Quiz — 62947805b45cd_SD22_MFK_CHKB_MIL_correction_BP2022_pascal_énoncé.pdf

Question 1 sur 10 20:00

[{"id":97624,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et la dérivée d'une constante est 0. Donc 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\": \"6x² + 2\", \"c\": \"3x + 2\", \"d\": \"6x - 5\"}}","_debug_options_count":4},{"id":97625,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour terme général uₙ = 3 × 2ⁿ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Ici, uₙ = 3 × 2ⁿ, donc l'affirmation est vraie.","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":97626,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n - 3) quand n tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 - 3\/n). Quand n → ∞, 1\/n → 0, donc la limite est 2\/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\": \"2\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":97627,"question":"La probabilité conditionnelle P(A|B) est définie par :","option_a":"P(A ∩ B)\/P(B)","option_b":"P(A) × P(B)","option_c":"P(A) + P(B)","option_d":"P(A) - P(B)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, P(A|B) = P(A ∩ B)\/P(B), à condition que P(B) ≠ 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\": \"P(A ∩ B)\/P(B)\", \"b\": \"P(A) × P(B)\", \"c\": \"P(A) + P(B)\", \"d\": \"","_debug_options_count":4},{"id":97628,"question":"L’équation différentielle y' + 2y = 0 a pour solution générale y = Ce^{-2x}.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’équation différentielle y' + 2y = 0 est une équation linéaire du premier ordre. Sa solution générale est y = Ce^{-2x}, où C est une constante réelle.","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":97629,"question":"Quelle est la solution de l’équation différentielle y'' - 3y' + 2y = 0 ?","option_a":"y = Ce^{x} + De^{2x}","option_b":"y = Ce^{x} + De^{-2x}","option_c":"y = Ce^{-x} + De^{-2x}","option_d":"y = Ce^{2x} + De^{-x}","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’équation caractéristique est r² - 3r + 2 = 0, dont les racines sont r = 1 et r = 2. La solution générale est donc y = Ce^{x} + De^{2x}.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"y = Ce^{x} + De^{2x}\", \"b\": \"y = Ce^{x} + De^{-2x}\", \"c\": \"y = Ce","_debug_options_count":4},{"id":97630,"question":"Dans un repère orthonormé, l’équation x² + y² + 2x - 4y + 1 = 0 représente :","option_a":"Un cercle de centre (-1, 2) et de rayon 2","option_b":"Un cercle de centre (1, -2) et de rayon √2","option_c":"Une droite","option_d":"Une parabole","option_e":"","option_f":"","bonne_reponse":"a","explication":"En complétant le carré, on obtient (x + 1)² + (y - 2)² = 4. Il s’agit donc d’un cercle de centre (-1, 2) et de rayon 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\": \"Un cercle de centre (-1, 2) et de rayon 2\", \"b\": \"Un cercle de ce","_debug_options_count":4},{"id":97631,"question":"La fonction f(x) = x³ - 3x² + 4 est croissante sur l’intervalle [-1, 3].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x s’annule en x = 0 et x = 2. f'(x) est négative sur ]0, 2[, donc la fonction n’est pas croissante sur [-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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":97632,"question":"Quelle est la probabilité d’obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/36","option_b":"1\/6","option_c":"1\/12","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 6 × 6 = 36 issues possibles. Un seul cas correspond à un double 6 (6 et 6), donc la probabilité est 1\/36.","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\/36\", \"b\": \"1\/6\", \"c\": \"1\/12\", \"d\": \"1\/18\"}}","_debug_options_count":4},{"id":97633,"question":"La fonction exponentielle est toujours positive sur ℝ.","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, car e^x \u003E 0 pour tout x ∈ ℝ.","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}]