Quiz — math.pdf

Question 1 sur 10 20:00

[{"id":3174,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. -∞","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite d'un polynôme à l'infini est déterminée par le terme de plus haut degré. Ici, (2x²)\/(x²) = 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. 2\", \"c\": \"C. -∞\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":3175,"question":"Une suite croissante et majorée est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est un théorème fondamental : toute suite croissante et majorée converge vers une limite finie.","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":3176,"question":"Quel est le déterminant d'une matrice 2x2 A = [[a, b], [c, d]] ?","option_a":"A. a*d - b*c","option_b":"B. a*c + b*d","option_c":"C. a + d","option_d":"D. a*b - c*d","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le déterminant d'une matrice 2x2 est calculé par la formule ad - bc.","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. a*d - b*c\", \"b\": \"B. a*c + b*d\", \"c\": \"C. a + d\", \"d\": \"D. a*b","_debug_options_count":4},{"id":3177,"question":"La dérivée de la fonction f(x) = ln(x) est :","option_a":"A. 1\/x","option_b":"B. x","option_c":"C. e^x","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(x) est 1\/x, une propriété fondamentale des 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\": \"A. 1\/x\", \"b\": \"B. x\", \"c\": \"C. e^x\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":3178,"question":"Une variable aléatoire suit une loi normale N(μ, σ²). Quelle est la probabilité P(X ≤ μ) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une loi normale centrée en μ, P(X ≤ μ) = 0.5 car la distribution est symétrique.","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":3179,"question":"Résolvez l'équation différentielle y' + 2y = 0.","option_a":"A. y = Ce^(-2x)","option_b":"B. y = Ce^(2x)","option_c":"C. y = C*ln(x)","option_d":"D. y = Cx","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale de y' + 2y = 0 est y = Ce^(-2x), obtenue par intégration.","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*ln(x)\", \"","_debug_options_count":4},{"id":3180,"question":"Quelle est la valeur de l'intégrale ∫(0 à 1) x² dx ?","option_a":"A. 1\/3","option_b":"B. 1","option_c":"C. 0","option_d":"D. 1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de x² entre 0 et 1 vaut [x³\/3] de 0 à 1 = 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\", \"c\": \"C. 0\", \"d\": \"D. 1\/2\"}}","_debug_options_count":4},{"id":3181,"question":"Une matrice carrée est inversible si et seulement si son déterminant est nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une matrice est inversible si et seulement si son déterminant est différent de zéro.","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":3182,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x³ - 2x + 1 au point d'abscisse 1 ?","option_a":"A. 1","option_b":"B. 3","option_c":"C. -2","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur est f'(1) = 3*(1)² - 2 = 1. La réponse correcte est 1, mais l'option B (3) est la dérivée en x=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\", \"b\": \"B. 3\", \"c\": \"C. -2\", \"d\": \"D. 0\"}}","_debug_options_count":4},{"id":3183,"question":"La fonction f(x) = e^(-x²) est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction 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}]