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Änderungen von Dokument BPE 1 Einheitsübergreifend

Zuletzt geändert von Holger Engels am 2025/01/12 21:23
Von Version 117.1
bearbeitet von Holger Engels
am 2025/01/12 21:23
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 89.1
bearbeitet von Martin Rathgeb
am 2025/01/07 21:41
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

Seiteneigenschaften
Dokument-Autor
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1 -XWiki.holgerengels
1 +XWiki.martinrathgeb
Inhalt
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1 1  {{aufgabe id="Arithmagon Darstellungsformen" afb="II" kompetenzen="K2, K4" tags="problemlösen" quelle="Martin Rathgeb" cc="BY-SA" zeit="8"}}
2 2  (% class="abc" %)
3 3  1. (((Fülle in folgenden Darstellungsformen einer Geraden die Lücken.
4 -[[image:Arithmagon Lineare Funktionen Formen.svg||width="500"]]
4 +(% class="border slim" %)
5 +| |{{formula}}y=\square 3\cdot (x-1)+\square{{/formula}} |
6 +|{{formula}}y=\square \cdot (x-2){{/formula}} |Graph: fallende Gerade in KooSyS ohne Skalierung |{{formula}}y=\square \cdot x+\square{{/formula}}
7 +| |{{formula}}\frac{x}{\square}+\frac{y}{\square}=1{{/formula}} |
8 +
5 5  )))
6 6  1. (((Nenne die Werte der charakteristischen Größen der Geraden:
7 -1. (((
8 -(% class="border" %)
9 -|**Lage der Geraden** |Abschnitt |Schnittpunkt
10 -|y-Achse |{{formula}}b={{/formula}} |{{formula}}S_y(\qquad|\qquad){{/formula}}
11 -|x-Achse |{{formula}}x_0={{/formula}} |{{formula}}S_x(\qquad|\qquad)=N{{/formula}}
11 +1. (((//Lage//.
12 +i. y-Achsenabschnitt {{formula}}b{{/formula}} mit y-Achsenschnittpunkt {{formula}}S_y{{/formula}}
13 +ii. x-Achsenabschnitt {{formula}}x_0{{/formula}} mit x-Achsenschnittpunkt {{formula}}S_x=N{{/formula}}
12 12  )))
13 -1. (((
14 -(% class="border" %)
15 -|**Kovariation des linearen Zusammenhangs** | Parameterwert bzw. Beschreibung
16 -|Monotonie |
17 -|Steigung |{{formula}}m=\hspace{1cm}{{/formula}}
18 -|Krümmung |{{formula}}\qquad{{/formula}}
15 +1. (((//Kovariation//.
16 +i. Steigung {{formula}}m{{/formula}}
17 +ii. Krümmung
19 19  )))
20 20  )))
21 21  {{/aufgabe}}
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23 23  {{aufgabe id="Formen von Geradengleichungen" afb="II" kompetenzen="K2, K4" quelle="Martin Rathgeb" cc="BY-SA" zeit="12"}}
24 24  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.
25 25  (% class="border slim" %)
26 -|Hauptform |{{formula}}y=m\cdot x+b{{/formula}}|(Spezialfall der PSF {{formula}}x_P=0{{/formula}})
27 -|Punkt-Steigungs-Form (PSF)|{{formula}}y=m\cdot (x-x_P)+y_P{{/formula}}|
28 -|Produktform |{{formula}}y=m \cdot (x-x_0){{/formula}}|(Spezialfall der PSF {{formula}}y_P=0{{/formula}})
29 -|Achsenabschnittsform |{{formula}}\frac{x}{x_0}+\frac{y}{y_0}=1{{/formula}}|(hier: normiert)
30 -|Allgemeine Form |{{formula}}A x + B y + C = 0{{/formula}}|(hier: nicht normiert, aber {{formula}}=0{{/formula}})
25 +|Hauptform |{{formula}}y=m\cdot x+b{{/formula}}
26 +|Punkt-Steigungs-Form |{{formula}}y=m\cdot (x-x_P)+y_P{{/formula}}
27 +|Produktform |{{formula}}y=m \cdot (x-x_0){{/formula}}
28 +|Achsenabschnittsform |{{formula}}\frac{x}{x_0}+\frac{y}{y_0}=1{{/formula}}
29 +|Allgemeine Form |{{formula}}\alpha \cdot x + \beta \cdot y + \gamma = 0{{/formula}}
31 31  
32 32  (% class="abc" %)
33 33  1. (((Bestimme für jede Gleichungsform {{formula}}\ldots{{/formula}}
34 34  1. {{formula}}\ldots{{/formula}}, ob (und ggf. wie) sich die beiden //Winkelhalbierenden// (besondere Geraden) darstellen lassen.
35 35  1. {{formula}}\ldots{{/formula}}, ob (und ggf. wie) sich die //Parallelen zu den Koordinatenachsen// (Typen besonderer Geraden) darstellen lassen.
36 -1. {{formula}}\ldots{{/formula}}, welche charakteristischen Größen der Geraden sich direkt ablesen lassen; siehe hierzu das vorausgegangene Arithmagon.
35 +1. {{formula}}\ldots{{/formula}}, welche charakteristischen Größen der Geraden sich direkt ablesen lassen; vgl. dazu vorausgegangenes Arithmagon.
37 37  
38 38  )))
39 39  1. (((Erläutere, inwiefern {{formula}}\ldots{{/formula}}
Arithmagon Lineare Funktionen Formen.svg
Author
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1 -XWiki.holgerengels
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Author
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1 -XWiki.martinrathgeb
Größe
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1 -15.8 KB
Inhalt
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