Modele de subiecte tip BAC rezolvate

Variantă 2 - Subiect tip 1

TESTUL nr. 2

Subiect tip I.

1) Fie MathML (base64):PG1hdGg+CiAgICA8bWk+WjwvbWk+CiAgICA8bW8+PTwvbW8+CiAgICA8bWk+NCArIDNpPC9taT4KPC9tYXRoPg==. Calculați MathML (base64):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.

2) Determinați MathML (base64):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.

3) Rezolvați ecuația MathML (base64):PG1hdGg+CiAgICA8bXN1cD4KICAgICAgICA8bWk+MjwvbWk+CiAgICAgICAgPG1pPngrMjwvbWk+CiAgICA8L21zdXA+CiAgICA8bW8+KzwvbW8+CiAgICA8bXN1cD4KICAgICAgICA8bWk+MjwvbWk+CiAgICAgICAgPG1pPngrMTwvbWk+CiAgICA8L21zdXA+CiAgICA8bW8+KzwvbW8+CiAgICA8bXN1cD4KICAgICAgICA8bWk+MjwvbWk+CiAgICAgICAgPG1pPng8L21pPgogICAgPC9tc3VwPgogICAgPG1pPj08L21pPgogICAgPG1vPjE0PC9tbz4KPC9tYXRoPg== .

4) Fie MathML (base64):PG1hdGg+CiAgICA8bWk+QTwvbWk+CiAgICA8bWk+PTwvbWk+CiAgICA8bW8+ezwvbW8+CiAgICA8bWk+MTwvbWk+CiAgICA8bWk+LDwvbWk+CiAgICA8bWk+MjwvbWk+CiAgICA8bWk+LDwvbWk+CiAgICA8bWk+MzwvbWk+CiAgICA8bWk+LDwvbWk+CiAgICA8bWk+NDwvbWk+CiAgICA8bWk+LDwvbWk+CiAgICA8bWk+NTwvbWk+CiAgICA8bW8+fTwvbW8+CjwvbWF0aD4=. Scrieți raportul dintre numărul submulțimilor lui A și numărul submulțimilor cu 3 elemente ale lui A.

5) Fie A(4, 0), B(-4, 0), C(0, 6). Determinați coordonatele centrului cercului circumscris triunghiului ABC.

6) Rezolvați ecuația MathML (base64):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.

Variantă 2 - Subiect tip 2

TESTUL nr. 1

Subiect tip II.

1. Fie matricea ........

a) Determinați rangA.

b) Calculați .......

c) Arătați că .......

2. Fie G=(-2, 2) și legea de compoziție ....

a) G este parte stabilă a lui ... în raport cu ”o”.

b) Orice element din G este simetrizabil în raport cu legea ”o”.

c) Arătați că ......este izomorfism între .... și .... .

Variantă 2 - Subiect tip 3

Variantă 2 - Subiect tip 3