Quiz — 2-Serie.pdf

Question 1 sur 10 20:00

[{"id":17129,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"2x² + 3x","option_c":"x² + 3","option_d":"2x + 3x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (x^n)' = n*x^(n-1). Ainsi, f'(x) = 2x + 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\": \"2x + 3\", \"b\": \"2x² + 3x\", \"c\": \"x² + 3\", \"d\": \"2x + 3x - 5\"}}","_debug_options_count":4},{"id":17130,"question":"La fonction f(x) = e^x est-elle 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 a une dérivée toujours positive (e^x \u003E 0), donc elle est strictement croissante sur 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},{"id":17131,"question":"Quelle est l'intégrale de f(x) = 2x + 1 entre 0 et 2 ?","option_a":"6","option_b":"4","option_c":"5","option_d":"8","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale se calcule comme suit : ∫(2x+1)dx = x² + x. Évaluée entre 0 et 2, cela donne (4+2) - (0+0) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6\", \"b\": \"4\", \"c\": \"5\", \"d\": \"8\"}}","_debug_options_count":4},{"id":17132,"question":"Le nombre complexe z = 3 + 4i a pour module :","option_a":"5","option_b":"7","option_c":"25","option_d":"√7","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe z = a + bi est donné par |z| = √(a² + b²). Ici, |z| = √(9+16) = 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\": \"25\", \"d\": \"√7\"}}","_debug_options_count":4},{"id":17133,"question":"La suite (u_n) définie par u_n = (-1)^n est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La suite alterne entre -1 et 1, donc elle n'a pas de limite. Elle est divergente.","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":17134,"question":"Quelle est la solution de l'équation différentielle y' = 2y ?","option_a":"y = Ce^(2x)","option_b":"y = 2x + C","option_c":"y = Ce^(-2x)","option_d":"y = C*2^x","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation différentielle y' = ky a pour solution y = Ce^(kx). Ici, k=2, donc y = Ce^(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^(2x)\", \"b\": \"y = 2x + C\", \"c\": \"y = Ce^(-2x)\", \"d\": \"y = C","_debug_options_count":4},{"id":17135,"question":"Dans une loi normale N(μ, σ²), quel pourcentage de valeurs se situe entre μ-σ et μ+σ ?","option_a":"68%","option_b":"95%","option_c":"99%","option_d":"50%","option_e":"","option_f":"","bonne_reponse":"a","explication":"Environ 68% des valeurs d'une loi normale se situent dans l'intervalle [μ-σ, μ+σ] (règle des 68-95-99,7).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"68%\", \"b\": \"95%\", \"c\": \"99%\", \"d\": \"50%\"}}","_debug_options_count":4},{"id":17136,"question":"La matrice A = [[1, 2], [3, 4]] est-elle inversible ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une matrice est inversible si son déterminant est non nul. Ici, det(A) = (1*4) - (2*3) = -2 ≠ 0, donc elle est inversible.","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":17137,"question":"Quelle est la limite de (sin x)\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"π\/2","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est un résultat fondamental en analyse : lim(x→0) (sin x)\/x = 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\": \"0\", \"b\": \"1\", \"c\": \"∞\", \"d\": \"π\/2\"}}","_debug_options_count":4},{"id":17138,"question":"Soit la fonction f(x) = ln(x). Quelle est sa dérivée ?","option_a":"1\/x","option_b":"x","option_c":"e^x","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction logarithme népérien est f'(x) = 1\/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\": \"1\/x\", \"b\": \"x\", \"c\": \"e^x\", \"d\": \"1\"}}","_debug_options_count":4}]