===== 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.
miniaufgabe.js
==== Miniaufgaben ====
=== KW 4===
Primfaktorzerlegung von Nenner und Zähler, dann kürzen und als Kehrwert verrechnen!
miniAufgabe("#exofraction2","#solfraction2",[
[
"$$\\frac{165}{195}:\\frac{231}{52}$$",
"$$\\frac{4}{21}$$"
],
[
"$$\\frac{45}{50}:\\frac{45}{385}$$",
"$$\\frac{77}{10}$$"
],
[
"$$\\frac{55}{65}:\\frac{55}{143}$$",
"$$\\frac{11}{5}$$"
],
[
"$$\\frac{49}{55}:\\frac{49}{33}$$",
"$$\\frac{3}{5}$$"
],
[
"$$\\frac{147}{165}:\\frac{175}{66}$$",
"$$\\frac{42}{125}$$"
],
[
"$$\\frac{63}{165}:\\frac{245}{847}$$",
"$$\\frac{33}{25}$$"
],
[
"$$\\frac{75}{105}:\\frac{75}{175}$$",
"$$\\frac{5}{3}$$"
],
[
"$$\\frac{175}{165}:\\frac{105}{165}$$",
"$$\\frac{5}{3}$$"
],
[
"$$\\frac{75}{75}:\\frac{27}{50}$$",
"$$\\frac{50}{27}$$"
],
[
"$$\\frac{77}{26}:\\frac{55}{26}$$",
"$$\\frac{7}{5}$$"
],
[
"$$\\frac{105}{165}:\\frac{245}{539}$$",
"$$\\frac{7}{5}$$"
],
[
"$$\\frac{15}{25}:\\frac{9}{35}$$",
"$$\\frac{7}{3}$$"
],
[
"$$\\frac{105}{30}:\\frac{45}{110}$$",
"$$\\frac{77}{9}$$"
],
[
"$$\\frac{385}{78}:\\frac{539}{195}$$",
"$$\\frac{25}{14}$$"
],
[
"$$\\frac{105}{70}:\\frac{245}{385}$$",
"$$\\frac{33}{14}$$"
],
[
"$$\\frac{245}{66}:\\frac{343}{385}$$",
"$$\\frac{25}{6}$$"
],
[
"$$\\frac{15}{35}:\\frac{25}{49}$$",
"$$\\frac{21}{25}$$"
],
[
"$$\\frac{33}{39}:\\frac{55}{143}$$",
"$$\\frac{11}{5}$$"
],
[
"$$\\frac{77}{39}:\\frac{77}{143}$$",
"$$\\frac{11}{3}$$"
]
]," ");
=== KW 3===
Primfaktorzerlegung von Nenner und Zähler, dann kürzen und als Kehrwert verrechnen!
miniAufgabe("#exofraction1","#solfraction1",[
[
"$$\\frac{165}{195}:\\frac{231}{52}$$",
"$$\\frac{4}{21}$$"
],
[
"$$\\frac{45}{50}:\\frac{45}{385}$$",
"$$\\frac{77}{10}$$"
],
[
"$$\\frac{55}{65}:\\frac{55}{143}$$",
"$$\\frac{11}{5}$$"
],
[
"$$\\frac{49}{55}:\\frac{49}{33}$$",
"$$\\frac{3}{5}$$"
],
[
"$$\\frac{147}{165}:\\frac{175}{66}$$",
"$$\\frac{42}{125}$$"
],
[
"$$\\frac{63}{165}:\\frac{245}{847}$$",
"$$\\frac{33}{25}$$"
],
[
"$$\\frac{75}{105}:\\frac{75}{175}$$",
"$$\\frac{5}{3}$$"
],
[
"$$\\frac{175}{165}:\\frac{105}{165}$$",
"$$\\frac{5}{3}$$"
],
[
"$$\\frac{75}{75}:\\frac{27}{50}$$",
"$$\\frac{50}{27}$$"
],
[
"$$\\frac{77}{26}:\\frac{55}{26}$$",
"$$\\frac{7}{5}$$"
],
[
"$$\\frac{105}{165}:\\frac{245}{539}$$",
"$$\\frac{7}{5}$$"
],
[
"$$\\frac{15}{25}:\\frac{9}{35}$$",
"$$\\frac{7}{3}$$"
],
[
"$$\\frac{105}{30}:\\frac{45}{110}$$",
"$$\\frac{77}{9}$$"
],
[
"$$\\frac{385}{78}:\\frac{539}{195}$$",
"$$\\frac{25}{14}$$"
],
[
"$$\\frac{105}{70}:\\frac{245}{385}$$",
"$$\\frac{33}{14}$$"
],
[
"$$\\frac{245}{66}:\\frac{343}{385}$$",
"$$\\frac{25}{6}$$"
],
[
"$$\\frac{15}{35}:\\frac{25}{49}$$",
"$$\\frac{21}{25}$$"
],
[
"$$\\frac{33}{39}:\\frac{55}{143}$$",
"$$\\frac{11}{5}$$"
],
[
"$$\\frac{77}{39}:\\frac{77}{143}$$",
"$$\\frac{11}{3}$$"
]
]," ");
=== KW 2===
Berechnen Sie:
miniAufgabe("#exopascal1","#solpascal1",[["$$\\left(\\frac{b}{2}+2 v\\right)^4$$", "$$\\frac{b^4}{16}+b^3 v+6 b^2 v^2+16 b v^3+16 v^4$$"], ["$$(3 a-2 b)^3$$", "$$27 a^3-54 a^2 b+36 a b^2-8 b^3$$"], ["$$\\left(\\frac{c}{3}+3 d\\right)^5$$","$$\\frac{c^5}{243}+\\frac{5 c^4 d}{27}+\\frac{10 c^3 d^2}{3}+30c^2 d^3+135 c d^4+243 d^5$$"], ["$$(2 a-2 b)^3$$", "$$8 a^3-24 a^2 b+24 a b^2-8 b^3$$"], ["$$(c+3 d)^3$$", "$$c^3+9 c^2 d+27 c d^2+27 d^3$$"], ["$$\\left(2u-\\frac{v}{4}\\right)^3$$","$$8 u^3-3 u^2 v+\\frac{3 u v^2}{8}-\\frac{v^3}{64}$$"], ["$$\\left(\\frac{a}{2}-\\frac{b}{3}\\right)^4$$","$$\\frac{a^4}{16}-\\frac{a^3 b}{6}+\\frac{a^2 b^2}{6}-\\frac{2ab^3}{27}+\\frac{b^4}{81}$$"],["$$\\left(\\frac{x}{4}-\\frac{y}{2}\\right)^5$$", "$$\\frac{x^5}{1024}-\\frac{5 x^4 y}{512}+\\frac{5 x^3 y^2}{128}-\\frac{5 x^2 y^3}{64}+\\frac{5 x y^4}{64}-\\frac{y^5}{32}$$"]],
" ");
=== KW 1 ===
Berechnen Sie:
miniAufgabe("#exobruchrechnen3","#solbruchrechnen3",
[["$$\\left(\\frac{3}{2}+\\frac{7}{3}\\right):\\frac{46}{21}$$", "$$\\left(\\frac{9}{6}+\\frac{14}{6}\\right):\\frac{46}{21}=\\frac{23}{6}:\\frac{46}{21}=\\frac{7}{4}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{31}\\right)-\\frac{3}{2}$$", "$$\\frac{31}{10}-\\frac{3}{2}=\\frac{31}{10}-\\frac{15}{10}=\\frac{8}{5}$$"], ["$$\\left(\\frac{1}{2}-\\frac{5}{4}\\right):\\frac{9}{28}$$", "$$\\left(\\frac{2}{4}-\\frac{5}{4}\\right):\\frac{9}{28}=-\\frac{3}{4}:\\frac{9}{28}=-\\frac{7}{3}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{25}\\right)-\\frac{4}{3}$$", "$$\\frac{5}{2}-\\frac{4}{3}=\\frac{15}{6}-\\frac{8}{6}=\\frac{7}{6}$$"], ["$$\\left(\\frac{2}{3}-\\frac{9}{5}\\right)\\cdot\\left(-\\frac{15}{34}\\right)$$", "$$\\left(\\frac{10}{15}-\\frac{27}{15}\\right)\\cdot-\\frac{15}{34}=-\\frac{17}{15}\\cdot-\\frac{15}{34}=\\frac{1}{2}$$"], ["$$\\left(\\frac{5}{2}-\\frac{7}{5}\\right)\\cdot\\frac{50}{33}$$", "$$\\left(\\frac{25}{10}-\\frac{14}{10}\\right)\\cdot\\frac{50}{33}=\\frac{11}{10}\\cdot\\frac{50}{33}=\\frac{5}{3}$$"], ["$$\\left(\\frac{9}{2}-\\frac{7}{5}\\right):\\frac{31}{15}$$", "$$\\left(\\frac{45}{10}-\\frac{14}{10}\\right):\\frac{31}{15}=\\frac{31}{10}:\\frac{31}{15}=\\frac{3}{2}$$"], ["$$\\frac{3}{5}:\\frac{18}{65}-\\frac{2}{3}$$", "$$\\frac{13}{6}-\\frac{2}{3}=\\frac{13}{6}-\\frac{4}{6}=\\frac{3}{2}$$"], ["$$\\left(\\frac{7}{4}-\\frac{3}{2}\\right)\\cdot\\frac{8}{3}$$", "$$\\left(\\frac{7}{4}-\\frac{6}{4}\\right)\\cdot\\frac{8}{3}=\\frac{1}{4}\\cdot\\frac{8}{3}=\\frac{2}{3}$$"], ["$$\\left(\\frac{2}{3}-\\frac{5}{2}\\right):\\frac{11}{7}$$", "$$\\left(\\frac{4}{6}-\\frac{15}{6}\\right):\\frac{11}{7}=-\\frac{11}{6}:\\frac{11}{7}=-\\frac{7}{6}$$"]],
" ");
=== KW 50 ===
Berechnen Sie:
miniAufgabe("#exobruchrechnen2","#solbruchrechnen2",
[["$$\\left(\\frac{3}{2}+\\frac{7}{3}\\right):\\frac{46}{21}$$", "$$\\left(\\frac{9}{6}+\\frac{14}{6}\\right):\\frac{46}{21}=\\frac{23}{6}:\\frac{46}{21}=\\frac{7}{4}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{31}\\right)-\\frac{3}{2}$$", "$$\\frac{31}{10}-\\frac{3}{2}=\\frac{31}{10}-\\frac{15}{10}=\\frac{8}{5}$$"], ["$$\\left(\\frac{1}{2}-\\frac{5}{4}\\right):\\frac{9}{28}$$", "$$\\left(\\frac{2}{4}-\\frac{5}{4}\\right):\\frac{9}{28}=-\\frac{3}{4}:\\frac{9}{28}=-\\frac{7}{3}$$"], ["$$-\\frac{2}{5}:\\left(-\\frac{4}{25}\\right)-\\frac{4}{3}$$", "$$\\frac{5}{2}-\\frac{4}{3}=\\frac{15}{6}-\\frac{8}{6}=\\frac{7}{6}$$"], ["$$\\left(\\frac{2}{3}-\\frac{9}{5}\\right)\\cdot\\left(-\\frac{15}{34}\\right)$$", "$$\\left(\\frac{10}{15}-\\frac{27}{15}\\right)\\cdot-\\frac{15}{34}=-\\frac{17}{15}\\cdot-\\frac{15}{34}=\\frac{1}{2}$$"], ["$$\\left(\\frac{5}{2}-\\frac{7}{5}\\right)\\cdot\\frac{50}{33}$$", "$$\\left(\\frac{25}{10}-\\frac{14}{10}\\right)\\cdot\\frac{50}{33}=\\frac{11}{10}\\cdot\\frac{50}{33}=\\frac{5}{3}$$"], ["$$\\left(\\frac{9}{2}-\\frac{7}{5}\\right):\\frac{31}{15}$$", "$$\\left(\\frac{45}{10}-\\frac{14}{10}\\right):\\frac{31}{15}=\\frac{31}{10}:\\frac{31}{15}=\\frac{3}{2}$$"], ["$$\\frac{3}{5}:\\frac{18}{65}-\\frac{2}{3}$$", "$$\\frac{13}{6}-\\frac{2}{3}=\\frac{13}{6}-\\frac{4}{6}=\\frac{3}{2}$$"], ["$$\\left(\\frac{7}{4}-\\frac{3}{2}\\right)\\cdot\\frac{8}{3}$$", "$$\\left(\\frac{7}{4}-\\frac{6}{4}\\right)\\cdot\\frac{8}{3}=\\frac{1}{4}\\cdot\\frac{8}{3}=\\frac{2}{3}$$"], ["$$\\left(\\frac{2}{3}-\\frac{5}{2}\\right):\\frac{11}{7}$$", "$$\\left(\\frac{4}{6}-\\frac{15}{6}\\right):\\frac{11}{7}=-\\frac{11}{6}:\\frac{11}{7}=-\\frac{7}{6}$$"]],
" ");
=== KW 49 ===
Resultat als Bruch von Potenzen mit positiven Exponenten von Primzahlen.miniAufgabe("#exonegex_numberpower","#solnegex_numberpower",
[["$\\displaystyle \\frac{63^{-4}}{147^{-2}}$", "$\\displaystyle \\frac{63^{-4}}{147^{-2}} = \\frac{\\left(3^{2} \\cdot 7\\right)^{-4}}{\\left(3 \\cdot 7^{2}\\right)^{-2}} = \\frac{\\left(3 \\cdot 7^{2}\\right)^{2}}{\\left(3^{2} \\cdot 7\\right)^{4}} = \\frac{3^{2} \\cdot 7^{4}}{3^{8} \\cdot 7^{4}} = \\frac{1}{3^{6}}$"], ["$\\displaystyle \\frac{50^{-3}}{20^{-2}}$", "$\\displaystyle \\frac{50^{-3}}{20^{-2}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-3}}{\\left(2^{2} \\cdot 5\\right)^{-2}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{2}}{\\left(2 \\cdot 5^{2}\\right)^{3}} = \\frac{2^{4} \\cdot 5^{2}}{2^{3} \\cdot 5^{6}} = \\frac{2}{5^{4}}$"], ["$\\displaystyle \\frac{175^{-4}}{245^{-3}}$", "$\\displaystyle \\frac{175^{-4}}{245^{-3}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{-4}}{\\left(5 \\cdot 7^{2}\\right)^{-3}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{3}}{\\left(5^{2} \\cdot 7\\right)^{4}} = \\frac{5^{3} \\cdot 7^{6}}{5^{8} \\cdot 7^{4}} = \\frac{7^{2}}{5^{5}}$"], ["$\\displaystyle \\frac{50^{-2}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-2}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{2}} = \\frac{2^{8} \\cdot 5^{4}}{2^{2} \\cdot 5^{4}} = 2^{6}$"], ["$\\displaystyle \\frac{147^{-2}}{63^{-4}}$", "$\\displaystyle \\frac{147^{-2}}{63^{-4}} = \\frac{\\left(3 \\cdot 7^{2}\\right)^{-2}}{\\left(3^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(3^{2} \\cdot 7\\right)^{4}}{\\left(3 \\cdot 7^{2}\\right)^{2}} = \\frac{3^{8} \\cdot 7^{4}}{3^{2} \\cdot 7^{4}} = 3^{6}$"], ["$\\displaystyle \\frac{245^{-3}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-3}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-3}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{3}} = \\frac{5^{8} \\cdot 7^{4}}{5^{3} \\cdot 7^{6}} = \\frac{5^{5}}{7^{2}}$"], ["$\\displaystyle \\frac{50^{-3}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-3}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-3}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{3}} = \\frac{2^{8} \\cdot 5^{4}}{2^{3} \\cdot 5^{6}} = \\frac{2^{5}}{5^{2}}$"], ["$\\displaystyle \\frac{245^{-3}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-3}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-3}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{3}} = \\frac{5^{8} \\cdot 7^{4}}{5^{3} \\cdot 7^{6}} = \\frac{5^{5}}{7^{2}}$"], ["$\\displaystyle \\frac{50^{-2}}{20^{-4}}$", "$\\displaystyle \\frac{50^{-2}}{20^{-4}} = \\frac{\\left(2 \\cdot 5^{2}\\right)^{-2}}{\\left(2^{2} \\cdot 5\\right)^{-4}} = \\frac{\\left(2^{2} \\cdot 5\\right)^{4}}{\\left(2 \\cdot 5^{2}\\right)^{2}} = \\frac{2^{8} \\cdot 5^{4}}{2^{2} \\cdot 5^{4}} = 2^{6}$"], ["$\\displaystyle \\frac{245^{-2}}{175^{-4}}$", "$\\displaystyle \\frac{245^{-2}}{175^{-4}} = \\frac{\\left(5 \\cdot 7^{2}\\right)^{-2}}{\\left(5^{2} \\cdot 7\\right)^{-4}} = \\frac{\\left(5^{2} \\cdot 7\\right)^{4}}{\\left(5 \\cdot 7^{2}\\right)^{2}} = \\frac{5^{8} \\cdot 7^{4}}{5^{2} \\cdot 7^{4}} = 5^{6}$"]],
"
", "
");
ruby potenzen-und-brueche.rb 13