Quiz — exercice 5 _ mme tounsi .pdf

Question 1 sur 10 20:00

[{"id":127610,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2","option_d":"3x² + 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 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\": \"6x + 2\", \"b\": \"3x + 2\", \"c\": \"6x² + 2\", \"d\": \"3x² + 2x\"}}","_debug_options_count":4},{"id":127611,"question":"La limite de (sin x)\/x quand x tend vers 0 est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une limite fondamentale 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":127612,"question":"Soit une suite définie par uₙ₊₁ = 2uₙ + 3 avec u₀ = 1. Quelle est la valeur de u₂ ?","option_a":"11","option_b":"7","option_c":"13","option_d":"9","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calcul pas à pas : u₁ = 2*1 + 3 = 5, u₂ = 2*5 + 3 = 13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"11\", \"b\": \"7\", \"c\": \"13\", \"d\": \"9\"}}","_debug_options_count":4},{"id":127613,"question":"Dans une loi binomiale B(n,p), l'espérance est égale à :","option_a":"n*p","option_b":"n\/p","option_c":"p\/n","option_d":"n + p","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n*p.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"n*p\", \"b\": \"n\/p\", \"c\": \"p\/n\", \"d\": \"n + p\"}}","_debug_options_count":4},{"id":127614,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale :","option_a":"y = Ce^(-2x)","option_b":"y = Cx + 2","option_c":"y = Ce^(2x)","option_d":"y = C\/x","option_e":"","option_f":"","bonne_reponse":"a","explication":"Solution d'une équation différentielle linéaire du premier ordre : 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 = Cx + 2\", \"c\": \"y = Ce^(2x)\", \"d\": \"y = C","_debug_options_count":4},{"id":127615,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, si deux vecteurs sont orthogonaux, leur produit scalaire est égal à 0.","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":127616,"question":"Quelle est la limite de (e^x - 1)\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"e","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"C'est une forme indéterminée qui se résout par la règle de l'Hôpital : lim(x→0) (e^x - 1)\/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\": \"e\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":127617,"question":"Dans un triangle ABC, si AB² + AC² = BC², alors le triangle est :","option_a":"Rectangle en A","option_b":"Isocèle","option_c":"Équilatéral","option_d":"Rectangle en B","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, si AB² + AC² = BC², alors l'angle en A est droit.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Rectangle en A\", \"b\": \"Isocèle\", \"c\": \"Équilatéral\", \"d\": \"Rec","_debug_options_count":4},{"id":127618,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction ln(x) n'est définie que pour x \u003E 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},{"id":127619,"question":"Soit f(x) = x³ - 3x + 2. Combien de racines réelles cette fonction possède-t-elle ?","option_a":"1","option_b":"2","option_c":"3","option_d":"0","option_e":"","option_f":"","bonne_reponse":"b","explication":"En étudiant les variations de f(x), on trouve qu'elle possède 2 racines réelles (une racine double et une simple).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\", \"b\": \"2\", \"c\": \"3\", \"d\": \"0\"}}","_debug_options_count":4}]