Quiz — 74.DOC

Question 1 sur 10 20:00

[{"id":40600,"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. 3x + 2","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. 3x + 2\"","_debug_options_count":4},{"id":40601,"question":"L'intégrale de 0 à 1 de x² dx est égale à :","option_a":"A. 1\/3","option_b":"B. 1\/2","option_c":"C. 1","option_d":"D. 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de x² est x³\/3. Évaluée entre 0 et 1, cela donne (1³\/3) - (0³\/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\": \"A. 1\/3\", \"b\": \"B. 1\/2\", \"c\": \"C. 1\", \"d\": \"D. 2\"}}","_debug_options_count":4},{"id":40602,"question":"Vrai ou Faux ? La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel.","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":40603,"question":"Quelle est la limite de (sin x)\/x quand x tend vers 0 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une limite fondamentale en analyse : lim (x→0) sin x \/ x = 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. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4},{"id":40604,"question":"Vrai ou Faux ? Une suite croissante est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite croissante peut diverger vers +∞ (exemple : u_n = n).","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":40605,"question":"Quelle est la solution de l'équation différentielle y' = 2y ?","option_a":"A. y = Ce^(2x)","option_b":"B. y = Ce^(-2x)","option_c":"C. y = 2x + C","option_d":"D. y = x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation différentielle y' = ky a pour solution y = Ce^(kx). Ici, k=2, donc y = Ce^(2x).","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 = 2x + C\", \"d","_debug_options_count":4},{"id":40606,"question":"Vrai ou Faux ? La probabilité de l'événement certain est 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité de l'événement certain est 1, et celle de l'événement impossible est 0.","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":40607,"question":"Quelle est la valeur de l'intégrale de -1 à 1 de x^3 dx ?","option_a":"A. 0","option_b":"B. 1\/4","option_c":"C. 1","option_d":"D. 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction x^3 est impaire. L'intégrale d'une fonction impaire sur [-a; a] est toujours 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\": \"A. 0\", \"b\": \"B. 1\/4\", \"c\": \"C. 1\", \"d\": \"D. 2\"}}","_debug_options_count":4},{"id":40608,"question":"Vrai ou Faux ? Le produit scalaire de deux vecteurs orthogonaux est nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire égal à 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":40609,"question":"Quelle est la dérivée seconde de la fonction f(x) = x^3 ?","option_a":"A. 6x","option_b":"B. 3x²","option_c":"C. 6","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée première est f'(x) = 3x². La dérivée seconde est f''(x) = 6x.","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\", \"b\": \"B. 3x²\", \"c\": \"C. 6\", \"d\": \"D. 0\"}}","_debug_options_count":4}]