Quiz — Revision analyse + proba.pdf

Question 1 sur 10 20:00

[{"id":8425,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(2x² - x + 4) quand x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 3\/2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite d'un quotient de polynômes quand x tend vers l'infini est égale au rapport des coefficients dominants. Ici, 3x²\/2x² = 3\/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. 0\", \"b\": \"B. 3\/2\", \"c\": \"C. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4},{"id":8426,"question":"Soit X une variable aléatoire suivant une loi normale N(μ, σ²). Que vaut P(μ - σ ≤ X ≤ μ + σ) ?","option_a":"A. 0,68","option_b":"B. 0,95","option_c":"C. 0,99","option_d":"D. 0,50","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale, environ 68% des valeurs se situent dans l'intervalle [μ - σ, μ + σ].","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. 0,68\", \"b\": \"B. 0,95\", \"c\": \"C. 0,99\", \"d\": \"D. 0,50\"}}","_debug_options_count":4},{"id":8427,"question":"Vrai ou Faux ? La dérivée de la fonction f(x) = ln(x) est f'(x) = 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est bien 1\/x, c'est une propriété fondamentale des fonctions logarithmes.","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":8428,"question":"Quelle est l'intégrale indéfinie de f(x) = 2x + 3 ?","option_a":"A. x² + 3x + C","option_b":"B. x² + 3x","option_c":"C. 2x² + 3x + C","option_d":"D. x² + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 2x est x² et celle de 3 est 3x. On ajoute la constante d'intégration C.","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. x² + 3x + C\", \"b\": \"B. x² + 3x\", \"c\": \"C. 2x² + 3x + C\", \"d","_debug_options_count":4},{"id":8429,"question":"Soit X une variable aléatoire suivant une loi binomiale B(n=10, p=0,3). Que vaut E(X) ?","option_a":"A. 3","option_b":"B. 7","option_c":"C. 10","option_d":"D. 0,3","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n*p = 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\": \"A. 3\", \"b\": \"B. 7\", \"c\": \"C. 10\", \"d\": \"D. 0,3\"}}","_debug_options_count":4},{"id":8430,"question":"Vrai ou Faux ? Toute fonction continue sur un intervalle fermé [a,b] 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":8431,"question":"Quelle est la dérivée de la fonction f(x) = e^(2x) ?","option_a":"A. e^(2x)","option_b":"B. 2e^(2x)","option_c":"C. e^x","option_d":"D. 2e^x","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de e^(u(x)) est u'(x)*e^(u(x)). Ici, u(x)=2x, donc u'(x)=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. e^(2x)\", \"b\": \"B. 2e^(2x)\", \"c\": \"C. e^x\", \"d\": \"D. 2e^x\"}}","_debug_options_count":4},{"id":8432,"question":"Soit X une variable aléatoire suivant une loi uniforme sur [0,10]. Que vaut P(X ≤ 5) ?","option_a":"A. 0,5","option_b":"B. 0,1","option_c":"C. 1","option_d":"D. 0,2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi uniforme sur [a,b], P(X ≤ c) = (c-a)\/(b-a). Ici, (5-0)\/(10-0) = 0,5.","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. 0,5\", \"b\": \"B. 0,1\", \"c\": \"C. 1\", \"d\": \"D. 0,2\"}}","_debug_options_count":4},{"id":8433,"question":"Vrai ou Faux ? L'intégrale de 0 à 1 de x² dx vaut 1\/3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de x² est x³\/3. Évaluée entre 0 et 1, cela donne 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":8434,"question":"Quelle est la limite de la suite u_n = (n² + 1)\/(2n² - 3) quand n tend vers +∞ ?","option_a":"A. 0","option_b":"B. 1\/2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite d'une suite rationnelle est le rapport des coefficients dominants. Ici, n²\/2n² = 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. 0\", \"b\": \"B. 1\/2\", \"c\": \"C. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4}]