7/24/2019 flori_2009

1/3

CONCURSUL DE MATEMATIC FLORICA T. CMPANETAPA JUDEEAN, 21 FEBRUARIE 2009

Clasa a IV-a

1.Fiica, tatl i !"#ica a" $%&'("#) 90 *( a#i+ P(t( *-i a#i, tatl .a a.(a *( -&t -'i ./'ta iic(i, ia'!"#ica *( *-" -'i ./'ta act"al a tatl"i+ Alai ./'ta i(c'"ia $# &'((#t+

2.U# !l-c#-t( a'( 100 *( &a3i#i, #"%('-tat( *( la 1 la 100+ S( '"& *i# ac(ta, la $#ta%&la'(, 40 *(-i, a&-i ( ac( "%a #"%('(l-' c( %a'c5(a &a3i#il( '%a(+ Et( &-i!il ca ac(at "% i((3al c" 6007 J"tiicai8

3.O ca#titat( *( 120 3 *( &'"#( a -t $%&'it $# %-* (3al $# %ai %"lt( li+ :# .(*('(at'a#&-'t"l"i, &(#t'" a ( (.ita &i('*('il(, ;a t'a#('at c/t( "# ('t *i# ca#titat(a *( &'"#( *i# i(ca'(la*, -!i#/*";( at(l - #-" la* c" t-t at/t(a il-3'a%( *( &'"#( c/t( a" '%a $# i(ca'( *i# lil(i#iial(+

a) C/t( li a" -t la $#c(&"t7J"tiicai8 b) C/t( il-3'a%( *( &'"#( ('a" i#iial $# i(ca'( la*7 c) C/i l(i ;a" $#caat *i# ./#a'(a &'"#(l-' *i# la*a #-" -'%at, *ac "# il-3'a% *( &'"#( *(calitat(a $#t/i c-t < l(i, "# il-3'a% *( &'"#( *( calitat(a a *-"a c-t 4 l(i, ia' la i(ca'( 2il-3'a%( *( &'"#( *( calitatat(a $#t/i (=it c/t( 43 *( &'"#( *( calitat(a a *-"a7

Subiect elaborat de Dumitru Prial i Ctlin Budeanu

Clasa a V-a

1. N-t% c" 1 2 2009, ,+++++,a a a #"%('(l( 1, 2, >, 2009, c'i( $# alt -'*i#(+ A'tai c #"%'"l

( ) ( ) ( )1 2 20091 2 +++++++ 2009N a a a= + + + (t( &a'+ Et( &-i!il caN #" i( *i.ii!il c" < 7

2.:#t';"# &t'at ? ? "#t c'i(

7/24/2019 flori_2009

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CONCURSUL DE MATEMATIC FLORICA T. CMPANETAPA JUDEEAN, 21 FEBRUARIE 2009

Clasa a VI-a

1. a)Fi( &'-&-'ia ,a c

b d= c" t-i t('%(#ii #"%('( #at"'al(, at(l $#c/t d(t( *i.ii!il i c" b, i c"

c, ia' bi c"#t &'i%( $#t'( (l(+ D(%-#t'ai c bcd(t( &t'at &('(ct+ b)Dac "# (=t'(% al "#(i &'-&-'ii c" t-i t('%(#ii #"%('( #at"'al( #(#"l( (t( *i.ii!il c" i(ca'(*i# %(ii (i, a'tai c "%a t"t"'-' t('%(#il-' (t( *i.ii!il c" c(llalt (=t'(%+

Claudiu tefan Popa

2.Di# ca"a c'i(i (c-#-%ic(, &'("l "#(i %'i ( '(*"c( &t%/#al c" @0, ti%& *( n &t%/#i,"#*( , 2+n n

a)C-#i*('% c &'("l i#iial al %'ii (t( *( 42 *( l(i+ tii#* c, at"#ci c/#* (t( ca"l, (

&'-c(*(a la '-t"#i'(a &'("l"i *"& - a#"%it '(*"c('(, &(#t'" ca (l &-at i &ltit c" "#itil(%-#(ta'( (=it(#t( i c $# a n;a &t%/# &'("l aiat (t( ac(lai c" c(l *i# &t%/#a n 1, (al( n+ b)P'("&"#/#* ac"% c &'("'il( "cc(i. -!i#"t( "#t (=&'i%at( ' '-t"#i'( i c &'("l i#iialal %'ii (t( al(i, a'atai c "%a $#t'( &'("'il( %'ii *i# &'i%(l( n 1 &t%/#i i *"!l"l &'("l"i%'ii *i# a n;a &t%/# (t( al(i+ Claudiu tefan Popa

3.C-#i*('% t'i"#35i"l i-c(lABC, c" AB AC= i 0F G 90 +m BAC

7/24/2019 flori_2009

3/3

CONCURSUL DE MATEMATIC FLORICA T. CMPANETAPA JUDEEAN, 21 FEBRUARIE 2009

Clasa a VIII-a

1.a)D(t('%i#ai #"%('(l( $#t'(3i ai bc" &'-&'i(tat(a c 2 2 1 0+a b ab a b+ + + + =

'ecrea(ii Matematice )*+,,, b) Fi( n "# #"%' #at"'al *at+ D(t('%i#ai #"%('(l( '(al( t'ict &-iti.( , ,x y - &(#t'" ca'(,n nx y- y -x= = i +n- xy=

Neculai Hran'ecrea(ii Matematice +*+,,.

2.D(&'( "# #"%' #at"'al n.-% &"#( c a'( &'-&'i(tat(a PG *ac 2< 1n + i .-% &"#( c

a'( &'-&'i(tat(a $G *ac { }2< K , 2,4,