var imprimare m2 bac 2010 (1) - calificrile profesionale...

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calific ă rile profesionale; profilul tehnic, specializarea toate calific rile profesionale. 1 SUBIECTUL I (30p) Varianta 001 5p 1. S ă se calculeze 2 3 3! C + . 5p 2. S ă se determine solu ţ iile reale ale ecua ţ iei ( ) 5 log 3 4 2 x + = . 5p 3. S ă se calculeze 1 2 1 1 x x + , ş tiind c ă 1 x ş i 2 x sunt solu ţ iile ecua ţ iei 2 2 0 x x = . 5p 4. Se consider ă func ţ ia [ ] : 0,1 f \ , ( ) 2 f x x = − . S ă se determine mul ţ imea valorilor func ţ iei f . 5p 5. Fie punctele ( ) 2, 1 A ş i ( ) 1,3 B . S ă se determine numerele reale a ş i b astfel încât AB ai b j = + JJJG G G . 5p 6. Se consider ă triunghiul ABC cu 4, 7 AB AC = = ş i 3 BC = . S ă se calculeze m ă sura unghiului B . Varianta 1 1 SUBIECTUL II (30p) – Varianta 001 1. Se consider ă determinantul 1 2 3 2 3 1 3 1 2 x x x d x x x x x x = , unde 1 2 3 , , x x x \ sunt solu ţ iile ecua ţ iei 3 3 2 0 x x + = . 5p a) S ă se calculeze 1 2 3 x x x + + . 5p b) S ă se arate c ă 3 3 3 1 2 3 6 x x x + + = − . 5p c) S ă se calculeze valoarea determinantului . d 2. Pe mul ţ imea numerelor reale definim opera ţ ia 4 4 12 x y xy x y = + + + D . 5p 5p 5p 1 SUBIECTUL III (30p) – Varianta 001 1. Se consider ă func ţ ia { } : 1 f \ \ \ , ( ) 2 1 x f x x = + . 5p a) S ă se calculeze derivata func ţ iei f . 5p b) S ă se determine intervalele de monotonie ale func ţ iei f . 5p c) S ă se demonstreze c ă ( ) 4 pentru orice 1 f x x ≤ − < − . 2. Se consider ă func ţ ia ( ) 2 , 0 : , . 1, 0 x x e x f f x x x + = + > \ \ 5p 5p 0 1 ( ) . x f x dx 5p [ ] ( ) ( ) : 0;1 , g g x f x = \ .
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calific ă rile profesionale; profilul tehnic, specializarea toate calific rile profesionale. 222 SUBIECTUL I (30p) Varianta 002 5p 1. Se consider ă func ţ ia : f \ \ , ( ) 3 f x x = . S ă se determine ( ) ( ) ( ) ( ) 4 3 3 4 f f f f . 5p 2. S ă se determine solu ţ iile reale ale ecua ţ iei ( ) 2 2 log 2 log 3 x x + + = . 5p 3. S ă se rezolve în mul ţ imea numerelor întregi inecua ţ ia 2 5 5 1. x x + 5p 4. S ă se demonstreze c ă pentru orice x \ numerele 1 3 1, 3 x x + ş i 5 3 1 x + sunt termeni consecutivi într-o progresie aritmetic ă . 5p 5. În reperul cartezian xOy se consider ă punctele ( ) 4, 8 A ş i ( ) 6,3 . B S ă se determine coordonatele vectorului OA OB + JJJG JJJG . 5p 6. S ă se calculeze aria triunghiului ABC ş tiind c ă ( ) 2, 30 AC m BAC = = ° ) ş i 4 AB = . Varianta 2 2 SUBIECTUL II (30p) – Varianta 002 1. Se consider ă determinantul a b c d c a b b c a = , unde , , a b c \ . 5p 5p 5p 2 3 5 5 2 3 0 3 5 2 x x x x x x x x x = .
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