Quiz — 6756d514c70ec_Correction Révision DS1exercice3.pdf

Question 1 sur 10 20:00

[{"id":16879,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1\/2 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1\/2 ou x = -2","option_d":"x = 1 ou x = 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons l'équation : 2x² - 5x + 2 = 0. Le discriminant Δ = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 1\/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\": \"x = 1\/2 ou x = 2\", \"b\": \"x = 2 ou x = 1\/2\", \"c\": \"x = -1\/2 ou x =","_debug_options_count":4},{"id":16880,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 3. Elle est positive pour x \u003C -1 ou x \u003E 1, et négative pour -1 \u003C x \u003C 1. La fonction n'est donc pas croissante sur [-2, 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":16881,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² + 2x au point d'abscisse x = 1 ?","option_a":"2","option_b":"4","option_c":"3","option_d":"5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur de la tangente est donné par la dérivée f'(x) = 2x + 2. En x = 1, f'(1) = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"4\", \"c\": \"3\", \"d\": \"5\"}}","_debug_options_count":4},{"id":16882,"question":"L'équation ln(x) = 2 admet pour solution :","option_a":"x = e²","option_b":"x = 2e","option_c":"x = e\/2","option_d":"x = 1\/e²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation ln(x) = 2 équivaut à x = e² par définition de la fonction logarithme népérien.","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 = e²\", \"b\": \"x = 2e\", \"c\": \"x = e\/2\", \"d\": \"x = 1\/e²\"}}","_debug_options_count":4},{"id":16883,"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, 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},{"id":16884,"question":"Quelle est la limite de la fonction f(x) = (x² + 1)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"+∞","option_c":"-∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Quand x tend vers 1, le numérateur tend vers 2 et le dénominateur tend vers 0. La limite est donc +∞ si x tend vers 1 par la droite, et -∞ si x tend vers 1 par la gauche.","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\": \"+∞\", \"c\": \"-∞\", \"d\": \"1\"}}","_debug_options_count":4},{"id":16885,"question":"L'inéquation 3x - 5 \u003E 7 a pour solution :","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 12","option_d":"x \u003C 12\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons l'inéquation : 3x - 5 \u003E 7 → 3x \u003E 12 → 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 12\", \"d\": \"x \u003C 12\/3\"}}","_debug_options_count":4},{"id":16886,"question":"La fonction f(x) = √(x² + 1) est paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction f est paire si f(-x) = f(x). Ici, f(-x) = √((-x)² + 1) = √(x² + 1) = f(x). La fonction est donc paire.","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":16887,"question":"Quel est le domaine de définition de la fonction f(x) = √(4 - x²) ?","option_a":"[-2, 2]","option_b":"]-∞, 2]","option_c":"]-2, 2[","option_d":"[0, 2]","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction √(4 - x²) est définie lorsque 4 - x² ≥ 0, soit x² ≤ 4 → -2 ≤ x ≤ 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, 2]\", \"b\": \"]-∞, 2]\", \"c\": \"]-2, 2[\", \"d\": \"[0, 2]\"}}","_debug_options_count":4},{"id":16888,"question":"La dérivée de la fonction f(x) = e^(3x) est :","option_a":"3e^(3x)","option_b":"e^(3x)","option_c":"3x e^(3x)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(u(x)) est u'(x) e^(u(x)). Ici, u(x) = 3x, donc u'(x) = 3. La dérivée est 3e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3e^(3x)\", \"b\": \"e^(3x)\", \"c\": \"3x e^(3x)\", \"d\": \"e^(x)\"}}","_debug_options_count":4}]