Quiz — CORDS1-4S-21-22final.docx

Question 1 sur 10 20:00

[{"id":4646,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Résolvons l'équation 2x² - 5x + 2 = 0. Le discriminant Δ = (-5)² - 4*2*2 = 25 - 16 = 9. Les solutions sont x = (5 ± √9)\/4, soit x = 2 ou x = 0,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = 1 ou x = 2\", \"b\": \"x = 0,5 ou x = 2\", \"c\": \"x = -1 ou x = 2\",","_debug_options_count":4},{"id":4647,"question":"La fonction f(x) = x³ - 3x est dérivable sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x³ - 3x est une fonction polynomiale, donc dérivable sur ℝ. Sa dérivée est f'(x) = 3x² - 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":4648,"question":"Quelle est la limite de (3x² + 2x - 1)\/(2x² - x + 4) quand x tend vers +∞ ?","option_a":"0","option_b":"1,5","option_c":"3\/2","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour x → +∞, on divise le numérateur et le dénominateur par x² : (3 + 2\/x - 1\/x²)\/(2 - 1\/x + 4\/x²) → 3\/2.","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\", \"b\": \"1,5\", \"c\": \"3\/2\", \"d\": \"+∞\"}}","_debug_options_count":4},{"id":4649,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0.","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 nul.","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":4650,"question":"Quelle est la dérivée de la fonction f(x) = (2x + 1)\/(x - 3) ?","option_a":"f'(x) = 2\/(x - 3)","option_b":"f'(x) = -7\/(x - 3)²","option_c":"f'(x) = 7\/(x - 3)²","option_d":"f'(x) = -2\/(x - 3)","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la formule de dérivation d'un quotient : f'(x) = [2(x - 3) - (2x + 1)*1]\/(x - 3)² = (2x - 6 - 2x - 1)\/(x - 3)² = -7\/(x - 3)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"f'(x) = 2\/(x - 3)\", \"b\": \"f'(x) = -7\/(x - 3)²\", \"c\": \"f'(x) = 7\/","_debug_options_count":4},{"id":4651,"question":"La fonction f(x) = |x| est dérivable en x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction valeur absolue n'est pas dérivable en x = 0 car sa dérivée à gauche (-1) diffère de sa dérivée à droite (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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":4652,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 ≤ 0 ?","option_a":"x ∈ [1, 3]","option_b":"x ∈ ]-∞, 1] ∪ [3, +∞[","option_c":"x ∈ [0, 4]","option_d":"x ∈ ]-∞, 0] ∪ [4, +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Résolvons x² - 4x + 3 ≤ 0. Les racines sont x = 1 et x = 3. Le polynôme est négatif entre ses racines, donc x ∈ [1, 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\": \"x ∈ [1, 3]\", \"b\": \"x ∈ ]-∞, 1] ∪ [3, +∞[\", \"c\": \"x ∈ ","_debug_options_count":4},{"id":4653,"question":"Le centre de gravité d'un triangle est l'intersection de ses médianes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, le centre de gravité d'un triangle est le point d'intersection de ses médianes.","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":4654,"question":"Quelle est l'espérance mathématique d'une variable aléatoire X suivant une loi binomiale B(n=10, p=0,3) ?","option_a":"E(X) = 3","option_b":"E(X) = 10","option_c":"E(X) = 0,3","option_d":"E(X) = 7","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi binomiale B(n, p), l'espérance 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\": \"E(X) = 3\", \"b\": \"E(X) = 10\", \"c\": \"E(X) = 0,3\", \"d\": \"E(X) = 7\"}}","_debug_options_count":4},{"id":4655,"question":"La fonction f(x) = e^x est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = e^x est f'(x) = e^x \u003E 0 pour tout x ∈ ℝ, donc la fonction est strictement 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}]