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lehrkraefte:blc:miniaufgaben [2020/02/16 20:41]
Ivo Blöchliger [17. Februar 2020 bis 21. Februar 2020] |
lehrkraefte:blc:miniaufgaben [2024/03/20 14:51]
Ivo Blöchliger [25. März 2024 bis 29. März 2024] |
| {{backlinks>.}} | ~~NOTOC~~ |
| | |
| ===== PDF Version ===== | |
| Für faule Äpfel unter den Geräten gibt es hier neu eine {{https://fginfo.ksbg.ch/~ivo/miniaufgaben.pdf|PDF-Version}} | |
| | |
| | |
| ===== Miniaufgaben ===== | ===== Miniaufgaben ===== |
| * Auf jede Lektion (ausser Prüfungslektionen) ist eine Miniaufgabe vorzubereiten. Am Anfang der Lektion wird eine Münze geworfen. Damit der Münzwurf gültig ist, muss sich die Münze mindestens 10 mal in der Luft drehen. Zeigt die Münze **Zahl**, wird eine Aufgabe in Form eines Kurztests geprüft. | * Auf jede Lektion (ausser Prüfungslektionen) ist eine Miniaufgabe vorzubereiten. Am Anfang der Lektion wird ein Würfel geworfen. Zeigt der Würfel eine Vier, Fünf oder Sechs, wird eine Aufgabe in Form eines Kurztests geprüft. |
| * Jeder Schüler hat 7 Joker für das gesamte 4. Schuljahr. Bei Meldung per e-mail oder Threema (HX3WS583) bis spätestens 12 h vor Lektionsbeginn wird der Schüler vom eventuellen Kurztest ersatzlos dispensiert. Zeigt die Münze Kopf, ist der Joker aber auch aufgebraucht! | * Jeder Schüler hat 5 Joker für das ganze Jahr. Diese werden über die [[lehrkraefte:blc:informatik:glf22:crypto:joker-chain|JokerChain]] verwaltet und können bis 23:59 am Vortag eingelöst werden. Bei Einsatz eines Jokers wird der Schüler vom eventuellen Kurztest ersatzlos dispensiert. Zeigt der Würfel 1-3, ist der Joker aber auch aufgebraucht! |
| | //Beachten Sie, dass via andere Kanäle keine Joker mehr eingelöst werden können. Bei Problemen werde ich Sie aber nach Möglichkeit unterstützen (mit genügend zeitlichem Vorlauf).// |
| * Der Minikurztest ist auf mitgebrachtem **A4-Papier im Hochformat** zu lösen. Ausgefranste Ränder, zerknittertes Papier, abgerissene Ecken und Übergrössen führen zu **Abzug**. | * Der Minikurztest ist auf mitgebrachtem **A4-Papier im Hochformat** zu lösen. Ausgefranste Ränder, zerknittertes Papier, abgerissene Ecken und Übergrössen führen zu **Abzug**. |
| * Der Name ist **oben rechts** zu notieren. | * Der Name ist **oben rechts** zu notieren. |
| * Die Prüfungsblätter können mehrmals verwendet werden, die Aufgaben sind aber sauber abzugrenzen. | * Die Prüfungsblätter können mehrmals verwendet werden, die Aufgaben sind aber sauber abzugrenzen. |
| | * Schreiben Sie nicht mit Rot oder einer schlecht lesbaren Farbe, wie z.B. gelb. (Ja, ja, jede Regel hat eine Geschichte). |
| | * Der Durchschnitt aller Miniaufgaben zählt als eine volle 6. Prüfungsnote. |
| |
| | <PRELOAD> |
| | miniaufgabe.js |
| | </PRELOAD> |
| |
| <JS> | ==== 18. März 2024 bis 22. März 2024 ==== |
| function generate(jQuery, idex, idsol, ex, sep="<br>", sep2="<br>", numex=3) { | === Dienstag 19. März 2024 === |
| var randperm=function(n) { | Maturaarbeitspräsentationen. Unterrichtsausfall |
| var a = []; | === Mittwoch 20. März 2024 === |
| for (var i=0; i<n; i++) { a[i]=i; } | Schreiben Sie den Term einmal als Binärbaum und einmal in Computer-Notation.<JS>miniAufgabe("#exotermanalyse1","#soltermanalyse1", |
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| var j = Math.floor(Math.random()*(n-i))+i; | " <hr> ", " <hr> "); |
| if (j>i) { | |
| var h = a[j]; | |
| a[j] = a[i]; | |
| a[i] = h; | |
| } | |
| } | |
| return a | |
| } | |
| var selec=randperm(ex.length); | |
| if (numex<1){ | |
| numex = ex.length; | |
| } | |
| for (var i=0; i<numex; i++) { | |
| jQuery(idex).append((i+1)+". "+ex[selec[i]][0]+sep); | |
| jQuery(idsol).append((i+1)+". "+ex[selec[i]][1]+sep2); | |
| } | |
| MathJax.Hub.Queue(["Typeset",MathJax.Hub,idex]); | |
| MathJax.Hub.Queue(["Typeset",MathJax.Hub,idsol]); | |
| } | |
| </JS> | |
| | |
| | |
| | |
| | |
| ==== 10. Februar 2020 bis 14. Februar 2020 ==== | |
| === Montag 10. Februar 2020 === | |
| | |
| Ein Lottospiel kostet für einen Tipp 1.-. Berechnen Sie den Erwartungswert aus der Sicht des Spielers.<JS>jQuery(function() {generate(jQuery, "#exoerwartungswertlotto","#solerwartungswertlotto", | |
| [["Es werden 4 aus 18 Zahlen gezogen. Die Quoten sind: 4 Richtige: 1000.- und 3 Richtige: 10.-.", "$P(4 \\text{ Richtige}) = \\frac{{4 \\choose 4} \\cdot {14 \\choose 0}}{{18 \\choose 4}} = \\frac{1\\cdot1}{3060} = \\frac{1}{3060}$<br>\n$P(3 \\text{ Richtige}) = \\frac{{4 \\choose 3} \\cdot {14 \\choose 1}}{{18 \\choose 4}} = \\frac{4\\cdot14}{3060} = \\frac{14}{765}$<br>$P(\\text{Kein Gewinn}) = 1 - P(4 \\text{ Richtige})-P(3 \\text{ Richtige}) = 1-\\frac{1}{3060}-\\frac{14}{765} = \\frac{1001}{1020}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{1001}{1020}+9 \\cdot \\frac{14}{765}+999 \\cdot \\frac{1}{3060} = -\\frac{25}{51} \\approx -0.49$."], ["Es werden 4 aus 19 Zahlen gezogen. Die Quoten sind: 4 Richtige: 1000.- und 3 Richtige: 10.-.", "$P(4 \\text{ Richtige}) = \\frac{{4 \\choose 4} \\cdot {15 \\choose 0}}{{19 \\choose 4}} = \\frac{1\\cdot1}{3876} = \\frac{1}{3876}$<br>\n$P(3 \\text{ Richtige}) = \\frac{{4 \\choose 3} \\cdot {15 \\choose 1}}{{19 \\choose 4}} = \\frac{4\\cdot15}{3876} = \\frac{5}{323}$<br>$P(\\text{Kein Gewinn}) = 1 - P(4 \\text{ Richtige})-P(3 \\text{ Richtige}) = 1-\\frac{1}{3876}-\\frac{5}{323} = \\frac{3815}{3876}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{3815}{3876}+9 \\cdot \\frac{5}{323}+999 \\cdot \\frac{1}{3876} = -\\frac{569}{969} \\approx -0.59$."], ["Es werden 4 aus 20 Zahlen gezogen. Die Quoten sind: 4 Richtige: 1000.- und 3 Richtige: 10.-.", "$P(4 \\text{ Richtige}) = \\frac{{4 \\choose 4} \\cdot {16 \\choose 0}}{{20 \\choose 4}} = \\frac{1\\cdot1}{4845} = \\frac{1}{4845}$<br>\n$P(3 \\text{ Richtige}) = \\frac{{4 \\choose 3} \\cdot {16 \\choose 1}}{{20 \\choose 4}} = \\frac{4\\cdot16}{4845} = \\frac{64}{4845}$<br>$P(\\text{Kein Gewinn}) = 1 - P(4 \\text{ Richtige})-P(3 \\text{ Richtige}) = 1-\\frac{1}{4845}-\\frac{64}{4845} = \\frac{956}{969}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{956}{969}+9 \\cdot \\frac{64}{4845}+999 \\cdot \\frac{1}{4845} = -\\frac{641}{969} \\approx -0.66$."], ["Es werden 4 aus 21 Zahlen gezogen. Die Quoten sind: 4 Richtige: 1000.- und 3 Richtige: 10.-.", "$P(4 \\text{ Richtige}) = \\frac{{4 \\choose 4} \\cdot {17 \\choose 0}}{{21 \\choose 4}} = \\frac{1\\cdot1}{5985} = \\frac{1}{5985}$<br>\n$P(3 \\text{ Richtige}) = \\frac{{4 \\choose 3} \\cdot {17 \\choose 1}}{{21 \\choose 4}} = \\frac{4\\cdot17}{5985} = \\frac{68}{5985}$<br>$P(\\text{Kein Gewinn}) = 1 - P(4 \\text{ Richtige})-P(3 \\text{ Richtige}) = 1-\\frac{1}{5985}-\\frac{68}{5985} = \\frac{1972}{1995}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{1972}{1995}+9 \\cdot \\frac{68}{5985}+999 \\cdot \\frac{1}{5985} = -\\frac{41}{57} \\approx -0.72$."], ["Es werden 4 aus 22 Zahlen gezogen. Die Quoten sind: 4 Richtige: 1000.- und 3 Richtige: 100.-.", "$P(4 \\text{ Richtige}) = \\frac{{4 \\choose 4} \\cdot {18 \\choose 0}}{{22 \\choose 4}} = \\frac{1\\cdot1}{7315} = \\frac{1}{7315}$<br>\n$P(3 \\text{ Richtige}) = \\frac{{4 \\choose 3} \\cdot {18 \\choose 1}}{{22 \\choose 4}} = \\frac{4\\cdot18}{7315} = \\frac{72}{7315}$<br>$P(\\text{Kein Gewinn}) = 1 - P(4 \\text{ Richtige})-P(3 \\text{ Richtige}) = 1-\\frac{1}{7315}-\\frac{72}{7315} = \\frac{7242}{7315}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{7242}{7315}+99 \\cdot \\frac{72}{7315}+999 \\cdot \\frac{1}{7315} = \\frac{177}{1463} \\approx 0.12$."], ["Es werden 5 aus 18 Zahlen gezogen. Die Quoten sind: 5 Richtige: 1000.- und 4 Richtige: 100.-.", "$P(5 \\text{ Richtige}) = \\frac{{5 \\choose 5} \\cdot {13 \\choose 0}}{{18 \\choose 5}} = \\frac{1\\cdot1}{8568} = \\frac{1}{8568}$<br>\n$P(4 \\text{ Richtige}) = \\frac{{5 \\choose 4} \\cdot {13 \\choose 1}}{{18 \\choose 5}} = \\frac{5\\cdot13}{8568} = \\frac{65}{8568}$<br>$P(\\text{Kein Gewinn}) = 1 - P(5 \\text{ Richtige})-P(4 \\text{ Richtige}) = 1-\\frac{1}{8568}-\\frac{65}{8568} = \\frac{1417}{1428}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{1417}{1428}+99 \\cdot \\frac{65}{8568}+999 \\cdot \\frac{1}{8568} = -\\frac{89}{714} \\approx -0.12$."], ["Es werden 5 aus 19 Zahlen gezogen. Die Quoten sind: 5 Richtige: 10000.- und 4 Richtige: 100.-.", "$P(5 \\text{ Richtige}) = \\frac{{5 \\choose 5} \\cdot {14 \\choose 0}}{{19 \\choose 5}} = \\frac{1\\cdot1}{11628} = \\frac{1}{11628}$<br>\n$P(4 \\text{ Richtige}) = \\frac{{5 \\choose 4} \\cdot {14 \\choose 1}}{{19 \\choose 5}} = \\frac{5\\cdot14}{11628} = \\frac{35}{5814}$<br>$P(\\text{Kein Gewinn}) = 1 - P(5 \\text{ Richtige})-P(4 \\text{ Richtige}) = 1-\\frac{1}{11628}-\\frac{35}{5814} = \\frac{11557}{11628}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{11557}{11628}+99 \\cdot \\frac{35}{5814}+9999 \\cdot \\frac{1}{11628} = \\frac{79}{171} \\approx 0.46$."], ["Es werden 5 aus 20 Zahlen gezogen. Die Quoten sind: 5 Richtige: 10000.- und 4 Richtige: 100.-.", "$P(5 \\text{ Richtige}) = \\frac{{5 \\choose 5} \\cdot {15 \\choose 0}}{{20 \\choose 5}} = \\frac{1\\cdot1}{15504} = \\frac{1}{15504}$<br>\n$P(4 \\text{ Richtige}) = \\frac{{5 \\choose 4} \\cdot {15 \\choose 1}}{{20 \\choose 5}} = \\frac{5\\cdot15}{15504} = \\frac{25}{5168}$<br>$P(\\text{Kein Gewinn}) = 1 - P(5 \\text{ Richtige})-P(4 \\text{ Richtige}) = 1-\\frac{1}{15504}-\\frac{25}{5168} = \\frac{203}{204}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{203}{204}+99 \\cdot \\frac{25}{5168}+9999 \\cdot \\frac{1}{15504} = \\frac{499}{3876} \\approx 0.13$."], ["Es werden 5 aus 21 Zahlen gezogen. Die Quoten sind: 5 Richtige: 10000.- und 4 Richtige: 100.-.", "$P(5 \\text{ Richtige}) = \\frac{{5 \\choose 5} \\cdot {16 \\choose 0}}{{21 \\choose 5}} = \\frac{1\\cdot1}{20349} = \\frac{1}{20349}$<br>\n$P(4 \\text{ Richtige}) = \\frac{{5 \\choose 4} \\cdot {16 \\choose 1}}{{21 \\choose 5}} = \\frac{5\\cdot16}{20349} = \\frac{80}{20349}$<br>$P(\\text{Kein Gewinn}) = 1 - P(5 \\text{ Richtige})-P(4 \\text{ Richtige}) = 1-\\frac{1}{20349}-\\frac{80}{20349} = \\frac{2252}{2261}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{2252}{2261}+99 \\cdot \\frac{80}{20349}+9999 \\cdot \\frac{1}{20349} = -\\frac{261}{2261} \\approx -0.12$."], ["Es werden 5 aus 22 Zahlen gezogen. Die Quoten sind: 5 Richtige: 10000.- und 4 Richtige: 100.-.", "$P(5 \\text{ Richtige}) = \\frac{{5 \\choose 5} \\cdot {17 \\choose 0}}{{22 \\choose 5}} = \\frac{1\\cdot1}{26334} = \\frac{1}{26334}$<br>\n$P(4 \\text{ Richtige}) = \\frac{{5 \\choose 4} \\cdot {17 \\choose 1}}{{22 \\choose 5}} = \\frac{5\\cdot17}{26334} = \\frac{85}{26334}$<br>$P(\\text{Kein Gewinn}) = 1 - P(5 \\text{ Richtige})-P(4 \\text{ Richtige}) = 1-\\frac{1}{26334}-\\frac{85}{26334} = \\frac{13124}{13167}$<br>Sei $X$ die Zufallsvariable, die den Gewinn bzw. Verlust angibt.<br>$E(X) = -1\\cdot \\frac{13124}{13167}+99 \\cdot \\frac{85}{26334}+9999 \\cdot \\frac{1}{26334} = -\\frac{3917}{13167} \\approx -0.30$."]], | |
| " <hr> ", "<hr>");}); | |
| </JS> | </JS> |
| <HTML> | <HTML> |
| <div id="exoerwartungswertlotto"></div> | <div id="exotermanalyse1"></div> |
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| </HTML> | </HTML> |
| <hidden Lösungen> | <hidden Lösungen> |
| | |
| <HTML> | <HTML> |
| <div id="solerwartungswertlotto"></div> | <div id="soltermanalyse1"></div> |
| | <div style='font-size:12px;color:gray;'>ruby termanalyse.rb 1</div> |
| </HTML> | </HTML> |
| | |
| </hidden> | </hidden> |
| |
| | ==== 25. März 2024 bis 29. März 2024 ==== |
| | === Dienstag 26. März 2024 === |
| === Donnerstag 13. Februar 2020 === | Leiten Sie ohne Hilfsmittel ab. Klammern Sie danach gemeinsame Faktoren aus. Weitere Vereinfachungen sind nicht nötig. |
| | <JS>miniAufgabe("#exoprod_ketten_nur_poly","#solprod_ketten_nur_poly", |
| Schreiben Sie folgende Summen aus:<JS>jQuery(function() {generate(jQuery, "#exosummen_ausschreiben","#solsummen_ausschreiben", | [["$\\left(-3x-13\\right)^{25} \\cdot \\left(8x^{4}+7x\\right)^{10}$", "$$\\begin{multline*}\\left(\\left(-3x-13\\right)^{25} \\cdot \\left(8x^{4}+7x\\right)^{10}\\right)' = \\\\\n25\\cdot \\left(-3x-13\\right)^{24}\\cdot \\left(-3)\\right) \\cdot \\left(8x^{4}+7x\\right)^{10} + \\left(-3x-13\\right)^{25} \\cdot 10 \\cdot \\left(8x^{4}+7x\\right)^{9} \\cdot \\left(32x^{3}+7)\\right) = \\\\\n5 \\cdot \\left(-3x-13\\right)^{24} \\cdot \\left(8x^{4}+7x\\right)^{9} \\cdot \\left[ 5 \\cdot \\left(-3\\right)\\cdot\\left(8x^{4}+7x\\right) + 2 \\cdot \\left(-3x-13\\right) \\cdot \\left(32x^{3}+7\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(9x-10\\right)^{20} \\cdot \\left(-3x^{4}-7x\\right)^{25}$", "$$\\begin{multline*}\\left(\\left(9x-10\\right)^{20} \\cdot \\left(-3x^{4}-7x\\right)^{25}\\right)' = \\\\\n20\\cdot \\left(9x-10\\right)^{19}\\cdot \\left(9)\\right) \\cdot \\left(-3x^{4}-7x\\right)^{25} + \\left(9x-10\\right)^{20} \\cdot 25 \\cdot \\left(-3x^{4}-7x\\right)^{24} \\cdot \\left(-12x^{3}-7)\\right) = \\\\\n5 \\cdot \\left(9x-10\\right)^{19} \\cdot \\left(-3x^{4}-7x\\right)^{24} \\cdot \\left[ 4 \\cdot \\left(9\\right)\\cdot\\left(-3x^{4}-7x\\right) + 5 \\cdot \\left(9x-10\\right) \\cdot \\left(-12x^{3}-7\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(11x+9\\right)^{25} \\cdot \\left(8x^{4}-6x\\right)^{15}$", "$$\\begin{multline*}\\left(\\left(11x+9\\right)^{25} \\cdot \\left(8x^{4}-6x\\right)^{15}\\right)' = \\\\\n25\\cdot \\left(11x+9\\right)^{24}\\cdot \\left(11)\\right) \\cdot \\left(8x^{4}-6x\\right)^{15} + \\left(11x+9\\right)^{25} \\cdot 15 \\cdot \\left(8x^{4}-6x\\right)^{14} \\cdot \\left(32x^{3}-6)\\right) = \\\\\n5 \\cdot \\left(11x+9\\right)^{24} \\cdot \\left(8x^{4}-6x\\right)^{14} \\cdot \\left[ 5 \\cdot \\left(11\\right)\\cdot\\left(8x^{4}-6x\\right) + 3 \\cdot \\left(11x+9\\right) \\cdot \\left(32x^{3}-6\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(3x^{7}+10x\\right)^{18} \\cdot \\left(7x+13\\right)^{27}$", "$$\\begin{multline*}\\left(\\left(3x^{7}+10x\\right)^{18} \\cdot \\left(7x+13\\right)^{27}\\right)' = \\\\\n18\\cdot \\left(3x^{7}+10x\\right)^{17}\\cdot \\left(21x^{6}+10)\\right) \\cdot \\left(7x+13\\right)^{27} + \\left(3x^{7}+10x\\right)^{18} \\cdot 27 \\cdot \\left(7x+13\\right)^{26} \\cdot \\left(7)\\right) = \\\\\n9 \\cdot \\left(3x^{7}+10x\\right)^{17} \\cdot \\left(7x+13\\right)^{26} \\cdot \\left[ 2 \\cdot \\left(21x^{6}+10\\right)\\cdot\\left(7x+13\\right) + 3 \\cdot \\left(3x^{7}+10x\\right) \\cdot \\left(7\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(5x-5\\right)^{42} \\cdot \\left(4x^{7}+13x\\right)^{12}$", "$$\\begin{multline*}\\left(\\left(5x-5\\right)^{42} \\cdot \\left(4x^{7}+13x\\right)^{12}\\right)' = \\\\\n42\\cdot \\left(5x-5\\right)^{41}\\cdot \\left(5)\\right) \\cdot \\left(4x^{7}+13x\\right)^{12} + \\left(5x-5\\right)^{42} \\cdot 12 \\cdot \\left(4x^{7}+13x\\right)^{11} \\cdot \\left(28x^{6}+13)\\right) = \\\\\n6 \\cdot \\left(5x-5\\right)^{41} \\cdot \\left(4x^{7}+13x\\right)^{11} \\cdot \\left[ 7 \\cdot \\left(5\\right)\\cdot\\left(4x^{7}+13x\\right) + 2 \\cdot \\left(5x-5\\right) \\cdot \\left(28x^{6}+13\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(8x^{6}-7x\\right)^{12} \\cdot \\left(-13x+7\\right)^{18}$", "$$\\begin{multline*}\\left(\\left(8x^{6}-7x\\right)^{12} \\cdot \\left(-13x+7\\right)^{18}\\right)' = \\\\\n12\\cdot \\left(8x^{6}-7x\\right)^{11}\\cdot \\left(48x^{5}-7)\\right) \\cdot \\left(-13x+7\\right)^{18} + \\left(8x^{6}-7x\\right)^{12} \\cdot 18 \\cdot \\left(-13x+7\\right)^{17} \\cdot \\left(-13)\\right) = \\\\\n6 \\cdot \\left(8x^{6}-7x\\right)^{11} \\cdot \\left(-13x+7\\right)^{17} \\cdot \\left[ 2 \\cdot \\left(48x^{5}-7\\right)\\cdot\\left(-13x+7\\right) + 3 \\cdot \\left(8x^{6}-7x\\right) \\cdot \\left(-13\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(4x^{7}+11x\\right)^{15} \\cdot \\left(-4x+10\\right)^{10}$", "$$\\begin{multline*}\\left(\\left(4x^{7}+11x\\right)^{15} \\cdot \\left(-4x+10\\right)^{10}\\right)' = \\\\\n15\\cdot \\left(4x^{7}+11x\\right)^{14}\\cdot \\left(28x^{6}+11)\\right) \\cdot \\left(-4x+10\\right)^{10} + \\left(4x^{7}+11x\\right)^{15} \\cdot 10 \\cdot \\left(-4x+10\\right)^{9} \\cdot \\left(-4)\\right) = \\\\\n5 \\cdot \\left(4x^{7}+11x\\right)^{14} \\cdot \\left(-4x+10\\right)^{9} \\cdot \\left[ 3 \\cdot \\left(28x^{6}+11\\right)\\cdot\\left(-4x+10\\right) + 2 \\cdot \\left(4x^{7}+11x\\right) \\cdot \\left(-4\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(5x^{5}+4\\right)^{28} \\cdot \\left(-13x-9\\right)^{21}$", "$$\\begin{multline*}\\left(\\left(5x^{5}+4\\right)^{28} \\cdot \\left(-13x-9\\right)^{21}\\right)' = \\\\\n28\\cdot \\left(5x^{5}+4\\right)^{27}\\cdot \\left(25x^{4})\\right) \\cdot \\left(-13x-9\\right)^{21} + \\left(5x^{5}+4\\right)^{28} \\cdot 21 \\cdot \\left(-13x-9\\right)^{20} \\cdot \\left(-13)\\right) = \\\\\n7 \\cdot \\left(5x^{5}+4\\right)^{27} \\cdot \\left(-13x-9\\right)^{20} \\cdot \\left[ 4 \\cdot \\left(25x^{4}\\right)\\cdot\\left(-13x-9\\right) + 3 \\cdot \\left(5x^{5}+4\\right) \\cdot \\left(-13\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(2x^{4}-13\\right)^{40} \\cdot \\left(-13x+12\\right)^{15}$", "$$\\begin{multline*}\\left(\\left(2x^{4}-13\\right)^{40} \\cdot \\left(-13x+12\\right)^{15}\\right)' = \\\\\n40\\cdot \\left(2x^{4}-13\\right)^{39}\\cdot \\left(8x^{3})\\right) \\cdot \\left(-13x+12\\right)^{15} + \\left(2x^{4}-13\\right)^{40} \\cdot 15 \\cdot \\left(-13x+12\\right)^{14} \\cdot \\left(-13)\\right) = \\\\\n5 \\cdot \\left(2x^{4}-13\\right)^{39} \\cdot \\left(-13x+12\\right)^{14} \\cdot \\left[ 8 \\cdot \\left(8x^{3}\\right)\\cdot\\left(-13x+12\\right) + 3 \\cdot \\left(2x^{4}-13\\right) \\cdot \\left(-13\\right) \\right] \\\\\n\\end{multline*}$$"], ["$\\left(3x^{5}-11\\right)^{12} \\cdot \\left(11x+3\\right)^{32}$", "$$\\begin{multline*}\\left(\\left(3x^{5}-11\\right)^{12} \\cdot \\left(11x+3\\right)^{32}\\right)' = \\\\\n12\\cdot \\left(3x^{5}-11\\right)^{11}\\cdot \\left(15x^{4})\\right) \\cdot \\left(11x+3\\right)^{32} + \\left(3x^{5}-11\\right)^{12} \\cdot 32 \\cdot \\left(11x+3\\right)^{31} \\cdot \\left(11)\\right) = \\\\\n4 \\cdot \\left(3x^{5}-11\\right)^{11} \\cdot \\left(11x+3\\right)^{31} \\cdot \\left[ 3 \\cdot \\left(15x^{4}\\right)\\cdot\\left(11x+3\\right) + 8 \\cdot \\left(3x^{5}-11\\right) \\cdot \\left(11\\right) \\right] \\\\\n\\end{multline*}$$"]], |
| [["$\\displaystyle \\sum_{a=3}^{n}{\\sqrt{i^2+a}} +\\sqrt{5}$", "$\\displaystyle \\sqrt{i^2+3}+\\sqrt{i^2+4}+\\sqrt{i^2+5}+\\ldots+\\sqrt{i^2+\\left(n-2\\right)}+\\sqrt{i^2+\\left(n-1\\right)}+\\sqrt{i^2+\\left(n\\right)}+\\sqrt{5}$"], ["$\\displaystyle \\sum_{i=3}^{n}{\\sqrt{i^2+a}} +\\sqrt{5}$", "$\\displaystyle \\sqrt{3^2+a}+\\sqrt{4^2+a}+\\sqrt{5^2+a}+\\ldots+\\sqrt{\\left(n-2\\right)^2+a}+\\sqrt{\\left(n-1\\right)^2+a}+\\sqrt{\\left(n\\right)^2+a}+\\sqrt{5}$"], ["$\\displaystyle \\sum_{i=m}^{42}{(i+a)^2} +(3+a)^2$", "$\\displaystyle (\\left(m\\right)+a)^2+(\\left(m+(1)\\right)+a)^2+(\\left(m+(2)\\right)+a)^2+\\ldots+(40+a)^2+(41+a)^2+(42+a)^2+(3+a)^2$"], ["$\\displaystyle \\sum_{a=m}^{42}{(i+a)^2} +(3+b)^2$", "$\\displaystyle (i+\\left(m\\right))^2+(i+\\left(m+(1)\\right))^2+(i+\\left(m+(2)\\right))^2+\\ldots+(i+40)^2+(i+41)^2+(i+42)^2+(3+b)^2$"], ["$\\displaystyle \\sum_{i=n}^{m}{a_{i}} -s_m$", "$\\displaystyle a_{\\left(n\\right)}+a_{\\left(n+(1)\\right)}+a_{\\left(n+(2)\\right)}+\\ldots+a_{\\left(m-2\\right)}+a_{\\left(m-1\\right)}+a_{\\left(m\\right)}-s_m$"], ["$\\displaystyle \\sum_{i=x}^{y}{f(i)} +f(3)$", "$\\displaystyle f(\\left(x\\right))+f(\\left(x+(1)\\right))+f(\\left(x+(2)\\right))+\\ldots+f(\\left(y-2\\right))+f(\\left(y-1\\right))+f(\\left(y\\right))+f(3)$"], ["$\\displaystyle \\sum_{i=2}^{20}{\\frac{i+2}{i}} -\\frac{7}{5}$", "$\\displaystyle \\frac{\\left(2\\right)+2}{\\left(2\\right)}+\\frac{\\left(2+(1)\\right)+2}{\\left(2+(1)\\right)}+\\frac{\\left(2+(2)\\right)+2}{\\left(2+(2)\\right)}+\\ldots+\\frac{\\left(20-2\\right)+2}{\\left(20-2\\right)}+\\frac{\\left(20-1\\right)+2}{\\left(20-1\\right)}+\\frac{\\left(20\\right)+2}{\\left(20\\right)}-\\frac{7}{5}$"]], | " <br><hr> "); |
| " <br> ");}); | |
| </JS> | </JS> |
| <HTML> | <HTML> |
| <div id="exosummen_ausschreiben"></div> | <div id="exoprod_ketten_nur_poly"></div> |
| |
| </HTML> | </HTML> |
| <hidden Lösungen> | <hidden Lösungen> |
| | |
| <HTML> | <HTML> |
| <div id="solsummen_ausschreiben"></div> | <div id="solprod_ketten_nur_poly"></div> |
| | <div style='font-size:12px;color:gray;'>ruby ableiten-von-hand.rb 12</div> |
| </HTML> | </HTML> |
| </hidden> | |
| |
| | </hidden> |
| |
| ==== 17. Februar 2020 bis 21. Februar 2020 ==== | === Mittwoch 27. März 2024 === |
| === Montag 17. Februar 2020 === | Leiten Sie ohne Hilfsmittel ab. Klammern Sie danach gemeinsame Faktoren aus. Weitere Vereinfachungen sind nicht nötig. |
| Berechnen Sie den Mittelwert $\mu$ und den Median $\tilde x$ für die folgenden zwei Wertereihen. | <JS>miniAufgabe("#exoquotient_ketten_nur_poly","#solquotient_ketten_nur_poly", |
| <JS>jQuery(function() {generate(jQuery, "#exomeanmed","#solmeanmed", | [["$\\frac{ \\left(-11x+7\\right)^{36} }{ \\left(-5x^{5}-2\\right)^{16} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-11x+7\\right)^{36} }{ \\left(-5x^{5}-2\\right)^{16} }\\right)' = \\\\\n\\frac{ 36\\cdot \\left(-11x+7\\right)^{35}\\cdot \\left(-11)\\right) \\cdot \\left(-5x^{5}-2\\right)^{16} - \\left(-11x+7\\right)^{36} \\cdot 16 \\cdot \\left(-5x^{5}-2\\right)^{15} \\cdot \\left(-25x^{4})\\right) }{ \\left(\\left(-5x^{5}-2\\right)^{16}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-11x+7\\right)^{35} \\cdot \\left(-5x^{5}-2\\right)^{15} \\cdot \\left[ 9 \\cdot \\left(-11\\right) \\cdot \\left(-5x^{5}-2\\right) - 4 \\cdot \\left(-11x+7\\right) \\cdot \\left(-25x^{4}\\right) \\right] }{ \\left(-5x^{5}-2\\right)^{32} }= \\\\\n\\frac{ 4 \\cdot \\left(-11x+7\\right)^{35} \\cdot \\left[ 9 \\cdot \\left(-11\\right) \\cdot \\left(-5x^{5}-2\\right) - 4 \\cdot \\left(-11x+7\\right) \\cdot \\left(-25x^{4}\\right) \\right] }{ \\left(-5x^{5}-2\\right)^{17} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}+7x\\right)^{28} }{ \\left(5x+3\\right)^{8} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}+7x\\right)^{28} }{ \\left(5x+3\\right)^{8} }\\right)' = \\\\\n\\frac{ 28\\cdot \\left(2x^{4}+7x\\right)^{27}\\cdot \\left(8x^{3}+7)\\right) \\cdot \\left(5x+3\\right)^{8} - \\left(2x^{4}+7x\\right)^{28} \\cdot 8 \\cdot \\left(5x+3\\right)^{7} \\cdot \\left(5)\\right) }{ \\left(\\left(5x+3\\right)^{8}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(2x^{4}+7x\\right)^{27} \\cdot \\left(5x+3\\right)^{7} \\cdot \\left[ 7 \\cdot \\left(8x^{3}+7\\right) \\cdot \\left(5x+3\\right) - 2 \\cdot \\left(2x^{4}+7x\\right) \\cdot \\left(5\\right) \\right] }{ \\left(5x+3\\right)^{16} }= \\\\\n\\frac{ 4 \\cdot \\left(2x^{4}+7x\\right)^{27} \\cdot \\left[ 7 \\cdot \\left(8x^{3}+7\\right) \\cdot \\left(5x+3\\right) - 2 \\cdot \\left(2x^{4}+7x\\right) \\cdot \\left(5\\right) \\right] }{ \\left(5x+3\\right)^{9} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-9x+12\\right)^{39} }{ \\left(-2x^{7}-12x\\right)^{26} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-9x+12\\right)^{39} }{ \\left(-2x^{7}-12x\\right)^{26} }\\right)' = \\\\\n\\frac{ 39\\cdot \\left(-9x+12\\right)^{38}\\cdot \\left(-9)\\right) \\cdot \\left(-2x^{7}-12x\\right)^{26} - \\left(-9x+12\\right)^{39} \\cdot 26 \\cdot \\left(-2x^{7}-12x\\right)^{25} \\cdot \\left(-14x^{6}-12)\\right) }{ \\left(\\left(-2x^{7}-12x\\right)^{26}\\right)^2} = \\\\\n\\frac{ 13 \\cdot \\left(-9x+12\\right)^{38} \\cdot \\left(-2x^{7}-12x\\right)^{25} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(-2x^{7}-12x\\right) - 2 \\cdot \\left(-9x+12\\right) \\cdot \\left(-14x^{6}-12\\right) \\right] }{ \\left(-2x^{7}-12x\\right)^{52} }= \\\\\n\\frac{ 13 \\cdot \\left(-9x+12\\right)^{38} \\cdot \\left[ 3 \\cdot \\left(-9\\right) \\cdot \\left(-2x^{7}-12x\\right) - 2 \\cdot \\left(-9x+12\\right) \\cdot \\left(-14x^{6}-12\\right) \\right] }{ \\left(-2x^{7}-12x\\right)^{27} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-5x+11\\right)^{28} }{ \\left(-2x^{5}+7x\\right)^{21} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-5x+11\\right)^{28} }{ \\left(-2x^{5}+7x\\right)^{21} }\\right)' = \\\\\n\\frac{ 28\\cdot \\left(-5x+11\\right)^{27}\\cdot \\left(-5)\\right) \\cdot \\left(-2x^{5}+7x\\right)^{21} - \\left(-5x+11\\right)^{28} \\cdot 21 \\cdot \\left(-2x^{5}+7x\\right)^{20} \\cdot \\left(-10x^{4}+7)\\right) }{ \\left(\\left(-2x^{5}+7x\\right)^{21}\\right)^2} = \\\\\n\\frac{ 7 \\cdot \\left(-5x+11\\right)^{27} \\cdot \\left(-2x^{5}+7x\\right)^{20} \\cdot \\left[ 4 \\cdot \\left(-5\\right) \\cdot \\left(-2x^{5}+7x\\right) - 3 \\cdot \\left(-5x+11\\right) \\cdot \\left(-10x^{4}+7\\right) \\right] }{ \\left(-2x^{5}+7x\\right)^{42} }= \\\\\n\\frac{ 7 \\cdot \\left(-5x+11\\right)^{27} \\cdot \\left[ 4 \\cdot \\left(-5\\right) \\cdot \\left(-2x^{5}+7x\\right) - 3 \\cdot \\left(-5x+11\\right) \\cdot \\left(-10x^{4}+7\\right) \\right] }{ \\left(-2x^{5}+7x\\right)^{22} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{6}+5x\\right)^{8} }{ \\left(11x+9\\right)^{28} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{6}+5x\\right)^{8} }{ \\left(11x+9\\right)^{28} }\\right)' = \\\\\n\\frac{ 8\\cdot \\left(2x^{6}+5x\\right)^{7}\\cdot \\left(12x^{5}+5)\\right) \\cdot \\left(11x+9\\right)^{28} - \\left(2x^{6}+5x\\right)^{8} \\cdot 28 \\cdot \\left(11x+9\\right)^{27} \\cdot \\left(11)\\right) }{ \\left(\\left(11x+9\\right)^{28}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(2x^{6}+5x\\right)^{7} \\cdot \\left(11x+9\\right)^{27} \\cdot \\left[ 2 \\cdot \\left(12x^{5}+5\\right) \\cdot \\left(11x+9\\right) - 7 \\cdot \\left(2x^{6}+5x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+9\\right)^{56} }= \\\\\n\\frac{ 4 \\cdot \\left(2x^{6}+5x\\right)^{7} \\cdot \\left[ 2 \\cdot \\left(12x^{5}+5\\right) \\cdot \\left(11x+9\\right) - 7 \\cdot \\left(2x^{6}+5x\\right) \\cdot \\left(11\\right) \\right] }{ \\left(11x+9\\right)^{29} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-5x-6\\right)^{8} }{ \\left(-5x^{5}-13x\\right)^{12} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-5x-6\\right)^{8} }{ \\left(-5x^{5}-13x\\right)^{12} }\\right)' = \\\\\n\\frac{ 8\\cdot \\left(-5x-6\\right)^{7}\\cdot \\left(-5)\\right) \\cdot \\left(-5x^{5}-13x\\right)^{12} - \\left(-5x-6\\right)^{8} \\cdot 12 \\cdot \\left(-5x^{5}-13x\\right)^{11} \\cdot \\left(-25x^{4}-13)\\right) }{ \\left(\\left(-5x^{5}-13x\\right)^{12}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-5x-6\\right)^{7} \\cdot \\left(-5x^{5}-13x\\right)^{11} \\cdot \\left[ 2 \\cdot \\left(-5\\right) \\cdot \\left(-5x^{5}-13x\\right) - 3 \\cdot \\left(-5x-6\\right) \\cdot \\left(-25x^{4}-13\\right) \\right] }{ \\left(-5x^{5}-13x\\right)^{24} }= \\\\\n\\frac{ 4 \\cdot \\left(-5x-6\\right)^{7} \\cdot \\left[ 2 \\cdot \\left(-5\\right) \\cdot \\left(-5x^{5}-13x\\right) - 3 \\cdot \\left(-5x-6\\right) \\cdot \\left(-25x^{4}-13\\right) \\right] }{ \\left(-5x^{5}-13x\\right)^{13} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-4x^{4}-3x\\right)^{20} }{ \\left(3x+5\\right)^{24} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-4x^{4}-3x\\right)^{20} }{ \\left(3x+5\\right)^{24} }\\right)' = \\\\\n\\frac{ 20\\cdot \\left(-4x^{4}-3x\\right)^{19}\\cdot \\left(-16x^{3}-3)\\right) \\cdot \\left(3x+5\\right)^{24} - \\left(-4x^{4}-3x\\right)^{20} \\cdot 24 \\cdot \\left(3x+5\\right)^{23} \\cdot \\left(3)\\right) }{ \\left(\\left(3x+5\\right)^{24}\\right)^2} = \\\\\n\\frac{ 4 \\cdot \\left(-4x^{4}-3x\\right)^{19} \\cdot \\left(3x+5\\right)^{23} \\cdot \\left[ 5 \\cdot \\left(-16x^{3}-3\\right) \\cdot \\left(3x+5\\right) - 6 \\cdot \\left(-4x^{4}-3x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+5\\right)^{48} }= \\\\\n\\frac{ 4 \\cdot \\left(-4x^{4}-3x\\right)^{19} \\cdot \\left[ 5 \\cdot \\left(-16x^{3}-3\\right) \\cdot \\left(3x+5\\right) - 6 \\cdot \\left(-4x^{4}-3x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+5\\right)^{25} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(2x^{4}+9x\\right)^{40} }{ \\left(3x+8\\right)^{30} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(2x^{4}+9x\\right)^{40} }{ \\left(3x+8\\right)^{30} }\\right)' = \\\\\n\\frac{ 40\\cdot \\left(2x^{4}+9x\\right)^{39}\\cdot \\left(8x^{3}+9)\\right) \\cdot \\left(3x+8\\right)^{30} - \\left(2x^{4}+9x\\right)^{40} \\cdot 30 \\cdot \\left(3x+8\\right)^{29} \\cdot \\left(3)\\right) }{ \\left(\\left(3x+8\\right)^{30}\\right)^2} = \\\\\n\\frac{ 10 \\cdot \\left(2x^{4}+9x\\right)^{39} \\cdot \\left(3x+8\\right)^{29} \\cdot \\left[ 4 \\cdot \\left(8x^{3}+9\\right) \\cdot \\left(3x+8\\right) - 3 \\cdot \\left(2x^{4}+9x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+8\\right)^{60} }= \\\\\n\\frac{ 10 \\cdot \\left(2x^{4}+9x\\right)^{39} \\cdot \\left[ 4 \\cdot \\left(8x^{3}+9\\right) \\cdot \\left(3x+8\\right) - 3 \\cdot \\left(2x^{4}+9x\\right) \\cdot \\left(3\\right) \\right] }{ \\left(3x+8\\right)^{31} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-9x+10\\right)^{16} }{ \\left(2x^{7}+5x\\right)^{40} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-9x+10\\right)^{16} }{ \\left(2x^{7}+5x\\right)^{40} }\\right)' = \\\\\n\\frac{ 16\\cdot \\left(-9x+10\\right)^{15}\\cdot \\left(-9)\\right) \\cdot \\left(2x^{7}+5x\\right)^{40} - \\left(-9x+10\\right)^{16} \\cdot 40 \\cdot \\left(2x^{7}+5x\\right)^{39} \\cdot \\left(14x^{6}+5)\\right) }{ \\left(\\left(2x^{7}+5x\\right)^{40}\\right)^2} = \\\\\n\\frac{ 8 \\cdot \\left(-9x+10\\right)^{15} \\cdot \\left(2x^{7}+5x\\right)^{39} \\cdot \\left[ 2 \\cdot \\left(-9\\right) \\cdot \\left(2x^{7}+5x\\right) - 5 \\cdot \\left(-9x+10\\right) \\cdot \\left(14x^{6}+5\\right) \\right] }{ \\left(2x^{7}+5x\\right)^{80} }= \\\\\n\\frac{ 8 \\cdot \\left(-9x+10\\right)^{15} \\cdot \\left[ 2 \\cdot \\left(-9\\right) \\cdot \\left(2x^{7}+5x\\right) - 5 \\cdot \\left(-9x+10\\right) \\cdot \\left(14x^{6}+5\\right) \\right] }{ \\left(2x^{7}+5x\\right)^{41} } \\\\\n\\end{multline*}$$"], ["$\\frac{ \\left(-13x+7\\right)^{25} }{ \\left(-2x^{7}-7\\right)^{10} }$", "$$\\begin{multline*}\\left(\\frac{ \\left(-13x+7\\right)^{25} }{ \\left(-2x^{7}-7\\right)^{10} }\\right)' = \\\\\n\\frac{ 25\\cdot \\left(-13x+7\\right)^{24}\\cdot \\left(-13)\\right) \\cdot \\left(-2x^{7}-7\\right)^{10} - \\left(-13x+7\\right)^{25} \\cdot 10 \\cdot \\left(-2x^{7}-7\\right)^{9} \\cdot \\left(-14x^{6})\\right) }{ \\left(\\left(-2x^{7}-7\\right)^{10}\\right)^2} = \\\\\n\\frac{ 5 \\cdot \\left(-13x+7\\right)^{24} \\cdot \\left(-2x^{7}-7\\right)^{9} \\cdot \\left[ 5 \\cdot \\left(-13\\right) \\cdot \\left(-2x^{7}-7\\right) - 2 \\cdot \\left(-13x+7\\right) \\cdot \\left(-14x^{6}\\right) \\right] }{ \\left(-2x^{7}-7\\right)^{20} }= \\\\\n\\frac{ 5 \\cdot \\left(-13x+7\\right)^{24} \\cdot \\left[ 5 \\cdot \\left(-13\\right) \\cdot \\left(-2x^{7}-7\\right) - 2 \\cdot \\left(-13x+7\\right) \\cdot \\left(-14x^{6}\\right) \\right] }{ \\left(-2x^{7}-7\\right)^{11} } \\\\\n\\end{multline*}$$"]], |
| [["a) 12, 18, 11, 11, 8 b) 5, 8, 4, 10, 8, 31 ", "a) $\\mu = 12$, $\\tilde x = 11$ b) $\\mu = 11$, $\\tilde x = 8$ "], ["a) 24, 15, 22, 26, -2 b) 10, 8, 15, 6, 12, 27 ", "a) $\\mu = 17$, $\\tilde x = 22$ b) $\\mu = 13$, $\\tilde x = 11$ "], ["a) 13, 8, 6, 5, 18 b) 15, 2, 7, 8, 10, 24 ", "a) $\\mu = 10$, $\\tilde x = 8$ b) $\\mu = 11$, $\\tilde x = 9$ "], ["a) 18, 12, 11, 18, 1 b) 20, 16, 7, 14, 14, 1 ", "a) $\\mu = 12$, $\\tilde x = 12$ b) $\\mu = 12$, $\\tilde x = 14$ "], ["a) 15, 22, 13, 19, 6 b) 16, 10, 14, 12, 19, -5 ", "a) $\\mu = 15$, $\\tilde x = 15$ b) $\\mu = 11$, $\\tilde x = 13$ "], ["a) 21, 13, 10, 8, 23 b) 11, 18, 11, 17, 17, 34 ", "a) $\\mu = 15$, $\\tilde x = 13$ b) $\\mu = 18$, $\\tilde x = 17$ "], ["a) 18, 17, 22, 23, 0 b) 10, 12, 12, 14, 6, 18 ", "a) $\\mu = 16$, $\\tilde x = 18$ b) $\\mu = 12$, $\\tilde x = 12$ "], ["a) 25, 17, 13, 16, 19 b) 16, 14, 17, 16, 23, 16 ", "a) $\\mu = 18$, $\\tilde x = 17$ b) $\\mu = 17$, $\\tilde x = 16$ "], ["a) 11, 8, 9, 10, 12 b) 19, 13, 20, 18, 17, 15 ", "a) $\\mu = 10$, $\\tilde x = 10$ b) $\\mu = 17$, $\\tilde x = \\frac{35}{2} = 17.5$ "], ["a) 14, 1, 7, 14, 14 b) 10, 13, 13, 21, 16, 17 ", "a) $\\mu = 10$, $\\tilde x = 14$ b) $\\mu = 15$, $\\tilde x = \\frac{29}{2} = 14.5$ "]], | " <br><hr> "); |
| " <hr> ", " <hr> ");}); | |
| </JS> | </JS> |
| <HTML> | <HTML> |
| <div id="exomeanmed"></div> | <div id="exoquotient_ketten_nur_poly"></div> |
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| </HTML> | </HTML> |
| <hidden Lösungen> | <hidden Lösungen> |
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| <div id="solmeanmed"></div> | <div id="solquotient_ketten_nur_poly"></div> |
| | <div style='font-size:12px;color:gray;'>ruby ableiten-von-hand.rb 13</div> |
| </HTML> | </HTML> |
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| === Donnerstag 20. Februar 2020 === | |
| Berechnen Sie Standardabweichung der folgenden Wertereihe. | |
| <JS>jQuery(function() {generate(jQuery, "#exostandardabweichung","#solstandardabweichung", | |
| [["20, 17, 13, 21, 9", "$\\mu = 16$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(16+1+9+25+49\\right) = \\frac{1}{4}\\cdot 100 = 25$ also $\\sigma = \\sqrt{25} = 5$"], ["18, 17, 20, 18, 12", "$\\mu = 17$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(1+0+9+1+25\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["7, 15, 13, 13, 12", "$\\mu = 12$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(25+9+1+1+0\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["21, 21, 18, 13, 7", "$\\mu = 16$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(25+25+4+9+81\\right) = \\frac{1}{4}\\cdot 144 = 36$ also $\\sigma = \\sqrt{36} = 6$"], ["15, 17, 14, 15, 9", "$\\mu = 14$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(1+9+0+1+25\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["14, 20, 14, 12, 15", "$\\mu = 15$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(1+25+1+9+0\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["11, 6, 14, 12, 12", "$\\mu = 11$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(0+25+9+1+1\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["13, 14, 9, 7, 17", "$\\mu = 12$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(1+4+9+25+25\\right) = \\frac{1}{4}\\cdot 64 = 16$ also $\\sigma = \\sqrt{16} = 4$"], ["21, 15, 15, 16, 13", "$\\mu = 16$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(25+1+1+0+9\\right) = \\frac{1}{4}\\cdot 36 = 9$ also $\\sigma = \\sqrt{9} = 3$"], ["15, 17, 11, 13, 4", "$\\mu = 12$, $\\sigma^2 = \\frac{1}{n-1} \\cdot \\sum_{i=1}^{n} (x_i-\\mu)^2 = \\frac{1}{4} \\cdot \\left(9+25+1+1+64\\right) = \\frac{1}{4}\\cdot 100 = 25$ also $\\sigma = \\sqrt{25} = 5$"]], | |
| " <hr> ", " <hr> ");}); | |
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| ==== Aufgaben vom aktuellen Jahr ==== | ==== Aufgaben vom aktuellen Jahr ==== |
| * [[lehrkraefte:blc:miniaufgaben:kw08-2020|KW8, 17. Februar 2020: Durchschnitt und Median berechnen, Standardabweichung berechnen]] | * [[lehrkraefte:blc:miniaufgaben:kw13-2024|KW13, 25. März 2024: Produkt- und Kettenregel auf Polynomterme anweden. Quotienten- und Kettenregel auf Polynomterme anweden.]] |
| * [[lehrkraefte:blc:miniaufgaben:kw07-2020|KW7, 10. Februar 2020: Erwartungswert im Lotto, Summen ausschreiben]] | * [[lehrkraefte:blc:miniaufgaben:kw12-2024|KW12, 18. März 2024: Terme als Baum und Computernotation notieren]] |
| * [[lehrkraefte:blc:miniaufgaben:kw06-2020|KW6, 3. Februar 2020: Wahrscheinlichkeitsrechnung mit Würfeln]] | * [[lehrkraefte:blc:miniaufgaben:kw10-2024|KW10, 4. März 2024: Ableiten mit Ketten- und Produktregel, Ableiten mit Ketten- und Quotientenregel]] |
| * [[lehrkraefte:blc:miniaufgaben:kw04-2020|KW4, 20. Januar 2020: Polynombrüche addieren, ausmultiplizieren und 2. binomische Formel]] | * [[lehrkraefte:blc:miniaufgaben:kw09-2024|KW9, 26. Februar 2024: Ableiten mit Kettenregel, Ableiten mit Produktregel]] |
| * [[lehrkraefte:blc:miniaufgaben:kw03-2020|KW3, 13. Januar 2020: Vierfeldtafeld und bedingte Wahrscheinlichkeit, Pokerwahrscheinlichkeiten]] | * [[lehrkraefte:blc:miniaufgaben:kw08-2024|KW8, 19. Februar 2024: $f'(x)=f(x)\cdot f'(0)$ für $f(x)=a^x$ zeigen, Funktionen als Verknüpfung zweier Funktionen schreiben.]] |
| * [[lehrkraefte:blc:miniaufgaben:kw02-2020|KW2, 6. Januar 2020: Mengenoperationen, Pokerwahrscheinlichkeiten]] | * [[lehrkraefte:blc:miniaufgaben:kw07-2024|KW7, 12. Februar 2024: $x^2$ und $x^3$ mit Grenzwert ableiten, Polynome mit Regeln ableiten.]] |
| * [[lehrkraefte:blc:miniaufgaben:kw50-2019|KW50, 16. Dezember 2019: Ausklammern und Kürzen, Wahrscheinlichkeiten im Urnen-Modell]] | * [[lehrkraefte:blc:miniaufgaben:kw06-2024|KW6, 5. Februar 2024: Grafisch ableiten.]] |
| * [[lehrkraefte:blc:miniaufgaben:kw49-2019|KW49, 9. Dezember 2019: Doppelbrüche mit Zahlen kürzen und in Primfaktoren zerlegen.]] | * [[lehrkraefte:blc:miniaufgaben:kw03-2024|KW3, 15. Januar 2024: Logarithmusgleichungen mit nötigem Basiswechsel]] |
| * [[lehrkraefte:blc:miniaufgaben:kw48-2019|KW48, 2. Dezember 2019: Binomialkoeffizienten berechnen, einfachste Kombinatorik-Aufgaben zu den Grundformeln.]] | * [[lehrkraefte:blc:miniaufgaben:kw02-2024|KW2, 8. Januar 2024: Logarithmengesetze anwenden, Logarthmusgleichung lösen, die auf eine quadratische Gleichung führt]] |
| * [[lehrkraefte:blc:miniaufgaben:kw47-2019|KW47, 25. November 2019: Permutationen von Buchstaben, ohne und mit Wiederholung]] | * [[lehrkraefte:blc:miniaufgaben:kw51-2023|KW51, 18. Dezember 2023: Logarithmusfunktionen ablesen, Exponentialgleichungen durch Logarthmieren lösen]] |
| * [[lehrkraefte:blc:miniaufgaben:kw46-2019|KW46, 18. November 2019: Parabeln aus Scheitelform skizzieren, Heiteres Funktionenraten einfach.]] | * [[lehrkraefte:blc:miniaufgaben:kw50-2023|KW50, 11. Dezember 2023: Einfache Exponentialgleichungen von Hand ohne Logarithmen, Einfache Logarithmen von Hand]] |
| * [[lehrkraefte:blc:miniaufgaben:kw45-2019|KW45, 11. November 2019: Ausmultiplizieren und Zusammenfassen, Trigowerte schätzen.]] | * [[lehrkraefte:blc:miniaufgaben:kw49-2023|KW49, 4. Dezember 2023: Exponentialfunktionen ablesen, Exponentialfunktion aus Text]] |
| * [[lehrkraefte:blc:miniaufgaben:kw44-2019|KW44, 4. November 2019: Abstand Parabel Ursprung mit TR, Parabeln skizzieren.]] | * [[lehrkraefte:blc:miniaufgaben:kw48-2023|KW48, 27. November 2023: Wertetabellen von Potenzfunktionen mit rationalen Basen, Funktionsgraphen transformieren einfach]] |
| * [[lehrkraefte:blc:miniaufgaben:kw43-2019|KW43, 28. Oktober 2019: Übersetzung Algebra <-> Deutsch, Kurvendiskussion mit TR]] | * [[lehrkraefte:blc:miniaufgaben:kw47-2023|KW47, 20. November 2023: Potenzgesetze in $\mathbb{N}$ beweisen, Potenzgesetze in Vereinfachungen anwenden.]] |
| * [[lehrkraefte:blc:miniaufgaben:kw42-2019|KW42, 21. Oktober 2019: Auf einen Bruchstrich zusammenfassen und faktorisieren, Kurvendiskussion mit TR]] | * KW46, 13. November 2023: Keine Miniaufgaben |
| * [[lehrkraefte:blc:miniaufgaben:kw38-2019|KW38, 23. September 2019: Ausmultiplizeren, Zusammenfassen, Faktorisieren]] | * [[lehrkraefte:blc:miniaufgaben:kw45-2023|KW45, 6. November 2023: Arithmetische Reihe berechnen, $a_0$, $a_1$ als quadratische Polynome gegben, berechne $a_2$.]] |
| * [[lehrkraefte:blc:miniaufgaben:kw37-2019|KW37, 16. September 2019: Ableiten mit Produktregel]] | * [[lehrkraefte:blc:miniaufgaben:kw44-2023|KW44, 30. Oktober 2023: Summenzeichen ausschreiben, Implizite Teilsummen von AF und AG mit Summenzeichen schreiben.]] |
| * [[lehrkraefte:blc:miniaufgaben:kw36-2019|KW36, 9. September 2019: Funktionen entschachteln, Kettenregel]] | * [[lehrkraefte:blc:miniaufgaben:kw43-2023|KW43, 23. Oktober 2023: GF oder AF aus drei Gliedern bestimmen (mit Bruchzahlen)]] |
| * [[lehrkraefte:blc:miniaufgaben:kw35-2019|KW35, 2. September 2019: Ableiten mit Produktregel]] | * [[lehrkraefte:blc:miniaufgaben:kw39-2023|KW39, 25. September 2023: Parameter von AF aus zwei Gliedern, Parameter von GF aus zwei Gliedern]] |
| * [[lehrkraefte:blc:miniaufgaben:kw34-2019|KW34, 26. August 2019: Exponentialgleichungen, Faktorisieren]] | * [[lehrkraefte:blc:miniaufgaben:kw38-2023|KW38, 18. September 2023: Ganzzahlige Potenzen auswendig lernen, AF/GF implizit zu explizit]] |
| * [[lehrkraefte:blc:miniaufgaben:kw33-2019|KW33, 19. August 2019: Polynome ableiten, Potenzgesetze beweisen ]] | * [[lehrkraefte:blc:miniaufgaben:kw37-2023|KW37, 11. September 2023: Strecke zu gleichseitigem Dreieck ergänzen.]] |
| | * [[lehrkraefte:blc:miniaufgaben:kw36-2023|KW36, 4. September 2023: Vektoren auf gewünschte Länge skalieren (mit Brüchen), Strecke zum Quadrat ergänzen.]] |
| | * [[lehrkraefte:blc:miniaufgaben:kw35-2023|KW35, 28. August 2023: Länge von Vektoren in Normalform]] |
| | * [[lehrkraefte:blc:miniaufgaben:kw34-2023|KW34, 21. August 2023: POV-Ray Code für Rotationen und Translation eines orientierten Torus produzieren, Gleichmässige Bewegung beschreiben, in mathematischer Notation und POV-Ray Code]] |
| | * [[lehrkraefte:blc:miniaufgaben:kw33-2023|KW33, 14. August 2023: Kugeln, Zylinder und Kegel in POV-Ray Syntax beschreiben]] |
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| === Ältere Aufgaben === | === Ältere Aufgaben === |
| * [[lehrkraefte:blc:miniaufgaben:Vierte-Klasse19-20|Aufgaben vom 4. Jahr 19/20]] | * [[lehrkraefte:blc:miniaufgaben:zweite-klasse22-23|Aufgaben vom 2. Jahr 22/23]] |
| * [[lehrkraefte:blc:miniaufgaben:Dritte-Klasse|Aufgaben vom 3. Jahr 18/19]] | * [[lehrkraefte:blc:miniaufgaben:erste-klasse21-22|Aufgaben vom 1. Jahr 21/22]] |
| * [[lehrkraefte:blc:miniaufgaben:Zweite-Klasse|Aufgaben vom 2. Jahr 17/18]] | * [[lehrkraefte:blc:miniaufgaben:vierte-klasse19-20|Aufgaben vom 4. Jahr 19/20]] |
| | * [[lehrkraefte:blc:miniaufgaben:vierte-klasse18-19|Aufgaben vom 4. Jahr 18/19]] |
| | * [[lehrkraefte:blc:miniaufgaben:Dritte-Klasse|Aufgaben vom 3. Jahr 17/18]] |
| | * [[lehrkraefte:blc:miniaufgaben:Zweite-Klasse|Aufgaben vom 2. Jahr 16/17]] |
| * [[lehrkraefte:ks:wochenaufgaben|Aufgaben von S. Knaus]] | * [[lehrkraefte:ks:wochenaufgaben|Aufgaben von S. Knaus]] |
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