Quiz — serie n2 femme top50.pdf

Question 1 sur 10 20:00

[{"id":65336,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 3x² + 2x ?","option_a":"3x² - 6x + 2","option_b":"x² - 3x + 2","option_c":"3x² - 6x","option_d":"x³ - 3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : f'(x) = 3x² - 6x + 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\": \"3x² - 6x + 2\", \"b\": \"x² - 3x + 2\", \"c\": \"3x² - 6x\", \"d\": \"x³ ","_debug_options_count":4},{"id":65337,"question":"La fonction f(x) = 1\/x est-elle continue sur ℝ* ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = 1\/x est continue sur son ensemble de définition ℝ*, mais pas sur ℝ car elle n'est pas définie en x=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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":65338,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"x² + x","option_c":"2x² + x + C","option_d":"x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale d'une fonction affine s'obtient en intégrant chaque terme : ∫(2x + 1) dx = x² + x + C, où C est la constante d'intégration.","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 + C\", \"b\": \"x² + x\", \"c\": \"2x² + x + C\", \"d\": \"x² + 2x","_debug_options_count":4},{"id":65339,"question":"Soit un triangle ABC rectangle en A. Si AB = 3 et AC = 4, quelle est la longueur de BC ?","option_a":"5","option_b":"7","option_c":"√7","option_d":"√13","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 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\": \"5\", \"b\": \"7\", \"c\": \"√7\", \"d\": \"√13\"}}","_debug_options_count":4},{"id":65340,"question":"La suite définie par uₙ = n² + 2n est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, uₙ₊₁ - uₙ = (n+1)² + 2(n+1) - (n² + 2n) = 2n + 3, qui dépend de n.","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":65341,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1 ou x = -2","option_d":"x = 1\/2 ou x = 2","option_e":"","option_f":"","bonne_reponse":"d","explication":"En utilisant la formule des racines d'un polynôme du second degré, on trouve x = [5 ± √(25 - 16)] \/ 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\": \"d\", \"options\": {\"a\": \"x = 1 ou x = 2\", \"b\": \"x = 2 ou x = 1\/2\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":65342,"question":"Soit f une fonction définie sur ℝ telle que f'(x) \u003E 0 pour tout x. Que peut-on dire de f ?","option_a":"f est décroissante","option_b":"f est constante","option_c":"f est croissante","option_d":"f est périodique","option_e":"","option_f":"","bonne_reponse":"c","explication":"Si la dérivée d'une fonction est strictement positive sur un intervalle, alors la fonction est strictement croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"f est décroissante\", \"b\": \"f est constante\", \"c\": \"f est croissa","_debug_options_count":4},{"id":65343,"question":"L'équation cos(x) = 0 a-t-elle des solutions dans l'intervalle [0, π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction cosinus s'annule en x = π\/2 dans l'intervalle [0, π], donc l'équation a des solutions.","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":65344,"question":"Quelle est la limite de (3n² + 2n - 1)\/(2n² - 5) quand n tend vers l'infini ?","option_a":"0","option_b":"3\/2","option_c":"∞","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n², on obtient (3 + 2\/n - 1\/n²)\/(2 - 5\/n²), dont la limite est 3\/2 quand n tend vers l'infini.","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\": \"3\/2\", \"c\": \"∞\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":65345,"question":"Soit un cercle de rayon 5 cm. Quelle est son aire ?","option_a":"25π cm²","option_b":"10π cm²","option_c":"5π cm²","option_d":"50π cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un cercle est donnée par la formule A = πr², donc A = π × 5² = 25π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"25π cm²\", \"b\": \"10π cm²\", \"c\": \"5π cm²\", \"d\": \"50π cm²\"}}","_debug_options_count":4}]