Quiz — P-EX06-19-OB.pdf

Question 1 sur 10 20:00

[{"id":44200,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"5 - 6x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (-5x)' = -5, et (2)' = 0. Donc f'(x) = 6x - 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\": \"6x - 5\", \"b\": \"3x - 5\", \"c\": \"6x² - 5\", \"d\": \"5 - 6x\"}}","_debug_options_count":4},{"id":44201,"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 s'annule en x = ±1. La fonction est décroissante sur [-1, 1] et croissante sur [-2, -1] et [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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":44202,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"x = 1","option_b":"x = 2","option_c":"x = 3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"b","explication":"8 peut s'écrire 2³, donc 2^(x+1) = 2³ ⇒ x+1 = 3 ⇒ x = 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\": \"x = 1\", \"b\": \"x = 2\", \"c\": \"x = 3\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":44203,"question":"La suite définie par uₙ = (2n + 1)\/(n + 3) est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En calculant la limite de uₙ quand n tend vers l'infini, on obtient 2. La suite est donc convergente vers 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":44204,"question":"Quelle est l'intégrale de f(x) = 4x³ entre 0 et 2 ?","option_a":"8","option_b":"16","option_c":"32","option_d":"4","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de 4x³ est x⁴. Évaluée entre 0 et 2, on obtient 2⁴ - 0⁴ = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"8\", \"b\": \"16\", \"c\": \"32\", \"d\": \"4\"}}","_debug_options_count":4},{"id":44205,"question":"La fonction f(x) = ln(x) est définie pour x \u003E 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction logarithme népérien est définie uniquement pour les valeurs strictement positives de 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":44206,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 ≤ 0 ?","option_a":"x ∈ [2, 3]","option_b":"x ∈ ]-∞, 2] ∪ [3, +∞[","option_c":"x ∈ [1, 6]","option_d":"x ∈ ]-∞, 1] ∪ [6, +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines de x² - 5x + 6 sont 2 et 3. Le trinôme est négatif entre ses racines, donc 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 ∈ [2, 3]\", \"b\": \"x ∈ ]-∞, 2] ∪ [3, +∞[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":44207,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé a 3 faces paires (2, 4, 6) sur 6 faces possibles, donc la probabilité est 3\/6 = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":44208,"question":"Quelle est la limite de la fonction f(x) = (x² + 1)\/x quand x tend vers 0+ ?","option_a":"0","option_b":"+∞","option_c":"-∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Quand x tend vers 0+, (x² + 1)\/x ≈ 1\/x, qui tend vers +∞.","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":44209,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire égal à 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}]