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Zuletzt geändert von Holger Engels am 2025/03/13 07:51
Von Version 123.4
bearbeitet von Holger Engels
am 2025/03/10 15:12
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Auf Version 129.2
bearbeitet von Holger Engels
am 2025/03/12 20:50
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Zusammenfassung

Details

Seiteneigenschaften
Inhalt
... ... @@ -18,10 +18,10 @@
18 18  - Näherungslösungen
19 19  
20 20  Gleichungen:
21 -x+y = e --> y = e - x
22 -x*y = e --> y = e / x
23 -e^y = x --> y = {{{ln(x)}}}
24 -{{(lehrende}}
21 +{{formula}}x\pm y = e \Rightarrow y = e \mp x{{/formula}}
22 +{{formula}}x*y = e \Rightarrow y = e / x{{/formula}}
23 +{{formula}}e^y = x \Rightarrow y = \ln(x){{/formula}}
24 +{{/lehrende}}
25 25  
26 26  {{aufgabe id="Gleichungen aufstellen I" afb="II" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe, Martina Wagner" cc="BY-SA" zeit="5"}}
27 27  Nenne jeweils eine passende Gleichung:
... ... @@ -40,7 +40,7 @@
40 40  
41 41  {{aufgabe id="Darstellungen zuordnen" afb="II" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe" cc="BY-SA" zeit="6"}}
42 42  Ordne zu:
43 -(% class="border slim " %)
43 +(% class="border slim" %)
44 44  |Implizite Gleichungen|Explizite Gleichungen|Wertetabellen|Schaubilder
45 45  |{{formula}} x^{-3} = 8 {{/formula}}|{{formula}} x = \sqrt[3]{8} {{/formula}}|(((
46 46  |x|0|1|2|3
... ... @@ -52,11 +52,11 @@
52 52  )))|[[image:2^-xund8.svg||width="200px"]]
53 53  |{{formula}} 2^{-x} = 8 {{/formula}}|{{formula}} x = \log_{2}(8) {{/formula}} |(((
54 54  |x|0|1|2|3
55 -|y|1|\frac{1}{2}|\frac{1}{4}|\frac{1}{8}
55 +|y|1|{{formula}}\frac{1}{2}{{/formula}}|{{formula}}\frac{1}{4}{{/formula}}|{{formula}}\frac{1}{8}{{/formula}}
56 56  )))|[[image:x^3und8.svg||width="200px"]]
57 57  |{{formula}} 2^x = 8 {{/formula}}|{{formula}} x = x = \frac{1}{\sqrt[3]{8}} {{/formula}} |(((
58 58  |x|0|1|2|3
59 -|y|n.d.|1|\frac{1}{8}|\frac{1}{27}
59 +|y|n.d.|1|{{formula}}\frac{1}{8}{{/formula}}|{{formula}}\frac{1}{27}{{/formula}}
60 60  )))|[[image:x^-3und8.svg||width="200px"]]
61 61  {{/aufgabe}}
62 62  
... ... @@ -83,8 +83,148 @@
83 83  {{/aufgabe}}
84 84  
85 85  {{aufgabe id="Gleichungen gemeinsamer Form" afb="I" kompetenzen="K5" quelle="Martin Rathgeb" cc="BY-SA" zeit="6"}}
86 -(% class="abc" %)
87 -Aufgabe als Dokument im Anhang ‚unten‘.
86 +(%class="abc"%)
87 +1. (((
88 +(%class="border slim"%)
89 +|(%align="center" width="160"%){{formula}}x^{-2}-4x^{-1}+3=0{{/formula}}
90 +
91 +{{formula}}u:=\_\_\_{{/formula}}
92 +⬊|(%align="center" width="160"%){{formula}}x^{2e}-4x^e+3=0{{/formula}}
93 +
94 +{{formula}}u:=\_\_\_{{/formula}}
95 +🠗|(%align="center" width="160"%){{formula}}e^{2x}-4e^x+3=0{{/formula}}
96 +
97 +{{formula}}u:=\_\_\_{{/formula}}
98 +⬋
99 +||(%align="center"%){{formula}}u^2-4u+3=0{{/formula}}
100 +(((
101 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
102 +|
103 +
104 +
105 +)))
106 +
107 +{{formula}}u_1=\_\_\_\quad;\quad u_2=\_\_\_{{/formula}}|
108 +|(%align="center"%)(((⬋
109 +{{formula}}\_\_\_:=u{{/formula}}
110 +(((
111 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
112 +|
113 +
114 +
115 +)))
116 +)))|(%align="center"%)(((🠗
117 +{{formula}}\_\_\_:=u{{/formula}}
118 +(((
119 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
120 +|
121 +
122 +
123 +)))
124 +)))|(%align="center"%)(((⬊
125 +{{formula}}\_\_\_:=u{{/formula}}
126 +(((
127 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
128 +|
129 +
130 +
131 +)))
132 +)))
133 +)))
134 +1. (((
135 +(%class="border slim"%)
136 +|(%align="center" width="160"%){{formula}}x^{-2}-3x^{-1}=0{{/formula}}
137 +
138 +{{formula}}u:=\_\_\_{{/formula}}
139 +⬊|(%align="center" width="160"%){{formula}}x^{2e}-3x^e=0{{/formula}}
140 +
141 +{{formula}}u:=\_\_\_{{/formula}}
142 +🠗|(%align="center" width="160"%){{formula}}e^{2x}-3e^x=0{{/formula}}
143 +
144 +{{formula}}u:=\_\_\_{{/formula}}
145 +⬋
146 +||(%align="center"%){{formula}}u^2-3u=0{{/formula}}
147 +(((
148 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
149 +|
150 +
151 +
152 +)))
153 +
154 +{{formula}}u_1=\_\_\_\quad;\quad u_2=\_\_\_{{/formula}}|
155 +|(%align="center"%)(((⬋
156 +{{formula}}\_\_\_:=u{{/formula}}
157 +(((
158 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
159 +|
160 +
161 +
162 +)))
163 +)))|(%align="center"%)(((🠗
164 +{{formula}}\_\_\_:=u{{/formula}}
165 +(((
166 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
167 +|
168 +
169 +
170 +)))
171 +)))|(%align="center"%)(((⬊
172 +{{formula}}\_\_\_:=u{{/formula}}
173 +(((
174 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
175 +|
176 +
177 +
178 +)))
179 +)))
180 +)))
181 +1. (((
182 +(%class="border slim"%)
183 +|(%align="center" width="160"%){{formula}}x^{-2}-2x^{-1}+3=0{{/formula}}
184 +
185 +{{formula}}u:=\_\_\_{{/formula}}
186 +⬊|(%align="center" width="160"%){{formula}}x^{2e}-2x^e+3=0{{/formula}}
187 +
188 +{{formula}}u:=\_\_\_{{/formula}}
189 +🠗|(%align="center" width="160"%){{formula}}e^{2x}-2e^x+3=0{{/formula}}
190 +
191 +{{formula}}u:=\_\_\_{{/formula}}
192 +⬋
193 +||(%align="center"%){{formula}}u^2-2u+3=0{{/formula}}
194 +(((
195 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
196 +|
197 +
198 +
199 +)))
200 +
201 +{{formula}}u_1=\_\_\_\quad;\quad u_2=\_\_\_{{/formula}}|
202 +|(%align="center"%)(((⬋
203 +{{formula}}\_\_\_:=u{{/formula}}
204 +(((
205 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
206 +|
207 +
208 +
209 +)))
210 +)))|(%align="center"%)(((🠗
211 +{{formula}}\_\_\_:=u{{/formula}}
212 +(((
213 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
214 +|
215 +
216 +
217 +)))
218 +)))|(%align="center"%)(((⬊
219 +{{formula}}\_\_\_:=u{{/formula}}
220 +(((
221 +(%class="border slim" style="width: 100%; margin-bottom: 0px"%)
222 +|
223 +
224 +
225 +)))
226 +)))
227 +)))
88 88  {{/aufgabe}}
89 89  
90 90  {{aufgabe id="Gleichungstypen einstudieren" afb="II" kompetenzen="K5" quelle="Elke Hallmann, Martin Rathgeb, Dirk Tebbe, Martina Wagner" cc="BY-SA" zeit="20"}}
... ... @@ -91,7 +91,7 @@
91 91  Bestimme die Lösung der folgenden Gleichungen:
92 92  
93 93  (% class="border slim " %)
94 -|Typ 1 Umkehroperationen|Typ 2 Ausklammern|Typ 3 Substitution
234 +|Typ 1 (Umkehroperationen)|Typ 2 (Ausklammern)|Typ 3 (Substitution)
95 95  |{{formula}}x^2 = 2{{/formula}}|{{formula}}x^2-2x = 0{{/formula}}|{{formula}}x^4-40x^2+144 = 0{{/formula}}
96 96  |{{formula}}x^4 = e{{/formula}}|{{formula}}2x^e = x^{2e}{{/formula}}|{{formula}}x^{2x}+x^e+1 = 0{{/formula}}
97 97  |{{formula}}e^x = e{{/formula}}|{{formula}}2e^x = e^{2x}{{/formula}}|{{formula}}10^{6x}-2\cdot 10^{3x}+1 = 0{{/formula}}