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Question 1 sur 10 20:00

[{"id":85200,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A) x = 2 ou x = 3","option_b":"B) x = -2 ou x = -3","option_c":"C) x = 1 ou x = 6","option_d":"D) x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation se factorise en (x-2)(x-3)=0, donc les solutions sont x=2 et 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 = 2 ou x = 3\", \"b\": \"B) x = -2 ou x = -3\", \"c\": \"C) x = 1 ou","_debug_options_count":4},{"id":85201,"question":"La fonction f(x) = 2x + 3 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine s'écrit sous la forme f(x)=ax+b, donc f(x)=2x+3 est bien affine.","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":85202,"question":"Quel est le discriminant d'une équation du second degré ax² + bx + c = 0 ?","option_a":"A) b² - 4ac","option_b":"B) a² - 4bc","option_c":"C) b² + 4ac","option_d":"D) 4a² - b²","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant d'une équation du second degré est donné par 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\": \"A) b² - 4ac\", \"b\": \"B) a² - 4bc\", \"c\": \"C) b² + 4ac\", \"d\": \"D)","_debug_options_count":4},{"id":85203,"question":"La fonction f(x) = x² est-elle décroissante sur l'intervalle ]-∞ ; 0[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction carrée est décroissante sur ]-∞ ; 0[ car sa dérivée f'(x)=2x est négative sur cet intervalle.","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":85204,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A) 0","option_b":"B) 3","option_c":"C) +∞","option_d":"D) -∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour x→+∞, on garde les termes de plus haut degré : f(x) ≈ 3x²\/x² = 3.","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) 3\", \"c\": \"C) +∞\", \"d\": \"D) -∞\"}}","_debug_options_count":4},{"id":85205,"question":"Un événement impossible a une probabilité de 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 égale à 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":85206,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + 5x - 1 ?","option_a":"A) 9x² - 4x + 5","option_b":"B) 6x² - 4x + 5","option_c":"C) 9x² - 4x - 1","option_d":"D) 3x² - 2x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée se calcule terme par terme : f'(x) = 9x² - 4x + 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) 9x² - 4x + 5\", \"b\": \"B) 6x² - 4x + 5\", \"c\": \"C) 9x² - 4x - ","_debug_options_count":4},{"id":85207,"question":"La somme des angles d'un triangle est-elle 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 : la somme des angles d'un triangle est toujours égale à 180°.","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":85208,"question":"Quelle est la formule de l'aire d'un disque de rayon r ?","option_a":"A) πr²","option_b":"B) 2πr","option_c":"C) πr","option_d":"D) 4πr²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un disque est donnée par la formule A = πr².","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) πr²\", \"b\": \"B) 2πr\", \"c\": \"C) πr\", \"d\": \"D) 4πr²\"}}","_debug_options_count":4},{"id":85209,"question":"Une suite géométrique de raison q \u003E 1 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si q \u003E 1, alors chaque terme est plus grand que le précédent, donc la suite est croissante.","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}]