Quiz — Analyse.ép.syn.pdf

Question 1 sur 10 20:00

[{"id":49960,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 3x","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d’une somme est la somme des dérivées. La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f’(x) = 2x + 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\", \"b\": \"x² + 3\", \"c\": \"2x + 3x\", \"d\": \"x + 3\"}}","_debug_options_count":4},{"id":49961,"question":"La fonction f(x) = 1\/x est définie sur ℝ.","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, donc son domaine de définition est ℝ*.","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":49962,"question":"Quelle est l’intégrale de f(x) = 2x entre 0 et 2 ?","option_a":"2","option_b":"4","option_c":"8","option_d":"16","option_e":"","option_f":"","bonne_reponse":"b","explication":"L’intégrale de 2x est x². Entre 0 et 2, cela donne 2² - 0² = 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\": \"8\", \"d\": \"16\"}}","_debug_options_count":4},{"id":49963,"question":"La limite de f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 est égale à :","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"On factorise : (x² - 1) = (x - 1)(x + 1). Donc f(x) = x + 1 pour x ≠ 1. La limite quand x→1 est donc 2.","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\": \"2\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":49964,"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":"La fonction exponentielle e^x est strictement positive pour tout x réel.","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":49965,"question":"Quelle est la primitive de f(x) = 3x² qui s’annule en x = 1 ?","option_a":"x³ + C","option_b":"x³ - 1","option_c":"x³ - 2","option_d":"x³","option_e":"","option_f":"","bonne_reponse":"b","explication":"La primitive de 3x² est x³ + C. Pour qu’elle s’annule en x = 1, on a 1³ + C = 0 ⇒ C = -1. Donc la primitive est x³ - 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\": \"x³ + C\", \"b\": \"x³ - 1\", \"c\": \"x³ - 2\", \"d\": \"x³\"}}","_debug_options_count":4},{"id":49966,"question":"La dérivée de f(x) = ln(x) est :","option_a":"1\/x","option_b":"x","option_c":"e^x","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction logarithme népérien ln(x) est 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\/x\", \"b\": \"x\", \"c\": \"e^x\", \"d\": \"1\"}}","_debug_options_count":4},{"id":49967,"question":"L’intégrale de f(x) = sin(x) entre 0 et π est égale à :","option_a":"0","option_b":"1","option_c":"2","option_d":"π","option_e":"","option_f":"","bonne_reponse":"b","explication":"L’intégrale de sin(x) est -cos(x). Entre 0 et π, cela donne -cos(π) - (-cos(0)) = -(-1) - (-1) = 2.","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\": \"2\", \"d\": \"π\"}}","_debug_options_count":4},{"id":49968,"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":"b","explication":"La dérivée f’(x) = 3x² - 3. Sur [-2 ; 2], f’(x) est négative entre -1 et 1, donc la fonction n’est pas croissante sur tout l’intervalle.","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":49969,"question":"Quelle est la valeur de l’intégrale de f(x) = e^x entre 0 et 1 ?","option_a":"e - 1","option_b":"1","option_c":"e","option_d":"2","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’intégrale de e^x est e^x. Entre 0 et 1, cela donne e^1 - e^0 = e - 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\": \"e - 1\", \"b\": \"1\", \"c\": \"e\", \"d\": \"2\"}}","_debug_options_count":4}]