Quiz — 645a485f9cb68_énoncé_Révision ds3 (Modèle 1).pdf

Question 1 sur 10 20:00

[{"id":17439,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynomiale se calcule terme par terme : la dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Donc 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\": \"6x + 2\", \"b\": \"3x² + 2\", \"c\": \"6x - 5\", \"d\": \"6x + 2x - 5\"}}","_debug_options_count":4},{"id":17440,"question":"Si X suit une loi binomiale de paramètres n=10 et p=0.3, alors E(X) = ?","option_a":"3","option_b":"7","option_c":"0.3","option_d":"10","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale est donnée par E(X) = n × p. Ici, E(X) = 10 × 0.3 = 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\": \"7\", \"c\": \"0.3\", \"d\": \"10\"}}","_debug_options_count":4},{"id":17441,"question":"Une suite est convergente si et seulement si elle est bornée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite convergente est toujours bornée, mais une suite bornée n'est pas nécessairement convergente (exemple : la suite (-1)^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":17442,"question":"Résoudre 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":"C'est une équation différentielle linéaire du premier ordre. La solution générale est 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\": \"a\", \"options\": {\"a\": \"y = Ce^(-2x)\", \"b\": \"y = Ce^(2x)\", \"c\": \"y = Cx\", \"d\": \"y = C\"}}","_debug_options_count":4},{"id":17443,"question":"Le module d'un nombre complexe z = a + ib est donné par :","option_a":"√(a² + b²)","option_b":"a² + b²","option_c":"|a| + |b|","option_d":"a + ib","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe z = a + ib est défini par |z| = √(a² + b²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"√(a² + b²)\", \"b\": \"a² + b²\", \"c\": \"|a| + |b|\", \"d\": \"a + ib","_debug_options_count":4},{"id":17444,"question":"Si une fonction est continue sur un intervalle [a, b], alors elle est dérivable sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction continue n'est pas nécessairement dérivable (exemple : f(x) = |x| en x=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":17445,"question":"Calculer la limite de la suite u_n = (2n + 1)\/(n + 3) quand n tend vers l'infini.","option_a":"2","option_b":"1\/3","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant le numérateur et le dénominateur par n, on obtient u_n = (2 + 1\/n)\/(1 + 3\/n). Quand n tend vers l'infini, u_n tend vers 2\/1 = 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\": \"2\", \"b\": \"1\/3\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":17446,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est égale à 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":17447,"question":"Quelle est la forme algébrique du nombre complexe z = 5(cos(π\/3) + i sin(π\/3)) ?","option_a":"5\/2 + i(5√3)\/2","option_b":"5 + i5","option_c":"5√3\/2 + i5\/2","option_d":"5 - i5","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant les formules cos(π\/3) = 1\/2 et sin(π\/3) = √3\/2, on obtient z = 5(1\/2 + i√3\/2) = 5\/2 + i(5√3)\/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\": \"5\/2 + i(5√3)\/2\", \"b\": \"5 + i5\", \"c\": \"5√3\/2 + i5\/2\", \"d\": \"5 ","_debug_options_count":4},{"id":17448,"question":"Si f est une fonction dérivable sur ℝ, alors f' est toujours continue sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction dérivable n'a pas nécessairement une dérivée continue (exemple : f(x) = x² sin(1\/x) pour x ≠ 0 et f(0) = 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}]