Quiz — Coprrection DS1 17-18.pdf

Question 1 sur 10 20:00

[{"id":7605,"question":"Quelle est la solution de l’équation 3x - 5 = 2x + 1 ?","option_a":"x = 4","option_b":"x = 6","option_c":"x = -4","option_d":"x = -6","option_e":"","option_f":"","bonne_reponse":"b","explication":"On isole x en soustrayant 2x des deux côtés : x - 5 = 1, puis on ajoute 5 : x = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = 4\", \"b\": \"x = 6\", \"c\": \"x = -4\", \"d\": \"x = -6\"}}","_debug_options_count":4},{"id":7606,"question":"La fonction f(x) = 2x² - 3x + 1 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction affine s’écrit sous la forme f(x) = ax + b. Ici, le terme x² indique qu’il s’agit d’une fonction du second degré.","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":7607,"question":"Quel est le développement de (x + 3)(2x - 1) ?","option_a":"2x² + 5x - 3","option_b":"2x² + 7x - 3","option_c":"2x² + 5x + 3","option_d":"2x² - 7x - 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"On utilise la distributivité : x*2x + x*(-1) + 3*2x + 3*(-1) = 2x² - x + 6x - 3 = 2x² + 5x - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2x² + 5x - 3\", \"b\": \"2x² + 7x - 3\", \"c\": \"2x² + 5x + 3\", \"d\": ","_debug_options_count":4},{"id":7608,"question":"L’inéquation 5 - 2x \u003E 3 est-elle équivalente à x \u003C 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"On soustrait 5 : -2x \u003E -2, puis on divise par -2 (en inversant le sens de l’inégalité) : x \u003C 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":7609,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"C’est une différence de carrés : x² - 9 = (x)² - (3)² = (x - 3)(x + 3).","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 - 3)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4},{"id":7610,"question":"La droite d’équation y = 2x + 5 passe-t-elle par le point A(1 ; 7) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"En remplaçant x par 1 : y = 2*1 + 5 = 7. Le point A(1 ; 7) appartient bien à la droite.","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":7611,"question":"Quel est le résultat de 3(2x - 4) - 2(5 - x) ?","option_a":"8x - 22","option_b":"8x - 2","option_c":"4x - 22","option_d":"4x - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"On développe : 6x - 12 - 10 + 2x = 8x - 22.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"8x - 22\", \"b\": \"8x - 2\", \"c\": \"4x - 22\", \"d\": \"4x - 2\"}}","_debug_options_count":4},{"id":7612,"question":"L’équation x² = 16 a-t-elle deux solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les solutions sont x = 4 et x = -4, donc deux solutions réelles distinctes.","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":7613,"question":"Quelle est la solution de l’inéquation -3x + 7 ≤ 1 ?","option_a":"x ≥ 2","option_b":"x ≤ 2","option_c":"x ≥ -2","option_d":"x ≤ -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"On soustrait 7 : -3x ≤ -6, puis on divise par -3 (en inversant le sens) : 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\": \"x ≥ 2\", \"b\": \"x ≤ 2\", \"c\": \"x ≥ -2\", \"d\": \"x ≤ -2\"}}","_debug_options_count":4},{"id":7614,"question":"La fonction g(x) = 4x - 7 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur (4) est positif, donc la fonction est strictement croissante.","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}]