Quiz — Série 5 - Portefeuilles de couverture - Corrigé.pdf

Question 1 sur 10 20:00

[{"id":31910,"question":"Quelle est la formule de la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A. f'(x) = 2x + 3","option_b":"B. f'(x) = x² + 3","option_c":"C. f'(x) = 2x - 5","option_d":"D. f'(x) = 3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 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. f'(x) = 2x + 3\", \"b\": \"B. f'(x) = x² + 3\", \"c\": \"C. f'(x) = 2","_debug_options_count":4},{"id":31911,"question":"L'équation x² - 4x + 4 = 0 a deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0. Une seule solution réelle double : x = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":31912,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 1 ?","option_a":"A. x \u003E 8","option_b":"B. x \u003C 8","option_c":"C. x \u003E 6","option_d":"D. x \u003C 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 7 \u003E 2x + 1 ⇒ x \u003E 8. La solution est x \u003E 8.","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 \u003E 8\", \"b\": \"B. x \u003C 8\", \"c\": \"C. x \u003E 6\", \"d\": \"D. x \u003C 6\"}}","_debug_options_count":4},{"id":31913,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","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":31914,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"A. x² + x + C","option_b":"B. x² + C","option_c":"C. 2x² + x + C","option_d":"D. x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 2x est x² et celle de 1 est x. Donc ∫(2x + 1) dx = x² + x + C.","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. x² + x + C\", \"b\": \"B. x² + C\", \"c\": \"C. 2x² + x + C\", \"d\": ","_debug_options_count":4},{"id":31915,"question":"La probabilité d'un événement certain est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement certain est égale à 1, tandis que celle 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\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":31916,"question":"Quelle est la solution de l'équation 2^(x+1) = 16 ?","option_a":"A. x = 3","option_b":"B. x = 4","option_c":"C. x = 2","option_d":"D. x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"2^(x+1) = 16 ⇒ 2^(x+1) = 2^4 ⇒ x + 1 = 4 ⇒ x = 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. x = 3\", \"b\": \"B. x = 4\", \"c\": \"C. x = 2\", \"d\": \"D. x = 5\"}}","_debug_options_count":4},{"id":31917,"question":"Le triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"5² + 12² = 25 + 144 = 169 = 13². Donc le triangle est rectangle en B.","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":31918,"question":"Quelle est la médiane d'un triangle ?","option_a":"A. Une droite qui passe par un sommet et le milieu du côté opposé","option_b":"B. Une droite perpendiculaire à un côté","option_c":"C. Une droite qui divise l'angle en deux angles égaux","option_d":"D. Une droite parallèle à un côté","option_e":"","option_f":"","bonne_reponse":"a","explication":"La médiane d'un triangle est une droite qui passe par un sommet et le milieu du côté opposé.","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. Une droite qui passe par un sommet et le milieu du côté oppo","_debug_options_count":4},{"id":31919,"question":"La fonction f(x) = sin(x) est périodique de période 2π.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction sin(x) est périodique de période 2π, car sin(x + 2π) = sin(x) pour tout 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}]