Quiz — EX21.pdf

Question 1 sur 10 20:00

[{"id":47408,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A) 6x + 2","option_b":"B) 3x + 2","option_c":"C) 6x² + 2x","option_d":"D) 6x + 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, la dérivée de 3x² est 6x, celle de 2x est 2, et la constante -5 disparaît.","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 + 2\", \"b\": \"B) 3x + 2\", \"c\": \"C) 6x² + 2x\", \"d\": \"D) 6x + ","_debug_options_count":4},{"id":47409,"question":"La limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers +∞ est égale à 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient (2 + 3\/x - 1\/x²)\/(1 - 4\/x²). Lorsque x tend vers +∞, les termes en 1\/x tendent vers 0, donc la limite est 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":47410,"question":"Quelle est la solution de l'équation 2^(x+1) = 16 ?","option_a":"A) x = 3","option_b":"B) x = 4","option_c":"C) x = 2","option_d":"D) x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"16 peut s'écrire 2^4. L'équation devient donc 2^(x+1) = 2^4, soit x+1 = 4, d'où 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\": \"A) x = 3\", \"b\": \"B) x = 4\", \"c\": \"C) x = 2\", \"d\": \"D) x = 5\"}}","_debug_options_count":4},{"id":47411,"question":"La fonction f(x) = x³ - 3x² + 2 est croissante sur l'intervalle ]-∞, 0[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x = 3x(x - 2). Sur ]-∞, 0[, f'(x) est positive (produit de deux termes négatifs), donc la fonction est croissante.","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":47412,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"A) 1\/6","option_b":"B) 1\/2","option_c":"C) 1\/3","option_d":"D) 2\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles. La probabilité est donc 3\/6 = 1\/2.","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) 1\/6\", \"b\": \"B) 1\/2\", \"c\": \"C) 1\/3\", \"d\": \"D) 2\/3\"}}","_debug_options_count":4},{"id":47413,"question":"La suite définie par uₙ = (n² + 1)\/n est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En simplifiant, uₙ = n + 1\/n. Lorsque n tend vers +∞, uₙ tend vers +∞, donc la suite est divergente.","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":47414,"question":"Quelle est la valeur de l'intégrale ∫(2x + 1)dx entre 0 et 2 ?","option_a":"A) 4","option_b":"B) 6","option_c":"C) 8","option_d":"D) 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 2x est x² et celle de 1 est x. Évaluée entre 0 et 2, on obtient (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\": \"b\", \"options\": {\"a\": \"A) 4\", \"b\": \"B) 6\", \"c\": \"C) 8\", \"d\": \"D) 2\"}}","_debug_options_count":4},{"id":47415,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction logarithme népérien ln(x) est définie uniquement pour x \u003E 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":47416,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"A) x ∈ [2, 3]","option_b":"B) x ∈ ]-∞, 2] ∪ [3, +∞[","option_c":"C) x ∈ [0, 5]","option_d":"D) x ∈ ]-∞, 1] ∪ [6, +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le trinôme x² - 5x + 6 se factorise en (x-2)(x-3). Le signe est négatif entre les racines, donc x ∈ [2, 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) x ∈ [2, 3]\", \"b\": \"B) x ∈ ]-∞, 2] ∪ [3, +∞[\", \"c\": \"","_debug_options_count":4},{"id":47417,"question":"La loi binomiale B(n, p) a pour espérance np.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n, p) est bien égale à np, où n est le nombre d'essais et p la probabilité de succès.","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}]