Quiz — 65b8d0598bba4_Exercice 2 corrigé.pdf

Question 1 sur 10 20:00

[{"id":37610,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"x = -6","option_b":"x = 6","option_c":"x = -4","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvez l'équation : 2x - 5 = 3x + 1 → 2x - 3x = 1 + 5 → -x = 6 → x = -6.","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 = -6\", \"b\": \"x = 6\", \"c\": \"x = -4\", \"d\": \"x = 4\"}}","_debug_options_count":4},{"id":37611,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² - 4x + 3 a un discriminant positif (Δ = 4 \u003E 0), donc elle prend des valeurs négatives entre ses racines (x = 1 et x = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":37612,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2x","option_d":"f'(x) = 3x² + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2 (dérivée terme à terme).","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) = 6x + 2\", \"b\": \"f'(x) = 3x + 2\", \"c\": \"f'(x) = 6x² + 2x\",","_debug_options_count":4},{"id":37613,"question":"L'inéquation x² - 5x + 6 \u003E 0 est-elle vérifiée pour x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour x = 1, x² - 5x + 6 = 1 - 5 + 6 = 2 \u003E 0. L'inéquation est donc vérifiée pour x = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":37614,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 2x + 5 ?","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ -12","option_d":"x ≥ -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvez l'inéquation : 3x - 7 ≤ 2x + 5 → 3x - 2x ≤ 5 + 7 → x ≤ 12.","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 ≤ 12\", \"b\": \"x ≥ 12\", \"c\": \"x ≤ -12\", \"d\": \"x ≥ -12\"}}","_debug_options_count":4},{"id":37615,"question":"La fonction f(x) = (2x + 1)\/(x - 3) est-elle définie pour x = 3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = (2x + 1)\/(x - 3) n'est pas définie pour x = 3 car le dénominateur s'annule (division par zéro).","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":37616,"question":"Quelle est la solution de l'équation |2x - 3| = 5 ?","option_a":"x = 4 ou x = -1","option_b":"x = 1 ou x = -4","option_c":"x = 4 ou x = 1","option_d":"x = -1 ou x = -4","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation |2x - 3| = 5 donne deux cas : 2x - 3 = 5 → x = 4 ou 2x - 3 = -5 → x = -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\": \"x = 4 ou x = -1\", \"b\": \"x = 1 ou x = -4\", \"c\": \"x = 4 ou x = 1\", ","_debug_options_count":4},{"id":37617,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x + 2 change de signe (Δ = 12 \u003E 0), donc la fonction n'est pas toujours croissante.","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":37618,"question":"Quelle est la solution de l'équation √(x + 3) = x - 1 ?","option_a":"x = 2","option_b":"x = 3","option_c":"x = 1","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"d","explication":"Résolvez l'équation : √(x + 3) = x - 1 → x + 3 = (x - 1)² → x + 3 = x² - 2x + 1 → x² - 3x - 2 = 0. Les solutions sont x = (3 ± √17)\/2. Seule x = 4 est valide (vérification dans l'équation initiale).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"x = 2\", \"b\": \"x = 3\", \"c\": \"x = 1\", \"d\": \"x = 4\"}}","_debug_options_count":4},{"id":37619,"question":"La fonction f(x) = e^(2x) + x est-elle dérivable sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = e^(2x) + x est dérivable sur ℝ car e^(2x) et x sont dérivables sur ℝ.","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}]