Quiz — série 17- révision 1 prototype d'examen.pdf

Question 1 sur 10 20:00

[{"id":10263,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x - 5","option_d":"6x² + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0. Donc 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\": \"3x² + 2\", \"c\": \"6x + 2x - 5\", \"d\": \"6x² + 2\"}}","_debug_options_count":4},{"id":10264,"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 un résultat fondamental en analyse : lim(x→0) sin(x)\/x = 1, utilisé pour les dérivées des fonctions trigonométriques.","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":10265,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quel est le terme u₃ ?","option_a":"18","option_b":"54","option_c":"81","option_d":"27","option_e":"","option_f":"","bonne_reponse":"b","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 2 × 3³ = 2 × 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"18\", \"b\": \"54\", \"c\": \"81\", \"d\": \"27\"}}","_debug_options_count":4},{"id":10266,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale :","option_a":"y = Ce^(2x)","option_b":"y = Ce^(-2x)","option_c":"y = Ce^(x\/2)","option_d":"y = Ce^(-x\/2)","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation y' + 2y = 0 est une EDL du 1er ordre. Sa solution générale est 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\": \"b\", \"options\": {\"a\": \"y = Ce^(2x)\", \"b\": \"y = Ce^(-2x)\", \"c\": \"y = Ce^(x\/2)\", \"d\": \"y =","_debug_options_count":4},{"id":10267,"question":"Dans une classe de 30 élèves, 18 sont des filles. La probabilité de choisir une fille au hasard est de :","option_a":"0,3","option_b":"0,4","option_c":"0,6","option_d":"0,8","option_e":"","option_f":"","bonne_reponse":"c","explication":"La probabilité est le rapport du nombre de cas favorables sur le nombre total de cas. Ici, 18\/30 = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0,3\", \"b\": \"0,4\", \"c\": \"0,6\", \"d\": \"0,8\"}}","_debug_options_count":4},{"id":10268,"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, deux vecteurs orthogonaux ont un produit scalaire égal à 0, car cos(90°) = 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":10269,"question":"Soit f une fonction continue sur [a, b]. Le théorème des valeurs intermédiaires garantit que :","option_a":"f atteint toutes les valeurs entre f(a) et f(b)","option_b":"f est dérivable sur [a, b]","option_c":"f est constante sur [a, b]","option_d":"f est strictement monotone sur [a, b]","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème des valeurs intermédiaires stipule que si f est continue sur [a, b], alors elle prend toutes les valeurs intermédiaires entre f(a) et f(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\": \"f atteint toutes les valeurs entre f(a) et f(b)\", \"b\": \"f est dé","_debug_options_count":4},{"id":10270,"question":"Un dé équilibré est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le chiffre 6 ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"c","explication":"La probabilité d'obtenir un 6 en un lancer est 1\/6. Pour deux lancers indépendants, c'est (1\/6) × (1\/6) = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/12\", \"c\": \"1\/36\", \"d\": \"1\/18\"}}","_debug_options_count":4},{"id":10271,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, e^x \u003E 0 pour tout x réel. C'est une propriété fondamentale de la fonction exponentielle.","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":10272,"question":"Soit A et B deux événements indépendants d'un même univers. Alors P(A ∩ B) = :","option_a":"P(A) + P(B)","option_b":"P(A) × P(B)","option_c":"P(A) - P(B)","option_d":"P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux événements sont indépendants si et seulement si P(A ∩ B) = P(A) × P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"P(A) + P(B)\", \"b\": \"P(A) × P(B)\", \"c\": \"P(A) - P(B)\", \"d\": \"P(A)","_debug_options_count":4}]