Quiz — P-PB27-40-FM.pdf

Question 1 sur 10 20:00

[{"id":72698,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = 3x² + 2x - 5 est f'(x) = 6x + 2, car la dérivée de x² est 2x et celle de x est 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\": \"6x + 2\", \"b\": \"3x² + 2\", \"c\": \"6x - 5\", \"d\": \"3x + 2\"}}","_debug_options_count":4},{"id":72700,"question":"L'équation x² - 5x + 6 = 0 a deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3)=0, donc elle a deux solutions réelles : x=2 et x=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":72702,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"x² + C","option_c":"2x² + x + C","option_d":"x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 2x est x² et celle de 1 est x, donc le résultat est x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x² + x + C\", \"b\": \"x² + C\", \"c\": \"2x² + x + C\", \"d\": \"x + C\"}}","_debug_options_count":4},{"id":72703,"question":"La fonction f(x) = sin(x) est périodique de période π.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction sin(x) est périodique de période 2π, car sin(x + 2π) = sin(x) pour tout x.","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":72705,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"x=1","option_b":"x=2","option_c":"x=0","option_d":"x=3","option_e":"","option_f":"","bonne_reponse":"b","explication":"2^(x+1) = 8 équivaut à 2^(x+1) = 2^3, donc x+1=3 et x=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\": \"x=1\", \"b\": \"x=2\", \"c\": \"x=0\", \"d\": \"x=3\"}}","_debug_options_count":4},{"id":72707,"question":"Le triangle ABC avec AB=5, BC=12 et AC=13 est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le triangle est rectangle car 5² + 12² = 25 + 144 = 169 = 13² (théorème de Pythagore).","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":72708,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"Indéterminée","option_e":"","option_f":"","bonne_reponse":"b","explication":"La limite est 2, car (x² - 1)\/(x - 1) = (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1, donc lim(x→1) (x+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\": \"1\", \"c\": \"2\", \"d\": \"Indéterminée\"}}","_debug_options_count":4},{"id":72710,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 possibles, donc la probabilité est 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":72712,"question":"Quelle est la solution de l'équation ln(x) = 0 ?","option_a":"x=0","option_b":"x=1","option_c":"x=e","option_d":"x=10","option_e":"","option_f":"","bonne_reponse":"b","explication":"ln(x) = 0 équivaut à x = e^0 = 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\": \"x=0\", \"b\": \"x=1\", \"c\": \"x=e\", \"d\": \"x=10\"}}","_debug_options_count":4},{"id":72713,"question":"La fonction f(x) = x³ est 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) = x³ est f'(x) = 3x² ≥ 0 pour tout x, donc la fonction est croissante sur ℝ.","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}]