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Zuletzt geändert von Holger Engels am 2025/03/13 07:51
Von Version 111.4
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Auf Version 90.2
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22 22  e^y = x --> y = ln(x)
23 23  
24 24  {{aufgabe id="Gleichungen aufstellen I" afb="II" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe, Martina Wagner" cc="BY-SA" zeit="5"}}
25 -Nenne jeweils eine passende Gleichung:
26 -
27 -Die Gleichung kann ich nach x auflösen, indem ich{{formula}} \ldots {{/formula}}
25 +Nenne eine passende Gleichung. Die Gleichung kann ich nach x auflösen, indem ich {{formula}} \ldots {{/formula}}
28 28  (% class="abc" %)
29 29  1. {{formula}} \ldots {{/formula}} die Terme auf beiden Seiten durch 5 dividiere und damit die Lösung {{formula}} x = \frac{2}{5} {{/formula}} erhalte.
30 30  1. {{formula}} \ldots {{/formula}} von beiden Termen die 5-te Wurzel ziehe und damit die Lösung {{formula}} x = \sqrt[5]{2} {{/formula}} erhalte.
... ... @@ -37,18 +37,7 @@
37 37  {{/aufgabe}}
38 38  
39 39  {{aufgabe id="Darstellungen zuordnen" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
40 -Ordne zu:
41 -(% class="border slim " %)
42 -|Implizite Gleichungen|Explizite Gleichungen|Wertetabellen|Schaubilder
43 -|{{formula}} x^3 = 8 {{/formula}}|{{formula}} x = \sqrt[3]{8} {{/formula}}|(((
44 -|x|0|1|2|3
45 -|y|1|2|4|8
46 -)))|[[image:2^xund8.svg||width="200px"]]
47 -|{{formula}} 2^x = 8 {{/formula}}|{{formula}} x = \log_{2}(8) {{/formula}} |(((
48 -|x|0|1|2|3
49 -|y|0|1|8|27
50 -)))|[[image:x^3und8.svg||width="200px"]]
51 -
38 +Ordne zu!
52 52  (% class="abc" %)
53 53  1. (((Gleichungen (implizite und explizite):
54 54  1. {{formula}} x^3 = 8 {{/formula}}
... ... @@ -67,8 +67,8 @@
67 67  |y|0|1|8|27
68 68  )))
69 69  1. zwei Graphen
70 -[[image:2^xund8.svg||width="200px"]]
71 -[[image:x^3und8.svg||width="200px"]]
57 +[[image:8und2^x.svg||width="200px"]]
58 +[[image:x^3 und 8.svg||width="200px"]]
72 72  {{/aufgabe}}
73 73  
74 74  {{aufgabe id="Logarithmen auswerten" afb="II" kompetenzen="K4,K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="10"}}
... ... @@ -77,23 +77,23 @@
77 77  [[image:Logarithmus_neu.svg||width="600px"]]
78 78  
79 79  (% class="abc" %)
80 -1. {{formula}} \log_{10}(0.1) {{/formula}}
81 -1. {{formula}} \log_{100}(0.1) {{/formula}}
82 -1. {{formula}} \log_{0.1}(0.1) {{/formula}}
67 +1. {{formula}} \log_{10}(10) {{/formula}}
68 +1. {{formula}} \log_{100}(10) {{/formula}}
69 +1. {{formula}} \log_{11}(10) {{/formula}}
83 83  1. {{formula}} \log_{10}(1000) {{/formula}}
84 84  1. {{formula}} \log_{10}(50) {{/formula}}
85 -1. {{formula}} \log_{0.1}(1000) {{/formula}}
72 +1. {{formula}} \log_{11}(1000) {{/formula}}
86 86  1. {{formula}} \log_{10}(1) {{/formula}}
87 87  1. {{formula}} \log_{100}(10) {{/formula}}
88 88  1. {{formula}} \log_{10}(10) {{/formula}}
89 89  {{/aufgabe}}
90 90  
91 -{{aufgabe id="Exponentialgleichungen lösen (graphisch versus rechnerisch)" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
78 +{{aufgabe id="Exponentialgleichungen lösen (graphisch vs rechnerisch)" afb="I" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="5"}}
92 92  (% class="abc" %)
93 93  Ermittle die Lösung der Gleichung {{formula}} 2^x = 5 {{/formula}} graphisch und rechnerisch.
94 94  {{/aufgabe}}
95 95  
96 -{{aufgabe id="Exponentialgleichungen Lösbarkeit (graphisch versus rechnerisch)" afb="I" kompetenzen="K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="6"}}
83 +{{aufgabe id="Exponentialgleichungen Lösbarkeit (graphisch vs rechnerisch)" afb="I" kompetenzen="K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="6"}}
97 97  (% class="abc" %)
98 98  Gegeben sind die beiden Gleichungen {{formula}} x^2 = a {{/formula}} und {{formula}} 2^x = a {{/formula}} für {{formula}} a \in \mathbb{R} {{/formula}}. Untersuche ihre Lösbarkeit in Abhängigkeit von {{formula}} a {{/formula}}.
99 99  {{formula}} c = a^b\:; \qquad c = \sqrt[a]{b}\:; \qquad c = \log_a(b)\:. {{/formula}}
... ... @@ -100,15 +100,15 @@
100 100  {{/aufgabe}}
101 101  
102 102  
103 -{{aufgabe id="Gleichungstypen einstudieren" afb="II" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe, Martina Wagner" cc="BY-SA" zeit="20"}}
90 +{{aufgabe id="Gleichungstypen einstudieren" afb="II" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe, Martina Wagner" cc="BY-SA" zeit="5"}}
104 104  Bestimme die Lösung der folgenden Gleichungen:
105 105  
106 106  (% class="border slim " %)
107 -|Typ 1 Umkehroperationen|Typ 2 Ausklammern|Typ 3 Substitution
108 -|{{formula}}x^2 = 2{{/formula}}|{{formula}}x^2-2x = 0{{/formula}}|{{formula}}x^4-40x^2+144 = 0{{/formula}}
109 -|{{formula}}x^4 = e{{/formula}}|{{formula}}2x^e = x^{2e}{{/formula}}|{{formula}}x^{2x}+x^e+1 = 0{{/formula}}
110 -|{{formula}}e^x = e{{/formula}}|{{formula}}2e^x = e^{2x}{{/formula}}|{{formula}}10^{6x}-2\cdot 10^{3x}+1 = 0{{/formula}}
111 -|{{formula}}3e^x = \frac{1}{2}e^{-x}{{/formula}}|{{formula}}x\cdot 3^x+4\cdot 3^x = 0{{/formula}}|{{formula}}3e^x-1 = \frac{1}{3}e^{-x}{{/formula}}
94 +|{{formula}}Typ 1 Umkehroperationen {{/formula}}|Typ 2 Ausklammern|Typ 3 Substitution
95 +|{{formula}}Typ 2 Ausklammern {{/formula}}|2|1
96 +|{{formula}}f-(x){{/formula}}|0|0
97 +|{{formula}}f_3(x){{/formula}}|2|2
98 +|{{formula}}f_4(x){{/formula}}|2|1
112 112  {{/aufgabe}}
113 113  
114 114  Nenne eine passende Gleichung. Die Gleichung kann ich nach x auflösen, indem ich {{formula}} \ldots {{/formula}}
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