Quiz — Devoir de controle n1 2022Bac math (1).pdf

Question 1 sur 10 20:00

[{"id":25874,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2x","option_c":"6x² + 2","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"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\": \"3x² + 2x\", \"c\": \"6x² + 2\", \"d\": \"3x + 2\"}}","_debug_options_count":4},{"id":25875,"question":"La suite définie par uₙ = n² + 1 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour tout n, uₙ₊₁ - uₙ = (n+1)² + 1 - (n² + 1) = 2n + 1 \u003E 0. La suite est donc croissante.","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":25876,"question":"Quelle est l’équation d’une droite parallèle à l’axe des abscisses passant par le point A(2, -3) ?","option_a":"y = -3","option_b":"x = 2","option_c":"y = 2x - 3","option_d":"x = -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une droite parallèle à l’axe des abscisses a une équation de la forme y = k. Comme elle passe par A(2, -3), k = -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\": \"y = -3\", \"b\": \"x = 2\", \"c\": \"y = 2x - 3\", \"d\": \"x = -3\"}}","_debug_options_count":4},{"id":25877,"question":"Soit X une variable aléatoire suivant une loi binomiale B(10, 0.4). Quelle est l’espérance de X ?","option_a":"4","option_b":"6","option_c":"0.4","option_d":"10","option_e":"","option_f":"","bonne_reponse":"a","explication":"L’espérance d’une loi binomiale B(n, p) est E(X) = n × p. Ici, E(X) = 10 × 0.4 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"4\", \"b\": \"6\", \"c\": \"0.4\", \"d\": \"10\"}}","_debug_options_count":4},{"id":25878,"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, le produit scalaire de deux vecteurs orthogonaux 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":25879,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² + 1) quand x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"+∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (2 + 3\/x - 1\/x²)\/(1 + 1\/x²). La limite est donc 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\": \"+∞\", \"d\": \"1\"}}","_debug_options_count":4},{"id":25880,"question":"Soit la fonction f(x) = e^(3x). Quelle est sa dérivée ?","option_a":"e^(3x)","option_b":"3e^(3x)","option_c":"e^(x)","option_d":"3e^(x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de e^(u(x)) est u'(x) × e^(u(x)). Ici, u(x) = 3x, donc u'(x) = 3. Ainsi, f'(x) = 3e^(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"e^(3x)\", \"b\": \"3e^(3x)\", \"c\": \"e^(x)\", \"d\": \"3e^(x)\"}}","_debug_options_count":4},{"id":25881,"question":"Un algorithme de dichotomie permet de résoudre une équation du type f(x) = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dichotomie est une méthode numérique qui permet de trouver une solution approchée d’une équation du type f(x) = 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":25882,"question":"Quelle est la solution de l’inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003E 6","option_d":"x \u003C 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant l’inéquation : 2x - 5 \u003E 3x + 1 → -x \u003E 6 → x \u003C -6 (en multipliant par -1, on change le sens de l’inégalité).","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 -6\", \"b\": \"x \u003E -6\", \"c\": \"x \u003E 6\", \"d\": \"x \u003C 6\"}}","_debug_options_count":4},{"id":25883,"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) est définie uniquement pour x \u003E 0. Elle n’est pas définie pour x ≤ 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}]