miniaufgabe.js
==== 4. Juni 2018 bis 8. Juni 2018 ====
=== Dienstag 5. Juni 2018 ===
Ausfall der Mathematikstunden. Repetieren Sie die {{lehrkraefte:blc:math:unterlagen:trigonometrie-sv.pdf|Trigonometrie}}, Seite 71/72 bis und mit Aufgabe 222. Es wird am Freitag 8. Juni einen Kurztest darüber geben (zählt 25% einer Prüfungsnote).
=== Freitag 8. Juni 2018 ===
Kurztest Trigonometrie.
==== 11. Juni 2018 bis 15. Juni 2018 ====
=== Dienstag 12. Juni 2018 ===
Ausmultiplizieren, zusammenfassen und zuletzt faktorisieren.miniAufgabe("#exoausmulundbinom","#solausmulundbinom",
[["$\\left(\\frac{3}{4}x-\\frac{3}{2}\\right)\\cdot\\left(-\\frac{10}{9}x+\\frac{9}{7}\\right)+\\left(-\\frac{9}{7}x+\\frac{18}{7}\\right)\\cdot\\left(-\\frac{77}{54}x+\\frac{83}{36}\\right)$", "$-\\frac{5}{6}x^2+\\frac{27}{28}x+\\frac{5}{3}x-\\frac{27}{14}+\\frac{11}{6}x^2-\\frac{83}{28}x-\\frac{11}{3}x+\\frac{83}{14}=x^2-4x+4 = \\left(x-2\\right)^2$"], ["$\\left(\\frac{1}{2}x+\\frac{3}{2}\\right)\\cdot\\left(\\frac{9}{2}x-\\frac{1}{2}\\right)+\\left(-\\frac{4}{7}x-\\frac{12}{7}\\right)\\cdot\\left(\\frac{35}{16}x-\\frac{91}{16}\\right)$", "$\\frac{9}{4}x^2-\\frac{1}{4}x+\\frac{27}{4}x-\\frac{3}{4}-\\frac{5}{4}x^2+\\frac{13}{4}x-\\frac{15}{4}x+\\frac{39}{4}=x^2+6x+9 = \\left(x+3\\right)^2$"], ["$\\left(-\\frac{1}{2}x-\\frac{1}{2}\\right)\\cdot\\left(-\\frac{4}{9}x-\\frac{10}{9}\\right)+\\left(\\frac{2}{3}x+\\frac{38}{21}\\right)\\cdot\\left(\\frac{7}{6}x+\\frac{14}{3}\\right)$", "$\\frac{2}{9}x^2+\\frac{5}{9}x+\\frac{2}{9}x+\\frac{5}{9}+\\frac{7}{9}x^2+\\frac{28}{9}x+\\frac{19}{9}x+\\frac{76}{9}=x^2+6x+9 = \\left(x+3\\right)^2$"], ["$\\left(\\frac{8}{3}x-\\frac{7}{6}\\right)\\cdot\\left(-\\frac{3}{10}x-\\frac{3}{5}\\right)+\\left(\\frac{1}{3}x+\\frac{11}{36}\\right)\\cdot\\left(\\frac{27}{5}x+\\frac{54}{5}\\right)$", "$-\\frac{4}{5}x^2-\\frac{8}{5}x+\\frac{7}{20}x+\\frac{7}{10}+\\frac{9}{5}x^2+\\frac{18}{5}x+\\frac{33}{20}x+\\frac{33}{10}=x^2+4x+4 = \\left(x+2\\right)^2$"], ["$\\left(\\frac{1}{3}x+\\frac{2}{3}\\right)\\cdot\\left(\\frac{9}{5}x+\\frac{1}{3}\\right)+\\left(\\frac{9}{4}x+\\frac{9}{2}\\right)\\cdot\\left(\\frac{8}{45}x+\\frac{68}{81}\\right)$", "$\\frac{3}{5}x^2+\\frac{1}{9}x+\\frac{6}{5}x+\\frac{2}{9}+\\frac{2}{5}x^2+\\frac{17}{9}x+\\frac{4}{5}x+\\frac{34}{9}=x^2+4x+4 = \\left(x+2\\right)^2$"], ["$\\left(\\frac{4}{3}x-\\frac{8}{3}\\right)\\cdot\\left(\\frac{9}{14}x-\\frac{7}{2}\\right)+\\left(\\frac{8}{7}x-\\frac{16}{7}\\right)\\cdot\\left(\\frac{1}{8}x+\\frac{7}{3}\\right)$", "$\\frac{6}{7}x^2-\\frac{14}{3}x-\\frac{12}{7}x+\\frac{28}{3}+\\frac{1}{7}x^2+\\frac{8}{3}x-\\frac{2}{7}x-\\frac{16}{3}=x^2-4x+4 = \\left(x-2\\right)^2$"], ["$\\left(\\frac{3}{7}x+\\frac{6}{7}\\right)\\cdot\\left(-\\frac{7}{15}x-\\frac{1}{3}\\right)+\\left(-\\frac{2}{3}x-\\frac{25}{21}\\right)\\cdot\\left(-\\frac{9}{5}x-\\frac{18}{5}\\right)$", "$-\\frac{1}{5}x^2-\\frac{1}{7}x-\\frac{2}{5}x-\\frac{2}{7}+\\frac{6}{5}x^2+\\frac{12}{5}x+\\frac{15}{7}x+\\frac{30}{7}=x^2+4x+4 = \\left(x+2\\right)^2$"], ["$\\left(\\frac{2}{3}x-\\frac{2}{3}\\right)\\cdot\\left(\\frac{15}{4}x-\\frac{3}{4}\\right)+\\left(-\\frac{10}{9}x-\\frac{70}{9}\\right)\\cdot\\left(\\frac{27}{20}x-\\frac{63}{20}\\right)$", "$\\frac{5}{2}x^2-\\frac{1}{2}x-\\frac{5}{2}x+\\frac{1}{2}-\\frac{3}{2}x^2+\\frac{7}{2}x-\\frac{21}{2}x+\\frac{49}{2}=x^2-10x+25 = \\left(x-5\\right)^2$"], ["$\\left(-\\frac{5}{2}x-\\frac{9}{4}\\right)\\cdot\\left(\\frac{2}{25}x+\\frac{2}{5}\\right)+\\left(\\frac{1}{3}x+\\frac{7}{15}\\right)\\cdot\\left(\\frac{18}{5}x+\\frac{21}{2}\\right)$", "$-\\frac{1}{5}x^2-x-\\frac{9}{50}x-\\frac{9}{10}+\\frac{6}{5}x^2+\\frac{7}{2}x+\\frac{42}{25}x+\\frac{49}{10}=x^2+4x+4 = \\left(x+2\\right)^2$"], ["$\\left(\\frac{5}{4}x+\\frac{5}{2}\\right)\\cdot\\left(\\frac{14}{25}x-\\frac{2}{3}\\right)+\\left(-\\frac{4}{5}x-\\frac{8}{5}\\right)\\cdot\\left(-\\frac{3}{8}x-\\frac{85}{24}\\right)$", "$\\frac{7}{10}x^2-\\frac{5}{6}x+\\frac{7}{5}x-\\frac{5}{3}+\\frac{3}{10}x^2+\\frac{17}{6}x+\\frac{3}{5}x+\\frac{17}{3}=x^2+4x+4 = \\left(x+2\\right)^2$"]],
"
", "
", 3);});
=== Freitag 15. Juni 2018 ===
Zusammenfassen, ausklammern, kürzen, Resultat als Vielfaches einer Potenz von $x$:
miniAufgabe("#exovereinfachenAusklammern","#solvereinfachenAusklammern",
[["$\\displaystyle \\frac{\\frac{5}{9} \\cdot x^{-5} \\cdot \\frac{1}{x^{-9}} +\\frac{1}{3} \\cdot x^{5} \\cdot \\frac{1}{x^{-4}}}{\\frac{4}{5} \\cdot x^{8} \\cdot \\frac{1}{x^{-8}} +\\frac{12}{25} \\cdot x^{3} \\cdot \\frac{1}{x^{-18}}}$", "$\\displaystyle \\frac{\\frac{5}{9}\\cdot x^{4} +\\frac{1}{3}\\cdot x^{9}}{\\frac{4}{5}\\cdot x^{16} +\\frac{12}{25}\\cdot x^{21}} = \\frac{\\frac{1}{9}\\cdot x^{4} \\cdot \\left(5 +3\\cdot x^{5}\\right)}{\\frac{4}{25}\\cdot x^{16} \\cdot \\left(5 +3\\cdot x^{5}\\right)} = \\frac{1}{9} \\cdot \\frac{25}{4} \\cdot x^{-12} = \\frac{25}{36}\\cdot x^{-12}$"], ["$\\displaystyle \\frac{\\frac{4}{9} \\cdot x^{6} \\cdot \\frac{1}{x^{-9}} +\\frac{2}{9} \\cdot x^{3} \\cdot \\frac{1}{x^{-4}}}{\\frac{1}{7} \\cdot x^{7} \\cdot \\frac{1}{x^{2}} +\\frac{1}{14} \\cdot x^{6} \\cdot \\frac{1}{x^{9}}}$", "$\\displaystyle \\frac{\\frac{4}{9}\\cdot x^{15} +\\frac{2}{9}\\cdot x^{7}}{\\frac{1}{7}\\cdot x^{5} +\\frac{1}{14}\\cdot x^{-3}} = \\frac{\\frac{2}{9}\\cdot x^{7} \\cdot \\left(2\\cdot x^{8} +1\\right)}{\\frac{1}{14}\\cdot x^{-3} \\cdot \\left(2\\cdot x^{8} +1\\right)} = \\frac{2}{9} \\cdot 14 \\cdot x^{10} = \\frac{28}{9}\\cdot x^{10}$"], ["$\\displaystyle \\frac{\\frac{7}{5} \\cdot x^{6} \\cdot \\frac{1}{x^{-4}} +\\frac{5}{3} \\cdot x^{5} \\cdot \\frac{1}{x^{-8}}}{\\frac{3}{4} \\cdot x^{2} \\cdot \\frac{1}{x^{-6}} +\\frac{25}{28} \\cdot x^{6} \\cdot \\frac{1}{x^{-5}}}$", "$\\displaystyle \\frac{\\frac{7}{5}\\cdot x^{10} +\\frac{5}{3}\\cdot x^{13}}{\\frac{3}{4}\\cdot x^{8} +\\frac{25}{28}\\cdot x^{11}} = \\frac{\\frac{1}{15}\\cdot x^{10} \\cdot \\left(21 +25\\cdot x^{3}\\right)}{\\frac{1}{28}\\cdot x^{8} \\cdot \\left(21 +25\\cdot x^{3}\\right)} = \\frac{1}{15} \\cdot 28 \\cdot x^{2} = \\frac{28}{15}\\cdot x^{2}$"], ["$\\displaystyle \\frac{\\frac{2}{3} \\cdot x^{8} \\cdot \\frac{1}{x^{-8}} +\\frac{1}{3} \\cdot x^{8} \\cdot \\frac{1}{x^{2}}}{\\frac{3}{5} \\cdot x^{3} \\cdot \\frac{1}{x^{-6}} +\\frac{3}{10} \\cdot x^{-3} \\cdot \\frac{1}{x^{-2}}}$", "$\\displaystyle \\frac{\\frac{2}{3}\\cdot x^{16} +\\frac{1}{3}\\cdot x^{6}}{\\frac{3}{5}\\cdot x^{9} +\\frac{3}{10}\\cdot x^{-1}} = \\frac{\\frac{1}{3}\\cdot x^{6} \\cdot \\left(2\\cdot x^{10} +1\\right)}{\\frac{3}{10}\\cdot x^{-1} \\cdot \\left(2\\cdot x^{10} +1\\right)} = \\frac{1}{3} \\cdot \\frac{10}{3} \\cdot x^{7} = \\frac{10}{9}\\cdot x^{7}$"], ["$\\displaystyle \\frac{\\frac{3}{2} \\cdot x^{2} \\cdot \\frac{1}{x^{-3}} +\\frac{3}{8} \\cdot x^{9} \\cdot \\frac{1}{x^{-8}}}{\\frac{1}{2} \\cdot x^{4} \\cdot \\frac{1}{x^{-5}} +\\frac{1}{8} \\cdot x^{5} \\cdot \\frac{1}{x^{-16}}}$", "$\\displaystyle \\frac{\\frac{3}{2}\\cdot x^{5} +\\frac{3}{8}\\cdot x^{17}}{\\frac{1}{2}\\cdot x^{9} +\\frac{1}{8}\\cdot x^{21}} = \\frac{\\frac{3}{8}\\cdot x^{5} \\cdot \\left(4 +1\\cdot x^{12}\\right)}{\\frac{1}{8}\\cdot x^{9} \\cdot \\left(4 +1\\cdot x^{12}\\right)} = \\frac{3}{8} \\cdot 8 \\cdot x^{-4} = 3\\cdot x^{-4}$"], ["$\\displaystyle \\frac{\\frac{1}{4} \\cdot x^{6} \\cdot \\frac{1}{x^{-4}} +\\frac{9}{5} \\cdot x^{6} \\cdot \\frac{1}{x^{-9}}}{\\frac{7}{2} \\cdot x^{9} \\cdot \\frac{1}{x^{5}} +\\frac{126}{5} \\cdot x^{-4} \\cdot \\frac{1}{x^{-13}}}$", "$\\displaystyle \\frac{\\frac{1}{4}\\cdot x^{10} +\\frac{9}{5}\\cdot x^{15}}{\\frac{7}{2}\\cdot x^{4} +\\frac{126}{5}\\cdot x^{9}} = \\frac{\\frac{1}{20}\\cdot x^{10} \\cdot \\left(5 +36\\cdot x^{5}\\right)}{\\frac{7}{10}\\cdot x^{4} \\cdot \\left(5 +36\\cdot x^{5}\\right)} = \\frac{1}{20} \\cdot \\frac{10}{7} \\cdot x^{6} = \\frac{1}{14}\\cdot x^{6}$"], ["$\\displaystyle \\frac{\\frac{9}{7} \\cdot x^{3} \\cdot \\frac{1}{x^{-2}} +\\frac{9}{4} \\cdot x^{5} \\cdot \\frac{1}{x^{-6}}}{\\frac{4}{5} \\cdot x^{7} \\cdot \\frac{1}{x^{-5}} +\\frac{7}{5} \\cdot x^{8} \\cdot \\frac{1}{x^{-10}}}$", "$\\displaystyle \\frac{\\frac{9}{7}\\cdot x^{5} +\\frac{9}{4}\\cdot x^{11}}{\\frac{4}{5}\\cdot x^{12} +\\frac{7}{5}\\cdot x^{18}} = \\frac{\\frac{9}{28}\\cdot x^{5} \\cdot \\left(4 +7\\cdot x^{6}\\right)}{\\frac{1}{5}\\cdot x^{12} \\cdot \\left(4 +7\\cdot x^{6}\\right)} = \\frac{9}{28} \\cdot 5 \\cdot x^{-7} = \\frac{45}{28}\\cdot x^{-7}$"], ["$\\displaystyle \\frac{\\frac{3}{2} \\cdot x^{9} \\cdot \\frac{1}{x^{4}} +\\frac{1}{3} \\cdot x^{8} \\cdot \\frac{1}{x^{-8}}}{\\frac{5}{2} \\cdot x^{3} \\cdot \\frac{1}{x^{-9}} +\\frac{5}{9} \\cdot x^{8} \\cdot \\frac{1}{x^{-15}}}$", "$\\displaystyle \\frac{\\frac{3}{2}\\cdot x^{5} +\\frac{1}{3}\\cdot x^{16}}{\\frac{5}{2}\\cdot x^{12} +\\frac{5}{9}\\cdot x^{23}} = \\frac{\\frac{1}{6}\\cdot x^{5} \\cdot \\left(9 +2\\cdot x^{11}\\right)}{\\frac{5}{18}\\cdot x^{12} \\cdot \\left(9 +2\\cdot x^{11}\\right)} = \\frac{1}{6} \\cdot \\frac{18}{5} \\cdot x^{-7} = \\frac{3}{5}\\cdot x^{-7}$"], ["$\\displaystyle \\frac{\\frac{3}{2} \\cdot x^{2} \\cdot \\frac{1}{x^{-6}} +\\frac{1}{8} \\cdot x^{5} \\cdot \\frac{1}{x^{-6}}}{\\frac{8}{7} \\cdot x^{7} \\cdot \\frac{1}{x^{3}} +\\frac{2}{21} \\cdot x^{-3} \\cdot \\frac{1}{x^{-10}}}$", "$\\displaystyle \\frac{\\frac{3}{2}\\cdot x^{8} +\\frac{1}{8}\\cdot x^{11}}{\\frac{8}{7}\\cdot x^{4} +\\frac{2}{21}\\cdot x^{7}} = \\frac{\\frac{1}{8}\\cdot x^{8} \\cdot \\left(12 +1\\cdot x^{3}\\right)}{\\frac{2}{21}\\cdot x^{4} \\cdot \\left(12 +1\\cdot x^{3}\\right)} = \\frac{1}{8} \\cdot \\frac{21}{2} \\cdot x^{4} = \\frac{21}{16}\\cdot x^{4}$"], ["$\\displaystyle \\frac{\\frac{1}{2} \\cdot x^{6} \\cdot \\frac{1}{x^{-5}} +\\frac{5}{7} \\cdot x^{8} \\cdot \\frac{1}{x^{3}}}{\\frac{1}{7} \\cdot x^{-3} \\cdot \\frac{1}{x^{-7}} +\\frac{10}{49} \\cdot x^{2} \\cdot \\frac{1}{x^{4}}}$", "$\\displaystyle \\frac{\\frac{1}{2}\\cdot x^{11} +\\frac{5}{7}\\cdot x^{5}}{\\frac{1}{7}\\cdot x^{4} +\\frac{10}{49}\\cdot x^{-2}} = \\frac{\\frac{1}{14}\\cdot x^{5} \\cdot \\left(7\\cdot x^{6} +10\\right)}{\\frac{1}{49}\\cdot x^{-2} \\cdot \\left(7\\cdot x^{6} +10\\right)} = \\frac{1}{14} \\cdot 49 \\cdot x^{7} = \\frac{7}{2}\\cdot x^{7}$"]],
"
", "
", 3);});