Differences

This shows you the differences between two versions of the page.

--- lehrkraefte:blc:miniaufgaben:kw26-2018 [2018/08/11 20:17]
Ivo Blöchliger created
+++ lehrkraefte:blc:miniaufgaben:kw26-2018 [2020/08/09 15:20] (current)
@@ Line 1: / Line 1: @@
-<JS>
+<PRELOAD>
-function generate(jQuery, idex, idsol, ex, sep="<br>", sep2="<br>", numex=3) {
+miniaufgabe.js
-    var randperm=function(n) {
+</PRELOAD>
-	var a = [];
-	for (var i=0; i<n; i++) { a[i]=i; }
-	for (var i=0; i<n; i++) {
-	    var j = Math.floor(Math.random()*(n-i))+i;
-	    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)+". &nbsp; "+ex[selec[i]][0]+sep);
-       jQuery(idsol).append((i+1)+". &nbsp; "+ex[selec[i]][1]+sep2);
-    }
-}
-</JS>
-==== 11. Juni 2018 bis 15. Juni 2018 ====
-=== Dienstag 12. Juni 2018 ===
-Ausmultiplizieren, zusammenfassen und zuletzt faktorisieren.<JS>jQuery(function() {generate(jQuery, "#exoausmulundbinom","#solausmulundbinom",
-[["$\\left(\\frac{3}{4}x-\\frac{3}{2}\\right)\\cdot\\left(-\\frac{10}{9}x+\\frac{9}{7}\\right)+\\left(-\\frac{9}{7}x+\\frac{18}{7}\\right)\\cdot\\left(-\\frac{77}{54}x+\\frac{83}{36}\\right)$", "$-\\frac{5}{6}x^2+\\frac{27}{28}x+\\frac{5}{3}x-\\frac{27}{14}+\\frac{11}{6}x^2-\\frac{83}{28}x-\\frac{11}{3}x+\\frac{83}{14}=x^2-4x+4 = \\left(x-2\\right)^2$"], ["$\\left(\\frac{1}{2}x+\\frac{3}{2}\\right)\\cdot\\left(\\frac{9}{2}x-\\frac{1}{2}\\right)+\\left(-\\frac{4}{7}x-\\frac{12}{7}\\right)\\cdot\\left(\\frac{35}{16}x-\\frac{91}{16}\\right)$", "$\\frac{9}{4}x^2-\\frac{1}{4}x+\\frac{27}{4}x-\\frac{3}{4}-\\frac{5}{4}x^2+\\frac{13}{4}x-\\frac{15}{4}x+\\frac{39}{4}=x^2+6x+9 = \\left(x+3\\right)^2$"], ["$\\left(-\\frac{1}{2}x-\\frac{1}{2}\\right)\\cdot\\left(-\\frac{4}{9}x-\\frac{10}{9}\\right)+\\left(\\frac{2}{3}x+\\frac{38}{21}\\right)\\cdot\\left(\\frac{7}{6}x+\\frac{14}{3}\\right)$", "$\\frac{2}{9}x^2+\\frac{5}{9}x+\\frac{2}{9}x+\\frac{5}{9}+\\frac{7}{9}x^2+\\frac{28}{9}x+\\frac{19}{9}x+\\frac{76}{9}=x^2+6x+9 = \\left(x+3\\right)^2$"], ["$\\left(\\frac{8}{3}x-\\frac{7}{6}\\right)\\cdot\\left(-\\frac{3}{10}x-\\frac{3}{5}\\right)+\\left(\\frac{1}{3}x+\\frac{11}{36}\\right)\\cdot\\left(\\frac{27}{5}x+\\frac{54}{5}\\right)$", "$-\\frac{4}{5}x^2-\\frac{8}{5}x+\\frac{7}{20}x+\\frac{7}{10}+\\frac{9}{5}x^2+\\frac{18}{5}x+\\frac{33}{20}x+\\frac{33}{10}=x^2+4x+4 = \\left(x+2\\right)^2$"], ["$\\left(\\frac{1}{3}x+\\frac{2}{3}\\right)\\cdot\\left(\\frac{9}{5}x+\\frac{1}{3}\\right)+\\left(\\frac{9}{4}x+\\frac{9}{2}\\right)\\cdot\\left(\\frac{8}{45}x+\\frac{68}{81}\\right)$", "$\\frac{3}{5}x^2+\\frac{1}{9}x+\\frac{6}{5}x+\\frac{2}{9}+\\frac{2}{5}x^2+\\frac{17}{9}x+\\frac{4}{5}x+\\frac{34}{9}=x^2+4x+4 = \\left(x+2\\right)^2$"], ["$\\left(\\frac{4}{3}x-\\frac{8}{3}\\right)\\cdot\\left(\\frac{9}{14}x-\\frac{7}{2}\\right)+\\left(\\frac{8}{7}x-\\frac{16}{7}\\right)\\cdot\\left(\\frac{1}{8}x+\\frac{7}{3}\\right)$", "$\\frac{6}{7}x^2-\\frac{14}{3}x-\\frac{12}{7}x+\\frac{28}{3}+\\frac{1}{7}x^2+\\frac{8}{3}x-\\frac{2}{7}x-\\frac{16}{3}=x^2-4x+4 = \\left(x-2\\right)^2$"], ["$\\left(\\frac{3}{7}x+\\frac{6}{7}\\right)\\cdot\\left(-\\frac{7}{15}x-\\frac{1}{3}\\right)+\\left(-\\frac{2}{3}x-\\frac{25}{21}\\right)\\cdot\\left(-\\frac{9}{5}x-\\frac{18}{5}\\right)$", "$-\\frac{1}{5}x^2-\\frac{1}{7}x-\\frac{2}{5}x-\\frac{2}{7}+\\frac{6}{5}x^2+\\frac{12}{5}x+\\frac{15}{7}x+\\frac{30}{7}=x^2+4x+4 = \\left(x+2\\right)^2$"], ["$\\left(\\frac{2}{3}x-\\frac{2}{3}\\right)\\cdot\\left(\\frac{15}{4}x-\\frac{3}{4}\\right)+\\left(-\\frac{10}{9}x-\\frac{70}{9}\\right)\\cdot\\left(\\frac{27}{20}x-\\frac{63}{20}\\right)$", "$\\frac{5}{2}x^2-\\frac{1}{2}x-\\frac{5}{2}x+\\frac{1}{2}-\\frac{3}{2}x^2+\\frac{7}{2}x-\\frac{21}{2}x+\\frac{49}{2}=x^2-10x+25 = \\left(x-5\\right)^2$"], ["$\\left(-\\frac{5}{2}x-\\frac{9}{4}\\right)\\cdot\\left(\\frac{2}{25}x+\\frac{2}{5}\\right)+\\left(\\frac{1}{3}x+\\frac{7}{15}\\right)\\cdot\\left(\\frac{18}{5}x+\\frac{21}{2}\\right)$", "$-\\frac{1}{5}x^2-x-\\frac{9}{50}x-\\frac{9}{10}+\\frac{6}{5}x^2+\\frac{7}{2}x+\\frac{42}{25}x+\\frac{49}{10}=x^2+4x+4 = \\left(x+2\\right)^2$"], ["$\\left(\\frac{5}{4}x+\\frac{5}{2}\\right)\\cdot\\left(\\frac{14}{25}x-\\frac{2}{3}\\right)+\\left(-\\frac{4}{5}x-\\frac{8}{5}\\right)\\cdot\\left(-\\frac{3}{8}x-\\frac{85}{24}\\right)$", "$\\frac{7}{10}x^2-\\frac{5}{6}x+\\frac{7}{5}x-\\frac{5}{3}+\\frac{3}{10}x^2+\\frac{17}{6}x+\\frac{3}{5}x+\\frac{17}{3}=x^2+4x+4 = \\left(x+2\\right)^2$"]],
-" <br><hr> ", " <br><hr> ", 3);});
-</JS>
-<HTML>
-<div id="exoausmulundbinom"></div>
-</HTML>
-<hidden Lösungen>
-<HTML>
-<div id="solausmulundbinom"></div>
-</HTML>
-</hidden>
-=== Freitag 15. Juni 2018 ===
-Zusammenfassen, ausklammern, kürzen, Resultat als Vielfaches einer Potenz von $x$:
-<JS>jQuery(function() {generate(jQuery, "#exovereinfachenAusklammern","#solvereinfachenAusklammern",
-[["$\\displaystyle \\frac{\\frac{5}{9} \\cdot x^{-5} \\cdot \\frac{1}{x^{-9}} +\\frac{1}{3} \\cdot x^{5} \\cdot \\frac{1}{x^{-4}}}{\\frac{4}{5} \\cdot x^{8} \\cdot \\frac{1}{x^{-8}} +\\frac{12}{25} \\cdot x^{3} \\cdot \\frac{1}{x^{-18}}}$", "$\\displaystyle \\frac{\\frac{5}{9}\\cdot x^{4} +\\frac{1}{3}\\cdot x^{9}}{\\frac{4}{5}\\cdot x^{16} +\\frac{12}{25}\\cdot x^{21}} = \\frac{\\frac{1}{9}\\cdot x^{4} \\cdot \\left(5 +3\\cdot x^{5}\\right)}{\\frac{4}{25}\\cdot x^{16} \\cdot \\left(5 +3\\cdot x^{5}\\right)} = \\frac{1}{9} \\cdot \\frac{25}{4} \\cdot x^{-12} = \\frac{25}{36}\\cdot x^{-12}$"], ["$\\displaystyle \\frac{\\frac{4}{9} \\cdot x^{6} \\cdot \\frac{1}{x^{-9}} +\\frac{2}{9} \\cdot x^{3} \\cdot \\frac{1}{x^{-4}}}{\\frac{1}{7} \\cdot x^{7} \\cdot \\frac{1}{x^{2}} +\\frac{1}{14} \\cdot x^{6} \\cdot \\frac{1}{x^{9}}}$", "$\\displaystyle \\frac{\\frac{4}{9}\\cdot x^{15} +\\frac{2}{9}\\cdot x^{7}}{\\frac{1}{7}\\cdot x^{5} +\\frac{1}{14}\\cdot x^{-3}} = \\frac{\\frac{2}{9}\\cdot x^{7} \\cdot \\left(2\\cdot x^{8} +1\\right)}{\\frac{1}{14}\\cdot x^{-3} \\cdot \\left(2\\cdot x^{8} +1\\right)} = \\frac{2}{9} \\cdot 14 \\cdot x^{10} = \\frac{28}{9}\\cdot x^{10}$"], ["$\\displaystyle \\frac{\\frac{7}{5} \\cdot x^{6} \\cdot \\frac{1}{x^{-4}} +\\frac{5}{3} \\cdot x^{5} \\cdot \\frac{1}{x^{-8}}}{\\frac{3}{4} \\cdot x^{2} \\cdot \\frac{1}{x^{-6}} +\\frac{25}{28} \\cdot x^{6} \\cdot \\frac{1}{x^{-5}}}$", "$\\displaystyle \\frac{\\frac{7}{5}\\cdot x^{10} +\\frac{5}{3}\\cdot x^{13}}{\\frac{3}{4}\\cdot x^{8} +\\frac{25}{28}\\cdot x^{11}} = \\frac{\\frac{1}{15}\\cdot x^{10} \\cdot \\left(21 +25\\cdot x^{3}\\right)}{\\frac{1}{28}\\cdot x^{8} \\cdot \\left(21 +25\\cdot x^{3}\\right)} = \\frac{1}{15} \\cdot 28 \\cdot x^{2} = \\frac{28}{15}\\cdot x^{2}$"], ["$\\displaystyle \\frac{\\frac{2}{3} \\cdot x^{8} \\cdot \\frac{1}{x^{-8}} +\\frac{1}{3} \\cdot x^{8} \\cdot \\frac{1}{x^{2}}}{\\frac{3}{5} \\cdot x^{3} \\cdot \\frac{1}{x^{-6}} +\\frac{3}{10} \\cdot x^{-3} \\cdot \\frac{1}{x^{-2}}}$", "$\\displaystyle \\frac{\\frac{2}{3}\\cdot x^{16} +\\frac{1}{3}\\cdot x^{6}}{\\frac{3}{5}\\cdot x^{9} +\\frac{3}{10}\\cdot x^{-1}} = \\frac{\\frac{1}{3}\\cdot x^{6} \\cdot \\left(2\\cdot x^{10} +1\\right)}{\\frac{3}{10}\\cdot x^{-1} \\cdot \\left(2\\cdot x^{10} +1\\right)} = \\frac{1}{3} \\cdot \\frac{10}{3} \\cdot x^{7} = \\frac{10}{9}\\cdot x^{7}$"], ["$\\displaystyle \\frac{\\frac{3}{2} \\cdot x^{2} \\cdot \\frac{1}{x^{-3}} +\\frac{3}{8} \\cdot x^{9} \\cdot \\frac{1}{x^{-8}}}{\\frac{1}{2} \\cdot x^{4} \\cdot \\frac{1}{x^{-5}} +\\frac{1}{8} \\cdot x^{5} \\cdot \\frac{1}{x^{-16}}}$", "$\\displaystyle \\frac{\\frac{3}{2}\\cdot x^{5} +\\frac{3}{8}\\cdot x^{17}}{\\frac{1}{2}\\cdot x^{9} +\\frac{1}{8}\\cdot x^{21}} = \\frac{\\frac{3}{8}\\cdot x^{5} \\cdot \\left(4 +1\\cdot x^{12}\\right)}{\\frac{1}{8}\\cdot x^{9} \\cdot \\left(4 +1\\cdot x^{12}\\right)} = \\frac{3}{8} \\cdot 8 \\cdot x^{-4} = 3\\cdot x^{-4}$"], ["$\\displaystyle \\frac{\\frac{1}{4} \\cdot x^{6} \\cdot \\frac{1}{x^{-4}} +\\frac{9}{5} \\cdot x^{6} \\cdot \\frac{1}{x^{-9}}}{\\frac{7}{2} \\cdot x^{9} \\cdot \\frac{1}{x^{5}} +\\frac{126}{5} \\cdot x^{-4} \\cdot \\frac{1}{x^{-13}}}$", "$\\displaystyle \\frac{\\frac{1}{4}\\cdot x^{10} +\\frac{9}{5}\\cdot x^{15}}{\\frac{7}{2}\\cdot x^{4} +\\frac{126}{5}\\cdot x^{9}} = \\frac{\\frac{1}{20}\\cdot x^{10} \\cdot \\left(5 +36\\cdot x^{5}\\right)}{\\frac{7}{10}\\cdot x^{4} \\cdot \\left(5 +36\\cdot x^{5}\\right)} = \\frac{1}{20} \\cdot \\frac{10}{7} \\cdot x^{6} = \\frac{1}{14}\\cdot x^{6}$"], ["$\\displaystyle \\frac{\\frac{9}{7} \\cdot x^{3} \\cdot \\frac{1}{x^{-2}} +\\frac{9}{4} \\cdot x^{5} \\cdot \\frac{1}{x^{-6}}}{\\frac{4}{5} \\cdot x^{7} \\cdot \\frac{1}{x^{-5}} +\\frac{7}{5} \\cdot x^{8} \\cdot \\frac{1}{x^{-10}}}$", "$\\displaystyle \\frac{\\frac{9}{7}\\cdot x^{5} +\\frac{9}{4}\\cdot x^{11}}{\\frac{4}{5}\\cdot x^{12} +\\frac{7}{5}\\cdot x^{18}} = \\frac{\\frac{9}{28}\\cdot x^{5} \\cdot \\left(4 +7\\cdot x^{6}\\right)}{\\frac{1}{5}\\cdot x^{12} \\cdot \\left(4 +7\\cdot x^{6}\\right)} = \\frac{9}{28} \\cdot 5 \\cdot x^{-7} = \\frac{45}{28}\\cdot x^{-7}$"], ["$\\displaystyle \\frac{\\frac{3}{2} \\cdot x^{9} \\cdot \\frac{1}{x^{4}} +\\frac{1}{3} \\cdot x^{8} \\cdot \\frac{1}{x^{-8}}}{\\frac{5}{2} \\cdot x^{3} \\cdot \\frac{1}{x^{-9}} +\\frac{5}{9} \\cdot x^{8} \\cdot \\frac{1}{x^{-15}}}$", "$\\displaystyle \\frac{\\frac{3}{2}\\cdot x^{5} +\\frac{1}{3}\\cdot x^{16}}{\\frac{5}{2}\\cdot x^{12} +\\frac{5}{9}\\cdot x^{23}} = \\frac{\\frac{1}{6}\\cdot x^{5} \\cdot \\left(9 +2\\cdot x^{11}\\right)}{\\frac{5}{18}\\cdot x^{12} \\cdot \\left(9 +2\\cdot x^{11}\\right)} = \\frac{1}{6} \\cdot \\frac{18}{5} \\cdot x^{-7} = \\frac{3}{5}\\cdot x^{-7}$"], ["$\\displaystyle \\frac{\\frac{3}{2} \\cdot x^{2} \\cdot \\frac{1}{x^{-6}} +\\frac{1}{8} \\cdot x^{5} \\cdot \\frac{1}{x^{-6}}}{\\frac{8}{7} \\cdot x^{7} \\cdot \\frac{1}{x^{3}} +\\frac{2}{21} \\cdot x^{-3} \\cdot \\frac{1}{x^{-10}}}$", "$\\displaystyle \\frac{\\frac{3}{2}\\cdot x^{8} +\\frac{1}{8}\\cdot x^{11}}{\\frac{8}{7}\\cdot x^{4} +\\frac{2}{21}\\cdot x^{7}} = \\frac{\\frac{1}{8}\\cdot x^{8} \\cdot \\left(12 +1\\cdot x^{3}\\right)}{\\frac{2}{21}\\cdot x^{4} \\cdot \\left(12 +1\\cdot x^{3}\\right)} = \\frac{1}{8} \\cdot \\frac{21}{2} \\cdot x^{4} = \\frac{21}{16}\\cdot x^{4}$"], ["$\\displaystyle \\frac{\\frac{1}{2} \\cdot x^{6} \\cdot \\frac{1}{x^{-5}} +\\frac{5}{7} \\cdot x^{8} \\cdot \\frac{1}{x^{3}}}{\\frac{1}{7} \\cdot x^{-3} \\cdot \\frac{1}{x^{-7}} +\\frac{10}{49} \\cdot x^{2} \\cdot \\frac{1}{x^{4}}}$", "$\\displaystyle \\frac{\\frac{1}{2}\\cdot x^{11} +\\frac{5}{7}\\cdot x^{5}}{\\frac{1}{7}\\cdot x^{4} +\\frac{10}{49}\\cdot x^{-2}} = \\frac{\\frac{1}{14}\\cdot x^{5} \\cdot \\left(7\\cdot x^{6} +10\\right)}{\\frac{1}{49}\\cdot x^{-2} \\cdot \\left(7\\cdot x^{6} +10\\right)} = \\frac{1}{14} \\cdot 49 \\cdot x^{7} = \\frac{7}{2}\\cdot x^{7}$"]],
-" <br><hr> ", " <br><hr> ", 3);});
-</JS>
-<HTML>
-<div id="exovereinfachenAusklammern"></div>
-</HTML>
-<hidden Lösungen>
-<HTML>
-<div id="solvereinfachenAusklammern"></div>
-</HTML>
-</hidden>
 ==== 18. Juni 2018 bis 22. Juni 2018 ====
 === Dienstag 19. Juni 2018 ===
 Lösen Sie schrittweise von Hand auf.
 <JS>
-jQuery(function() {generate(jQuery, "#exos3","#sol3",
+miniAufgabe("#exos3","#sol3",
 [["${{7x}\\over{6}}+{{4}\\over{3}}={{3x}\\over{4}}+{{5}\\over{3}}$", "$\\begin{align*}{{7x}\\over{6}}+{{4}\\over{3}} &= {{3x}\\over{4}}+{{5}\\over{3}} && |\\cdot 12\\\\\n14x+16 &= 9x+20 && |-\\left(9x+16\\right)\\\\\n5x &= 4 && |:5\\\\\nx &= {{4}\\over{5}}\n\\end{align*}$"], ["${{13x}\\over{8}}+{{3}\\over{8}}={{7x}\\over{5}}+{{39}\\over{40}}$", "$\\begin{align*}{{13x}\\over{8}}+{{3}\\over{8}} &= {{7x}\\over{5}}+{{39}\\over{40}} && |\\cdot 40\\\\\n65x+15 &= 56x+39 && |-\\left(56x+15\\right)\\\\\n9x &= 24 && |:9\\\\\nx &= {{8}\\over{3}}\n\\end{align*}$"], ["${{39x}\\over{40}}+{{5}\\over{8}}={{7x}\\over{8}}+{{4}\\over{5}}$", "$\\begin{align*}{{39x}\\over{40}}+{{5}\\over{8}} &= {{7x}\\over{8}}+{{4}\\over{5}} && |\\cdot 40\\\\\n39x+25 &= 35x+32 && |-\\left(35x+25\\right)\\\\\n4x &= 7 && |:4\\\\\nx &= {{7}\\over{4}}\n\\end{align*}$"], ["${{51x}\\over{56}}+{{7}\\over{8}}={{3x}\\over{4}}+{{27}\\over{28}}$", "$\\begin{align*}{{51x}\\over{56}}+{{7}\\over{8}} &= {{3x}\\over{4}}+{{27}\\over{28}} && |\\cdot 56\\\\\n51x+49 &= 42x+54 && |-\\left(42x+49\\right)\\\\\n9x &= 5 && |:9\\\\\nx &= {{5}\\over{9}}\n\\end{align*}$"], ["${{11x}\\over{4}}+{{5}\\over{6}}={{7x}\\over{3}}+{{13}\\over{12}}$", "$\\begin{align*}{{11x}\\over{4}}+{{5}\\over{6}} &= {{7x}\\over{3}}+{{13}\\over{12}} && |\\cdot 12\\\\\n33x+10 &= 28x+13 && |-\\left(28x+10\\right)\\\\\n5x &= 3 && |:5\\\\\nx &= {{3}\\over{5}}\n\\end{align*}$"], ["${{19x}\\over{12}}+{{8}\\over{3}}={{5x}\\over{4}}+{{35}\\over{12}}$", "$\\begin{align*}{{19x}\\over{12}}+{{8}\\over{3}} &= {{5x}\\over{4}}+{{35}\\over{12}} && |\\cdot 12\\\\\n19x+32 &= 15x+35 && |-\\left(15x+32\\right)\\\\\n4x &= 3 && |:4\\\\\nx &= {{3}\\over{4}}\n\\end{align*}$"], ["${{15x}\\over{14}}+{{6}\\over{7}}={{3x}\\over{4}}+{{8}\\over{7}}$", "$\\begin{align*}{{15x}\\over{14}}+{{6}\\over{7}} &= {{3x}\\over{4}}+{{8}\\over{7}} && |\\cdot 28\\\\\n30x+24 &= 21x+32 && |-\\left(21x+24\\right)\\\\\n9x &= 8 && |:9\\\\\nx &= {{8}\\over{9}}\n\\end{align*}$"], ["${{22x}\\over{9}}+{{8}\\over{3}}={{5x}\\over{3}}+3$", "$\\begin{align*}{{22x}\\over{9}}+{{8}\\over{3}} &= {{5x}\\over{3}}+3 && |\\cdot 9\\\\\n22x+24 &= 15x+27 && |-\\left(15x+24\\right)\\\\\n7x &= 3 && |:7\\\\\nx &= {{3}\\over{7}}\n\\end{align*}$"], ["${{29x}\\over{14}}+{{5}\\over{7}}={{7x}\\over{4}}+{{8}\\over{7}}$", "$\\begin{align*}{{29x}\\over{14}}+{{5}\\over{7}} &= {{7x}\\over{4}}+{{8}\\over{7}} && |\\cdot 28\\\\\n58x+20 &= 49x+32 && |-\\left(49x+20\\right)\\\\\n9x &= 12 && |:9\\\\\nx &= {{4}\\over{3}}\n\\end{align*}$"], ["$x+{{5}\\over{9}}={{3x}\\over{4}}+{{11}\\over{9}}$", "$\\begin{align*}x+{{5}\\over{9}} &= {{3x}\\over{4}}+{{11}\\over{9}} && |\\cdot 36\\\\\n36x+20 &= 27x+44 && |-\\left(27x+20\\right)\\\\\n9x &= 24 && |:9\\\\\nx &= {{8}\\over{3}}\n\\end{align*}$"]],
 "<hr>"