Quiz — item 74 sousse 2017 UGD.pdf

Question 1 sur 10 20:00

[{"id":36610,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 5x - 2 ?","option_a":"6x + 5","option_b":"3x + 5","option_c":"6x² + 5x","option_d":"3x² + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme est obtenue en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 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\": \"6x + 5\", \"b\": \"3x + 5\", \"c\": \"6x² + 5x\", \"d\": \"3x² + 5\"}}","_debug_options_count":4},{"id":36611,"question":"La fonction f(x) = 1\/x est continue sur son ensemble de définition.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = 1\/x est continue sur ℝ*, mais pas en x=0 où elle n'est pas définie.","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":36612,"question":"Quel est le produit scalaire de deux vecteurs u(2, -3) et v(-1, 4) ?","option_a":"-14","option_b":"14","option_c":"10","option_d":"-10","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le produit scalaire se calcule par u·v = (2)(-1) + (-3)(4) = -2 -12 = -14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-14\", \"b\": \"14\", \"c\": \"10\", \"d\": \"-10\"}}","_debug_options_count":4},{"id":36613,"question":"La suite définie par uₙ = 3n + 2 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 3, donc elle est arithmétique.","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":36614,"question":"Quelle est la forme trigonométrique du nombre complexe z = -1 + i√3 ?","option_a":"2(cos(2π\/3) + i sin(2π\/3))","option_b":"2(cos(π\/3) + i sin(π\/3))","option_c":"√2(cos(3π\/4) + i sin(3π\/4))","option_d":"2(cos(π\/2) + i sin(π\/2))","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module de z est 2 et son argument est 2π\/3, donc z = 2(cos(2π\/3) + i sin(2π\/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\": \"2(cos(2π\/3) + i sin(2π\/3))\", \"b\": \"2(cos(π\/3) + i sin(π\/3))\",","_debug_options_count":4},{"id":36615,"question":"La loi binomiale B(n,p) a pour espérance E(X) = np.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n,p) est bien E(X) = np, où n est le nombre d'essais et p la probabilité de succès.","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":36616,"question":"Quelle est l'équation de la tangente à la courbe y = x² + 3x au point d'abscisse x=1 ?","option_a":"y = 5x - 1","option_b":"y = 5x + 1","option_c":"y = 3x + 5","option_d":"y = x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La tangente a pour équation y = f'(1)(x-1) + f(1). Ici, f'(x)=2x+3, donc f'(1)=5 et f(1)=4. L'équation est y=5x-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\": \"y = 5x - 1\", \"b\": \"y = 5x + 1\", \"c\": \"y = 3x + 5\", \"d\": \"y = x + ","_debug_options_count":4},{"id":36617,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac peut être positif, nul ou négatif selon les valeurs de a, b et c.","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":36618,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"En factorisant, f(x) = (x-1)(x+1)\/(x-1) = x+1 pour x≠1. Donc lim(x→1) f(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":36619,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les nombres pairs sont 2, 4 et 6, soit 3 issues favorables sur 6 possibles. La probabilité est donc 3\/6 = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]