Show pageOld revisionsBacklinksBack to top This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ===== Miniaufgaben ===== * Jeweils am Freitag wird eine Miniaufgabe geprüft. * Der Minikurztest ist auf mitgebrachtem **A4-Papier im Hochformat** zu lösen. Der Name ist **oben rechts** zu notieren. * Die Prüfungsblätter können mehrmals verwendet werden, die Aufgaben sind aber sauber abzugrenzen. <PRELOAD> miniaufgabe.js </PRELOAD> ==== Miniaufgaben ==== === KW 4=== Primfaktorzerlegung von Nenner und Zähler, dann kürzen und als Kehrwert verrechnen! <JS>miniAufgabe("#exofraction2","#solfraction2",[ [ "$$\\frac{165}{195}:\\frac{231}{52}$$", "$$\\frac{4}{21}$$" ], [ "$$\\frac{45}{50}:\\frac{45}{385}$$", "$$\\frac{77}{10}$$" ], [ "$$\\frac{55}{65}:\\frac{55}{143}$$", "$$\\frac{11}{5}$$" ], [ "$$\\frac{49}{55}:\\frac{49}{33}$$", "$$\\frac{3}{5}$$" ], [ "$$\\frac{147}{165}:\\frac{175}{66}$$", "$$\\frac{42}{125}$$" ], [ "$$\\frac{63}{165}:\\frac{245}{847}$$", "$$\\frac{33}{25}$$" ], [ "$$\\frac{75}{105}:\\frac{75}{175}$$", "$$\\frac{5}{3}$$" ], [ "$$\\frac{175}{165}:\\frac{105}{165}$$", "$$\\frac{5}{3}$$" ], [ "$$\\frac{75}{75}:\\frac{27}{50}$$", "$$\\frac{50}{27}$$" ], [ "$$\\frac{77}{26}:\\frac{55}{26}$$", "$$\\frac{7}{5}$$" ], [ "$$\\frac{105}{165}:\\frac{245}{539}$$", "$$\\frac{7}{5}$$" ], [ "$$\\frac{15}{25}:\\frac{9}{35}$$", "$$\\frac{7}{3}$$" ], [ "$$\\frac{105}{30}:\\frac{45}{110}$$", "$$\\frac{77}{9}$$" ], [ "$$\\frac{385}{78}:\\frac{539}{195}$$", "$$\\frac{25}{14}$$" ], [ "$$\\frac{105}{70}:\\frac{245}{385}$$", "$$\\frac{33}{14}$$" ], [ "$$\\frac{245}{66}:\\frac{343}{385}$$", "$$\\frac{25}{6}$$" ], [ "$$\\frac{15}{35}:\\frac{25}{49}$$", "$$\\frac{21}{25}$$" ], [ "$$\\frac{33}{39}:\\frac{55}{143}$$", "$$\\frac{11}{5}$$" ], [ "$$\\frac{77}{39}:\\frac{77}{143}$$", "$$\\frac{11}{3}$$" ] ]," ");</JS> <HTML> <div id="exofraction2"> </div> </HTML> <hidden Lösungen> <HTML> <div id="solfraction2"></div> </HTML> </hidden> === KW 3=== Primfaktorzerlegung von Nenner und Zähler, dann kürzen und als Kehrwert verrechnen! <JS>miniAufgabe("#exofraction1","#solfraction1",[ [ "$$\\frac{165}{195}:\\frac{231}{52}$$", "$$\\frac{4}{21}$$" ], [ "$$\\frac{45}{50}:\\frac{45}{385}$$", "$$\\frac{77}{10}$$" ], [ "$$\\frac{55}{65}:\\frac{55}{143}$$", "$$\\frac{11}{5}$$" ], [ "$$\\frac{49}{55}:\\frac{49}{33}$$", "$$\\frac{3}{5}$$" ], [ "$$\\frac{147}{165}:\\frac{175}{66}$$", "$$\\frac{42}{125}$$" ], [ "$$\\frac{63}{165}:\\frac{245}{847}$$", "$$\\frac{33}{25}$$" ], [ "$$\\frac{75}{105}:\\frac{75}{175}$$", "$$\\frac{5}{3}$$" ], [ "$$\\frac{175}{165}:\\frac{105}{165}$$", "$$\\frac{5}{3}$$" ], [ "$$\\frac{75}{75}:\\frac{27}{50}$$", "$$\\frac{50}{27}$$" ], [ "$$\\frac{77}{26}:\\frac{55}{26}$$", "$$\\frac{7}{5}$$" ], [ "$$\\frac{105}{165}:\\frac{245}{539}$$", "$$\\frac{7}{5}$$" ], [ "$$\\frac{15}{25}:\\frac{9}{35}$$", "$$\\frac{7}{3}$$" ], [ "$$\\frac{105}{30}:\\frac{45}{110}$$", "$$\\frac{77}{9}$$" ], [ "$$\\frac{385}{78}:\\frac{539}{195}$$", "$$\\frac{25}{14}$$" ], [ "$$\\frac{105}{70}:\\frac{245}{385}$$", "$$\\frac{33}{14}$$" ], [ "$$\\frac{245}{66}:\\frac{343}{385}$$", "$$\\frac{25}{6}$$" ], [ "$$\\frac{15}{35}:\\frac{25}{49}$$", "$$\\frac{21}{25}$$" ], [ "$$\\frac{33}{39}:\\frac{55}{143}$$", "$$\\frac{11}{5}$$" ], [ "$$\\frac{77}{39}:\\frac{77}{143}$$", "$$\\frac{11}{3}$$" ] ]," ");</JS> <HTML> <div id="exofraction1"> </div> </HTML> <hidden Lösungen> <HTML> <div id="solfraction1"></div> </HTML> </hidden> === KW 2=== Berechnen Sie: <JS>miniAufgabe("#exopascal1","#solpascal1",[["$$\\left(\\frac{b}{2}+2 v\\right)^4$$", "$$\\frac{b^4}{16}+b^3 v+6 b^2 v^2+16 b v^3+16 v^4$$"], ["$$(3 a-2 b)^3$$", "$$27 a^3-54 a^2 b+36 a b^2-8 b^3$$"], ["$$\\left(\\frac{c}{3}+3 d\\right)^5$$","$$\\frac{c^5}{243}+\\frac{5 c^4 d}{27}+\\frac{10 c^3 d^2}{3}+30c^2 d^3+135 c d^4+243 d^5$$"], ["$$(2 a-2 b)^3$$", "$$8 a^3-24 a^2 b+24 a b^2-8 b^3$$"], ["$$(c+3 d)^3$$", "$$c^3+9 c^2 d+27 c d^2+27 d^3$$"], ["$$\\left(2u-\\frac{v}{4}\\right)^3$$","$$8 u^3-3 u^2 v+\\frac{3 u v^2}{8}-\\frac{v^3}{64}$$"], ["$$\\left(\\frac{a}{2}-\\frac{b}{3}\\right)^4$$","$$\\frac{a^4}{16}-\\frac{a^3 b}{6}+\\frac{a^2 b^2}{6}-\\frac{2ab^3}{27}+\\frac{b^4}{81}$$"],["$$\\left(\\frac{x}{4}-\\frac{y}{2}\\right)^5$$", "$$\\frac{x^5}{1024}-\\frac{5 x^4 y}{512}+\\frac{5 x^3 y^2}{128}-\\frac{5 x^2 y^3}{64}+\\frac{5 x y^4}{64}-\\frac{y^5}{32}$$"]], " "); </JS> <HTML> <div id="exopascal1"></div> </HTML> <hidden Lösungen> <HTML> <div id="solpascal1"></div> </HTML> </hidden> === KW 1 === Berechnen Sie: <JS>miniAufgabe("#exobruchrechnen3","#solbruchrechnen3", [["$$\\left(\\frac{3}{2}+\\frac{7}{3}\\right):\\frac{46}{21}$$", "$$\\left(\\frac{9}{6}+\\frac{14}{6}\\right):\\frac{46}{21}=\\frac{23}{6}:\\frac{46}{21}=\\frac{7}{4}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{31}\\right)-\\frac{3}{2}$$", "$$\\frac{31}{10}-\\frac{3}{2}=\\frac{31}{10}-\\frac{15}{10}=\\frac{8}{5}$$"], ["$$\\left(\\frac{1}{2}-\\frac{5}{4}\\right):\\frac{9}{28}$$", "$$\\left(\\frac{2}{4}-\\frac{5}{4}\\right):\\frac{9}{28}=-\\frac{3}{4}:\\frac{9}{28}=-\\frac{7}{3}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{25}\\right)-\\frac{4}{3}$$", "$$\\frac{5}{2}-\\frac{4}{3}=\\frac{15}{6}-\\frac{8}{6}=\\frac{7}{6}$$"], ["$$\\left(\\frac{2}{3}-\\frac{9}{5}\\right)\\cdot\\left(-\\frac{15}{34}\\right)$$", "$$\\left(\\frac{10}{15}-\\frac{27}{15}\\right)\\cdot-\\frac{15}{34}=-\\frac{17}{15}\\cdot-\\frac{15}{34}=\\frac{1}{2}$$"], ["$$\\left(\\frac{5}{2}-\\frac{7}{5}\\right)\\cdot\\frac{50}{33}$$", "$$\\left(\\frac{25}{10}-\\frac{14}{10}\\right)\\cdot\\frac{50}{33}=\\frac{11}{10}\\cdot\\frac{50}{33}=\\frac{5}{3}$$"], ["$$\\left(\\frac{9}{2}-\\frac{7}{5}\\right):\\frac{31}{15}$$", "$$\\left(\\frac{45}{10}-\\frac{14}{10}\\right):\\frac{31}{15}=\\frac{31}{10}:\\frac{31}{15}=\\frac{3}{2}$$"], ["$$\\frac{3}{5}:\\frac{18}{65}-\\frac{2}{3}$$", "$$\\frac{13}{6}-\\frac{2}{3}=\\frac{13}{6}-\\frac{4}{6}=\\frac{3}{2}$$"], ["$$\\left(\\frac{7}{4}-\\frac{3}{2}\\right)\\cdot\\frac{8}{3}$$", "$$\\left(\\frac{7}{4}-\\frac{6}{4}\\right)\\cdot\\frac{8}{3}=\\frac{1}{4}\\cdot\\frac{8}{3}=\\frac{2}{3}$$"], ["$$\\left(\\frac{2}{3}-\\frac{5}{2}\\right):\\frac{11}{7}$$", "$$\\left(\\frac{4}{6}-\\frac{15}{6}\\right):\\frac{11}{7}=-\\frac{11}{6}:\\frac{11}{7}=-\\frac{7}{6}$$"]], " "); </JS> <HTML> <div id="exobruchrechnen3"></div> </HTML> <hidden Lösungen> <HTML> <div id="solbruchrechnen3"></div> </HTML> </hidden> === KW 50 === Berechnen Sie: <JS>miniAufgabe("#exobruchrechnen2","#solbruchrechnen2", [["$$\\left(\\frac{3}{2}+\\frac{7}{3}\\right):\\frac{46}{21}$$", "$$\\left(\\frac{9}{6}+\\frac{14}{6}\\right):\\frac{46}{21}=\\frac{23}{6}:\\frac{46}{21}=\\frac{7}{4}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{31}\\right)-\\frac{3}{2}$$", "$$\\frac{31}{10}-\\frac{3}{2}=\\frac{31}{10}-\\frac{15}{10}=\\frac{8}{5}$$"], ["$$\\left(\\frac{1}{2}-\\frac{5}{4}\\right):\\frac{9}{28}$$", "$$\\left(\\frac{2}{4}-\\frac{5}{4}\\right):\\frac{9}{28}=-\\frac{3}{4}:\\frac{9}{28}=-\\frac{7}{3}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{25}\\right)-\\frac{4}{3}$$", "$$\\frac{5}{2}-\\frac{4}{3}=\\frac{15}{6}-\\frac{8}{6}=\\frac{7}{6}$$"], ["$$\\left(\\frac{2}{3}-\\frac{9}{5}\\right)\\cdot\\left(-\\frac{15}{34}\\right)$$", "$$\\left(\\frac{10}{15}-\\frac{27}{15}\\right)\\cdot-\\frac{15}{34}=-\\frac{17}{15}\\cdot-\\frac{15}{34}=\\frac{1}{2}$$"], ["$$\\left(\\frac{5}{2}-\\frac{7}{5}\\right)\\cdot\\frac{50}{33}$$", "$$\\left(\\frac{25}{10}-\\frac{14}{10}\\right)\\cdot\\frac{50}{33}=\\frac{11}{10}\\cdot\\frac{50}{33}=\\frac{5}{3}$$"], ["$$\\left(\\frac{9}{2}-\\frac{7}{5}\\right):\\frac{31}{15}$$", "$$\\left(\\frac{45}{10}-\\frac{14}{10}\\right):\\frac{31}{15}=\\frac{31}{10}:\\frac{31}{15}=\\frac{3}{2}$$"], ["$$\\frac{3}{5}:\\frac{18}{65}-\\frac{2}{3}$$", "$$\\frac{13}{6}-\\frac{2}{3}=\\frac{13}{6}-\\frac{4}{6}=\\frac{3}{2}$$"], ["$$\\left(\\frac{7}{4}-\\frac{3}{2}\\right)\\cdot\\frac{8}{3}$$", "$$\\left(\\frac{7}{4}-\\frac{6}{4}\\right)\\cdot\\frac{8}{3}=\\frac{1}{4}\\cdot\\frac{8}{3}=\\frac{2}{3}$$"], ["$$\\left(\\frac{2}{3}-\\frac{5}{2}\\right):\\frac{11}{7}$$", "$$\\left(\\frac{4}{6}-\\frac{15}{6}\\right):\\frac{11}{7}=-\\frac{11}{6}:\\frac{11}{7}=-\\frac{7}{6}$$"]], " "); </JS> <HTML> <div id="exobruchrechnen2"></div> </HTML> <hidden Lösungen> <HTML> <div id="solbruchrechnen2"></div> </HTML> </hidden> === KW 49 === Resultat als Bruch von Potenzen mit positiven Exponenten von Primzahlen.<JS>miniAufgabe("#exonegex_numberpower","#solnegex_numberpower", [["$\\displaystyle \\frac{63^{-4}}{147^{-2}}$", "$\\displaystyle \\frac{63^{-4}}{147^{-2}} = \\frac{\\left(3^{2} \\cdot 7\\right)^{-4}}{\\left(3 \\cdot 7^{2}\\right)^{-2}} = \\frac{\\left(3 \\cdot 7^{2}\\right)^{2}}{\\left(3^{2} \\cdot 7\\right)^{4}} = \\frac{3^{2} \\cdot 7^{4}}{3^{8} \\cdot 7^{4}} = \\frac{1}{3^{6}}$"], ["$\\displaystyle \\frac{50^{-3}}{20^{-2}}$", "$\\displaystyle \\frac{50^{-3}}{20^{-2}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-3}}{\\left(2^{2} \\cdot 5\\right)^{-2}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{2}}{\\left(2 \\cdot 5^{2}\\right)^{3}} = \\frac{2^{4} \\cdot 5^{2}}{2^{3} \\cdot 5^{6}} = \\frac{2}{5^{4}}$"], ["$\\displaystyle \\frac{175^{-4}}{245^{-3}}$", "$\\displaystyle \\frac{175^{-4}}{245^{-3}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{-4}}{\\left(5 \\cdot 7^{2}\\right)^{-3}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{3}}{\\left(5^{2} \\cdot 7\\right)^{4}} = \\frac{5^{3} \\cdot 7^{6}}{5^{8} \\cdot 7^{4}} = \\frac{7^{2}}{5^{5}}$"], ["$\\displaystyle \\frac{50^{-2}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-2}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{2}} = \\frac{2^{8} \\cdot 5^{4}}{2^{2} \\cdot 5^{4}} = 2^{6}$"], ["$\\displaystyle \\frac{147^{-2}}{63^{-4}}$", "$\\displaystyle \\frac{147^{-2}}{63^{-4}} = \\frac{\\left(3 \\cdot 7^{2}\\right)^{-2}}{\\left(3^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(3^{2} \\cdot 7\\right)^{4}}{\\left(3 \\cdot 7^{2}\\right)^{2}} = \\frac{3^{8} \\cdot 7^{4}}{3^{2} \\cdot 7^{4}} = 3^{6}$"], ["$\\displaystyle \\frac{245^{-3}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-3}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-3}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{3}} = \\frac{5^{8} \\cdot 7^{4}}{5^{3} \\cdot 7^{6}} = \\frac{5^{5}}{7^{2}}$"], ["$\\displaystyle \\frac{50^{-3}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-3}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-3}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{3}} = \\frac{2^{8} \\cdot 5^{4}}{2^{3} \\cdot 5^{6}} = \\frac{2^{5}}{5^{2}}$"], ["$\\displaystyle \\frac{245^{-3}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-3}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-3}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{3}} = \\frac{5^{8} \\cdot 7^{4}}{5^{3} \\cdot 7^{6}} = \\frac{5^{5}}{7^{2}}$"], ["$\\displaystyle \\frac{50^{-2}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-2}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{2}} = \\frac{2^{8} \\cdot 5^{4}}{2^{2} \\cdot 5^{4}} = 2^{6}$"], ["$\\displaystyle \\frac{245^{-2}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-2}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-2}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{2}} = \\frac{5^{8} \\cdot 7^{4}}{5^{2} \\cdot 7^{4}} = 5^{6}$"]], " <hr> ", " <hr> "); </JS> <HTML> <div id="exonegex_numberpower"></div> </HTML> <hidden Lösungen> <HTML> <div id="solnegex_numberpower"></div> <div style='font-size:12px;color:gray;'>ruby potenzen-und-brueche.rb 13</div> </HTML> </hidden> lehrkraefte/ks/enp.txt Last modified: 2022/01/26 22:37by Simon Knaus