Quiz — 6633ab186f774_Corrigé_Epreuve N°5.pdf

Question 1 sur 10 20:00

[{"id":20289,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = 10","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 2x des deux côtés et en ajoutant 5, on obtient x = 12.","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 = -12\", \"d\": \"x = 10\"}}","_debug_options_count":4},{"id":20290,"question":"La fonction f(x) = 2x² - 8x + 5 est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b. Ici, f(x) est une fonction du second degré (présence de x²).","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":20291,"question":"Quel est le discriminant de l'équation x² - 6x + 9 = 0 ?","option_a":"Δ = 0","option_b":"Δ = 36","option_c":"Δ = -36","option_d":"Δ = 12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant Δ = b² - 4ac = (-6)² - 4(1)(9) = 36 - 36 = 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\": \"Δ = 0\", \"b\": \"Δ = 36\", \"c\": \"Δ = -36\", \"d\": \"Δ = 12\"}}","_debug_options_count":4},{"id":20292,"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":"Une fonction affine a pour forme f(x) = ax + b, dont la représentation graphique est 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":20293,"question":"Résolvez l'inéquation 2x - 3 \u003E 5.","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En ajoutant 3 puis en divisant par 2, on obtient x \u003E 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 \u003E 4\", \"b\": \"x \u003C 4\", \"c\": \"x \u003E 1\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4},{"id":20294,"question":"La somme des angles d'un triangle est égale à 180 degrés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale de la géométrie plane : la somme des angles d'un triangle est toujours de 180°.","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":20295,"question":"Quel est le coefficient directeur de la droite d'équation y = -3x + 2 ?","option_a":"-3","option_b":"2","option_c":"3","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans l'équation y = ax + b, a représente le coefficient directeur. Ici, a = -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\": \"-3\", \"b\": \"2\", \"c\": \"3\", \"d\": \"-2\"}}","_debug_options_count":4},{"id":20296,"question":"L'équation x² + 4 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = 0² - 4(1)(4) = -16 \u003C 0. L'équation n'a donc pas de solution réelle.","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":20297,"question":"Factorisez l'expression 4x² - 9.","option_a":"(2x - 3)(2x + 3)","option_b":"(4x - 9)(x + 1)","option_c":"(x - 3)(4x + 3)","option_d":"(2x + 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il s'agit d'une identité remarquable de la forme a² - b² = (a - b)(a + b) avec a = 2x 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\": \"(2x - 3)(2x + 3)\", \"b\": \"(4x - 9)(x + 1)\", \"c\": \"(x - 3)(4x + 3)\"","_debug_options_count":4},{"id":20298,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","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}]