Quiz — synthèse 2-3.pdf

Question 1 sur 10 20:00

[{"id":21069,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15","option_c":"x = 3","option_d":"x = 10","option_e":"","option_f":"","bonne_reponse":"a","explication":"On isole x : 3x = 15 → x = 5. C'est une équation du 1er degré classique.","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 = 5\", \"b\": \"x = 15\", \"c\": \"x = 3\", \"d\": \"x = 10\"}}","_debug_options_count":4},{"id":21070,"question":"La fonction f(x) = 2x + 3 est-elle une fonction 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. Ici, a = 2 et b = 3, donc c'est bien une fonction 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":21071,"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 identité remarquable : a² - b² = (a - b)(a + b). Ici, a = x et b = 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":21072,"question":"L'inéquation 2x + 1 \u003E 5 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"On résout : 2x \u003E 4 → x \u003E 2. L'inégalité change de sens si on multiplie par un nombre négatif.","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 2\", \"b\": \"x \u003C 2\", \"c\": \"x \u003E 3\", \"d\": \"x \u003C 3\"}}","_debug_options_count":4},{"id":21073,"question":"La représentation graphique d'une fonction linéaire est toujours une droite passant par l'origine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction linéaire s'écrit f(x) = ax. Sa représentation graphique est une droite passant par (0,0).","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":21074,"question":"Quelle est la valeur de f(2) pour f(x) = x² - 4x + 5 ?","option_a":"1","option_b":"5","option_c":"-3","option_d":"3","option_e":"","option_f":"","bonne_reponse":"b","explication":"On remplace x par 2 : f(2) = 4 - 8 + 5 = 1. Attention à bien respecter les priorités opératoires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\", \"b\": \"5\", \"c\": \"-3\", \"d\": \"3\"}}","_debug_options_count":4},{"id":21075,"question":"L'équation x² + 4x + 4 = 0 admet :","option_a":"Deux solutions distinctes","option_b":"Une solution double","option_c":"Aucune solution","option_d":"Trois solutions","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est un carré parfait : (x + 2)² = 0 → x = -2 (solution double).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Deux solutions distinctes\", \"b\": \"Une solution double\", \"c\": \"Auc","_debug_options_count":4},{"id":21076,"question":"La fonction f(x) = -3x + 7 est-elle décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur est -3 (négatif), donc la fonction est décroissante 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":21077,"question":"Quelle est la solution de l'inéquation -2x + 6 ≤ 0 ?","option_a":"x ≥ 3","option_b":"x ≤ 3","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"On résout : -2x ≤ -6 → x ≥ 3 (l'inégalité change de sens car on divise par un nombre négatif).","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\", \"b\": \"x ≤ 3\", \"c\": \"x \u003E 3\", \"d\": \"x \u003C 3\"}}","_debug_options_count":4},{"id":21078,"question":"La somme des angles d'un triangle est égale à :","option_a":"90°","option_b":"180°","option_c":"360°","option_d":"270°","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une propriété fondamentale de la géométrie euclidienne : la somme des angles d'un triangle est toujours 180°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"90°\", \"b\": \"180°\", \"c\": \"360°\", \"d\": \"270°\"}}","_debug_options_count":4}]