Quiz — 6740b0ea9c871_CORREC EX LDD.pdf

Question 1 sur 10 20:00

[{"id":42855,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) quand x tend vers +∞ ?","option_a":"A) 3","option_b":"B) 0","option_c":"C) +∞","option_d":"D) -∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"La limite d'un quotient de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 3x²\/x² = 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) 0\", \"c\": \"C) +∞\", \"d\": \"D) -∞\"}}","_debug_options_count":4},{"id":42856,"question":"L'équation x² + 2x + 5 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = 4 - 20 = -16 \u003C 0, donc pas de solution réelle.","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":42857,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"A) 1\/(2x + 1)","option_b":"B) 2\/(2x + 1)","option_c":"C) 1\/(x + 1)","option_d":"D) 2x\/(2x + 1)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 2x + 1, donc u' = 2. Ainsi, f'(x) = 2\/(2x + 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\": \"A) 1\/(2x + 1)\", \"b\": \"B) 2\/(2x + 1)\", \"c\": \"C) 1\/(x + 1)\", \"d\": \"","_debug_options_count":4},{"id":42858,"question":"La fonction f(x) = e^(-x²) est-elle paire ou impaire ?","option_a":"A) Paire","option_b":"B) Impaire","option_c":"C) Ni paire ni impaire","option_d":"D) Les deux","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction f est paire si f(-x) = f(x). Ici, f(-x) = e^(-(-x)²) = e^(-x²) = f(x).","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) Paire\", \"b\": \"B) Impaire\", \"c\": \"C) Ni paire ni impaire\", \"d\":","_debug_options_count":4},{"id":42859,"question":"L'intégrale ∫(de 0 à 1) x² dx est égale à :","option_a":"A) 1\/3","option_b":"B) 1\/2","option_c":"C) 1","option_d":"D) 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de x^n est x^(n+1)\/(n+1). Ici, ∫x² dx = 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\": \"A) 1\/3\", \"b\": \"B) 1\/2\", \"c\": \"C) 1\", \"d\": \"D) 0\"}}","_debug_options_count":4},{"id":42860,"question":"Une variable aléatoire X suit une loi normale N(0,1). Quelle est la probabilité P(X ≤ 0) ?","option_a":"A) 0,5","option_b":"B) 0","option_c":"C) 1","option_d":"D) 0,34","option_e":"","option_f":"","bonne_reponse":"a","explication":"La loi normale centrée réduite est symétrique par rapport à 0. 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\": \"a\", \"options\": {\"a\": \"A) 0,5\", \"b\": \"B) 0\", \"c\": \"C) 1\", \"d\": \"D) 0,34\"}}","_debug_options_count":4},{"id":42861,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc oui.","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":42862,"question":"Quelle est la solution de l'inéquation 3x - 5 \u003E 7 ?","option_a":"A) x \u003E 4","option_b":"B) x \u003C 4","option_c":"C) x \u003E 12","option_d":"D) x \u003C 12\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 5 \u003E 7 ⇒ 3x \u003E 12 ⇒ x \u003E 4.","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 \u003E 4\", \"b\": \"B) x \u003C 4\", \"c\": \"C) x \u003E 12\", \"d\": \"D) x \u003C 12\/3\"}","_debug_options_count":4},{"id":42863,"question":"La fonction f(x) = x³ - 3x² + 2 est-elle convexe sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La convexité se détermine par le signe de la dérivée seconde. f''(x) = 6x - 6. f''(x) \u003C 0 pour x \u003C 1, donc la fonction n'est pas convexe sur ℝ.","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":42864,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² au point d'abscisse 2 ?","option_a":"A) 2","option_b":"B) 4","option_c":"C) 1","option_d":"D) 0","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur de la tangente est f'(2). f'(x) = 2x, donc f'(2) = 4.","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) 2\", \"b\": \"B) 4\", \"c\": \"C) 1\", \"d\": \"D) 0\"}}","_debug_options_count":4}]