Quiz — correction ex2+4 S34 mr jalleli.pdf

Question 1 sur 10 20:00

[{"id":2283,"question":"Quelle est l'équation de la droite passant par les points A(1, 2) et B(3, 4) ?","option_a":"y = x + 1","option_b":"y = 2x - 1","option_c":"y = x + 2","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation de la droite passant par deux points se calcule avec la formule y = mx + b, où m = (y2 - y1)\/(x2 - x1). Ici, m = (4-2)\/(3-1) = 1, puis on utilise un point pour trouver b : 2 = 1*1 + b → b = 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\": \"y = x + 1\", \"b\": \"y = 2x - 1\", \"c\": \"y = x + 2\", \"d\": \"y = 2x + 1","_debug_options_count":4},{"id":2284,"question":"La distance entre les points A(2, 3) et B(5, 7) est égale à √(18).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La distance se calcule avec la formule √[(x2-x1)² + (y2-y1)²]. Ici, √[(5-2)² + (7-3)²] = √(9 + 16) = √25 = 5 ≠ √18. L'affirmation est donc fausse.","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":2285,"question":"Soit une suite (Un) définie par U0 = 2 et Un+1 = 3Un - 1. Quelle est la valeur de U2 ?","option_a":"14","option_b":"17","option_c":"11","option_d":"20","option_e":"","option_f":"","bonne_reponse":"a","explication":"U1 = 3*U0 - 1 = 3*2 - 1 = 5. U2 = 3*U1 - 1 = 3*5 - 1 = 14. La bonne réponse est donc 14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"14\", \"b\": \"17\", \"c\": \"11\", \"d\": \"20\"}}","_debug_options_count":4},{"id":2286,"question":"La limite de la suite (Un) définie par Un = (2n² + 3n + 1)\/(n² + 5) quand n tend vers l'infini est :","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour trouver la limite, on divise chaque terme par n² : (2 + 3\/n + 1\/n²)\/(1 + 5\/n²). Quand n → ∞, les termes en 1\/n et 1\/n² tendent vers 0, donc la limite est 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":2287,"question":"Une suite géométrique de raison q = -2 et de premier terme U0 = 3 a pour terme général Un = 3 * (-2)^n.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, une suite géométrique de raison q a pour terme général Un = U0 * q^n. Ici, U0 = 3 et q = -2, donc Un = 3 * (-2)^n. L'affirmation est vraie.","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":2288,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"f'(x) = 6x - 5","option_b":"f'(x) = 3x - 5","option_c":"f'(x) = 6x + 2","option_d":"f'(x) = 3x² - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = d(3x²)\/dx - d(5x)\/dx + d(2)\/dx = 6x - 5 + 0 = 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\": \"f'(x) = 6x - 5\", \"b\": \"f'(x) = 3x - 5\", \"c\": \"f'(x) = 6x + 2\", \"d","_debug_options_count":4},{"id":2289,"question":"Soit une fonction f définie par f(x) = (x² + 1)\/(x - 2). Son domaine de définition est :","option_a":"ℝ \\ {2}","option_b":"ℝ","option_c":"[2, +∞[","option_d":"]-∞, 2[","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction est définie pour tout x réel sauf ceux qui annulent le dénominateur. Ici, x - 2 = 0 → x = 2. Le domaine de définition est donc ℝ privé de 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\": \"ℝ \\\\ {2}\", \"b\": \"ℝ\", \"c\": \"[2, +∞[\", \"d\": \"]-∞, 2[\"}}","_debug_options_count":4},{"id":2290,"question":"La fonction f(x) = x³ - 3x a pour dérivée f'(x) = 3x² - 3. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x³ est 3x² et la dérivée de -3x est -3. Donc f'(x) = 3x² - 3. L'affirmation est vraie.","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":2291,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 2 ou x = 1\/2","option_b":"x = -2 ou x = -1\/2","option_c":"x = 1 ou x = 2","option_d":"x = 0 ou x = 5\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"On résout l'équation avec le discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 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\": \"x = 2 ou x = 1\/2\", \"b\": \"x = -2 ou x = -1\/2\", \"c\": \"x = 1 ou x = ","_debug_options_count":4},{"id":2292,"question":"La fonction f(x) = e^(2x) a pour dérivée f'(x) = 2e^(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de e^(u(x)) est u'(x) * e^(u(x)). Ici, u(x) = 2x, donc u'(x) = 2. Ainsi, f'(x) = 2e^(2x). L'affirmation est vraie.","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}]