Quiz — _ملخّص+تمارين نمذجة.pdf

Question 1 sur 10 20:00

[{"id":15019,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"2x² + 3","option_c":"x² + 3","option_d":"2x + 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 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\": \"2x + 3\", \"b\": \"2x² + 3\", \"c\": \"x² + 3\", \"d\": \"2x + 5\"}}","_debug_options_count":4},{"id":15020,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour terme général :","option_a":"uₙ = 3 * 2ⁿ","option_b":"uₙ = 3 * n²","option_c":"uₙ = 2 * 3ⁿ","option_d":"uₙ = 3 + 2n","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général d'une suite géométrique est uₙ = u₀ * qⁿ. Ici, uₙ = 3 * 2ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"uₙ = 3 * 2ⁿ\", \"b\": \"uₙ = 3 * n²\", \"c\": \"uₙ = 2 * 3ⁿ\", ","_debug_options_count":4},{"id":15021,"question":"Vrai ou Faux ? La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle eˣ est strictement positive pour tout x réel.","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":15022,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² + 1) quand x tend vers +∞ ?","option_a":"3","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient f(x) = (3 + 2\/x - 1\/x²)\/(1 + 1\/x²). La limite est donc 3\/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\": \"3\", \"b\": \"1\", \"c\": \"2\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":15023,"question":"Vrai ou Faux ? 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 : uₙ = n). Elle n'est pas forcément convergente.","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":15024,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les nombres pairs sont 2, 4 et 6. Il y a 3 cas favorables sur 6 possibles, donc P = 3\/6 = 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\": \"1\/2\", \"b\": \"1\/3\", \"c\": \"1\/6\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":15025,"question":"Vrai ou Faux ? La fonction f(x) = ln(x) est définie pour x ≤ 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction logarithme népérien ln(x) est définie uniquement pour x \u003E 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},{"id":15026,"question":"Quelle est la solution de l'équation différentielle y' = 2y avec y(0) = 5 ?","option_a":"y = 5e²ˣ","option_b":"y = 5eˣ","option_c":"y = 2e⁵ˣ","option_d":"y = 5 + 2x","option_e":"","option_f":"","bonne_reponse":"b","explication":"La solution générale est y = Ce²ˣ. Avec y(0) = 5, on trouve C = 5. Donc y = 5e²ˣ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"y = 5e²ˣ\", \"b\": \"y = 5eˣ\", \"c\": \"y = 2e⁵ˣ\", \"d\": \"y = 5 + 2","_debug_options_count":4},{"id":15027,"question":"Vrai ou Faux ? La dérivée de sin(x) est cos(x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de sin(x) est bien cos(x), une propriété fondamentale en analyse.","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":15028,"question":"Quelle est l'intégrale de f(x) = 3x² entre 0 et 2 ?","option_a":"4","option_b":"8","option_c":"12","option_d":"16","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'intégrale de 3x² est x³. Entre 0 et 2, on obtient 2³ - 0³ = 8 - 0 = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"4\", \"b\": \"8\", \"c\": \"12\", \"d\": \"16\"}}","_debug_options_count":4}]