Quiz — ds40809.pdf

Question 1 sur 10 20:00

[{"id":133927,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 10","option_c":"x = 5","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"En isolant x, on obtient 3x - 2x = 5 + 7, soit x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = 12\", \"b\": \"x = 10\", \"c\": \"x = 5\", \"d\": \"x = 2\"}}","_debug_options_count":4},{"id":133928,"question":"La fonction f(x) = x² - 4x + 4 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette fonction est un carré parfait : f(x) = (x - 2)² ≥ 0 pour tout x réel.","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":133929,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"1","option_b":"25","option_c":"16","option_d":"9","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = (-5)² - 4*1*6 = 25 - 24 = 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\": \"1\", \"b\": \"25\", \"c\": \"16\", \"d\": \"9\"}}","_debug_options_count":4},{"id":133930,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de :","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc P = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":133931,"question":"La dérivée de la fonction f(x) = 3x³ - 2x² + x est :","option_a":"f'(x) = 9x² - 4x + 1","option_b":"f'(x) = 3x² - 2x + 1","option_c":"f'(x) = 9x² - 4x","option_d":"f'(x) = 6x² - 4x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En dérivant terme à terme, on obtient f'(x) = 9x² - 4x + 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\": \"f'(x) = 9x² - 4x + 1\", \"b\": \"f'(x) = 3x² - 2x + 1\", \"c\": \"f'(x)","_debug_options_count":4},{"id":133932,"question":"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":133933,"question":"Quel est le volume d'un cylindre de rayon 3 cm et de hauteur 5 cm ?","option_a":"45π cm³","option_b":"30π cm³","option_c":"15π cm³","option_d":"9π cm³","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume V = πr²h = π*3²*5 = 45π cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"45π cm³\", \"b\": \"30π cm³\", \"c\": \"15π cm³\", \"d\": \"9π cm³\"}}","_debug_options_count":4},{"id":133934,"question":"Une suite arithmétique de premier terme 2 et de raison 3 a pour terme général :","option_a":"uₙ = 2 + 3n","option_b":"uₙ = 2 + 3(n-1)","option_c":"uₙ = 3n - 1","option_d":"uₙ = 3 + 2n","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule générale d'une suite arithmétique est uₙ = u₁ + (n-1)r.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"uₙ = 2 + 3n\", \"b\": \"uₙ = 2 + 3(n-1)\", \"c\": \"uₙ = 3n - 1\", \"","_debug_options_count":4},{"id":133935,"question":"La médiane d'un ensemble de données est toujours égale à la moyenne.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane et la moyenne sont égales uniquement si la distribution est symétrique.","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":133936,"question":"Quel est le résultat de l'intégrale ∫(2x + 1)dx ?","option_a":"x² + x + C","option_b":"x² + 2x + C","option_c":"2x² + x + C","option_d":"x² + x","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\": \"x² + x + C\", \"b\": \"x² + 2x + C\", \"c\": \"2x² + x + C\", \"d\": \"x²","_debug_options_count":4}]