Quiz — controle 3-3.pdf

Question 1 sur 10 20:00

[{"id":40940,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A) 6x + 2","option_b":"B) 3x² + 2","option_c":"C) 6x - 5","option_d":"D) 2x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","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) 6x + 2\", \"b\": \"B) 3x² + 2\", \"c\": \"C) 6x - 5\", \"d\": \"D) 2x + 2","_debug_options_count":4},{"id":40941,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = 0, donc l'équation admet une solution réelle double (x = 2).","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":40942,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3)\/(x² - 1) lorsque x tend vers l'infini ?","option_a":"A) 0","option_b":"B) 2","option_c":"C) +∞","option_d":"D) -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) ≈ 2 pour x grand.","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) 2\", \"c\": \"C) +∞\", \"d\": \"D) -1\"}}","_debug_options_count":4},{"id":40943,"question":"La probabilité d'un événement A est P(A) = 0,3. Quelle est la probabilité de l'événement contraire ?","option_a":"A) 0,3","option_b":"B) 0,7","option_c":"C) 0,5","option_d":"D) 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité de l'événement contraire est P(A̅) = 1 - P(A) = 0,7.","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) 0,3\", \"b\": \"B) 0,7\", \"c\": \"C) 0,5\", \"d\": \"D) 1\"}}","_debug_options_count":4},{"id":40944,"question":"Une suite est définie par uₙ₊₁ = 2uₙ + 3 avec u₀ = 1. Quelle est la valeur de u₂ ?","option_a":"A) 5","option_b":"B) 7","option_c":"C) 9","option_d":"D) 11","option_e":"","option_f":"","bonne_reponse":"c","explication":"u₁ = 2*1 + 3 = 5, u₂ = 2*5 + 3 = 13. La bonne réponse est 13 (option C).","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) 5\", \"b\": \"B) 7\", \"c\": \"C) 9\", \"d\": \"D) 11\"}}","_debug_options_count":4},{"id":40945,"question":"La fonction f(x) = x³ - 3x est-elle strictement croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Sa dérivée f'(x) = 3x² - 3 s'annule en x = ±1, donc la fonction n'est pas strictement croissante.","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":40946,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = ln(x) au point d'abscisse x = 1 ?","option_a":"A) 0","option_b":"B) 1","option_c":"C) e","option_d":"D) -1","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de ln(x) est f'(x) = 1\/x, donc f'(1) = 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\": \"A) 0\", \"b\": \"B) 1\", \"c\": \"C) e\", \"d\": \"D) -1\"}}","_debug_options_count":4},{"id":40947,"question":"Dans une classe de 30 élèves, 12 portent des lunettes. Quelle est la probabilité qu'un élève choisi au hasard ne porte pas de lunettes ?","option_a":"A) 0,4","option_b":"B) 0,6","option_c":"C) 0,8","option_d":"D) 0,2","option_e":"","option_f":"","bonne_reponse":"b","explication":"18 élèves ne portent pas de lunettes, donc P = 18\/30 = 0,6.","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) 0,4\", \"b\": \"B) 0,6\", \"c\": \"C) 0,8\", \"d\": \"D) 0,2\"}}","_debug_options_count":4},{"id":40948,"question":"La suite uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite alterne entre -1 et 1, donc elle n'a pas de limite (divergente).","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":40949,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"A) x \u003C -6","option_b":"B) x \u003E -6","option_c":"C) x \u003C 6","option_d":"D) x \u003E 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En simplifiant, on obtient -6 \u003E x, soit x \u003C -6.","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) x \u003C -6\", \"b\": \"B) x \u003E -6\", \"c\": \"C) x \u003C 6\", \"d\": \"D) x \u003E 6\"}}","_debug_options_count":4}]