Quiz — 78.DOC

Question 1 sur 10 20:00

[{"id":37760,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x² + 3x","option_d":"3x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : (x²)' = 2x et (3x)' = 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\": \"2x + 3\", \"b\": \"x² + 3\", \"c\": \"2x² + 3x\", \"d\": \"3x - 5\"}}","_debug_options_count":4},{"id":37761,"question":"La suite définie par uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite est convergente si elle admet une limite finie. Ici, uₙ alterne entre -1 et 1, donc elle n'a pas de limite.","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":37762,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"1","option_b":"0","option_c":"Leur norme","option_d":"Indéterminé","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux vecteurs orthogonaux ont un produit scalaire égal à 0, car cos(90°) = 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\": \"1\", \"b\": \"0\", \"c\": \"Leur norme\", \"d\": \"Indéterminé\"}}","_debug_options_count":4},{"id":37763,"question":"L'intégrale ∫₀¹ x² dx vaut :","option_a":"1\/3","option_b":"1","option_c":"2\/3","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de x² entre 0 et 1 est [x³\/3]₀¹ = 1\/3 - 0 = 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\"}}","_debug_options_count":4},{"id":37764,"question":"La fonction exponentielle est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour tout x réel, eˣ \u003E 0. C'est une propriété fondamentale de la fonction exponentielle.","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":37765,"question":"Quelle est la solution de l'équation différentielle y' = 2y ?","option_a":"y = e^(2x)","option_b":"y = 2x + C","option_c":"y = Ce^(2x)","option_d":"y = x² + C","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'équation y' = 2y a pour solution générale y = Ce^(2x), où C est une constante réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"y = e^(2x)\", \"b\": \"y = 2x + C\", \"c\": \"y = Ce^(2x)\", \"d\": \"y = x²","_debug_options_count":4},{"id":37766,"question":"Le nombre complexe i² est égal à :","option_a":"1","option_b":"-1","option_c":"i","option_d":"0","option_e":"","option_f":"","bonne_reponse":"b","explication":"Par définition, i est l'unité imaginaire telle que i² = -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\": \"1\", \"b\": \"-1\", \"c\": \"i\", \"d\": \"0\"}}","_debug_options_count":4},{"id":37767,"question":"La probabilité d'un événement impossible est :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un événement impossible a une probabilité de 0, tandis qu'un événement certain a une probabilité de 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":37768,"question":"Quelle est la limite de la suite uₙ = (1 + 1\/n)ⁿ quand n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"e","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"Cette suite converge vers le nombre e (≈ 2,718), base du logarithme naturel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"e\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":37769,"question":"Le déterminant d'une matrice triangulaire est égal :","option_a":"Au produit des éléments diagonaux","option_b":"À la somme des éléments diagonaux","option_c":"À 0","option_d":"À 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une matrice triangulaire, le déterminant est le produit des éléments de la diagonale principale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Au produit des éléments diagonaux\", \"b\": \"À la somme des élé","_debug_options_count":4}]