Quiz — ZetaDe2.pdf

Question 1 sur 10 20:00

[{"id":97459,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 3x","option_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\": \"2x + 3\", \"b\": \"x² + 3\", \"c\": \"2x + 3x\", \"d\": \"x + 3\"}}","_debug_options_count":4},{"id":97460,"question":"Une suite géométrique de raison q = -2 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique converge uniquement si |q| \u003C 1. Ici, |q| = 2 \u003E 1, donc elle diverge.","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":97461,"question":"Soit X une variable aléatoire suivant une loi normale N(0,1). Que vaut P(X ≤ 0) ?","option_a":"0","option_b":"0.5","option_c":"1","option_d":"0.34","option_e":"","option_f":"","bonne_reponse":"b","explication":"La loi normale centrée réduite est symétrique autour de 0. Donc P(X ≤ 0) = 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\": \"0\", \"b\": \"0.5\", \"c\": \"1\", \"d\": \"0.34\"}}","_debug_options_count":4},{"id":97462,"question":"L'intégrale ∫(de 0 à 1) x² dx vaut :","option_a":"1\/2","option_b":"1\/3","option_c":"1","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"b","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\": \"b\", \"options\": {\"a\": \"1\/2\", \"b\": \"1\/3\", \"c\": \"1\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":97463,"question":"Une suite arithmétique de raison r = 0 est-elle constante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si r = 0, tous les termes de la suite sont égaux à u₀. Elle est donc 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":97464,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"1","option_d":"1\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par n, on obtient (2 + 1\/n)\/(1 + 3\/n). La limite est donc 2\/1 = 2.","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\": \"2\", \"c\": \"1\", \"d\": \"1\/3\"}}","_debug_options_count":4},{"id":97465,"question":"Soit f une fonction continue sur [a,b]. Le théorème des valeurs intermédiaires garantit que :","option_a":"f est dérivable sur [a,b]","option_b":"f prend toutes les valeurs entre f(a) et f(b)","option_c":"f est croissante sur [a,b]","option_d":"f est constante sur [a,b]","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème des valeurs intermédiaires stipule que f prend toutes les valeurs intermédiaires entre f(a) et f(b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"f est dérivable sur [a,b]\", \"b\": \"f prend toutes les valeurs ent","_debug_options_count":4},{"id":97466,"question":"La probabilité d'un événement impossible est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité d'un événement impossible est bien égale 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":97467,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce^(-2x)","option_b":"y = Ce^(2x)","option_c":"y = Cx","option_d":"y = C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation différentielle linéaire du premier ordre y' + 2y = 0 a pour solution 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\": \"y = Ce^(-2x)\", \"b\": \"y = Ce^(2x)\", \"c\": \"y = Cx\", \"d\": \"y = C\"}}","_debug_options_count":4},{"id":97468,"question":"Soit une fonction f définie par f(x) = e^(-x²). Que vaut f'(x) ?","option_a":"-2xe^(-x²)","option_b":"e^(-x²)","option_c":"-x²e^(-x²)","option_d":"2xe^(-x²)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la dérivée d'une fonction composée, f'(x) = -2x * e^(-x²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-2xe^(-x²)\", \"b\": \"e^(-x²)\", \"c\": \"-x²e^(-x²)\", \"d\": \"2xe^(-x","_debug_options_count":4}]