Quiz — 2017 co.pdf

Question 1 sur 10 20:00

[{"id":77126,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 3","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite est égale au rapport des coefficients dominants : 3x²\/x² = 3.","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\", \"c\": \"C. +∞\", \"d\": \"D. -∞\"}}","_debug_options_count":4},{"id":77127,"question":"La suite définie par uₙ = 2n² - 5n + 1 est-elle croissante à partir d'un certain rang ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La suite est croissante car sa dérivée (4n - 5) devient positive pour n ≥ 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":77128,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x² + 3) ?","option_a":"A. (4x)\/(2x² + 3)","option_b":"B. (2x)\/(2x² + 3)","option_c":"C. 4x\/(2x² + 3)","option_d":"D. (4x²)\/(2x² + 3)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u, ici u = 2x² + 3 donc u' = 4x.","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. (4x)\/(2x² + 3)\", \"b\": \"B. (2x)\/(2x² + 3)\", \"c\": \"C. 4x\/(2x²","_debug_options_count":4},{"id":77129,"question":"L'équation eˣ = 5 admet-elle une solution réelle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle est strictement croissante et prend toutes les valeurs de ℝ⁺, 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":77130,"question":"Quelle est l'intégrale de f(x) = 3x² + 2x - 1 entre 0 et 2 ?","option_a":"A. 8","option_b":"B. 12","option_c":"C. 10","option_d":"D. 6","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégrale de 3x² est x³, de 2x est x² et de -1 est -x. Calcul entre 0 et 2 : (8 + 4 - 2) - 0 = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 8\", \"b\": \"B. 12\", \"c\": \"C. 10\", \"d\": \"D. 6\"}}","_debug_options_count":4},{"id":77131,"question":"La fonction f(x) = x³ - 3x² + 4 est-elle convexe sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée seconde f''(x) = 6x - 6 n'est pas toujours positive, 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":77132,"question":"Quelle est la solution de l'inéquation ln(x) \u003E 1 ?","option_a":"A. x \u003E 0","option_b":"B. x \u003E e","option_c":"C. x \u003C e","option_d":"D. x \u003E 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"ln(x) \u003E 1 équivaut à x \u003E e^1, soit x \u003E e.","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. x \u003E 0\", \"b\": \"B. x \u003E e\", \"c\": \"C. x \u003C e\", \"d\": \"D. x \u003E 1\"}}","_debug_options_count":4},{"id":77133,"question":"La suite géométrique de premier terme 2 et de raison 0,5 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite géométrique de raison |q| \u003C 1 est convergente vers 0.","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":77134,"question":"Quelle est la valeur de la somme S = Σ (de k=1 à 5) (2k + 1) ?","option_a":"A. 25","option_b":"B. 35","option_c":"C. 45","option_d":"D. 55","option_e":"","option_f":"","bonne_reponse":"c","explication":"S = (2+1) + (4+1) + (6+1) + (8+1) + (10+1) = 3 + 5 + 7 + 9 + 11 = 35.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. 25\", \"b\": \"B. 35\", \"c\": \"C. 45\", \"d\": \"D. 55\"}}","_debug_options_count":4},{"id":77135,"question":"La fonction f(x) = x⁴ - 4x³ + 6x² est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = x⁴ + 4x³ + 6x² ≠ f(x), donc elle n'est pas paire.","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}]