Quiz — 65be3f5704e69_Corrigé-Révision DC2.pdf

Question 1 sur 10 20:00

[{"id":9773,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 3","option_c":"x = 15\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés : 3x = 15, puis on divise par 3 : x = 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\": \"x = 5\", \"b\": \"x = 3\", \"c\": \"x = 15\/3\", \"d\": \"x = 15\"}}","_debug_options_count":4},{"id":9774,"question":"Le triangle ABC est rectangle en A avec AB = 3 cm et AC = 4 cm. Quelle est la longueur de BC ?","option_a":"5 cm","option_b":"7 cm","option_c":"1 cm","option_d":"6 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5 cm\", \"b\": \"7 cm\", \"c\": \"1 cm\", \"d\": \"6 cm\"}}","_debug_options_count":4},{"id":9775,"question":"Vrai ou Faux : La fonction f(x) = x² est toujours croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² est décroissante sur ]-∞, 0] et croissante sur [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":9776,"question":"Quelle est la dérivée de la fonction f(x) = 4x³ - 2x + 1 ?","option_a":"f'(x) = 12x² - 2","option_b":"f'(x) = 12x² - 2x","option_c":"f'(x) = 4x² - 2","option_d":"f'(x) = 12x - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 4x³ est 12x², celle de -2x est -2, et celle de 1 est 0. Donc f'(x) = 12x² - 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\": \"f'(x) = 12x² - 2\", \"b\": \"f'(x) = 12x² - 2x\", \"c\": \"f'(x) = 4x²","_debug_options_count":4},{"id":9777,"question":"Vrai ou Faux : L'inverse de 0,2 est 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'inverse de 0,2 est 1\/0,2 = 5, donc l'affirmation est 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":9778,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003E -2","option_c":"x \u003C 2","option_d":"x \u003E 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"On soustrait 3 des deux côtés : 2x \u003E 4, puis on divise par 2 : x \u003E 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\": \"x \u003E 2\", \"b\": \"x \u003E -2\", \"c\": \"x \u003C 2\", \"d\": \"x \u003E 5\"}}","_debug_options_count":4},{"id":9779,"question":"Vrai ou Faux : La somme des angles d'un triangle est égale à 180°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale de la géométrie plane.","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":9780,"question":"Quelle est la factorisation de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une identité remarquable de la forme a² - b² = (a - b)(a + 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\": \"(x - 3)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4},{"id":9781,"question":"Vrai ou Faux : La médiane d'un triangle est toujours perpendiculaire à un côté.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane est une droite joignant un sommet au milieu du côté opposé, mais elle n'est pas toujours perpendiculaire.","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":9782,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"On factorise : (x - 2)(x - 3) = 0, donc x = 2 ou 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\": \"x = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4}]