Quiz — MATH S2.pdf

Question 1 sur 10 20:00

[{"id":91217,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = 2","option_d":"x = 4\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 5 = 7 ⇒ 3x = 12 ⇒ x = 4. Cette équation linéaire est résolue en isolant x.","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\", \"b\": \"x = 12\/3\", \"c\": \"x = 2\", \"d\": \"x = 4\/3\"}}","_debug_options_count":4},{"id":91218,"question":"La fonction f(x) = 2x + 1 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur (2) est positif, donc la fonction est strictement croissante 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},{"id":91219,"question":"Quel est le résultat de (x + 3)(x - 2) ?","option_a":"x² + x - 6","option_b":"x² + 5x - 6","option_c":"x² - 6x + 1","option_d":"x² + x + 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"Développement : x² - 2x + 3x - 6 = x² + x - 6. Utilisez la distributivité (identité remarquable).","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 - 6\", \"b\": \"x² + 5x - 6\", \"c\": \"x² - 6x + 1\", \"d\": \"x²","_debug_options_count":4},{"id":91220,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est l'énoncé du théorème de Pythagore, valable uniquement pour les triangles rectangles.","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":91221,"question":"Quelle est la médiane de la série : 5, 7, 8, 10, 12 ?","option_a":"7","option_b":"8","option_c":"9","option_d":"10","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane est la valeur centrale après rangement : 5, 7, \u003Cstrong\u003E8\u003C\/strong\u003E, 10, 12. Ici, il y a un nombre impair de termes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"7\", \"b\": \"8\", \"c\": \"9\", \"d\": \"10\"}}","_debug_options_count":4},{"id":91222,"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":"C'est une fonction du second degré avec a=1\u003E0, donc elle admet un minimum (sommet de la parabole).","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":91223,"question":"Résolvez le système : { 2x + y = 5 ; x - y = 1 }. La solution est :","option_a":"(2, 1)","option_b":"(-1, 7)","option_c":"(1, 3)","option_d":"(3, -1)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En additionnant les deux équations : 3x = 6 ⇒ x=2. Puis y=5-2x=1. Solution : (2,1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(2, 1)\", \"b\": \"(-1, 7)\", \"c\": \"(1, 3)\", \"d\": \"(3, -1)\"}}","_debug_options_count":4},{"id":91224,"question":"Le cosinus d'un angle aigu dans un triangle rectangle est toujours inférieur à 1. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le cosinus d'un angle aigu est compris entre 0 et 1 (inclus), car il s'agit d'un rapport de longueurs.","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":91225,"question":"Quelle est l'image de 3 par la fonction f(x) = -2x + 7 ?","option_a":"1","option_b":"13","option_c":"-1","option_d":"7","option_e":"","option_f":"","bonne_reponse":"c","explication":"f(3) = -2*3 + 7 = -6 + 7 = 1. Remplacez x par 3 dans l'expression de f.","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\", \"b\": \"13\", \"c\": \"-1\", \"d\": \"7\"}}","_debug_options_count":4},{"id":91226,"question":"La droite d'équation y = -3x + 2 passe-t-elle par le point A(1, -1) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour x=1, y = -3*1 + 2 = -1. Le point A(1, -1) vérifie l'équation, donc la droite passe par 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}]