FS10 Matematik Problemregning Maj 2015

!"#$%&'(&)" .,"#(/012%+,"#$% *+,*,"#$%&'&()*+&,-! .*/',0%&*1-! 2*34-

!

! FP10 Matematik Maj 2015

=>&%&,)!,*%,-!

!

?>*))&'@4>A-!

!56!7&83&+9&#!:;5<

B#C-

! Mikkel Dahl

D#(!,#CD,3*>!*#(!0!*>3-

!BRI10SH

E0>)F,)G$#&,A&)!)0/,C-

!

5

5

!

34 5'&/67'+$#22%/18/+89/2:$/'2/;#/:/$%<$:=7%9

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

A4 J'2:%&2%+/?%9/1#+;+K&9&:&=%+

A43/L:,/?%9/;%+%=&:&= S!LM!O!<I!O!:K!O!5;;! M!O!<I!L!:K: :K:!O!:K!L!<I;; <I;;!O!5;;!L! ////// ///// GFBBBB/?$

//////A4A/>(#+/?'&=%/?:$$:$:2%+/@+4/?:&*2 !!!!!!N'<;!L!MN;!+0,! !!!!!!I5K;'MN;!L /////////G4IGAI/?$/@+/?:&

A4F/>(#+/,2#+/%&/@+#M%&29%$ M!O!NK!O!5;;;'5;;! IM;!O!5;!L!IM;; IM;;'5;;!L +#-$#1)<#'2(/'(/*)&8($1%#0()($)1&$,$=/0' !!!!!!A4C/>(#+/?'&=%/?:$$:$:2%+/@+/2:?% !!!!!!N!O!<;!L! //////>(/)'$(03()<($*&/)1.$)#)"$./$8=*+()2)'2-(/ ))))))A4I/>(#+/?'&=%/2:?%+/#=/?:&*22%+ ))))))5;;;'MN;!L //////>($)82%%()6.)%20')&8($)!$01.2& $$$$$$A4G/O:&9/1+%?/2:$/%&/1*&"2:#&,1+%?,"+:12 3456) A4BD/01.2& !!CDB/?$ FCN

///////F4/.&2'$/@%+,#&%+/:&9$'=2/@8/7#,@:2'$%+/:/P'&?'+"

?49 >(#+/?'&=%/@:=%+/#=/"(:&9%+ RA#&/,&3!0!=TU&>!L ?4@ Q%=&/%2/9:'=+'? / FDHF3D

?4? >'+/67'+$#22%/+%2/:/,:&/@8,2'&9R 789&/:002$89&$&20$;:&<1$90$<2$;/2=02$%>1?<2&$1$;:&>2@2?$>9&$1?</9A0 ICM L:,/?%9/%&/;%+%=&:&= ///////MI;;;'V;;;L ICK P*/,"'$/;%,"+:(% B20$A2??2.=?10/1A2$9?09/$9;$=2?A2<9A2$C&'$C2&=:?$2&$@D>?0$;9/<2?<2$;&9$!""EF!"(+ G43CADIH

C4/O:=*+1S$=%+

A49)P*/,"'$/2%=&%

A4@)>(#+/?'&=%/1%$2%+ >($)($)2)#%')#G$1(%'($)2)1265$): A4?)>(#+/?'&=%/,"+'(%+%9%/1%$2%+ >($)($)2)#%')!"+$*+$#8($(0()1(%'($)2)1265$)9;; A4A)L:,/'2/1#+?$%&/"'&/#?,"+:(%, :J:OW,J5XJ,OW,J:X ,O,JMO,JM ?Y!T/C?$T/C A4:/>'+/67'+$#22%/+%2/:/,:&/@8,2'&9R H9*$789&/:002$89&$&20$1$=1?$CI=09?<*$<9$?$J/1>2&$A9?A20$:A$C/K==20$<2$=9..2$9?09/$ A9?A2$=:.$<2$AL&$1$<2?$9?<2?$;:&.2/

I4/P:#1'&2:,"%/2+%"'&2%+

,'( Q%=&/%&/9:#1'&2:,"/2+%"'&2

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