Quiz — 66413eb6de107_enoncé - prototypes d'examen 2.pdf

Question 1 sur 10 20:00

[{"id":27260,"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. 6x - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : 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. 6x - 2","_debug_options_count":4},{"id":27261,"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":"La fonction exponentielle e^x est strictement positive pour tout réel 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":27262,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quelle est la valeur de u₃ ?","option_a":"A. 6","option_b":"B. 18","option_c":"C. 54","option_d":"D. 162","option_e":"","option_f":"","bonne_reponse":"c","explication":"u₃ = u₀ × q³ = 2 × 27 = 54.","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. 6\", \"b\": \"B. 18\", \"c\": \"C. 54\", \"d\": \"D. 162\"}}","_debug_options_count":4},{"id":27263,"question":"L'intégrale ∫(2x + 1)dx entre 0 et 2 vaut :","option_a":"A. 4","option_b":"B. 5","option_c":"C. 6","option_d":"D. 8","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale se calcule comme [x² + x] entre 0 et 2, soit (4 + 2) - (0 + 0) = 6.","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. 4\", \"b\": \"B. 5\", \"c\": \"C. 6\", \"d\": \"D. 8\"}}","_debug_options_count":4},{"id":27264,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":27265,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x) \/ (x² + 1) lorsque x tend vers +∞ ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 3","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (3 + 2\/x) \/ (1 + 1\/x²), donc la limite est 3.","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. +∞\"}}","_debug_options_count":4},{"id":27266,"question":"Dans un repère orthonormé, l'équation d'un cercle de centre (2, -1) et de rayon 3 est :","option_a":"A. (x-2)² + (y+1)² = 3","option_b":"B. (x+2)² + (y-1)² = 9","option_c":"C. (x-2)² + (y+1)² = 9","option_d":"D. (x-2)² + (y-1)² = 3","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'équation d'un cercle de centre (a,b) et de rayon r est (x-a)² + (y-b)² = r².","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. (x-2)² + (y+1)² = 3\", \"b\": \"B. (x+2)² + (y-1)² = 9\", \"c\": ","_debug_options_count":4},{"id":27267,"question":"La fonction logarithme népérien ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"ln(x) n'est défini que 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\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":27268,"question":"Soit f une fonction continue sur [a, b]. Le théorème des valeurs intermédiaires garantit que :","option_a":"A. f est dérivable sur [a, b]","option_b":"B. f prend toutes les valeurs entre f(a) et f(b)","option_c":"C. f est croissante sur [a, b]","option_d":"D. f est constante sur [a, b]","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème des valeurs intermédiaires stipule que f prend toutes les valeurs intermédiaires entre f(a) et f(b).","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. f est dérivable sur [a, b]\", \"b\": \"B. f prend toutes les vale","_debug_options_count":4},{"id":27269,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"A. y = Ce^(-2x)","option_b":"B. y = Ce^(2x)","option_c":"C. y = Cx + 2","option_d":"D. y = C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation différentielle linéaire du premier ordre y' + 2y = 0 a pour solution générale y = Ce^(-2x).","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 = Cx + 2\", \"d","_debug_options_count":4}]