Quiz — serie 2 p2.pdf

Question 1 sur 10 20:00

[{"id":38090,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 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\": \"6x + 2\", \"b\": \"3x² + 2\", \"c\": \"6x - 5\", \"d\": \"3x + 2\"}}","_debug_options_count":4},{"id":38091,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique.","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":38092,"question":"Quel est le résultat de l'intégrale ∫(4x³ - 2x) dx ?","option_a":"x⁴ - x² + C","option_b":"4x⁴ - 2x² + C","option_c":"x⁴ - x²","option_d":"4x⁴ - x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale se calcule terme par terme : ∫4x³ dx = x⁴ et ∫-2x dx = -x², d'où x⁴ - x² + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x⁴ - x² + C\", \"b\": \"4x⁴ - 2x² + C\", \"c\": \"x⁴ - x²\", \"d\":","_debug_options_count":4},{"id":38093,"question":"Dans une expérience aléatoire, la probabilité d'un événement A est P(A) = 0,3. Quelle est la probabilité de l'événement contraire ?","option_a":"0,7","option_b":"0,3","option_c":"0,5","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité de l'événement contraire est P(Ā) = 1 - P(A) = 1 - 0,3 = 0,7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,7\", \"b\": \"0,3\", \"c\": \"0,5\", \"d\": \"1\"}}","_debug_options_count":4},{"id":38094,"question":"La fonction f(x) = (x² + 1)\/x est-elle définie pour 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 car le dénominateur s'annule, ce qui rend l'expression indéfinie.","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":38095,"question":"Quelle est la limite de la fonction f(x) = (3x² - 2x + 1)\/(x² + 1) quand x tend vers l'infini ?","option_a":"3","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (3 - 2\/x + 1\/x²)\/(1 + 1\/x²). Quand x tend vers l'infini, les termes en 1\/x tendent vers 0, d'où la limite 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":38096,"question":"Un sac contient 5 boules rouges et 3 boules bleues. Quelle est la probabilité de tirer une boule rouge ?","option_a":"5\/8","option_b":"3\/8","option_c":"5\/3","option_d":"8\/5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 5 boules rouges sur un total de 8 boules. La probabilité est donc 5\/8.","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\/8\", \"b\": \"3\/8\", \"c\": \"5\/3\", \"d\": \"8\/5\"}}","_debug_options_count":4},{"id":38097,"question":"La fonction f(x) = x³ - 3x est-elle 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 s'annule en x = ±1. La fonction n'est pas croissante sur tout l'intervalle [-2, 2] car elle décroît entre -1 et 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":38098,"question":"Quel est le produit scalaire de deux vecteurs u(2, -1) et v(-3, 4) ?","option_a":"-10","option_b":"10","option_c":"5","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le produit scalaire se calcule par u·v = (2)(-3) + (-1)(4) = -6 -4 = -10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-10\", \"b\": \"10\", \"c\": \"5\", \"d\": \"-5\"}}","_debug_options_count":4},{"id":38099,"question":"La suite définie par uₙ = 2ⁿ est-elle géométrique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est géométrique si le rapport entre deux termes consécutifs est constant. Ici, uₙ₊₁\/uₙ = 2, donc elle est géométrique.","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}]