Quiz — Enoncé.pdf

Question 1 sur 10 20:00

[{"id":50738,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"f'(x) = 6x - 5","option_b":"f'(x) = 3x - 5","option_c":"f'(x) = 6x² - 5","option_d":"f'(x) = 3x² - 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 : (ax^n)' = n·a·x^(n-1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f'(x) = 6x - 5\", \"b\": \"f'(x) = 3x - 5\", \"c\": \"f'(x) = 6x² - 5\", ","_debug_options_count":4},{"id":50739,"question":"La suite définie par uₙ₊₁ = 2uₙ + 1 et u₀ = 0 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, u₁ = 1, u₂ = 3, donc u₂ - u₁ ≠ u₁ - u₀.","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":50740,"question":"Quelle est l'expression de la probabilité conditionnelle P(A|B) ?","option_a":"P(A|B) = P(A ∩ B) \/ P(B)","option_b":"P(A|B) = P(A) + P(B)","option_c":"P(A|B) = P(A) × P(B)","option_d":"P(A|B) = P(B) \/ P(A)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité conditionnelle P(A|B) se calcule comme le rapport de la probabilité de l'intersection A ∩ B sur la probabilité de B.","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(A ∩ B) \/ P(B)\", \"b\": \"P(A|B) = P(A) + P(B)\", \"c\": \"P","_debug_options_count":4},{"id":50741,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à :","option_a":"0","option_b":"1","option_c":"-1","option_d":"Leur norme","option_e":"","option_f":"","bonne_reponse":"a","explication":"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\": \"0\", \"b\": \"1\", \"c\": \"-1\", \"d\": \"Leur norme\"}}","_debug_options_count":4},{"id":50742,"question":"L'équation différentielle y' = 2y + 3 admet-elle une solution constante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une solution constante y = k vérifie y' = 0. En substituant, on obtient 0 = 2k + 3 ⇒ k = -3\/2. La solution constante existe donc.","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":50743,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/(2n² - 3) quand n tend vers l'infini ?","option_a":"1\/2","option_b":"0","option_c":"+∞","option_d":"-∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour calculer la limite, on divise le numérateur et le dénominateur par n² : (1 + 1\/n²)\/(2 - 3\/n²) → 1\/2 quand n → ∞.","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\/2\", \"b\": \"0\", \"c\": \"+∞\", \"d\": \"-∞\"}}","_debug_options_count":4},{"id":50744,"question":"La fonction exponentielle est-elle 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 exp(x) est définie pour tout x réel et vérifie exp(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},{"id":50745,"question":"Quelle est la primitive de f(x) = 4x³ - 2x + 1 ?","option_a":"F(x) = x⁴ - x² + x + C","option_b":"F(x) = 12x² - 2 + C","option_c":"F(x) = x⁴ - x² + 1","option_d":"F(x) = 4x⁴ - x² + x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive s'obtient en intégrant terme à terme : ∫4x³ dx = x⁴, ∫-2x dx = -x², ∫1 dx = x. La constante C est ajoutée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"F(x) = x⁴ - x² + x + C\", \"b\": \"F(x) = 12x² - 2 + C\", \"c\": \"F(","_debug_options_count":4},{"id":50746,"question":"Dans une expérience aléatoire, si P(A) = 0,3 et P(B) = 0,4 avec A et B incompatibles, alors P(A ∪ B) = ?","option_a":"0,7","option_b":"0,12","option_c":"0,1","option_d":"0,2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour deux événements incompatibles, P(A ∪ B) = P(A) + P(B) = 0,3 + 0,4 = 0,7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,7\", \"b\": \"0,12\", \"c\": \"0,1\", \"d\": \"0,2\"}}","_debug_options_count":4},{"id":50747,"question":"La fonction f(x) = ln(x) est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction logarithme népérien ln(x) n'est définie que pour x \u003E 0. Elle n'est donc pas définie 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}]