Quiz — 67d003155e9cc_Corrigé-Devoir de synthèse n°2.pdf

Question 1 sur 10 20:00

[{"id":10043,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x² - 5","option_c":"6x - 5x","option_d":"6x² - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6x - 5\", \"b\": \"3x² - 5\", \"c\": \"6x - 5x\", \"d\": \"6x² - 5\"}}","_debug_options_count":4},{"id":10044,"question":"L'intégrale ∫(2x + 1) dx entre 0 et 2 vaut :","option_a":"6","option_b":"4","option_c":"5","option_d":"7","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calculez l'intégrale indéfinie : x² + x, puis évaluez entre 0 et 2 : (4 + 2) - (0 + 0) = 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\": \"6\", \"b\": \"4\", \"c\": \"5\", \"d\": \"7\"}}","_debug_options_count":4},{"id":10045,"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":"Une fonction dérivable est nécessairement continue, mais l'inverse n'est pas toujours vrai.","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":10046,"question":"Quelle est la solution de l'équation x² - 4x + 3 = 0 ?","option_a":"x = 1 ou x = 3","option_b":"x = -1 ou x = 3","option_c":"x = 1 ou x = -3","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Factorisez : (x - 1)(x - 3) = 0, donc x = 1 ou x = 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\": \"x = 1 ou x = 3\", \"b\": \"x = -1 ou x = 3\", \"c\": \"x = 1 ou x = -3\", ","_debug_options_count":4},{"id":10047,"question":"Vrai ou Faux ? La probabilité conditionnelle P(A|B) est toujours inférieure à P(A).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"P(A|B) peut être supérieure à P(A) si B favorise A (exemple : P(A) = 0.3, P(A|B) = 0.5).","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":10048,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² - 4) quand x tend vers +∞ ?","option_a":"3","option_b":"0","option_c":"∞","option_d":"2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Divisez numérateur et dénominateur par x² : (3 + 2\/x - 1\/x²)\/(1 - 4\/x²) → 3\/1 = 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\": \"3\", \"b\": \"0\", \"c\": \"∞\", \"d\": \"2\"}}","_debug_options_count":4},{"id":10049,"question":"Vrai ou Faux ? Une primitive de f(x) = e^x est F(x) = e^x + C.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^x + C est bien e^x, donc c'est une primitive valide.","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":10050,"question":"Quelle est l'aire sous la courbe de f(x) = x² entre x = 0 et x = 1 ?","option_a":"1\/3","option_b":"1","option_c":"2\/3","option_d":"0.5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calculez l'intégrale ∫x² dx entre 0 et 1 : [x³\/3]₀¹ = 1\/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\": \"1\/3\", \"b\": \"1\", \"c\": \"2\/3\", \"d\": \"0.5\"}}","_debug_options_count":4},{"id":10051,"question":"Vrai ou Faux ? Deux droites parallèles dans l'espace n'ont pas de point d'intersection.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans l'espace, deux droites parallèles n'ont aucun point commun (elles sont strictement parallèles).","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":10052,"question":"Quelle est la solution de l'inéquation 2x - 5 ≤ 3x + 1 ?","option_a":"x ≥ -6","option_b":"x ≤ -6","option_c":"x ≥ 6","option_d":"x ≤ 6","option_e":"","option_f":"","bonne_reponse":"b","explication":"Réarrangez : -5 - 1 ≤ 3x - 2x → -6 ≤ x → x ≥ -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\": \"x ≥ -6\", \"b\": \"x ≤ -6\", \"c\": \"x ≥ 6\", \"d\": \"x ≤ 6\"}}","_debug_options_count":4}]