengen von lgs
  • ebenen
  • geraden
  • lagebeziehungen
  • wahrschein
  • wahrscheinlichkeitsrechnung

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Written for

  • Secondary school
  • Gymnasium
  • Mathematik
  • 1
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Content preview

x
Vektorrechnung
x 3


3
-




2
Punkte A(xIX,xy Bsp.:AS21
-
1137 Dunkte

1


3 bzw. Alanazlag) B(41015)
ei x
2


"

X
B(bilbelbs) â AB
=




(Y (0 52)
= =
=
B A
=
-




Richtungsvektor



5 Bx
=
(=I) (==) A
=
= =

-

B Gegenvektor



Bistder Gegenvektor von AB! BE=-


Die
Länge eines Vektors, istd er Betragd. Vektors!

â ()
=




Betrag:(â)
22 1 = +
3 14 3,74
+ = =




A B



S. 145;Nr.7, isr FB=-c?


a. A(21114), B(31317), ((21518), D(11315) b. A(11 -112), B(31010), ((316 (1), D(-51010) 2. AC01415), B(1717), ((111815), D(41515)

A =(==g):() x



B (= i) (3) (8 )-(E) 55 (= 8) ()
=
=
Es
=

=


-parallelogramm Parallelogramm
=


=
=
kein =




=(= a) (i) (i (3) (=8)
=

=




i
=


=




a.A(51112), B(61213), (61215), D(51114)

B (= ) (E)
=
=


~


( (5 2) (21)
=
=
=
= -


(2) =
-
As
23 = -




Beschreibung von Geraden S. 148




.
Geraden sind angegeben durch einen Punkt (durch den die Gerade läuft) und durch ihre Richtung.

.
Der Punktw ird durch den Ortsuektor zum Punkt definiert, die
Richtung durch den Richtungsverter = (?)
·

Es giltd ann für alle Punkte der Geraden E
g:
(8) r(?)
=
+




mitr et


(
r()*naavaranquett
r 10:
=
:

Gerade:I'=(Y)
-s
+

+ Bsp.:P11141-2)

(i)
e
auf
3x
i =



Punkt-Richtungsform liegt der
er



Punkte der
Geraden sind z. B.:r 1 : =
(2)
=

, Windschief
·S. 1 5 2.




2 Geraden kommen zueinander


n schneidend sein (Schnittpunkt)

Parallel sein (gleiche Richtungen!
31 windschief sein (aneinander vorbeilaufend)

I identisch sein




153
Vorgehensweise zur
Untersuchung:S.



S. 155; Nr. 191 -g: = (=) r.(a);h:=
+ (8) s.()
=
+




9:= (z) r.(2);n == (?) t.(i)
=
+
=
+
(5):() () =




entspricht3 Gleichungen: -> sind parallel!

I. r.2 4
=
=2.2=4 u P(012-13):

1.1.4 8
= = 2.4 8
= = (8) s.() (5)
=
+
=




(GS:1.6 + Es 0
= 1-6


#.r.1 2
=
=) r 2 =
1 =) r 2
=


einsetzen in 1&2 Es =
-
6 1:5

(2) () = -
sind parallel! S:-18 einsetzen!
-




echt parallel oder identisch?: #. 2.1.( 18)
- = -
36X


D(11213): #0 +3.) 18) -
-
= 45X


E (3) t.(()
=
+
(3)
=

(as:1.3 + 45: 1- 3 -> Graphen sind parallel!
echt



4t = -
21:4


t -
= -
einsetzen!


1.6 +
8.( z) -
2
=




2 2
=
v



#1.4 2.)
+
-
z) 3 =




3:3



-> Die Graphen sind identisch zueinander!

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