Quiz — correction ex 5 série 27 Mr arrbbiii.pdf

Question 1 sur 10 20:00

[{"id":64966,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"3x - 5","option_c":"6x² - 5","option_d":"3x² - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme est obtenue en appliquant la règle de dérivation : (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 - 5\", \"d\": \"3x² - 5\"}}","_debug_options_count":4},{"id":64967,"question":"Une suite croissante est toujours convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une suite croissante peut diverger vers +∞ (exemple : u_n = n). Elle n'est convergente que si elle est majorée.","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":64968,"question":"Soit une variable aléatoire X suivant une loi binomiale B(n=10, p=0.3). Quelle est son espérance ?","option_a":"3","option_b":"0.3","option_c":"10","option_d":"7","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n*p = 10*0.3 = 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\": \"3\", \"b\": \"0.3\", \"c\": \"10\", \"d\": \"7\"}}","_debug_options_count":4},{"id":64969,"question":"Le déterminant d'une matrice triangulaire est égal au produit des éléments de sa diagonale.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale des matrices triangulaires : det(A) = produit des éléments diagonaux.","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":64970,"question":"Quelle est la limite de la suite u_n = (2n² + 3n + 1)\/(n² - 5) quand n tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par n², on obtient lim(u_n) = 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\": \"0\", \"c\": \"1\", \"d\": \"+∞\"}}","_debug_options_count":4},{"id":64971,"question":"Une matrice carrée est inversible si et seulement si son déterminant est strictement positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une matrice est inversible si son déterminant est non nul (≠ 0), pas nécessairement positif.","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":64972,"question":"Soit f une fonction dérivable sur [a,b] telle que f(a)=f(b). Quel théorème s'applique ?","option_a":"Théorème de Pythagore","option_b":"Théorème des valeurs intermédiaires","option_c":"Théorème de Rolle","option_d":"Théorème de Gauss","option_e":"","option_f":"","bonne_reponse":"c","explication":"Le théorème de Rolle stipule que si f est dérivable sur [a,b] et f(a)=f(b), alors il existe c dans ]a,b[ tel que f'(c)=0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Théorème de Pythagore\", \"b\": \"Théorème des valeurs intermédi","_debug_options_count":4},{"id":64973,"question":"La variance d'une variable aléatoire X est toujours positive ou nulle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La variance mesure la dispersion des valeurs autour de l'espérance. Elle est toujours ≥ 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":64974,"question":"Résoudre l'inéquation 2x - 3 \u003E 5x + 1.","option_a":"x \u003C -4\/3","option_b":"x \u003E -4\/3","option_c":"x \u003C 4\/3","option_d":"x \u003E 4\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x : 2x - 5x \u003E 1 + 3 → -3x \u003E 4 → x \u003C -4\/3 (en divisant par un nombre négatif, l'inégalité change de sens).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x \u003C -4\/3\", \"b\": \"x \u003E -4\/3\", \"c\": \"x \u003C 4\/3\", \"d\": \"x \u003E 4\/3\"}}","_debug_options_count":4},{"id":64975,"question":"Soit A une matrice 2x2 telle que A² = I (matrice identité). Que peut-on dire de A ?","option_a":"A est symétrique","option_b":"A est inversible et A⁻¹ = A","option_c":"A est triangulaire","option_d":"A est nulle","option_e":"","option_f":"","bonne_reponse":"b","explication":"Si A² = I, alors A est inversible et son inverse est A lui-même (A⁻¹ = A).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A est symétrique\", \"b\": \"A est inversible et A⁻¹ = A\", \"c\": \"","_debug_options_count":4}]