Änderungen von Dokument BPE 3.1 Eigenschaften und Formen
Zuletzt geändert von Holger Engels am 2025/04/09 13:57
Von Version 93.1
bearbeitet von Holger Engels
am 2024/12/17 18:04
am 2024/12/17 18:04
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Auf Version 121.1
bearbeitet von Holger Engels
am 2024/12/18 14:18
am 2024/12/18 14:18
Änderungskommentar:
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Zusammenfassung
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Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)
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Anhänge (2 geändert, 9 hinzugefügt, 2 gelöscht)
- Polynome_zuordnen-Grad_drei.ggb
- Polynome_zuordnen-Grad_vier.ggb
- Polynome_zuordnen-Grad_vier.png
- geogebra_polynome_dritten_Grades.png
- 1-fach.svg
- 2-fach.svg
- 3-fach.svg
- 4-fach.svg
- 5-fach.svg
- Arithmagon Quadratische Formen.svg
- Polynome_zuordnen-Grad_drei.svg
- Polynome_zuordnen-Grad_vier.svg
- Vielfachheiten.ggb
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... ... @@ -2,15 +2,36 @@ 2 2 3 3 [[Kompetenzen.K5]] Ich kenne die allgemeine Form der Polynomfunktion 4 4 [[Kompetenzen.K4]] Ich kenne die Produktform der Polynomfunktion 5 -[[Kompetenzen.K3]] [[Kompetenzen.K4]] Ich kann die für den Anwendungsfall geeignete Darstellungsform wählen 6 -[[Kompetenzen.K1]] [[Kompetenzen.K4]] Ich kann die Wahl der Darstellungsform im Anwendungskontext begründen 5 +[[Kompetenzen.K4]] Ich kenne die Scheitelform der quadratischen Funktion [[→ BPE 2.2>>BPE_2_2]] 6 +[[Kompetenzen.K4]] Ich kann Polynomfunktionen mithilfe unterschiedlicher Darstellungsformen beschreiben 7 +[[Kompetenzen.K1]] [[Kompetenzen.K6]] Ich kann die Wahl der Form im mathematischen Kontext begründen 8 +[[Kompetenzen.K1]] [[Kompetenzen.K3]] [[Kompetenzen.K6]] Ich kann die Wahl der Form im anwendungsorientierten Kontext begründen [[→ BPE 3.5>>BPE_3_5]] 7 7 10 +Wiederholen (qF): Darstellungsformen von quadratischen Funktionen (SF, PF, HF) 11 +Wiederholen (qF): Eingehen auf verschiedene Eigenschaften (Vorteile, Nachteile) der DF 12 +Kennen: algebraische DF von PF, HF von Polynomfunktionen 13 +Input: Vorgegebene Schaubilder vergleichen (Gemeinsamkeiten, Unterschiede) 14 +"Beschreiben": Form 'fühlen' (Globalverhalten, Lokalverhalten); vgl. Buchstaben-Formen (N, W) Nulltellentypen (einfach vs mehrfach (gerade vs ungerade)) 15 + 8 8 {{lernende}} 9 9 [[Nullstellen und Vielfachheiten interaktiv>>https://kmap.eu/app/browser/Mathematik/Ganzrationale%20Funktionen/Produktform#erkunden]] 10 10 {{/lernende}} 11 11 12 -{{aufgabe id="Schaubilder zuordnen Teil 1" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" zeit="5"}} 13 -[[image:geogebra_polynome_dritten_Grades.png||width=600 style=float:right]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl. 20 +{{aufgabe id="Vielfachheiten von Nullstellen" afb="I" kompetenzen="K4" quelle="Holger Engels" cc="by-sa" zeit="4"}} 21 +Ordne zu und schreibe dahinter jeweils "schneidet", "berührt" "schmiegt sich an", wobei //Anschmiegen// und //Schneiden// miteinander vereinbar sind, //Berühren// und //Schneiden// jedoch nicht. Siehe [[Vielfachheiten von Schnittstellen>>Glossar.WebHome||anchor=HVielfachheitenvonSchnittstellen]]. 22 +|[[image:3-fach.svg||width=100]]| |1-fach | 23 +|[[image:4-fach.svg||width=100]]| |2-fach | 24 +|[[image:2-fach.svg||width=100]]| |3-fach | 25 +|[[image:5-fach.svg||width=100]]| |4-fach | 26 +|[[image:1-fach.svg||width=100]]| |5-fach | 27 +{{/aufgabe}} 28 + 29 +{{aufgabe id="Arithmagon Quadratische Formen" afb="I" kompetenzen="K4" quelle="Martina Wagner" cc="by-sa" zeit="5"}} 30 +[[image:Arithmagon Quadratische Formen.svg||width=500 style=float:left]] 31 +{{/aufgabe}} 32 + 33 +{{aufgabe id="Schaubilder zuordnen Teil 1" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="5"}} 34 +[[image:Polynome_zuordnen-Grad_drei.svg||width=500 style=float:right]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl. 14 14 (% style="list-style: alphastyle" %) 15 15 1. {{formula}}f_1(x)=x^3{{/formula}} 16 16 1. {{formula}}f_2(x)=-x^2\cdot(x-3){{/formula}} ... ... @@ -19,11 +19,11 @@ 19 19 1. {{formula}}f_5(x)=-x^3-2\,x^2+2{{/formula}} 20 20 {{/aufgabe}} 21 21 22 -{{aufgabe id="Schaubilder zuordnen Teil 2" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" zeit="5"}} 23 -[[image:Polynome_zuordnen-Grad_vier. png||width=600 style="float:right"]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl.43 +{{aufgabe id="Schaubilder zuordnen Teil 2" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="5"}} 44 +[[image:Polynome_zuordnen-Grad_vier.svg||width=500 style="float:right"]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl. 24 24 (% style="list-style: alphastyle" %) 25 25 1. {{formula}}f_1(x)=-0{,}25\,x^4{{/formula}} 26 -1. {{formula}}f_2(x)=-0{,}5\,x^4-1{,}5\,x^3-1{,}5\,x^2 -1{{/formula}}47 +1. {{formula}}f_2(x)=-0{,}5\,x^4-1{,}5\,x^3-1{,}5\,x^2+1{{/formula}} 27 27 1. {{formula}}f_3(x)=-x^4{{/formula}} 28 28 1. {{formula}}f_4(x)=-x^4-x^3+2x^2+2{{/formula}} 29 29 1. {{formula}}f_5(x)=-0{,}3\cdot (x+2)^2\cdot(x-2)^2+4{{/formula}} ... ... @@ -34,14 +34,7 @@ 34 34 [[image:Graphen Produktform.png||width=600]] 35 35 {{/aufgabe}} 36 36 37 -{{aufgabe id="Skizzieren" afb="I" kompetenzen="K4" quelle="Juliane Maier" cc="BY-SA"}} 38 -Gegeben ist die Funktion {{formula}}f{{/formula}} mit {{formula}}D=\mathbb{R}{{/formula}}. Skizziere den Funktionsgraphen. 39 -(% class="abc" %) 40 -1. {{formula}}f(x)=(x-2)^3{{/formula}} 41 -1. {{formula}}f(x)=x^4-x^2{{/formula}} 42 -{{/aufgabe}} 43 - 44 -{{aufgabe id="Immer, manchmal, nie" afb="III" kompetenzen="K1,K5" quelle="Niklas Wunder, Katharina Schneider" zeit="12"}} 58 +{{aufgabe id="Immer, manchmal, nie" afb="III" kompetenzen="K1,K5" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="12"}} 45 45 Beurteile, ob die folgenden Aussagen immer, nie oder manchmal unter bestimmten Bedingungen zutreffen. Begründe deine Entscheidung. 46 46 (% style="list-style: alphastyle" %) 47 47 1. Der Graph von {{formula}}f{{/formula}} mit {{formula}}f(x)=-3\cdot x^n {{/formula}} verläuft für ein gerades n von links unten nach rechts unten. ... ... @@ -52,8 +52,16 @@ 52 52 1. Durch die beiden Punkte P(-2|1) und Q(2|2) verläuft kein Graph einer Funktion vierten Grades. 53 53 {{/aufgabe}} 54 54 69 +{{aufgabe id="Vieta" afb="II" kompetenzen="K2,K5" quelle="Martin Rathgeb, Martina Wagner" cc="BY-SA" zeit="10"}} 70 +Ermittle die fehlenden Zahlen bzw. Terme. 71 +(% class="abc" %) 72 +1. {{formula}}x^2+\square x + \square=(x-5)(x+7){{/formula}} 73 +1. {{formula}}x^2+\square x - 12=(x-4)(x-\square){{/formula}} 74 +1. {{formula}}x^2-12 x + \square=(x-4)(x-\square){{/formula}} 75 +1. {{formula}}x^2+\square x + \square=(x-a)(x-b){{/formula}} 76 +{{/aufgabe}} 55 55 56 -{{aufgabe id="Darstellungsformen umwandeln" afb="II" kompetenzen="K5" quelle="Niklas Wunder, Katharina Schneider" zeit="15"}} 78 +{{aufgabe id="Darstellungsformen umwandeln" afb="II" kompetenzen="K5" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="15"}} 57 57 Wandle in die entsprechend andere Darstellungsform um (Hauptform bzw. Produktform). 58 58 (% style="list-style: alphastyle" %) 59 59 1. {{formula}}f(x)=-\frac{1}{16}\cdot (x-2)^2\cdot (x-8){{/formula}} ... ... @@ -64,12 +64,12 @@ 64 64 Hinweis: Die Funktion //f// besitzt nur die Nullstellen {{formula}} x_1 =-2, x_2=1 {{/formula}} und {{formula}} x_3 =3 {{/formula}}. 65 65 {{/aufgabe}} 66 66 67 -{{aufgabe id="Parabelmaschine" afb="II" kompetenzen="K2, K5" tags="problemlösen" quelle="Simon Oswald" cc="BY-SA" zeit="20"}} 89 +{{aufgabe id="Parabelmaschine" afb="II" kompetenzen="K2, K5" tags="problemlösen" quelle="Simon Oswald" cc="BY-SA" cc="by-sa" zeit="20"}} 68 68 [[image:Parabelmaschine.PNG||width="240" style="float: right"]] 69 69 Denke dir zwei Zahlen, eine positiv, eine negativ. 70 70 Wenn du diese Zahlen quadrierst, erhältst du zwei Punkte auf der Normalparabel. 71 71 72 -Ermitt eln Sie, wo die Verbindungslinie dieser zwei Punkte die y-Achse schneidet!94 +Ermittle, wo die Verbindungslinie dieser zwei Punkte die y-Achse schneidet! 73 73 74 74 {{lehrende}} 75 75 **Variante :** Offene Aufgabe für den Unterricht & für die Klassenarbeit
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... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
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... ... @@ -1,0 +1,1 @@ 1 +XWiki.holgerengels - Größe
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