Quiz — 283.._sujet 4.pdf

Question 1 sur 10 20:00

[{"id":33180,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = -2","option_c":"x = 2","option_d":"x = -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 5 = 2x + 7 → 3x - 2x = 7 + 5 → 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 = 2\", \"d\": \"x = -12\"}}","_debug_options_count":4},{"id":33181,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction s'annule en x=1 et x=3, elle est donc négative entre ces valeurs.","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":33182,"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":"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":33183,"question":"La dérivée de f(x) = 5x³ - 2x² + x est f'(x) = 15x² - 4x + 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée est correcte : f'(x) = 15x² - 4x + 1.","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":33184,"question":"Quelle est la limite de (2x² + 3x - 1)\/(x² - 1) quand x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant par x², on obtient (2 + 3\/x - 1\/x²)\/(1 - 1\/x²) → 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\": \"2\", \"b\": \"0\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":33185,"question":"L'inéquation 2x - 7 \u003E 3x + 1 a pour solution x \u003C -8.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"2x - 7 \u003E 3x + 1 → -x \u003E 8 → x \u003C -8.","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":33186,"question":"Quel est le développement de (x + 2)(x - 3) ?","option_a":"x² - x - 6","option_b":"x² + x - 6","option_c":"x² - 6x + 6","option_d":"x² + 5x - 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"(x + 2)(x - 3) = x² - 3x + 2x - 6 = x² - x - 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² - x - 6\", \"b\": \"x² + x - 6\", \"c\": \"x² - 6x + 6\", \"d\": \"x² ","_debug_options_count":4},{"id":33187,"question":"La fonction f(x) = 1\/x est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction n'est pas définie en x = 0, donc non dérivable.","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":33188,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2, 3]","option_b":"x ∈ ]-∞, 2] ∪ [3, +∞[","option_c":"x ∈ [0, 5]","option_d":"x ∈ R","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines sont x=2 et x=3, la parabole est négative entre ces valeurs.","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, 3]\", \"b\": \"x ∈ ]-∞, 2] ∪ [3, +∞[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":33189,"question":"La fonction f(x) = sin(x) est-elle périodique de période 2π ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction sinus a une période de 2π.","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}]