Quiz — correction bac blanc laghouat 2016 suj1.pdf

Question 1 sur 10 20:00

[{"id":36650,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A : 2x + 3","option_b":"B : x² + 3","option_c":"C : 2x - 5","option_d":"D : x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A : 2x + 3\", \"b\": \"B : x² + 3\", \"c\": \"C : 2x - 5\", \"d\": \"D : x +","_debug_options_count":4},{"id":36651,"question":"Soit une suite géométrique de raison q = 2 et de premier terme u₀ = 3. Quel est le terme u₃ ?","option_a":"A : 6","option_b":"B : 12","option_c":"C : 24","option_d":"D : 48","option_e":"","option_f":"","bonne_reponse":"c","explication":"u₃ = u₀ × q³ = 3 × 2³ = 3 × 8 = 24.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A : 6\", \"b\": \"B : 12\", \"c\": \"C : 24\", \"d\": \"D : 48\"}}","_debug_options_count":4},{"id":36652,"question":"Vrai ou Faux : Une fonction dérivable est toujours continue.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Toute fonction dérivable en un point est continue en ce point. C'est une propriété fondamentale du calcul différentiel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36653,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3 ?","option_a":"A : x \u003E 1","option_b":"B : x \u003E 4","option_c":"C : x \u003C 4","option_d":"D : x \u003C 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"2x - 5 \u003E 3 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A : x \u003E 1\", \"b\": \"B : x \u003E 4\", \"c\": \"C : x \u003C 4\", \"d\": \"D : x \u003C 1\"}","_debug_options_count":4},{"id":36654,"question":"Vrai ou Faux : La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36655,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² + 1) quand x tend vers l'infini ?","option_a":"A : 0","option_b":"B : 3","option_c":"C : +∞","option_d":"D : -∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant le numérateur et le dénominateur par x², on obtient f(x) = (3 + 2\/x - 1\/x²)\/(1 + 1\/x²). Quand x → ∞, f(x) → 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A : 0\", \"b\": \"B : 3\", \"c\": \"C : +∞\", \"d\": \"D : -∞\"}}","_debug_options_count":4},{"id":36656,"question":"Vrai ou Faux : Une suite arithmétique a une raison constante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite arithmétique est définie par une différence constante entre deux termes consécutifs, appelée raison.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36657,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 2x + 1 ?","option_a":"A : x⁴ - x² + x + C","option_b":"B : 12x² - 2 + C","option_c":"C : x⁴ - x² + C","option_d":"D : 4x⁴ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 4x³ est x⁴, celle de -2x est -x², et celle de 1 est x. On ajoute la constante C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A : x⁴ - x² + x + C\", \"b\": \"B : 12x² - 2 + C\", \"c\": \"C : x⁴","_debug_options_count":4},{"id":36658,"question":"Vrai ou Faux : Si deux événements sont incompatibles, leur probabilité conjointe est nulle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux événements incompatibles ne peuvent pas se produire simultanément, donc P(A ∩ B) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36659,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"A : y = Ce^(-2x)","option_b":"B : y = Ce^(2x)","option_c":"C : y = C - 2x","option_d":"D : y = Cx","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce^(-2x), où C est une constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A : y = Ce^(-2x)\", \"b\": \"B : y = Ce^(2x)\", \"c\": \"C : y = C - 2x\",","_debug_options_count":4}]