Quiz — (حل سلسلة مجموعة النقط(1.pdf · version 1.pdf

Question 1 sur 10 20:00

[{"id":79614,"question":"Quelle est la distance entre les points A(2, 3) et B(5, 7) ?","option_a":"5","option_b":"√13","option_c":"√25","option_d":"√29","option_e":"","option_f":"","bonne_reponse":"d","explication":"La distance AB = √[(5-2)² + (7-3)²] = √(9 + 16) = √25 = 5. La réponse correcte est donc √25.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"5\", \"b\": \"√13\", \"c\": \"√25\", \"d\": \"√29\"}}","_debug_options_count":4},{"id":79615,"question":"Les points A(1, 2), B(3, 4) et C(5, 6) sont-ils alignés ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Calculons le déterminant des vecteurs AB et AC : (3-1)(6-2) - (4-2)(5-1) = 8 - 8 = 0. Les points sont donc alignés. Réponse : Vrai.","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":79616,"question":"Quelle est l'équation de la droite passant par les points A(0, 1) et B(2, 5) ?","option_a":"y = 2x + 1","option_b":"y = x + 1","option_c":"y = 2x - 1","option_d":"y = x - 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La pente m = (5-1)\/(2-0) = 2. L'équation est y = 2x + 1 (car la droite passe par (0,1)).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"y = 2x + 1\", \"b\": \"y = x + 1\", \"c\": \"y = 2x - 1\", \"d\": \"y = x - 1","_debug_options_count":4},{"id":79617,"question":"Le milieu du segment [AB] avec A(4, -1) et B(-2, 3) a pour coordonnées :","option_a":"(1, 1)","option_b":"(1, -1)","option_c":"(2, 1)","option_d":"(0, 1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les coordonnées du milieu sont ((4 + (-2))\/2, (-1 + 3)\/2) = (1, 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\": \"(1, 1)\", \"b\": \"(1, -1)\", \"c\": \"(2, 1)\", \"d\": \"(0, 1)\"}}","_debug_options_count":4},{"id":79618,"question":"La droite d'équation y = -3x + 2 passe-t-elle par le point C(1, -1) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x = 1 dans l'équation, on obtient y = -3(1) + 2 = -1. Le point C(1, -1) appartient donc à la droite. Réponse : Vrai.","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":79619,"question":"Quel est le vecteur directeur de la droite d'équation 2x - 3y + 5 = 0 ?","option_a":"(2, -3)","option_b":"(-3, 2)","option_c":"(3, 2)","option_d":"(2, 3)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une équation ax + by + c = 0, le vecteur directeur est (b, -a). Ici, le vecteur est (-3, -2), soit (3, 2) en simplifiant. La réponse correcte est (3, 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\": \"(2, -3)\", \"b\": \"(-3, 2)\", \"c\": \"(3, 2)\", \"d\": \"(2, 3)\"}}","_debug_options_count":4},{"id":79620,"question":"Les points A(0, 0), B(1, 1) et C(2, 2) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les points A, B et C appartiennent à la droite y = x. Ils sont donc colinéaires. Réponse : Vrai.","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":79621,"question":"Quelle est l'équation du cercle de centre O(0, 0) et de rayon 3 ?","option_a":"x² + y² = 9","option_b":"x² + y² = 3","option_c":"x² + y² = 6","option_d":"x² + y² = 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation d'un cercle de centre (a,b) et rayon r est (x-a)² + (y-b)² = r². Ici, l'équation est x² + y² = 9.","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 + y² = 9\", \"b\": \"x² + y² = 3\", \"c\": \"x² + y² = 6\", \"d\": ","_debug_options_count":4},{"id":79622,"question":"Le vecteur AB avec A(1, 2) et B(4, 6) a pour coordonnées :","option_a":"(3, 4)","option_b":"(5, 8)","option_c":"(4, 6)","option_d":"(3, 8)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les coordonnées du vecteur AB sont (4-1, 6-2) = (3, 4).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(3, 4)\", \"b\": \"(5, 8)\", \"c\": \"(4, 6)\", \"d\": \"(3, 8)\"}}","_debug_options_count":4},{"id":79623,"question":"La droite d'équation y = 4x - 1 est-elle parallèle à la droite y = 4x + 3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux droites sont parallèles si elles ont la même pente. Ici, les deux droites ont une pente de 4. Réponse : Vrai.","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}]