Ministerul Educaţiei, Cercetării şi Inovării 
Centrul Naţional pentru Curriculum şi Evaluare în Învăţământul Preuniversitar 
Soluţie 
10 1. ( 1+ i )20 = ( 1+ i )2 = (   2i )10 = −1024 . 
2. f ( f ( x )) =  1 
 f   
= x 
x 
  
, (−10) + (−9) + ...+ (−1) +1+ ...+10 = 0 . 
3. Funcţia este strict crescătoare, fiind compunere de funcţii strict crescătoare, deci funcţia f este injectivă. 
5! 5! 
4. 
− 6 ⋅ = 0 
. 
2! 3!2! 
5. 
( ) 
2 2 
m m − + −= 
3 4 1 11 
+ 
3 4 
⇒ 
m∈{−10;0} . 
6. cos75D − cos15D = −2sin 45D sin30D , 
D = 2 D = 1 
⇒ 2 
sin 45 ,sin 30 
2 2 
D − D = − . 
cos75 cos15 
BACALAUREAT 2009-MATEMATICĂ - Proba D, tipul subiectului MT1, programa M1 
2

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  • 1. Ministerul Educaţiei, Cercetării şi Inovării Centrul Naţional pentru Curriculum şi Evaluare în Învăţământul Preuniversitar Soluţie 10 1. ( 1+ i )20 = ( 1+ i )2 = (   2i )10 = −1024 . 2. f ( f ( x )) =  1  f   = x x   , (−10) + (−9) + ...+ (−1) +1+ ...+10 = 0 . 3. Funcţia este strict crescătoare, fiind compunere de funcţii strict crescătoare, deci funcţia f este injectivă. 5! 5! 4. − 6 ⋅ = 0 . 2! 3!2! 5. ( ) 2 2 m m − + −= 3 4 1 11 + 3 4 ⇒ m∈{−10;0} . 6. cos75D − cos15D = −2sin 45D sin30D , D = 2 D = 1 ⇒ 2 sin 45 ,sin 30 2 2 D − D = − . cos75 cos15 BACALAUREAT 2009-MATEMATICĂ - Proba D, tipul subiectului MT1, programa M1 2