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Question 1 sur 10 20:00

[{"id":66711,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x - 5","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 + 2\", \"c\": \"6x + 2x - 5\", \"d\": \"3x + 2\"}}","_debug_options_count":4},{"id":66712,"question":"L'intégrale de 0 à 2 de la fonction f(x) = x² est égale à :","option_a":"4\/3","option_b":"8\/3","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'intégrale de x² est x³\/3. Calculée entre 0 et 2 : (2³\/3) - (0³\/3) = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"4\/3\", \"b\": \"8\/3\", \"c\": \"2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":66713,"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 + 2n","option_c":"uₙ = 3 × n²","option_d":"uₙ = 2 × 3ⁿ","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une suite géométrique, uₙ = u₀ × qⁿ = 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 + 2n\", \"c\": \"uₙ = 3 × n²\", ","_debug_options_count":4},{"id":66714,"question":"Vrai ou Faux ? La dérivée de eˣ est eˣ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction exponentielle eˣ est bien eˣ, c'est une propriété fondamentale.","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":66715,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Un dé a 6 faces : 1, 2, 3, 4, 5, 6. Les nombres pairs sont 2, 4, 6 → 3 cas favorables sur 6 → 1\/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\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":66716,"question":"Vrai ou Faux ? L'intégrale d'une fonction positive sur un intervalle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si f(x) ≥ 0 sur [a; b], alors ∫ₐᵇ f(x) dx ≥ 0, car l'aire sous la courbe est positive ou nulle.","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":66717,"question":"La limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini est :","option_a":"0","option_b":"2","option_c":"1\/3","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant numérateur et dénominateur par n : uₙ = (2 + 1\/n)\/(1 + 3\/n) → limite = 2\/1 = 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\": \"0\", \"b\": \"2\", \"c\": \"1\/3\", \"d\": \"1\"}}","_debug_options_count":4},{"id":66718,"question":"Vrai ou Faux ? La dérivée de ln(x) est 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction logarithme népérien ln(x) est bien 1\/x 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":66719,"question":"Quelle est la valeur moyenne de la fonction f(x) = x² sur l'intervalle [0; 2] ?","option_a":"4\/3","option_b":"8\/3","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"La valeur moyenne est (1\/(2-0)) × ∫₀² x² dx = (1\/2) × (8\/3) = 4\/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\": \"4\/3\", \"b\": \"8\/3\", \"c\": \"2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":66720,"question":"Vrai ou Faux ? Une suite arithmétique a une raison constante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, une suite arithmétique a une différence constante entre deux termes consécutifs, appelée raison.","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}]