Quiz — 1586627019_3-2 Exercice d'application_Question2.pdf

Question 1 sur 10 20:00

[{"id":36530,"question":"Quelle est la solution de l'équation 3x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2\/3","option_b":"x = -1 ou x = 2\/3","option_c":"x = 1 ou x = -2\/3","option_d":"x = -1 ou x = -2\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons l'équation 3x² - 5x + 2 = 0. Le discriminant Δ = (-5)² - 4×3×2 = 25 - 24 = 1. Les solutions sont x = (5 ± √1)\/6, soit x = 1 ou x = 2\/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 = 2\/3\", \"b\": \"x = -1 ou x = 2\/3\", \"c\": \"x = 1 ou x = -","_debug_options_count":4},{"id":36531,"question":"La fonction f(x) = x³ - 3x est décroissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [-1, 1] car 3x² ≤ 3. La fonction est donc décroissante sur cet intervalle. L'affirmation est fausse.","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":36532,"question":"Quelle est la forme factorisée de x³ - 8 ?","option_a":"(x - 2)(x² + 2x + 4)","option_b":"(x - 2)(x² - 2x + 4)","option_c":"(x + 2)(x² - 2x + 4)","option_d":"(x + 2)(x² + 2x + 4)","option_e":"","option_f":"","bonne_reponse":"a","explication":"x³ - 8 est une différence de cubes : x³ - 2³ = (x - 2)(x² + 2x + 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 - 2)(x² + 2x + 4)\", \"b\": \"(x - 2)(x² - 2x + 4)\", \"c\": \"(x + ","_debug_options_count":4},{"id":36533,"question":"Si f(x) = 2x + 3 et g(x) = x² - 1, alors (f ∘ g)(x) = ?","option_a":"2x² + 5","option_b":"2x² - 1","option_c":"2x² + 1","option_d":"4x² + 6x + 5","option_e":"","option_f":"","bonne_reponse":"b","explication":"","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2x² + 5\", \"b\": \"2x² - 1\", \"c\": \"2x² + 1\", \"d\": \"4x² + 6x + 5\"","_debug_options_count":4},{"id":36534,"question":"La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour tout x réel, eˣ \u003E 0. La fonction exponentielle est donc toujours positive.","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":36535,"question":"Quelle est la limite de (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"0","option_b":"2","option_c":"4","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"d","explication":"La fonction (x² - 4)\/(x - 2) se simplifie en (x + 2) pour x ≠ 2. La limite lorsque x tend vers 2 est donc 4. Cependant, la fonction n'est pas définie en x = 2, donc la limite n'existe pas en tant que telle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"4\", \"d\": \"La limite n'existe pas\"}}","_debug_options_count":4},{"id":36536,"question":"Soit f(x) = ln(x). Quelle est la dérivée de f en x = 1 ?","option_a":"0","option_b":"1","option_c":"-1","option_d":"e","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de ln(x) est 1\/x. En x = 1, f'(1) = 1\/1 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"-1\", \"d\": \"e\"}}","_debug_options_count":4},{"id":36537,"question":"L'équation x² + y² = 25 représente un cercle de centre (0, 0) et de rayon 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² + y² = r² représente un cercle de centre (0, 0) et de rayon r. Ici, r = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36538,"question":"Quelle est la solution de l'inéquation -2x + 5 ≥ 1 ?","option_a":"x ≤ 2","option_b":"x ≥ 2","option_c":"x ≤ -2","option_d":"x ≥ -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons -2x + 5 ≥ 1 → -2x ≥ -4 → x ≤ 2 (en divisant par un nombre négatif, on change le sens de l'inégalité).","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 ≤ -2\", \"d\": \"x ≥ -2\"}}","_debug_options_count":4},{"id":36539,"question":"La fonction f(x) = 1\/x est définie pour tout x réel.","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. L'affirmation est donc fausse.","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}]