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Ministerul Educa釘iei, Cercetrii i Inovrii 
Centrul Na釘ional pentru Curriculum i Evaluare 樽n nv釘m但ntul Preuniversitar 
Solu釘ie 
1. ( 3 + 7)2 = 3 + 2 21 + 7 =10 + 2 21 ; 4,5 < 21 < 4,69 < 2 21 < 9,2 ,deci 錚錚( 3 + 7)2 錚刻 =19 . 
2. 
 x   x    錚 1 
錚 x 
錚 錚 
2 1 3 2 2 3 3 
  +    +   
    
x x x x 
x x x x 
 ; ( )( ) 
1 0,1 2 0 1,2 
錚 錚 
0 0 
1 1 2 12 1 
x 
錚 錚 錚 錚 
 
k k 
JJG JJG JJG JJG 
A B C 
JJG G G 
a 
= =  = 
A R R 
BACALAUREAT 2009-MATEMATIC - Proba D, tipul subiectului MT1, programa M1 
1 
,1 
2 
錚 錚 
. 
3. 3 2  x = 2  x2  x = (2  x)3  (2  x)(x2  4x + 3) = 0 x{1;2;3} . 
4. 
2 49 
3 2 
1 49 
k k 
k 
Tk C x y 
+ 
錚 錚 
= 錚 錚 
錚 錚 
錚 錚 
; 2(49 ) 
28 
3 2 
k 
 
=  =  28 14 14 
T29 = C49 x y . 
5. 
3 
G 
r r r 
r 
+ + 
=  
rG = 2i + 2 j 
. 
6. 
3 
sin , 2 3. 
2 sin 
A

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  • 1. Ministerul Educa釘iei, Cercetrii i Inovrii Centrul Na釘ional pentru Curriculum i Evaluare 樽n nv釘m但ntul Preuniversitar Solu釘ie 1. ( 3 + 7)2 = 3 + 2 21 + 7 =10 + 2 21 ; 4,5 < 21 < 4,69 < 2 21 < 9,2 ,deci 錚錚( 3 + 7)2 錚刻 =19 . 2. x x 錚 1 錚 x 錚 錚 2 1 3 2 2 3 3 + + x x x x x x x x ; ( )( ) 1 0,1 2 0 1,2 錚 錚 0 0 1 1 2 12 1 x 錚 錚 錚 錚 k k JJG JJG JJG JJG A B C JJG G G a = = = A R R BACALAUREAT 2009-MATEMATIC - Proba D, tipul subiectului MT1, programa M1 1 ,1 2 錚 錚 . 3. 3 2 x = 2 x2 x = (2 x)3 (2 x)(x2 4x + 3) = 0 x{1;2;3} . 4. 2 49 3 2 1 49 k k k Tk C x y + 錚 錚 = 錚 錚 錚 錚 錚 錚 ; 2(49 ) 28 3 2 k = = 28 14 14 T29 = C49 x y . 5. 3 G r r r r + + = rG = 2i + 2 j . 6. 3 sin , 2 3. 2 sin A