Quiz — BAC BLANC 2017MT Lycee chara.pdf

Question 1 sur 10 20:00

[{"id":35990,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 1 ?","option_a":"3x² - 4x + 5","option_b":"3x² - 4x + 5x","option_c":"x² - 2x + 5","option_d":"3x² - 2x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'un polynôme s'obtient en appliquant la règle de dérivation terme à terme : (x³)' = 3x², (-2x²)' = -4x, (5x)' = 5, (-1)' = 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\": \"3x² - 4x + 5\", \"b\": \"3x² - 4x + 5x\", \"c\": \"x² - 2x + 5\", \"d\": ","_debug_options_count":4},{"id":35991,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quelle est la valeur de u₃ ?","option_a":"18","option_b":"54","option_c":"162","option_d":"6","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une suite géométrique, uₙ = u₀ × qⁿ. Ainsi, u₃ = 2 × 3³ = 2 × 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"18\", \"b\": \"54\", \"c\": \"162\", \"d\": \"6\"}}","_debug_options_count":4},{"id":35992,"question":"Vrai ou Faux ? La fonction exponentielle est toujours croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle f(x) = eˣ a pour dérivée f'(x) = eˣ, qui est strictement positive pour tout x réel. Elle est donc strictement croissante.","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":35993,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 5) lorsque x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour les limites à l'infini des fonctions rationnelles, on compare les degrés des polynômes. Ici, les termes dominants sont 2x² au numérateur et x² au dénominateur, 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\": \"0\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":35994,"question":"Vrai ou Faux ? Si deux événements A et B sont indépendants, alors P(A ∩ B) = P(A) × P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux événements sont indépendants si et seulement si P(A ∩ B) = P(A) × P(B). Cette propriété est fondamentale en probabilités.","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":35995,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 avec la condition initiale y(0) = 3 ?","option_a":"y = 3e⁻²ˣ","option_b":"y = 3e²ˣ","option_c":"y = -6e⁻²ˣ","option_d":"y = 6e²ˣ","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation y' + 2y = 0 a pour solution générale y = Ce⁻²ˣ. Avec y(0) = 3, on trouve C = 3, d'où y = 3e⁻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 = 3e⁻²ˣ\", \"b\": \"y = 3e²ˣ\", \"c\": \"y = -6e⁻²ˣ\", \"d\": \"y","_debug_options_count":4},{"id":35996,"question":"Vrai ou Faux ? La matrice identité est inversible et son inverse est elle-même.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La matrice identité Iₙ vérifie Iₙ × Iₙ = Iₙ, donc elle est inversible et son inverse est elle-même.","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":35997,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"c","explication":"Il y a 6 × 6 = 36 issues possibles en lançant deux dés. Un seul cas favorable correspond au double 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\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/12\", \"c\": \"1\/36\", \"d\": \"1\/18\"}}","_debug_options_count":4},{"id":35998,"question":"Vrai ou Faux ? Toute fonction continue sur un intervalle fermé est dérivable sur cet intervalle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux. Par exemple, la fonction f(x) = |x| est continue sur [-1, 1] mais n'est pas dérivable en x = 0.","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":35999,"question":"Quelle est l'aire du domaine délimité par la courbe y = x² et l'axe des abscisses entre x = 0 et x = 2 ?","option_a":"4\/3","option_b":"8\/3","option_c":"2","option_d":"4","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'aire est donnée par l'intégrale ∫₀² x² dx = [x³\/3]₀² = 8\/3 - 0 = 8\/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\": \"4\/3\", \"b\": \"8\/3\", \"c\": \"2\", \"d\": \"4\"}}","_debug_options_count":4}]