Quiz — Lycée Pilote Sfax - DS 2 2012.pdf

Question 1 sur 10 20:00

[{"id":69631,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 5","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc 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\": \"x² + 3\", \"c\": \"2x + 5\", \"d\": \"x + 3\"}}","_debug_options_count":4},{"id":69632,"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":69633,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x 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 x², on obtient (2 + 3\/x - 1\/x²)\/(1 - 4\/x²). La limite est donc 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":69634,"question":"Soit X une variable aléatoire suivant une loi binomiale B(n=10, p=0.3). Que vaut P(X=3) ?","option_a":"C(10,3) × 0.3³ × 0.7⁷","option_b":"C(10,3) × 0.3⁷ × 0.7³","option_c":"0.3³","option_d":"0.7⁷","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi binomiale, P(X=k) = C(n,k) × pᵏ × (1-p)ⁿ⁻ᵏ. Ici, P(X=3) = C(10,3) × 0.3³ × 0.7⁷.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"C(10,3) × 0.3³ × 0.7⁷\", \"b\": \"C(10,3) × 0.3⁷ × 0.7³\", \"","_debug_options_count":4},{"id":69635,"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":69636,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce⁻²ˣ","option_b":"y = Ce²ˣ","option_c":"y = Cx²","option_d":"y = C\/x²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce⁻²ˣ, où C est une constante.","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 = Ce²ˣ\", \"c\": \"y = Cx²\", \"d\": \"y = C\/x","_debug_options_count":4},{"id":69637,"question":"Soit une fonction f définie sur ℝ telle que f'(x) \u003E 0 pour tout x. Que peut-on dire de f ?","option_a":"f est décroissante","option_b":"f est constante","option_c":"f est croissante","option_d":"f est périodique","option_e":"","option_f":"","bonne_reponse":"c","explication":"Si la dérivée f'(x) est strictement positive pour tout x, alors la fonction f 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\": \"c\", \"options\": {\"a\": \"f est décroissante\", \"b\": \"f est constante\", \"c\": \"f est croissa","_debug_options_count":4},{"id":69638,"question":"Dans une classe de 30 élèves, 12 sont des filles. On choisit un élève au hasard. Quelle est la probabilité que ce soit une fille ?","option_a":"0.4","option_b":"0.3","option_c":"0.6","option_d":"0.5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité est le rapport du nombre de filles au nombre total d'élèves : 12\/30 = 0.4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.4\", \"b\": \"0.3\", \"c\": \"0.6\", \"d\": \"0.5\"}}","_debug_options_count":4},{"id":69639,"question":"La fonction f(x) = x³ - 3x² + 2x est convexe sur l'intervalle [-1, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée seconde f''(x) = 6x - 6. Sur [-1, 2], f''(x) change de signe (négative sur [-1,1], positive sur [1,2]), donc f n'est pas convexe sur tout l'intervalle.","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":69640,"question":"Quelle est l'aire du triangle ABC avec A(1,2), B(3,4) et C(5,2) ?","option_a":"2","option_b":"4","option_c":"6","option_d":"8","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'aire d'un triangle avec des coordonnées (x₁,y₁), (x₂,y₂), (x₃,y₃) est donnée par |(x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂))\/2|. Ici, l'aire est |(1(4-2) + 3(2-2) + 5(2-4))\/2| = |(2 + 0 - 10)\/2| = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"2\", \"b\": \"4\", \"c\": \"6\", \"d\": \"8\"}}","_debug_options_count":4}]