Quiz — 1 serie gzara.pdf

Question 1 sur 10 20:00

[{"id":27660,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"x² + 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : la dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 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\": \"6x² + 2\", \"c\": \"3x + 2\", \"d\": \"x² + 2x\"}}","_debug_options_count":4},{"id":27661,"question":"La suite définie par uₙ = 2n + 1 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 = 2(n+1)+1 - (2n+1) = 2, donc la suite est bien 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":27662,"question":"Quel est le déterminant d'une matrice 2x2 A = [[a, b], [c, d]] ?","option_a":"ad - bc","option_b":"a + d","option_c":"a*d","option_d":"b*c","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le déterminant d'une matrice 2x2 [[a, b], [c, d]] est calculé par la formule ad - bc.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"ad - bc\", \"b\": \"a + d\", \"c\": \"a*d\", \"d\": \"b*c\"}}","_debug_options_count":4},{"id":27663,"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 eˣ est définie pour tout réel x et prend uniquement des valeurs strictement positives (eˣ \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":27664,"question":"Quelle est l'intégrale de f(x) = 4x³ entre 0 et 2 ?","option_a":"16","option_b":"8","option_c":"32","option_d":"4","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 4x³ est x⁴. Évaluée entre 0 et 2, on obtient 2⁴ - 0⁴ = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"16\", \"b\": \"8\", \"c\": \"32\", \"d\": \"4\"}}","_debug_options_count":4},{"id":27665,"question":"Le produit scalaire de deux vecteurs orthogonaux est-il toujours nul ?","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 égal à zéro.","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":27666,"question":"Quelle est la limite de la suite uₙ = (n² + 1)\/n² quand n tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n², on obtient (1 + 1\/n²) → 1 quand n → ∞.","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\": \"∞\", \"d\": \"n\"}}","_debug_options_count":4},{"id":27667,"question":"La matrice identité 3x3 a-t-elle un déterminant égal à 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La matrice identité est triangulaire supérieure avec des 1 sur la diagonale. Son déterminant est le produit des éléments diagonaux, donc 1×1×1 = 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":27668,"question":"Quelle est la primitive de f(x) = 5x⁴ ?","option_a":"x⁵ + C","option_b":"5x⁵ + C","option_c":"x⁴ + C","option_d":"5x³ + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"La primitive de xⁿ est xⁿ⁺¹\/(n+1) + C. Ici, n=4, donc la primitive est x⁵\/5 + C, soit x⁵ + C (en absorbant 1\/5 dans la 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\": \"x⁵ + C\", \"b\": \"5x⁵ + C\", \"c\": \"x⁴ + C\", \"d\": \"5x³ + C\"}}","_debug_options_count":4},{"id":27669,"question":"Le théorème des valeurs intermédiaires s'applique-t-il à toute fonction continue sur un intervalle fermé ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème des valeurs intermédiaires stipule que si une fonction f est continue sur un intervalle [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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]