Quiz — Enoncé S4 EX.pdf

Question 1 sur 10 20:00

[{"id":6341,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"x = -6","option_b":"x = -4","option_c":"x = 4","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant l'équation, on obtient 2x - 5 = 3x + 1 → -5 - 1 = 3x - 2x → 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 = -4\", \"c\": \"x = 4\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":6342,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction est un polynôme du second degré avec un coefficient positif devant x², donc elle admet un minimum.","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":6343,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + x - 5 ?","option_a":"f'(x) = 9x² - 4x + 1","option_b":"f'(x) = 6x² - 4x + 1","option_c":"f'(x) = 9x² - 2x + 1","option_d":"f'(x) = 3x² - 2x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'un polynôme est obtenue en multipliant chaque terme par son exposant et en réduisant l'exposant de 1 : 3*3x² - 2*2x + 1 = 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) = 6x² - 4x + 1\", \"c\": \"f'(x)","_debug_options_count":4},{"id":6344,"question":"Le vecteur u(2, -3) et le vecteur v(-1, 4) sont-ils colinéaires ?","option_a":"Oui","option_b":"Non","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux vecteurs sont colinéaires si leurs coordonnées sont proportionnelles. Ici, 2\/-1 ≠ -3\/4, donc ils ne le sont pas.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Oui\", \"b\": \"Non\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":6345,"question":"La limite de la fonction f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 est-elle égale à 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En simplifiant, f(x) = (x - 1)(x + 1)\/(x - 1) = x + 1 pour x ≠ 1. Donc lim(x→1) f(x) = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":6346,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"Δ = 1","option_b":"Δ = 16","option_c":"Δ = 25","option_d":"Δ = 36","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant est donné par 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\": \"Δ = 1\", \"b\": \"Δ = 16\", \"c\": \"Δ = 25\", \"d\": \"Δ = 36\"}}","_debug_options_count":4},{"id":6347,"question":"La fonction f(x) = 1\/x est-elle définie en 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":6348,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 5 ?","option_a":"x \u003E 12","option_b":"x \u003E 2","option_c":"x \u003C 12","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant, on obtient 3x - 7 \u003E 2x + 5 → x \u003E 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 \u003E 12\", \"b\": \"x \u003E 2\", \"c\": \"x \u003C 12\", \"d\": \"x \u003C 2\"}}","_debug_options_count":4},{"id":6349,"question":"Le point A(2, 3) appartient-il à la droite d'équation y = 2x - 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 2 dans l'équation, on obtient y = 2*2 - 1 = 3, ce qui correspond aux coordonnées de A.","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":6350,"question":"Quelle est la primitive de la fonction f(x) = 4x³ - 3x² + 2x - 1 ?","option_a":"F(x) = x⁴ - x³ + x² - x + C","option_b":"F(x) = 12x² - 6x + 2 + C","option_c":"F(x) = x⁴ - x³ + x + C","option_d":"F(x) = 4x⁴ - 3x³ + 2x² - x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive est obtenue en augmentant chaque exposant de 1 et en divisant par le nouvel exposant : x⁴ - x³ + 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\": \"F(x) = x⁴ - x³ + x² - x + C\", \"b\": \"F(x) = 12x² - 6x + 2 + C","_debug_options_count":4}]