Barem de Evaluare Si de Notare

7/25/2019 Barem de Evaluare Si de Notare

1/33

BAREM DE EVALUARE I DE NOTARE

Varianta 6 Prof. Andone Elena

SUBIECTUL I (3 de !"n#te$

%. & ('!$

.29

('!$

3. ) *%) ) %) ) 3

('!$

+.x

2

x+1

('!$

'. 362

('!$6. 3 fe e laterale i do", -ae ('!$

SUBIECTUL II (3 de !"n#te$%. De/en ('!$. a 0 - 1 %') (%!$

a 1 +-) (%!$Se reol2a /i/te"l forat din #ele do", e#"a ii a 1 %) - 1 3 (3!$

3. |13| 1 3 4 %

(%!$|1+3| 1 % 0 3

(%!$|13| 0 |1+3| 1 31+1+3=23

(!$Re"ltat"l e/te n",r ira ional (%!$

+. a$ !re "l d"!, !ria /#"!ire e/te de 3 0 53 1 36 lei (!$!re "l d"!, a do"a /#"!ire e/te de 36 0 %536 1 376 lei (3!$-$ 3 0 353 1 37 lei ('!$

'. '6 1 (ab2 1

a2+b2 * a-

(!$'6 1 86 4 a- (%!$

a- 1 +' (%!$a- 1 ' (%!$


2/33

SUBIECTUL III (3 de !"n#te$

%. a$ ADCE 1 !aralelo9ra AD DE ) AD CE CE DE DCE

dre!t"n9:i# DE 1 ' 3

(3!$

t9 ( DAB $ 1 3 (DAB$ 1 6

(!$-$ EC 1 EB 1 ' #) (!$(CBE$ 1 6) de#i tri"n9:i"l BEC e/te e#:ilateral

(3!$

#$ Aria tra!e"l"i ABCD e/te

1253

4 #

(!$

Aria #olii de :;rtie e/te de 6 # 1253

4

(!$De#i !oate fi de#"!at (%!$

. a$ V 1 L 1 h :2=4950 cm3

('!$

-$V

1 1 15 20=6600cm3

(3!$Vpiatra 1 66 4 +7' 1 %6' #3

(!$

#$ A sticla=A tA b=2550 cm2

('!$

Varianta 8 Prof. Andone ElenaSUBIECTUL I (3 de !"n#te$

%. 8)(3$ ('!$. % ('!$3. 7)' 9 ('!$+. 3 ('!$

'. 7 3

('!$6. 6)6' ('!$

SUBIECTUL II (3 de !"n#te$


3/33

%. Ine#"a ia e/te e#:i2alent, #" 6< 0 4 % +< 0 %6< 4 +< % 0 % 4

< 7

(+!$

< e/te n",r nat"ral (%!$

. ?ie a!re "l "n"i @9 de -anane i b!re "l "n"i @9 de !orto#ale (%!$%+a 0 &- 1 &6 (%!$a 0 +- 1 %'& (%!$Reol2;nd /i/te"l forat din #ele do", e#"a ii o- ine #, % @9 de -anane #o/t, ' lei)

"n @9 de !orto#ale lei) (%!$de#i 3 @9 de -anane i % @9 de !orto#ale #o/t, %8 lei (%!$

3. Ra ionali, fie#are din terenii /"ei #" e

%. a$ A DMN 1 A ABCDA DCMAADNAMNB=

(!$60015010 (30x )5x=150+5x (3!$

-$ %' 0 '< 1 '< 1 ' < 1 % (!$a!li#, teorea l"i Pita9ora n tri"n9:i"l ADN i o- ine

DN 1 2

(3!$#$ Se 2erifi#, #" re#i!ro#a teoreei l"i Pita9ora #a tri"n9:i"l DMN e/te "n tri"n9:i

dre!t"n9:i# n N ('!$


4/33

. a$ V 1 L l h=240000 cm3

('!$

-$ Dre!tele DB i AD /"nt ne#o!lanare) AD BC) DB BC 1 =B>

"n9:i"l dintre #ele do", dre!te e/te "n9:i"l DBC. (!$

Tri"n9:i"l DBC e/te dre!t"n9:i# n C DB 1 ' 5

(!$

Co/ DBC 155 .

(%!$

#$ At1 (l L+L h+l h $ 1 (%!$

136 # (+!$

Varianta & Prof. Andrei Len" a


%. % ('!$. ('!$3. 88 ('!$+. ' ('!$'. %3 ('!$6. 3 ('!$

SUBIECTUL II (3 de !"n#te$%. De/enea, tetraed"l re9"lat (+!$Notea, tetraed"l re9"lat MNP (%!$

. %a 4 %6- 1 a * - 0 7a 4 %'- 1 (!$1%8 0 3(3a 4 '-$ 1 (!$

1%8 0 3 3 1 &6

(%!$3. Not, #" x n",r"l de !ro-lee reol2ate n !ria i de Andrei

(2p)

< 0 < 0 ' 0 < 0 % 0 < 0 %' 1 %%+< 1 3 1 %% +< 1 & < 1 (!ro-lee a reol2at Andrei n !ria i$ (!$Fn ni#io i n",r"l !ro-leelor reol2ate n" e/te !ri. (%!$

+. a$ f($ 1 3 4 3 1 *3 A()*3$

(%!$

f(%$ 1 3 % 4 3 1 B(%)$

(%!$Re!reentarea #elor do", !"n#te /a" alte do", !"n#te de !e 9rafi# #ore#t n /i/te"l

de a


5/33

-$ A(


6/33

AC A!

, (A$ 1 7T P A A

!2

1 A!C

2AC2 1 4 %6+ 1

36 AA!

1 6 #

(3!$

-$ ?ie DM D!

B) M ( D!

B$ d(D, D!

B) 1 DM

(%!$

DM =DD

! BD

D!B

(!$

=60 2041

1002 1

1241

2 1 6 82 #

(!$#$ +l1 + cm3 (%!$

?ie x n,l iea la #are /e ridi#, a!a V 1 A ABCD x

(%!$

+ cm3 1 & x x 1 + H &

(!$

x = ' # (%!$

Varianta 7 Prof. Andrei Len" a


%. + ('!$

. (* " %

('!$3. + ('!$

+. %7 ('!$'. 6 ('!$6. 6 ('!$

SUBIECTUL II (3 de !"n#te$%. De/enea, !ri/a tri"n9:i"lar, re9"lat, (+!$

Notea, !ri/a tri"n9:i"lar, re9"lat, (%!$

. ?ie x /"a !e #are o are Ni#oleta 3x 0x

3 0 8 1 &8

(!$


7/33

10x

3 0 8 1 &8 10x

3 1 6

(!$

x 1 6

3

10 1 8&

(%!$

3.1

a+b 1ab

ab

(%!$

E12121 0

3232 0 ... 0

2012201120122011

(3!$

E1 *% 0 2012

(%!$

+. a$f($ 1 3 02=2A(0,2) (%!$

f(%$ 1 3 12=1B(1,1) (%!$

Re!reentarea #elor do", !"n#te /a" alte do", !"n#te de !e 9rafi# #ore#t n /i/te"l

de a


8/33

+ x24x+1=(2x1)2 (%!$

7 y2+6y+1=(3y+1)2 (%!$

(2x1)2 %0 ) (3y+1)2

%0

(%!$4x

2

4 +x0 7 y2

0 6y0 ' 0

(%!$

SUBIECUL III (3 de !"n#te$%. a$ Not, VABCD !iraida) O #entr"l -aei ABCD) M ilo#"l lat"rii BC (%!$

Fn VOM(m(O$ 1 7$ V&2

1 VM2

* &M2

(!$OM a!otea -aei OM 1 + (%!$V&

2

1 5242 1 7 VO 1 3

(%!$

-$ A t=A l+Ab , A l=pb ap

2, Ab=l

2

(%!$

A l 14 8 5

2=80m2

(!$Ab=64m

2

A t=80m2+64m2=144m2 (%!$

& 144 m2+8 1m2=1160 m2 (%!$

#$ V 1A b h

3

(%!$

V 1

64 3

3 1 6+ m3

(3!$6+ H 3 1 %)(3$) de#i !ot /ta % de !er/oane n #ort. (%!$

. a$ ?ie ABCD tra!e"l dre!t"n9:i#) AB 1 %m) CD 1 &) m(B$ 1 6) (%!$CMAB MB 1 BC 1 +m (%!$

Fn CMB) m(M$ 1 7 CM2=BC2MB2CM2=4222=12 CM 1

3

(!$


9/33

PABCD 1 AB 0 BC 0 CD 0 AD 1 %m + +m + &m + 3 m 1 (%% 0 3 $m

(%!$

-$ A ABCD 1(AB+CD) CM

2

(!$

1(10+8) 23

2 1 %& 3m2 3 m

2

(3!$

#$ 3 17,50=580 l'i


10/33

+. a$ E(%$ 1 ( 11+2+ 1

12 ) : 21

12

(%!$

1 (1

3+ 1

1 ): 2

1=(1

33

3 ): 2

1

(%!$

123

(12)(!$

11

3

(%!$

-$ E(x$ 1x2+x+2(x+2)(x2)

: 2x

x2

(!$

12x

(x+2)(x2): 2x

x2

(%!$

1 2x(x+2)(x2)x22x =

1x+2

(!$

'. A(%) m$ #$ " f(%$ 1 m

(!$

f(%$ 1 % 0 % 1 3

(!$

m1 3 (%!$


%. a$ A 1 L l

(%!$

A 1 %' % 1 %' m

(!$A 1 %' :a (!$

-$ 7)38' tone 9r;" o- in"te de !e 3)8' :a ('!$#$ 7)38' t 1 738' @9 ('!$


11/33

. a$ MN linie ilo#ie n ABC MN AB) MN 1AB

2 1 3 #) dar AB AC

MN AC

(!$ M* (ABC)MN AC} Th 3 NE AC d(N) AC$ 1 NE

(%!$

Fn EMN) m(EMN$ 1 7Th Pita+ra

*N2=*M2+MN2=16+9=25

EN 1 ' # (!$

-$

ACMNAC*N

MN , *N(*MN)

} AC(EMN$

('!$

#$

(*AC) (ABC)=ACMNAC ,MN (ABC)*NAC , *N(*AC) } ((EAC$)(ABC$$ 1 (MN,NE$ 1 MNE

(3!$

/in(MNE$ 1cat p-s.

ip 1M*

N* 14

5

(!$

Varianta %% Prof. An9:el Mi:,i , Gior9i9,SUBIECTUL I (3 de !"n#te$%. %& ('!$. ' ('!$

3. 10/3

('!$

+. 3

('!$

'. 14

('!$6. a 1 6 i - 1 ('!$

SUBIECTUL II (3 de !"n#te$%. Re!reentarea #ore#t, a de/en"l"i ('!$


12/33

. (3+2+1)2

1 6 0 6+23+22

(!$

J(% 0 2 $(% 0 3 $ 0 1 6 0 6+23+22

(3!$3. l 1 )' (3!$

A 1 )6' (!$+. a$f($ 1 (3!$

0 m1 %) m1 & (!$-$A()6$)B(3)$ (3!$Re!reentarea #ore#t, a 9rafi#"l"i (!$

'. %' lei ('!$


%. a$ BC 1 + 2 #

('!$

-$ A 1 (B 0 -$ h/2

(3!$A 1 + # (!$#$ +' ('!$

. a$ AB 1 % (3!$

: 1 3 3

(!$

-$ A t=A l+2A b

(3!$A t 1 %(%& 0 3 $

(!$

#$ V 1 %& 3 3

(3!$+&6 d"-le (!$

Varianta % Prof. An9:el Mi:,i , Gior9i#,SUBIECTUL I (3 de !"n#te$%. ('!$. - ('!$3. x1 %% i y1 % ('!$+. % ('!$

'. d 1 119 #

('!$


13/33

6. A 1 3 3 #

('!$

SUBIECTUL II (3 de !"n#te$

%. Realiarea #ore#t, a de/en"l"i ('!$. < 0 1 3 %'< 0 1 ' (!$

d"-le (3!$

3. 0 3 ' 0 + 8 1 +'

(!$a 1 ) - 1 ') # 1 8 (3!$

+. a$ +a 1 6- (!$a 1 3 i - 1 (3!$

-$ Ma 1 (a+b) /2

(!$Ma 1 )'

(3!$

'. E(


14/33

Varianta %3 Prof. An9:el Mi:,i , Gior9i#,SUBIECTUL I (3 de !"n#te$%. 6 ('!$. & ('!$

3. %' ('!$+. /

('!$'. ('!$6. :a ('!$

SUBIECTUL II (3 de !"n#te$%. 8 ('!$. 1 % ('!$3. M 0 C 1 +)%(%$ (3!$

M 0 D 1 +)3($C 0 D 1 ')(3$Ad"n;nd #ele trei rela ii o- ine M 0 C 0 D 1 %3)6 M 0 C 0 D 1 6)& nlo#"ind n a#e/t, rela ie rela ia (%$

o- ine D 1 )8 leiDin rela ia ($ o- ine M 1 %)6 lei (!$ Din rela ia (3$ o- ine C 1 )' lei

+. a$f(6$ 1 6m0 ' 1 & (3!$m1 )' (!$

-$ ?ie B 1

pr&xA

AOB) m(B$ 1 7

T P

A&

2=B&2+AB2

(3!$A&

2=62+82=100A&=10- m (!$

'. |01|1 & *& 1 ! 4 % 1 & *8 1 ! 1 7 ! J*8)7

('!$


%. a$

VOM ) m(O$ 1 7

T P

VM

2=242+(33)

2=603a

p

=3672 m

(3!$

A t 13 18 367

2 1 &% 67 dm

(!$

-$ A b 1l234 1 &%

3 dm

(3!$


15/33

A t 1 A l+Ab=8167 2m2+8132m2=81(67+3)2m2 (!$

#$ V 1A b h

3 1 6+& 32m3

('!$

. a$ (AB 0 MC$ CB 1 3AD DM

(3!$

DM 1 3 # (!$

-$ Perietr" AB 0 BC 0 CM 0 MA (3!$

P 1 %& # (!$

#$ P 1 (AB+MC)/2

(!$

P 1 +' # (3!$

Varianta %+ Prof. Badea Daniela


%. *77 ('!$

. *+ ('!$3. ('!$+. 36 ('!$'. % ('!$6. ' ('!$

SUBIECTUL II (3 de !"n#te$%. De/enea, tetraed"l (+!$

Notea, tetraed"l (%!$

. " /"a !riit, aa i d,2

33+5 lei

(%!$

tata i d,60

100( 13 35)+3=

3

5 lei

(%!$

e#"a ia e/te2

33+5+

3

5+25=3

23

15=30 (!$

"1 ' lei (%!$


16/33

3. {11x2y=4020x19y=42(3!$

{x=4y=2

(!$

+. a$ x R * {0 41 }

(%!$

E(


17/33


%. a$ 22=L2+l2+h2676=64+36+h2h=25 (!$

A t 1 (#l + #$ + l$$ 1 876 #

(!$V1#l$ = % #3 (%!$

-$ %& D!

B, Q DB d(#$!%B) = #&

('p)D ! P

DP 12

3 "D ! P

D ! D 12

5 DP 1 % #

D ! P6 D! BD (#a I$

D ! P

D ! B =

P6

BD=

D ! 6

D ! D =

10

26

P6=50

13 #

VAMPD! 1 VMAPD !=AAPD ! 2 (M , ADD !)

3

c d(M)ADD$ 1 MN) ilo#"l l"i (AD$ MN 1AB

2 1 3 #

(%!$

AAPD ! 1AD PD!

2 1 + #

(!$

VMAPD! 1 + #3

(%!$

. a$ AM 1 MT 1 + 2 m TN 1 NB 1 2 m

(!$

L 1 (+ 2 0 2 $ 1 % 2 m

(3!$-$ R 1 6m R 1 +m r 1 m (%!$

31 1

/

2(72+r272 )=12/ m237,8m2 (!$


18/33

32 1 TN )' 1 2 m 1 )&

(%!$3 1 3132=37,82,82=34,98

(%!$

#$ Lr=2 / 7!=12/m37,8m=3780 cm (%!$

38& H 3 1 %6 (ar-" ti !e #ir#"ferin a rond"l"i$ (%!$ La 1 /(7+r )=6 /m18,9m=1890 cm (%!$

%&7 H 3 1 63 (ar-" ti$ (%!$?inaliare H %6 0 63 4 % 1 %&& ar-" ti (%!$

Varianta %' Prof. Badea Daniela

SUBIECTUL I (3 de !"n#te$%. x ('!$. 7 ('!$

3. 2

('!$

+.7

8

('!$'. 36 ('!$6. 36 ('!$

SUBIECTUL II (3 de !"n#te$%. De/en (+!$

Nota ii (%!$

.x+y+0+t

4 1 %7+

(%!$

< 13

5 y 13

5 0 13

5 t

(%!$

27

125t+

9

25t+

3

5t=1904 t=875 (!$

< 1 %&7 1 3%' 1 '' (%!$

3. a 0 6- 1 88 "a 0 - 1 88 4 +- (%!$

(a 0 -$ %% " (88 4 +-$ %%

(%!$


19/33

(774b ) 1177 11 } +- %%

(%!$?inaliare (!$

+. a$ #$ # +={M} f('$ 1 6 '('$ 1 6

(%!$

N(%*$ # + " '(%$ 1 *

(%!$

{5m+)=6m+)=2 (!$'(


20/33

SUBIECTUL III (3 de !"n#te$%. a$ #er#"rile a" diaetr"l de + #

% H + 1 '&' 1 +3 0 %3 1 +3 0 % 0 %Total 3' #o "le e (/eidi/#"ri$

-$ VAB i/o/#el #" m(AVB$ 1 +'

VNB dr. I/o/#el VN 1 NB 1 6 2

ANB dr. AB 1 l1 % 22 #

%)+l 2


21/33

3ABCD 1 &&(% 0 3 $ #

(!$

#$ 3MNP6= AC BD

(!$

ABCD ortodia9onal 3ABCD=AC BD

2

(%!$3ABCD

3MNP6 11

2

(!$

Varianta 3% Prof. Brea" Ni#olaeSUBIECTUL I (3 de !"n#te$%. + ('!$. % ('!$3. %6 ('!$+. 3 ('!$

'. + 3

('!$6. ('!$

SUBIECTUL II (3 de !"n#te$%. De/enea, dre!te !aralele t,iate de o /e#ant, (3!$

Un9:i"ri alterne*interne ar#ate #ore#t (!$

. A 1 {0 45 410415 420 425} B 1 {0 47 414 421 428435 4 424 49456 }

(!$

A B 1 {0 45 47 410 414 415 420 421 425428 435 442 4 49456 } are %+ eleente

(!$

A B 1 0 } are "n eleent

(%!$

3. {a+b=64a=3b+8(!$S"-/tit"i an !ria e#"a ie i o- ine +- 1 '6 (%!$

- 1 %+ a 1 ' (!$+. a$ de/fa#ere !arantee (3!$

red"#ere a terenilor a/eenea i o- inere a re"ltat"l"i (!$ -$ /e folo/e te !"n#t"l a$ (%!$


22/33

Cal#"le i o- inerea re"ltat"l"i ?(a$ 1 1

(a+1)(a2+a1)

(!$

Reol2area e#"a iei ?(a$ 11

a31 i re"ltat"l a1

(!$

'.2+323 1 0

3

(%!$

2+222 1

2 0 %

(%!$

5+26 1 2+3

(%!$

Cal#"le i re"ltat 3 Q

(!$


%. a$ Vpirami2.=A b h

3

(%!$

: 1 EO 122

(!$

VABCD*=26 #

3

(%!$

Vcrp=23 #

3

(%!$

-$ E? 1 AC 1 BD 1 2 #

('!$

#$ ABCD 8 BDE?) !,trate #" lat"ra de % #

(3!$


23/33

A ABCD=ABD*9 1% #

(!$

. a$ ABC i/o/#el #" hB 1 %

(3!$

A ABC=AC h B

2 1 6

(!$

-$ Da#, CCAB) at"n#i CC 12AABC

AB 1120

13

(!$

MN 1CC !

2 160

13

(%!$

A MNP6=L l=13

260

13=30 (!$

#$ din a/e,n,ri de tri"n9:i"riC C

!MNCC !

=NC

AC=

NP

AB

(!$

not, NP 1


24/33

Notea, !iraida (%!$

.2

3

a

b+1=

2

32

3+1=

13

92a+3b3b

=2a

3b+3b

3b=2

3

a

b+1

(!$

)(6$ 16

9=1

3

(%!$2

3

a

b+1=

2

32

3+1=

13

9

(!$3. Se notea, #" x ti!"l !ar#"r/ !e o/ n dr" /!re #oal,) #" yti!"l !ar#"r/ #"

a ina /!re #oal,. in;nd #ont #, ele2"l"i i tre-"ie a#ela i ti! d"/ #a i la ntor/

(er9;nd #" a#ela i ilo# de tran/!ort$) /#rieH

{x+y=452y=20(!$ 1 % (%!$< 1 3' (%!$< 1 8 (adi#, dr""l d"/*ntor/ !ar#"r/ !e o/$ (%!$

+. a$ Ale9erea #ore#t, a do", !"n#te #are a!ar in 9rafi#"l"i (+!$

Tra/area 9rafi#"l"i (%!$-$ < 1 f($ 1 * A() *$ (!$ 1 f(


25/33

Not;nd #" x n,l iea la #are a"n9e a!a) a2eH 3' 1 ' 4 x )

(!$< 1 %)8' d (%8)' #$ (%!$

-$

Vac:=5 4 32m3=602m3=60 l

(+!$V

1 1 6l 4 3'l 1 'l

(%!$

#$ Vac: 1 6l 1 6 d3 1 6 #3

(!$Vc-b 1 3 1 & #3

(!$

Vor intra 6H & 1 8' #"-"le e (%!$. a$ MP 1 & (%!$

N 1 6 (%!$

A r)2=MP N6

2

(!$

A r)2=86

2 1 +

(%!$-$ A 2r 1 AB BC 1 %6 6 1 76

(%!$A ha=A2r2 Ar)2 (%!$

2 Ar)2 1 + 1 +&

(%!$Aha 1 76 4 +& 1 +&

(%!$Aha=2 A r)2 (%!$

#$ Cea ai are di/tan , dintre do", !"n#te ale dre!t"n9:i"l"i e/te l"n9iea

dia9onalei [AC]

(!$

?olo/ind teorea l"i Pita9ora /e o- ineH AC 1 162+62 1 292

(!$


26/33

?inaliare 292


27/33

< 4 3 1 < (%!$< 1 3 (%!$M(3)3$ (%!$

'. Ra ionaliea, n"itorii o- in;ndH

N 1 (21

1 +

327

47 (625)7 47

)7

(!$Ad"#e la a#ela i n"itor o- in;ndH

N 17 27+3262+5

77

(!$

?inaliare N 1 % N

(%!$SUBIECTUL III (3 de !"n#te$

%. a$ Pb=2 (6+5 )=22 ($ (!$

A l=Pb h=224=88 ($ (!$

&&H 1 ++ ( liniari$ (%!$

-$ V 1 L l :

(3!$

V 16 5 4

1 % (3

$(!$

#$ Not;nd #" x n,l iea la #are a"n9e ni/i!"l) a2eH 8' 1 6 5 x )

(!$

< 175

30

(!$< 1 )' ($ (%!$

. a$ Raa #er#"l"i #" diaetr"l AB 1 (%!$Raa #er#"l"i #" diaetr"l BC 1 % (%!$L"n9iea a do", /ei#er#"ri o!"/e e/te e9al, #" l"n9iea #er#"l"i. (!$

L"n9iea #er#"l"i 1 /

L"n9iea 9ard"l"i 1 (6 / 0 %$

(%!$-$ Aria dre!t"n9:i"l"i 1 & (%!$

Aria a do", dintre /eidi/#"ri (#" raa % $ 1 % /

(%!$


28/33

Aria #elorlalte do", /eidi/#"ri (#" raa $ 1 + /

(%!$

Aria teren"l"i 1 (& 0 ' / $

(%!$& 0 ' / 800+500 3,15=2375


29/33

75=53

(%!$a 1 (%!$

+. a$ Cal#"lea,f(*'$ 1 %+ (%!$f(+$ 1 *+ (%!$Re!reint, A(*')%+$ i B(+)*+$ (!$

Tra/ea, /e9ent"l n#:i/ [AB ]

(%!$

-$ + 4 < 0 2 1 +

(%!$

*< 1 * 2

(!$< 1 2 [5,4 ]

(!$

'. E(n$ 1 (n0 n * 3$(n0 n * '$ 0 % 1 [ ()2+) )3 ] [ ( )2+2) )5 ] 0 % (%!$

E(n$ 1 ()2+2))2 4 3( )

2+2) $ 4 '( )2+2) $ 0 %' 0 %

(%!$

E(n$ 1

()2+2))2

4 &(

)2+2)

$ 0 %6(%!$

E(n$ 1 ()2+2)4)2 ) !,trat !erfe#t) ) N

(!$


%. a$ n,l iea -lo#"l"i 13

216=24 ($

(!$Pb=4 16=64 ($ (!$

aria lateral, a -lo#"l"i 1 Pb h=64 24=1536 ($ (%!$

-$ dia9onala -aei !iraidei 1 %6 2 ($

(%!$

n,l iea !iraidei 11

416 1 + ($

(%!$


30/33

a!li#, teorea l"i Pita9oraH

"#:ia lateral, a !iraidei 1 42+(82)

2

1 % ($

(3!$

#$ a!otea !iraidei 1 144

64

1 + 5

(

$

(%!$

Arie a#o!eri 1 + 16 45

2 1 %& 5 ($

(!$

N",r i9le 1 %& 5 1 '6 5 1 25602

5 1 '8+ i9le

(!$

. a$ A2isc=/ 72

(!$A2isc=4050/

(!$A 2isc=12757,5 #

(%!$

-$ A )'acp'rit.=Ap.tratA 2isc (%!$

Ap.trat 1 %&' #

(3!$

A)'acp'rit. 1 '+68)' # (%!$

#$ Lat"ra !,trat"l"i :a "rat 1 (452)2+(452)

2

1 7 # (!$

S"nt ne#e/are 7 !l,#i (!$Pre "l 1 38& lei (%!$

Varianta 3' Prof. B"l9,r Delia ValentinaSUBIECTUL I (3 de !"n#te$

%.3

2

('!$. % ('!$

3.1

6

('!$


31/33

+.4

5

('!$'. 6 ('!$

6. %+ ('!$

SUBIECTUL II (3 de !"n#te$%. De/enea, !ri/a (+!$

Notea, !ri/a (%!$

. 32=

1

9

(%!$

24=

1

16

(%!$

o- ine a 15

12

(%!$

ad"#e1

3, 5

12,1

2 la a#ela i n"itor

(%!$

finaliare (%!$

3. Not;nd n1 n",r"l !o etelor ( n N$)x1 !re "l !o etei

2) x+225=340 (3!$

) x=145

(%!$

Din #ondi ia x

% x 1 %+' (lei$(%!$

+. a$ Ale9erea #ore#t, a do", !"n#te #are a!ar in 9rafi#"l"i (+!$Tra/area 9rafi#"l"i (%!$

-$ Not;nd #$&y 1 {A } ) #$&x={B } ) f($ 1 *3) A()*3$

(%!$

A 1&A&B

2

(%!$


32/33

4,5=3 &B

2

(%!$OB 1 3 B(3)$ f(3$ 1 m = 1

(2p)

'. (3x7)2

1 9x267x+7

(%!$(7+3x ) (73x )=79x2 (%!$

(3x+7)2

1 9x2+6 7x+7

(%!$

S 1 9x267x+7+2 (79x2 )+9x2+67x+7=28 (!$


%. a$ C" din datele !ro-leei #ele %6 #"-"ri /"nt a eate !e "n !,trat) a2e !e

l"n9iea !ri/ei + #"-"ri) !e l, iea !ri/ei + #"-"ri. (%!$L 1 % #) l1 % #) : 1 3 # (3!$

V 1 L l : 1 +3 #3

(%!$-$ Pentr" a a2ea -a, "n !,trat #" lat"ra de 6 # /"nt ne#e/are + #"-"ri) iar !entr" a

a2ea n,l iea #"-"l"i de 6 # /"nt ne#e/are #"-"ri /"!ra!"/e. (+!$Total #"-"ri 1 & (%!$

#$ Dr""l ini de la* la e/te dr""l dre!t) adi#, i!oten"a 9 91;1 )

"nde 91;1 #oin#ide #" * din de/f, "rarea lateral, a #"-"l"i.

(!$9 9

1 1 + 6 1 + (#$

(%!$9

1;

1 1 6 (#$

(%!$

A!li#;nd teorea l"i Pita9ora n 9 91;1 ) 9;1 1 6 17 (#$

(%!$

. a$ A 2isc=/ 72

(!$


33/33

A2isc 1 + /

(!$A2isc 1 %6

(%!$

-$ A +a0)=AA2isc (%!$

A 1 ' 3 +38'

(3!$A +a0) 1 3%%' (%!$

#$ P"n#tele /it"ate la di/tan , a

Date post:	27-Feb-2018
Category:	Documents
Upload:	olaru-untaru-cristina-madalina
View:	239 times
Download:	0 times

Barem de Evaluare Si de Notare

Documents