Quiz — 275.._Magazine Analyse BAC 2008.pdf

Question 1 sur 10 20:00

[{"id":33760,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A. 2x + 3","option_b":"B. x² + 3","option_c":"C. 2x + 5","option_d":"D. 3x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : la dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 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. 2x + 3\", \"b\": \"B. x² + 3\", \"c\": \"C. 2x + 5\", \"d\": \"D. 3x + 5\"","_debug_options_count":4},{"id":33761,"question":"L'intégrale ∫(3x² + 2x) dx est égale à :","option_a":"A. x³ + x² + C","option_b":"B. x³ + x + C","option_c":"C. 6x + 2 + C","option_d":"D. x³ + 2x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale d'une somme est la somme des intégrales. ∫3x² dx = x³ et ∫2x dx = x², donc l'intégrale est x³ + x² + 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. x³ + x² + C\", \"b\": \"B. x³ + x + C\", \"c\": \"C. 6x + 2 + C\", \"","_debug_options_count":4},{"id":33762,"question":"Une suite est convergente si et seulement si elle est bornée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite convergente est toujours bornée, mais une suite bornée n'est pas nécessairement convergente (exemple : la suite (-1)^n).","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":33763,"question":"Quelle est la solution générale de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^(-2x)","option_b":"B. y = Ce^(2x)","option_c":"C. y = C + e^(-2x)","option_d":"D. y = Cx + e^(-2x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une équation différentielle linéaire du premier ordre. La solution générale est y = Ce^(-2x), où C est une constante réelle.","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. y = Ce^(-2x)\", \"b\": \"B. y = Ce^(2x)\", \"c\": \"C. y = C + e^(-2x)","_debug_options_count":4},{"id":33764,"question":"La fonction f(x) = ln(x) est définie pour :","option_a":"A. x \u003E 0","option_b":"B. x ≥ 0","option_c":"C. x \u003C 0","option_d":"D. x ∈ ℝ","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction logarithme népérien ln(x) est définie uniquement pour les valeurs strictement positives de 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. x \u003E 0\", \"b\": \"B. x ≥ 0\", \"c\": \"C. x \u003C 0\", \"d\": \"D. x ∈ ℝ","_debug_options_count":4},{"id":33765,"question":"Si une fonction est dérivable en un point, alors elle est continue en ce point.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est un théorème fondamental : la dérivabilité implique la continuité, mais l'inverse n'est pas vrai.","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":33766,"question":"Quelle est la limite de la suite u_n = (n² + 1)\/(2n² + 3) quand n tend vers l'infini ?","option_a":"A. 0","option_b":"B. 1\/2","option_c":"C. 1","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n², on obtient lim (1 + 1\/n²)\/(2 + 3\/n²) = 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. 1\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":33767,"question":"L'équation différentielle y'' - 3y' + 2y = 0 a pour équation caractéristique :","option_a":"A. r² - 3r + 2 = 0","option_b":"B. r² + 3r + 2 = 0","option_c":"C. r² - 3r - 2 = 0","option_d":"D. r² + 3r - 2 = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une équation différentielle linéaire du second ordre à coefficients constants, l'équation caractéristique s'obtient en remplaçant y par r², y' par r et y'' par 1.","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. r² - 3r + 2 = 0\", \"b\": \"B. r² + 3r + 2 = 0\", \"c\": \"C. r² - ","_debug_options_count":4},{"id":33768,"question":"La fonction f(x) = e^(-x²) est paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","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), donc elle est paire.","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":33769,"question":"Quelle est l'intégrale ∫(1\/x) dx pour x \u003E 0 ?","option_a":"A. ln(x) + C","option_b":"B. 1\/x + C","option_c":"C. x + C","option_d":"D. e^x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de 1\/x est ln(x) + C, où C est une constante réelle, 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\": \"a\", \"options\": {\"a\": \"A. ln(x) + C\", \"b\": \"B. 1\/x + C\", \"c\": \"C. x + C\", \"d\": \"D. e^x +","_debug_options_count":4}]