Quiz — 64d39a1860253_corrigé_Révision.pdf

Question 1 sur 5 10:00

[{"id":1284,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"La limite n'existe pas","option_b":"2","option_c":"0","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour x tendant vers l'infini, on compare les termes dominants au numérateur et au dénominateur. Ici, 2x²\/x² = 2, donc la limite est 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\": \"La limite n'existe pas\", \"b\": \"2\", \"c\": \"0\", \"d\": \"1\"}}","_debug_options_count":4},{"id":1285,"question":"Soit une suite définie par u₀ = 1 et uₙ₊₁ = 2uₙ + 3. Quelle est l'expression de uₙ en fonction de n ?","option_a":"uₙ = 2ⁿ - 3","option_b":"uₙ = 2ⁿ + 3","option_c":"uₙ = 3 × 2ⁿ - 2","option_d":"uₙ = 2ⁿ - 1","option_e":"","option_f":"","bonne_reponse":"c","explication":"C'est une suite arithmético-géométrique. On résout l'équation l = 2l + 3 pour trouver la limite, puis on exprime uₙ en fonction de cette limite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"uₙ = 2ⁿ - 3\", \"b\": \"uₙ = 2ⁿ + 3\", \"c\": \"uₙ = 3 × 2ⁿ ","_debug_options_count":4},{"id":1286,"question":"Dans un triangle ABC rectangle en A, AB = 3 et AC = 4. Quelle est la longueur de BC ?","option_a":"5","option_b":"7","option_c":"√7","option_d":"25","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore : BC² = AB² + AC² = 9 + 16 = 25, donc BC = 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\": \"5\", \"b\": \"7\", \"c\": \"√7\", \"d\": \"25\"}}","_debug_options_count":4},{"id":1287,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 2x) ?","option_a":"(6x + 2)\/(3x² + 2x)","option_b":"(6x + 2) × ln(3x² + 2x)","option_c":"1\/(3x² + 2x)","option_d":"(3x² + 2x)\/(6x + 2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x² + 2x, donc u' = 6x + 2. Ainsi, f'(x) = (6x + 2)\/(3x² + 2x).","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)\/(3x² + 2x)\", \"b\": \"(6x + 2) × ln(3x² + 2x)\", \"c\": \"1\/","_debug_options_count":4},{"id":1288,"question":"Soit une variable aléatoire X suivant une loi normale N(0,1). Quelle est la probabilité P(-1 ≤ X ≤ 1) ?","option_a":"0,3413","option_b":"0,6826","option_c":"0,9544","option_d":"0,9974","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une loi normale centrée réduite, environ 68% des valeurs sont dans l'intervalle [-1, 1]. La probabilité exacte est 0,6826.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,3413\", \"b\": \"0,6826\", \"c\": \"0,9544\", \"d\": \"0,9974\"}}","_debug_options_count":4}]