Quiz — 65ed99b5affdf_Enoncé-Série N°36(Révision DS2).pdf

Question 1 sur 10 20:00

[{"id":5536,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"A. 6x - 5","option_b":"B. 3x - 5","option_c":"C. 6x² - 5","option_d":"D. 5x - 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la formule (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x - 5.","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 - 5\", \"b\": \"B. 3x - 5\", \"c\": \"C. 6x² - 5\", \"d\": \"D. 5x - 6","_debug_options_count":4},{"id":5537,"question":"L'équation x² - 4x + 3 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac = 16 - 12 = 4 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","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":5538,"question":"Soit la suite (uₙ) définie par u₀ = 2 et uₙ₊₁ = 3uₙ - 1. Quelle est la valeur de u₂ ?","option_a":"A. 14","option_b":"B. 17","option_c":"C. 20","option_d":"D. 23","option_e":"","option_f":"","bonne_reponse":"b","explication":"u₁ = 3*2 - 1 = 5, puis u₂ = 3*5 - 1 = 14. La réponse correcte est donc 14.","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. 14\", \"b\": \"B. 17\", \"c\": \"C. 20\", \"d\": \"D. 23\"}}","_debug_options_count":4},{"id":5539,"question":"La fonction f(x) = x³ - 3x² admet un extremum local en x = 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"f'(x) = 3x² - 6x. f'(1) = 0 et f''(1) = 6 \u003E 0, donc x = 1 est un minimum local.","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":5540,"question":"Quelle est la solution de l'inéquation -2x² + 5x - 2 \u003E 0 ?","option_a":"A. x ∈ ]1\/2 ; 2[","option_b":"B. x ∈ ]-∞ ; 1\/2[ ∪ ]2 ; +∞[","option_c":"C. x ∈ ]-∞ ; 1[","option_d":"D. x ∈ ]1 ; 2[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines de -2x² + 5x - 2 = 0 sont x = 1\/2 et x = 2. Le coefficient de x² est négatif, donc l'inéquation est vérifiée entre les 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 ∈ ]1\/2 ; 2[\", \"b\": \"B. x ∈ ]-∞ ; 1\/2[ ∪ ]2 ; +∞[\",","_debug_options_count":4},{"id":5541,"question":"La suite (uₙ) définie par uₙ = 2n + 1 est une suite arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La différence entre deux termes consécutifs est constante : uₙ₊₁ - uₙ = 2, donc c'est une suite arithmétique de raison 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":5542,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x² + 3x en x = 1 ?","option_a":"A. y = 5x - 1","option_b":"B. y = 5x + 1","option_c":"C. y = x + 5","option_d":"D. y = -5x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"f(1) = 4 et f'(x) = 2x + 3, donc f'(1) = 5. L'équation de la tangente est y = 5(x - 1) + 4 = 5x - 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. y = 5x - 1\", \"b\": \"B. y = 5x + 1\", \"c\": \"C. y = x + 5\", \"d\": \"","_debug_options_count":4},{"id":5543,"question":"La suite (uₙ) définie par uₙ = 1\/n converge vers 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Lorsque n tend vers l'infini, 1\/n tend vers 0. La suite converge donc 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":5544,"question":"Quelle est la valeur maximale de la fonction f(x) = -x² + 4x sur l'intervalle [0 ; 4] ?","option_a":"A. 0","option_b":"B. 4","option_c":"C. 8","option_d":"D. 12","option_e":"","option_f":"","bonne_reponse":"c","explication":"f'(x) = -2x + 4. Le maximum est atteint en x = 2, avec f(2) = -4 + 8 = 4. Cependant, la valeur maximale sur [0 ; 4] est f(2) = 4.","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. 4\", \"c\": \"C. 8\", \"d\": \"D. 12\"}}","_debug_options_count":4},{"id":5545,"question":"La fonction f(x) = e^x est toujours croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = e^x est f'(x) = e^x, qui est toujours positive. La fonction est donc 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}]