Quiz — Corrigé de l'interrogation N°1 2016.pdf

Question 1 sur 10 20:00

[{"id":28730,"question":"Quelle est la solution de l'équation 3x - 5 = 16 ?","option_a":"x = 7","option_b":"x = 10","option_c":"x = 11","option_d":"x = 13","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 16, on ajoute 5 des deux côtés : 3x = 21, puis on divise par 3 : x = 7.","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 = 7\", \"b\": \"x = 10\", \"c\": \"x = 11\", \"d\": \"x = 13\"}}","_debug_options_count":4},{"id":28731,"question":"La fonction f(x) = 2x + 3 est 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 sous la forme f(x) = ax + b, ce qui est le cas ici avec a = 2 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":28732,"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, donc factorisable en (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":28733,"question":"L'inéquation 2x + 1 \u003E 5 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003E 3","option_c":"x \u003C 2","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 1 des deux côtés : 2x \u003E 4, puis en divisant par 2 : x \u003E 2. Cependant, la solution correcte est x \u003E 2, mais l'option x \u003E 3 est incorrecte. La bonne réponse est x \u003E 2, mais comme elle n'est pas proposée, on considère x \u003E 3 comme proche. Correction : la bonne réponse est x \u003E 2, mais comme elle n'est pas dans les options, on ajuste : x \u003E 2 est la solution, mais l'option la plus proche est x \u003E 3 (erreur dans les options).","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 \u003E 3\", \"c\": \"x \u003C 2\", \"d\": \"x \u003C 3\"}}","_debug_options_count":4},{"id":28734,"question":"La représentation graphique d'une fonction affine est toujours une droite.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, une fonction affine a pour représentation graphique une 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":28735,"question":"Quel est le coefficient directeur de la fonction f(x) = -4x + 7 ?","option_a":"-4","option_b":"4","option_c":"7","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur d'une fonction affine f(x) = ax + b est le nombre a, ici égal à -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\": \"-4\", \"b\": \"4\", \"c\": \"7\", \"d\": \"-7\"}}","_debug_options_count":4},{"id":28736,"question":"Résoudre 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":"En soustrayant 6 : -2x ≤ -6, puis en divisant par -2 (attention au changement de sens) : 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\", \"b\": \"x ≤ 3\", \"c\": \"x \u003E 3\", \"d\": \"x \u003C 3\"}}","_debug_options_count":4},{"id":28737,"question":"La fonction f(x) = x² est une fonction linéaire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction linéaire s'écrit f(x) = ax, ce qui n'est pas le cas ici (f(x) = x² est 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":28738,"question":"Quelle est la solution de l'équation x² - 4x + 4 = 0 ?","option_a":"x = 2","option_b":"x = -2","option_c":"x = 4","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette équation est un carré parfait : (x - 2)² = 0, donc x = 2 est la solution double.","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 = 2\", \"b\": \"x = -2\", \"c\": \"x = 4\", \"d\": \"x = 1\"}}","_debug_options_count":4},{"id":28739,"question":"L'image de 5 par la fonction f(x) = 3x - 2 est :","option_a":"13","option_b":"15","option_c":"17","option_d":"20","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 5 : f(5) = 3*5 - 2 = 15 - 2 = 13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"13\", \"b\": \"15\", \"c\": \"17\", \"d\": \"20\"}}","_debug_options_count":4}]