Änderungen von Dokument BPE 1 Einheitsübergreifend

Zuletzt geändert von Holger Engels am 2025/01/12 21:23

Von 31.1 nach 30.1 Von 117.1 nach 116.1

Von Version 116.1

bearbeitet von Holger Engels
am 2025/01/12 21:23

Änderungskommentar: Neues Bild Arithmagon Lineare Funktionen Formen.svg hochladen

Auf Version 31.1

bearbeitet von Niklas Wunder
am 2024/10/15 13:54

Änderungskommentar: Es gibt keinen Kommentar für diese Version

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- Arithmagon Lineare Funktionen Formen.svg
- rhombus_with_lighter_colors.svg

Details

Seiteneigenschaften

Dokument-Autor

@@ -1,1 +1,1 @@
--XWiki.holgerengels
++XWiki.niklaswunder

Inhalt

@@ -1,77 +1,15 @@
--{{aufgabe id="Arithmagon Darstellungsformen" afb="II" kompetenzen="K2, K4" tags="problemlösen" quelle="Martin Rathgeb" cc="BY-SA" zeit="8"}}
--(% class="abc" %)
--1. (((Fülle in folgenden Darstellungsformen einer Geraden die Lücken.
--[[image:rhombus_with_lighter_colors.svg||width="500"]]
--)))
--1. (((Nenne die Werte der charakteristischen Größen der Geraden:
--1. (((
--(% class="border" %)
--|**Lage der Geraden** |Abschnitt |Schnittpunkt
--|y-Achse |{{formula}}b={{/formula}} |{{formula}}S_y(\qquad|\qquad){{/formula}}
--|x-Achse |{{formula}}x_0={{/formula}} |{{formula}}S_x(\qquad|\qquad)=N{{/formula}}
--)))
--1. (((
--(% class="border" %)
--|**Kovariation des linearen Zusammenhangs** | Parameterwert bzw. Beschreibung
--|Monotonie |
--|Steigung |{{formula}}m=\hspace{1cm}{{/formula}}
--|Krümmung |{{formula}}\qquad{{/formula}}
--)))
--)))
--{{/aufgabe}}
--
--{{aufgabe id="Formen von Geradengleichungen" afb="II" kompetenzen="K2, K4" quelle="Martin Rathgeb" cc="BY-SA" zeit="12"}}
--In der Literatur werden folgende Formen der Geradengleichung unterschieden, wobei {{formula}}P(x_P|y_P){{/formula}} ein beliebiger Punkt der Geraden sei; vgl. Merkhilfe, S. 3 und 5.
--(% class="border slim" %)
--|Hauptform |{{formula}}y=m\cdot x+b{{/formula}}|(Spezialfall der PSF {{formula}}x_P=0{{/formula}})
--|Punkt-Steigungs-Form (PSF)|{{formula}}y=m\cdot (x-x_P)+y_P{{/formula}}|
--|Produktform |{{formula}}y=m \cdot (x-x_0){{/formula}}|(Spezialfall der PSF {{formula}}y_P=0{{/formula}})
--|Achsenabschnittsform |{{formula}}\frac{x}{x_0}+\frac{y}{y_0}=1{{/formula}}|(hier: normiert)
--|Allgemeine Form |{{formula}}A x + B y + C = 0{{/formula}}|(hier: nicht normiert, aber {{formula}}=0{{/formula}})
--
--(% class="abc" %)
--1. (((Bestimme für jede Gleichungsform {{formula}}\ldots{{/formula}}
--1. {{formula}}\ldots{{/formula}}, ob (und ggf. wie) sich die beiden //Winkelhalbierenden// (besondere Geraden) darstellen lassen.
--1. {{formula}}\ldots{{/formula}}, ob (und ggf. wie) sich die //Parallelen zu den Koordinatenachsen// (Typen besonderer Geraden) darstellen lassen.
--1. {{formula}}\ldots{{/formula}}, welche charakteristischen Größen der Geraden sich direkt ablesen lassen; siehe hierzu das vorausgegangene Arithmagon.
--
--)))
--1. (((Erläutere, inwiefern {{formula}}\ldots{{/formula}}
--1. {{formula}}\ldots{{/formula}} die //Hauptform// und die //Produktform// zwei Spezialfälle der //Punkt-Steigungs-Form// sind.
--1. {{formula}}\ldots{{/formula}} nur die //Allgemeine Form// diese Bezeichnung mit Recht trägt; vgl. dazu a).
--
--)))
--1. Berechne aus den Parametern {{formula}}x_0, y_0{{/formula}} der Achsenabschnittsform die Steigung {{formula}}m{{/formula}}.
--{{/aufgabe}}
--
--{{aufgabe id="Klassenparty" afb="II" zeit="10" kompetenzen="K1,K3,K4,K5" quelle="Torben Würth" cc="BY-SA"}}
--Für eine Klassenparty stehen zwei Locations zur Verfügung. In der Almhütte muss für die Raummiete eine Gebühr von 20€ bezahlt werden, jedes Getränk kostet 2€. Im Hüttenzauber sind lediglich 2,5€ pro Getränk zu zahlen, eine Raummiete fällt nicht an.
--Begründe, für welche Location Du dich entscheiden würdest.
--{{/aufgabe}}
--
--{{aufgabe id="Parabel und Gerade" afb="II" zeit="30" kompetenzen="K4,K5" quelle="Torben Würth" cc="BY-SA"}}
--Gegeben ist die Funktionsgleichung {{formula}}f(x)=(x+2)^2-3{{/formula}} und ein zu ergänzendes Koordinatensystem.
--(% style="list-style: alphastyle" %)
--1. Zeichne den Funktionsgraphen in einem geeigneten Intervall.
--1. Berechne die Funktionswerte an den Stellen {{formula}}x=-3{{/formula}} und {{formula}}x=1{{/formula}}.
--1. Zeichne die Gerade {{formula}}g{{/formula}} durch die Punkte {{formula}}P_1(-3|-2){{/formula}} und {{formula}}P_2(1|6){{/formula}} ein.
--1. Berechne den Funktionsterm der Geraden {{formula}}g{{/formula}}.
--1. Ermittle den Bereich, in dem die Gerade über der {{formula}}x{{/formula}}-Achse verläuft.
--1. Bestimme den Funktionsterm einer Geraden {{formula}}h{{/formula}}, die senkrecht auf der Geraden {{formula}}g{{/formula}} steht und einen gemeinsamen Punkt mit {{formula}}f{{/formula}} und {{formula}}g{{/formula}} hat.
--{{/aufgabe}}
--
--{{aufgabe id="Wurzelfunktion" afb="II" zeit="20" kompetenzen="K4,K5" tags="" quelle="Torben Würth" cc="BY-SA"}}
--Gegeben ist die Funktionsgleichung {{formula}}f(x)=x^{\frac{2}{6}} {{/formula}}, eine zu ergänzende Wertetabelle und ein zu ergänzendes Koordinatensystem.
--
--((((% class="border" style="width:100%" %)
--|={{formula}}x{{/formula}}| | | | | | | | | | | | | | | | | |
++{{aufgabe id="" afb="III" zeit="20" kompetenzen="K2, K5" tags="" quelle="Torben Würth" cc="BY-SA"}}
++Gegeben ist die Funktion {{formula}}f(x)=x^{\frac{2}{6}} {{/formula}}
++  1. Gib den Funktionsterm in vereinfachter Schreiweise an.
++  1. Gib den Funktionsterm als Wurzelfunktion an.
++  1. Bestimme die maximale Definitionsmenge sowie den Wertebereich.
++  1. Zeichne die Funktion mit Hilfe einer Wertetabelle in einem geeigneten Intervall.
++
++ ((((% class="border" style="width:100%" %)
++|={{formula}}x{{/formula}}| | | | | | | | | | | | | | | | | |
  |={{formula}}f(x){{/formula}}||||||||||||||||||
  )))
--(% style="list-style: alphastyle" %)
--1. Gib den Funktionsterm in vereinfachter Schreibweise an.
--1. Gib den Funktionsterm als Wurzelfunktion an.
--1. Zeichne die Funktion mit Hilfe einer Wertetabelle in einem geeigneten Intervall.
--1. Bestimme den maximalen Definitionsbereich sowie den Wertebereich.
++  [[image:Achsenkreuz.svg||width="600px"]]
  {{/aufgabe}}
  {{aufgabe id="Gitterpunkte" afb="III" zeit="20" kompetenzen="K2, K5" tags="problemlösen" quelle="Problemlösegruppe" cc="BY-SA"}}
@@ -124,5 +124,5 @@
 . Erläutere, ob man auf derselben Fläche noch mehr Fußbälle unterbringen könnte. Wenn ja, skizziere eine mögliche Anordnung und gib möglichst genau an, wie viel Prozent mehr Fußbälle das sind.
  {{/aufgabe}}
--{{matrix/}}
++{{seitenreflexion/}}

Arithmagon Lineare Funktionen Formen.svg

Author

...	...	@@ -1,1 +1,0 @@
1		-XWiki.holgerengels

Größe

...	...	@@ -1,1 +1,0 @@
1		-22.8 KB

Inhalt

...	...	@@ -1,1 +1,0 @@
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rhombus_with_lighter_colors.svg

Author

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1		-XWiki.martinrathgeb

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Zuletzt besucht

Zuletzt geändert

unfertig	fertig
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