Quiz — corrigé série 3.pdf

Question 1 sur 10 20:00

[{"id":31710,"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":31711,"question":"L'intégrale de f(x) = 4x³ entre 0 et 2 vaut 16.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 4x³ est x⁴. Entre 0 et 2, cela donne 2⁴ - 0⁴ = 16. L'affirmation est donc 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":31712,"question":"Quelle est la limite de (2x² + 3x - 1)\/(x² - 1) quand x tend vers +∞ ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x², on obtient (2 + 3\/x - 1\/x²)\/(1 - 1\/x²). Quand x tend vers +∞, cela tend vers 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":31713,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3. Elle est négative pour x ∈ [-1, 1], donc la fonction est décroissante sur cet intervalle. L'affirmation est 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":31714,"question":"Quelle est la solution de l'équation 2^(x+1) = 16 ?","option_a":"x = 3","option_b":"x = 2","option_c":"x = 4","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"16 = 2⁴, donc 2^(x+1) = 2⁴. Par identification, x + 1 = 4, soit x = 3. La bonne réponse est x = 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\": \"x = 3\", \"b\": \"x = 2\", \"c\": \"x = 4\", \"d\": \"x = 1\"}}","_debug_options_count":4},{"id":31715,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé a 6 faces : 1, 2, 3, 4, 5, 6. Les nombres pairs sont 2, 4, 6, soit 3 cas favorables sur 6 possibles. La probabilité est donc 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":31716,"question":"Quelle est la valeur de la somme des angles d'un triangle ?","option_a":"90°","option_b":"180°","option_c":"360°","option_d":"270°","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des angles d'un triangle est toujours égale à 180°, quel que soit le type de triangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"90°\", \"b\": \"180°\", \"c\": \"360°\", \"d\": \"270°\"}}","_debug_options_count":4},{"id":31717,"question":"La fonction f(x) = ln(x) est définie pour x \u003E 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction logarithme népérien ln(x) n'est définie que pour x \u003E 0. L'affirmation est donc 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":31718,"question":"Quelle est la solution de l'équation différentielle y' = 2y avec y(0) = 3 ?","option_a":"y = 3e^(2x)","option_b":"y = 2e^(3x)","option_c":"y = 3e^x","option_d":"y = 2e^x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution générale de y' = 2y est y = Ce^(2x). Avec y(0) = 3, on obtient C = 3. Donc y = 3e^(2x).","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 = 3e^(2x)\", \"b\": \"y = 2e^(3x)\", \"c\": \"y = 3e^x\", \"d\": \"y = 2e^x","_debug_options_count":4},{"id":31719,"question":"Le nombre complexe z = 3 + 4i a pour module 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module de z = a + bi est √(a² + b²). Ici, √(3² + 4²) = √(9 + 16) = √25 = 5. 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}]