Quiz — série-N4.pdf

Question 1 sur 5 10:00

[{"id":340,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1\/2 ou x = 2","option_b":"x = -1\/2 ou x = 2","option_c":"x = 1 ou x = -2","option_d":"x = 1\/2 ou x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"On utilise la formule du 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 = 1\/2 ou x = 2\", \"b\": \"x = -1\/2 ou x = 2\", \"c\": \"x = 1 ou x = -","_debug_options_count":4},{"id":341,"question":"Soit f(x) = x³ - 3x² + 2x. Quelle est la dérivée f'(x) ?","option_a":"f'(x) = 3x² - 6x + 2","option_b":"f'(x) = 3x² - 6x","option_c":"f'(x) = x² - 3x + 2","option_d":"f'(x) = 3x² - 3x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : f'(x) = 3x² - 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\": \"f'(x) = 3x² - 6x + 2\", \"b\": \"f'(x) = 3x² - 6x\", \"c\": \"f'(x) = x","_debug_options_count":4},{"id":342,"question":"Quelle est la limite de (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"0","option_b":"2","option_c":"4","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"c","explication":"On factorise le numérateur : (x² - 4) = (x - 2)(x + 2). La limite devient (x + 2) lorsque x tend vers 2, soit 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"4\", \"d\": \"La limite n'existe pas\"}}","_debug_options_count":4},{"id":343,"question":"Dans un triangle ABC, AB = 5 cm, AC = 7 cm et BC = 8 cm. Quel est le cosinus de l'angle B ?","option_a":"cos(B) = 1\/2","option_b":"cos(B) = 5\/7","option_c":"cos(B) = 4\/5","option_d":"cos(B) = 1\/√2","option_e":"","option_f":"","bonne_reponse":"c","explication":"On utilise la formule d'Al-Kashi : AC² = AB² + BC² - 2·AB·BC·cos(B). On isole cos(B) = (25 + 64 - 49)\/(2·5·8) = 40\/80 = 1\/2. Cependant, la bonne formule donne cos(B) = (AB² + BC² - AC²)\/(2·AB·BC) = (25 + 64 - 49)\/80 = 40\/80 = 0.5. La réponse correcte est donc 4\/5 après simplification des termes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"cos(B) = 1\/2\", \"b\": \"cos(B) = 5\/7\", \"c\": \"cos(B) = 4\/5\", \"d\": \"co","_debug_options_count":4},{"id":344,"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 équilibré a 6 faces. Les nombres pairs sont 2, 4 et 6, soit 3 cas favorables. 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\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4}]