Quiz — 6996ef6e2a67d_corrigé ex 2 série 11.pdf

Question 1 sur 10 20:00

[{"id":107256,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 7 ?","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'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : f'(x) = 3x² - 4x + 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\": \"3x² - 4x + 5\", \"b\": \"3x² - 4x + 5x\", \"c\": \"x² - 2x + 5\", \"d\": ","_debug_options_count":4},{"id":107257,"question":"La suite définie par uₙ₊₁ = 2uₙ + 3 avec u₀ = 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, uₙ₊₁ - uₙ = uₙ + 3, qui n'est pas constant.","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":107258,"question":"Soit X une variable aléatoire suivant une loi binomiale B(n=10, p=0.3). Quelle est l'espérance de X ?","option_a":"3","option_b":"7","option_c":"0.3","option_d":"10","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi binomiale B(n,p), l'espérance est E(X) = n × p = 10 × 0.3 = 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\": \"3\", \"b\": \"7\", \"c\": \"0.3\", \"d\": \"10\"}}","_debug_options_count":4},{"id":107259,"question":"L'équation de la tangente à la courbe de f(x) = x² au point d'abscisse a = 2 est :","option_a":"y = 4x - 4","option_b":"y = 2x - 4","option_c":"y = 4x + 4","option_d":"y = x² + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La tangente a pour équation y = f'(a)(x - a) + f(a). Ici, f'(2) = 4 et f(2) = 4, donc y = 4(x - 2) + 4 = 4x - 4.","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 = 4x - 4\", \"b\": \"y = 2x - 4\", \"c\": \"y = 4x + 4\", \"d\": \"y = x² ","_debug_options_count":4},{"id":107260,"question":"La limite de la suite uₙ = (2n + 1)\/(n - 3) quand n tend vers l'infini est :","option_a":"2","option_b":"0","option_c":"1","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), dont 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":107261,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs sont orthogonaux si et seulement si leur produit scalaire est nul.","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":107262,"question":"Soit f(x) = e^(2x). Quelle est la dérivée de f ?","option_a":"2e^(2x)","option_b":"e^(2x)","option_c":"2xe^(2x-1)","option_d":"e^(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(u(x)) est u'(x) × e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 2 et f'(x) = 2e^(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\": \"2e^(2x)\", \"b\": \"e^(2x)\", \"c\": \"2xe^(2x-1)\", \"d\": \"e^(x)\"}}","_debug_options_count":4},{"id":107263,"question":"Une suite géométrique de raison q = -2 et de premier terme u₀ = 3 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite géométrique converge si et seulement si |q| \u003C 1. Ici, |q| = 2 \u003E 1, donc la suite diverge.","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":107264,"question":"L'équation cartésienne d'un plan dans l'espace est de la forme :","option_a":"ax + by + cz + d = 0","option_b":"y = mx + p","option_c":"x² + y² = r²","option_d":"(x-a)² + (y-b)² + (z-c)² = r²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation générale d'un plan dans l'espace est ax + by + cz + d = 0, où (a,b,c) est un vecteur normal au plan.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"ax + by + cz + d = 0\", \"b\": \"y = mx + p\", \"c\": \"x² + y² = r²\",","_debug_options_count":4},{"id":107265,"question":"Soit X une variable aléatoire d'espérance E(X) = 5 et d'écart-type σ(X) = 2. Que vaut E(3X + 2) ?","option_a":"17","option_b":"15","option_c":"10","option_d":"7","option_e":"","option_f":"","bonne_reponse":"b","explication":"Pour une variable aléatoire Y = aX + b, on a E(Y) = aE(X) + b. Ici, E(3X + 2) = 3 × 5 + 2 = 17.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"17\", \"b\": \"15\", \"c\": \"10\", \"d\": \"7\"}}","_debug_options_count":4}]