Quiz — 63399c1fe3ecc_Exercice 2 type devoir.pdf

Question 1 sur 10 20:00

[{"id":88548,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Donc f'(x) = 6x + 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\": \"6x + 2\", \"b\": \"6x² + 2\", \"c\": \"3x + 2\", \"d\": \"6x - 5\"}}","_debug_options_count":4},{"id":88549,"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 = (-4)² - 4*1*4 = 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":88550,"question":"Quel est le résultat de ∫(2x + 3) dx ?","option_a":"x² + 3x + C","option_b":"x² + 3x","option_c":"2x² + 3x + C","option_d":"2x² + 3x","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 2x est x² et celle de 3 est 3x. On ajoute la constante d'intégration 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 + 3x + C\", \"b\": \"x² + 3x\", \"c\": \"2x² + 3x + C\", \"d\": \"2x² ","_debug_options_count":4},{"id":88551,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est le théorème de Pythagore : a² + b² = c², où c est l'hypoténuse.","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":88552,"question":"Quelle est la valeur de sin(π\/2) ?","option_a":"0","option_b":"1","option_c":"-1","option_d":"√2\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"sin(π\/2) = 1, car π\/2 correspond à 90° et sin(90°) = 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\": \"0\", \"b\": \"1\", \"c\": \"-1\", \"d\": \"√2\/2\"}}","_debug_options_count":4},{"id":88553,"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":88554,"question":"Quel est le résultat de (3x + 2)(x - 5) ?","option_a":"3x² - 13x - 10","option_b":"3x² - 15x + 2x - 10","option_c":"3x² - 17x - 10","option_d":"3x² - 13x + 10","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant (3x + 2)(x - 5) = 3x² - 15x + 2x - 10 = 3x² - 13x - 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3x² - 13x - 10\", \"b\": \"3x² - 15x + 2x - 10\", \"c\": \"3x² - 17x -","_debug_options_count":4},{"id":88555,"question":"La médiane d'un triangle est une droite qui passe par un sommet et le milieu du côté opposé.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une médiane d'un triangle est une droite qui joint un sommet au 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":88556,"question":"Quelle est la solution de l'équation 2x - 7 = 3x + 1 ?","option_a":"x = -8","option_b":"x = 8","option_c":"x = -6","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"c","explication":"2x - 7 = 3x + 1 → -7 - 1 = 3x - 2x → -8 = x → x = -8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"x = -8\", \"b\": \"x = 8\", \"c\": \"x = -6\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":88557,"question":"Le produit de deux nombres négatifs est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Exemple : (-2) × (-3) = 6, qui est positif. Le produit de deux nombres négatifs est positif.","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}]