Quiz — Serie Prog 31.12.2021 Revision.pdf

Question 1 sur 10 20:00

[{"id":27020,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"A. 0","option_b":"B. 4","option_c":"C. Indéterminée","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction se simplifie en f(x) = x + 2 pour x ≠ 2. Ainsi, la limite est 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. 0\", \"b\": \"B. 4\", \"c\": \"C. Indéterminée\", \"d\": \"D. +∞\"}}","_debug_options_count":4},{"id":27021,"question":"La dérivée de la fonction f(x) = x³ - 3x² + 2x est f'(x) = 3x² - 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée correcte est f'(x) = 3x² - 6x + 2. L'affirmation est donc vraie.","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":27022,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"A. x = e","option_b":"B. x = e²","option_c":"C. x = 2","option_d":"D. x = 1\/e²","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation ln(x) = 2 équivaut à x = e².","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 = e\", \"b\": \"B. x = e²\", \"c\": \"C. x = 2\", \"d\": \"D. x = 1\/e²","_debug_options_count":4},{"id":27023,"question":"La fonction f(x) = x² est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée seconde f''(x) = 2 \u003E 0, donc la fonction est convexe 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":27024,"question":"Quelle est l'intégrale de f(x) = 3x² entre 0 et 1 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 3","option_d":"D. 1\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégrale de 3x² est x³. Entre 0 et 1, cela donne 1 - 0 = 1. L'option C (3) est incorrecte, la bonne réponse est 1 (option B). Correction : la bonne réponse est B (1).","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. 0\", \"b\": \"B. 1\", \"c\": \"C. 3\", \"d\": \"D. 1\/3\"}}","_debug_options_count":4},{"id":27025,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du discriminant est bien Δ = b² - 4ac.","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":27026,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 \u003C 0 ?","option_a":"A. x ∈ ]2; 3[","option_b":"B. x ∈ ]-∞; 2[ ∪ ]3; +∞[","option_c":"C. x ∈ ]-∞; +∞[","option_d":"D. x ∈ ∅","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines sont x = 2 et x = 3. Le polynôme est négatif entre ces deux racines.","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 ∈ ]2; 3[\", \"b\": \"B. x ∈ ]-∞; 2[ ∪ ]3; +∞[\", \"c\": \"","_debug_options_count":4},{"id":27027,"question":"La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour tout x réel, eˣ \u003E 0. L'affirmation est donc vraie.","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":27028,"question":"Quelle est la dérivée de la fonction f(x) = sin(2x) ?","option_a":"A. cos(2x)","option_b":"B. 2cos(2x)","option_c":"C. -2cos(2x)","option_d":"D. sin(2x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de sin(u) est u'cos(u). Ici, u = 2x, donc u' = 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. cos(2x)\", \"b\": \"B. 2cos(2x)\", \"c\": \"C. -2cos(2x)\", \"d\": \"D. si","_debug_options_count":4},{"id":27029,"question":"La probabilité d'un événement impossible est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, la probabilité d'un événement impossible est 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}]