Quiz — serie 30 p1.pdf

Question 1 sur 10 20:00

[{"id":8070,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x² - 4) lorsque x tend vers +∞ ?","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 en +∞ est celle de son 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":8071,"question":"La fonction f définie par f(x) = x³ - 3x + 1 est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction n'est donc pas strictement croissante sur ℝ.","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":8072,"question":"Quel est le déterminant d'une matrice triangulaire supérieure ?","option_a":"A. La somme des éléments diagonaux","option_b":"B. Le produit des éléments diagonaux","option_c":"C. 0","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une matrice triangulaire, le déterminant est égal au produit des éléments de la diagonale principale.","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. La somme des éléments diagonaux\", \"b\": \"B. Le produit des é","_debug_options_count":4},{"id":8073,"question":"Soit une suite géométrique de premier terme u₀ = 5 et de raison q = -2. Quelle est la valeur de u₃ ?","option_a":"A. -40","option_b":"B. 40","option_c":"C. -20","option_d":"D. 20","option_e":"","option_f":"","bonne_reponse":"a","explication":"u₃ = u₀ × q³ = 5 × (-2)³ = 5 × (-8) = -40.","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. -40\", \"b\": \"B. 40\", \"c\": \"C. -20\", \"d\": \"D. 20\"}}","_debug_options_count":4},{"id":8074,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale y(x) = Ce^(-2x) où C est une constante réelle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale de y' + 2y = 0 est bien y(x) = Ce^(-2x), avec C ∈ ℝ.","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":8075,"question":"Quelle est la dérivée de la fonction f(x) = ln(3x² + 1) ?","option_a":"A. 6x\/(3x² + 1)","option_b":"B. 3x\/(3x² + 1)","option_c":"C. 6x","option_d":"D. 1\/(3x² + 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 3x² + 1, donc u' = 6x. Ainsi, f'(x) = 6x\/(3x² + 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. 6x\/(3x² + 1)\", \"b\": \"B. 3x\/(3x² + 1)\", \"c\": \"C. 6x\", \"d\": \"D","_debug_options_count":4},{"id":8076,"question":"Soit un vecteur u(2, -3) dans un repère orthonormé. Quelle est la norme de u ?","option_a":"A. 1","option_b":"B. √13","option_c":"C. 5","option_d":"D. √5","option_e":"","option_f":"","bonne_reponse":"b","explication":"La norme de u est √(2² + (-3)²) = √(4 + 9) = √13.","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. √13\", \"c\": \"C. 5\", \"d\": \"D. √5\"}}","_debug_options_count":4},{"id":8077,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour tout x ∈ ℝ, e^x \u003E 0. La fonction exponentielle est donc toujours positive.","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":8078,"question":"Soit une variable aléatoire X suivant une loi normale N(μ, σ²). Quelle est la probabilité P(X ≤ μ) ?","option_a":"A. 0","option_b":"B. 0.5","option_c":"C. 1","option_d":"D. μ","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans une loi normale, la probabilité d'être inférieur ou égal à la moyenne μ est de 0.5.","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. 0.5\", \"c\": \"C. 1\", \"d\": \"D. μ\"}}","_debug_options_count":4},{"id":8079,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 \u003E 0 ?","option_a":"A. x ∈ ]2, 3[","option_b":"B. x ∈ ]-∞, 2[ ∪ ]3, +∞[","option_c":"C. x ∈ ℝ","option_d":"D. x ∈ {2, 3}","option_e":"","option_f":"","bonne_reponse":"b","explication":"Les racines de x² - 5x + 6 sont 2 et 3. Le polynôme est positif à l'extérieur des racines.","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 ∈ ]2, 3[\", \"b\": \"B. x ∈ ]-∞, 2[ ∪ ]3, +∞[\", \"c\": \"","_debug_options_count":4}]