Quiz — correction model1.2.pdf

Question 1 sur 10 20:00

[{"id":15629,"question":"Quelle est la solution de l’équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 2x = 7 + 5 → x = 12. Une erreur classique est d’oublier de regrouper les termes en 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 = 12\", \"b\": \"x = 2\", \"c\": \"x = -2\", \"d\": \"x = 5\"}}","_debug_options_count":4},{"id":15630,"question":"La fonction f(x) = 2x + 3 est-elle affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine s’écrit f(x) = ax + b, donc f(x) = 2x + 3 est bien affine.","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":15631,"question":"Quel est le coefficient directeur de la droite passant par les points A(1; 2) et B(3; 6) ?","option_a":"2","option_b":"4","option_c":"1","option_d":"3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur m = (6-2)\/(3-1) = 4\/2 = 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\", \"b\": \"4\", \"c\": \"1\", \"d\": \"3\"}}","_debug_options_count":4},{"id":15632,"question":"L’inéquation 2x - 1 \u003E 5 a pour solution x \u003E 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"2x \u003E 6 → x \u003E 3. La solution est correcte, mais attention aux erreurs de signe.","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":15633,"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":"x² - 9 est une différence de carrés : (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\": \"(x+3)²\"}}","_debug_options_count":4},{"id":15634,"question":"La droite d’équation y = -x + 4 passe-t-elle par le point C(2; 2) ?","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 + 4 = 2. Le point C 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":15635,"question":"Quel est le résultat de l’expression (3x² - 2x + 1) - (x² + 4x - 3) ?","option_a":"2x² - 6x + 4","option_b":"4x² + 2x - 2","option_c":"2x² - 2x + 4","option_d":"3x² - 6x + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"On soustrait terme à terme : 3x² - x² = 2x², -2x - 4x = -6x, 1 - (-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\": \"2x² - 6x + 4\", \"b\": \"4x² + 2x - 2\", \"c\": \"2x² - 2x + 4\", \"d\": ","_debug_options_count":4},{"id":15636,"question":"La fonction f(x) = x² est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction x² est décroissante sur ]-∞; 0] et croissante sur [0; +∞[.","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":15637,"question":"Quelle est l’équation de la médiatrice du segment [AB] avec A(0; 0) et B(4; 4) ?","option_a":"y = -x + 4","option_b":"y = x","option_c":"y = 2x","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le milieu de [AB] est (2; 2) et la pente de AB est 1, donc la médiatrice a une pente de -1. Son équation est y = -x + 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"y = -x + 4\", \"b\": \"y = x\", \"c\": \"y = 2x\", \"d\": \"x = 2\"}}","_debug_options_count":4},{"id":15638,"question":"Si f(x) = 3x - 1, alors f(2) = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"f(2) = 3*2 - 1 = 5. Le calcul est correct.","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}]