Quiz — Lycée Pilote Sousse - DC 1 2016 (+Corrigé).pdf

Question 1 sur 10 20:00

[{"id":23864,"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":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : x = 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\": \"x = 4\", \"b\": \"x = 12\/3\", \"c\": \"x = 2\", \"d\": \"x = 4\/3\"}}","_debug_options_count":4},{"id":23865,"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 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":23866,"question":"Quelle est l'image de 5 par la fonction f(x) = -x² + 4x ?","option_a":"f(5) = -5","option_b":"f(5) = 5","option_c":"f(5) = -25","option_d":"f(5) = 25","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 5 dans f(x) = -x² + 4x, on obtient f(5) = -25 + 20 = -5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f(5) = -5\", \"b\": \"f(5) = 5\", \"c\": \"f(5) = -25\", \"d\": \"f(5) = 25\"}","_debug_options_count":4},{"id":23867,"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":"b","explication":"En soustrayant 1 des deux côtés : 2x \u003E 4, puis en divisant par 2 : x \u003E 2. La solution est x \u003E 2, mais 2 n'est pas inclus.","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 \u003E 2\", \"b\": \"x \u003E 3\", \"c\": \"x \u003C 2\", \"d\": \"x \u003C 3\"}}","_debug_options_count":4},{"id":23868,"question":"La droite d'équation y = -3x + 1 passe-t-elle par le point (0, 1) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 0 dans l'équation, on obtient y = 1. Le point (0, 1) appartient donc 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":23869,"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":"En soustrayant 6 des deux côtés : -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":23870,"question":"La fonction f(x) = 5 est-elle une fonction constante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction constante est de la forme f(x) = k, où k est un nombre réel. Ici, f(x) = 5 est bien une fonction constante.","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":23871,"question":"Quelle est la solution de l'équation 4(x - 2) = 3x + 5 ?","option_a":"x = 13","option_b":"x = -13","option_c":"x = 3","option_d":"x = -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant : 4x - 8 = 3x + 5, puis en soustrayant 3x : x - 8 = 5, et enfin en ajoutant 8 : x = 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\": \"x = 13\", \"b\": \"x = -13\", \"c\": \"x = 3\", \"d\": \"x = -3\"}}","_debug_options_count":4},{"id":23872,"question":"L'équation x² = 9 a pour solutions :","option_a":"x = 3","option_b":"x = -3","option_c":"x = 3 et x = -3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"c","explication":"Les solutions de x² = 9 sont x = 3 et x = -3, car 3² = 9 et (-3)² = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"x = 3\", \"b\": \"x = -3\", \"c\": \"x = 3 et x = -3\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":23873,"question":"La fonction f(x) = -x + 7 est-elle décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine f(x) = ax + b est décroissante si a \u003C 0. Ici, a = -1, donc la fonction est décroissante.","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}]