Quiz — 1557506106_Exercice 2 A1 (concours national) correction.pdf

Question 1 sur 10 20:00

[{"id":43535,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12","option_c":"x = 2","option_d":"x = 6","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\", \"c\": \"x = 2\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":43536,"question":"Vrai ou Faux ? L'équation x² = 16 a deux solutions : x = 4 et x = -4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² = 16 admet bien deux solutions : x = 4 et x = -4, car (-4)² = 16 et 4² = 16.","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":43537,"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 : x² - 3² = (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":43538,"question":"Vrai ou Faux ? 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":43539,"question":"Quelle est la valeur de 2³ × 2⁴ ?","option_a":"2⁷","option_b":"2¹²","option_c":"4⁷","option_d":"16","option_e":"","option_f":"","bonne_reponse":"a","explication":"Lorsqu'on multiplie des puissances de même base, on additionne les exposants : 2³ × 2⁴ = 2^(3+4) = 2⁷.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2⁷\", \"b\": \"2¹²\", \"c\": \"4⁷\", \"d\": \"16\"}}","_debug_options_count":4},{"id":43540,"question":"Vrai ou Faux ? L'inéquation 2x + 1 \u003E 5 a pour solution x \u003E 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons 2x + 1 \u003E 5 : 2x \u003E 4 → x \u003E 2. La solution est donc x \u003E 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":43541,"question":"Quelle est la solution de l'équation (x + 1)(x - 3) = 0 ?","option_a":"x = -1 ou x = 3","option_b":"x = 1 ou x = -3","option_c":"x = 0","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un produit de facteurs est nul si l'un des facteurs est nul : x + 1 = 0 → x = -1, ou x - 3 = 0 → 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 = -1 ou x = 3\", \"b\": \"x = 1 ou x = -3\", \"c\": \"x = 0\", \"d\": \"x =","_debug_options_count":4},{"id":43542,"question":"Vrai ou Faux ? La fraction 3\/4 est égale à 0,75.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"3 divisé par 4 donne bien 0,75, donc 3\/4 = 0,75 est vrai.","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":43543,"question":"Quelle est la valeur de f(2) si f(x) = 5x - 1 ?","option_a":"9","option_b":"3","option_c":"11","option_d":"7","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour calculer f(2), on remplace x par 2 : f(2) = 5×2 - 1 = 10 - 1 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"9\", \"b\": \"3\", \"c\": \"11\", \"d\": \"7\"}}","_debug_options_count":4},{"id":43544,"question":"Vrai ou Faux ? L'équation 4x² - 12x + 9 = 0 a une solution double.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac = (-12)² - 4×4×9 = 144 - 144 = 0. Une solution double existe quand Δ = 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}]