Quiz — 240.._sujet-1 -sc.pdf

Question 1 sur 5 10:00

[{"id":124,"question":"Quelle est la solution de l'équation 3x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2\/3","option_b":"x = -1 ou x = 2\/3","option_c":"x = 1 ou x = -2\/3","option_d":"x = -1 ou x = -2\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation 3x² - 5x + 2 = 0 est une équation du second degré. En utilisant la formule des racines, on trouve Δ = 25 - 24 = 1. Les solutions sont donc x1 = (5 + 1)\/6 = 1 et x2 = (5 - 1)\/6 = 2\/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\": \"x = 1 ou x = 2\/3\", \"b\": \"x = -1 ou x = 2\/3\", \"c\": \"x = 1 ou x = -","_debug_options_count":4},{"id":125,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 4x² + 5x - 2 ?","option_a":"f'(x) = 3x² - 8x + 5","option_b":"f'(x) = 3x² - 4x + 5","option_c":"f'(x) = x² - 8x + 5","option_d":"f'(x) = 3x² - 8x - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme. Pour f(x) = x³ - 4x² + 5x - 2, on obtient f'(x) = 3x² - 8x + 5.","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 - 8x + 5\", \"b\": \"f'(x) = 3x² - 4x + 5\", \"c\": \"f'(x)","_debug_options_count":4},{"id":126,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/2","option_b":"1\/3","option_c":"2\/3","option_d":"1\/6","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un dé équilibré a 6 faces numérotées de 1 à 6. Les nombres pairs sont 2, 4 et 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\": \"1\/2\", \"b\": \"1\/3\", \"c\": \"2\/3\", \"d\": \"1\/6\"}}","_debug_options_count":4},{"id":127,"question":"Résolvez l'inéquation 2x - 3 \u003E 5x + 1.","option_a":"x \u003C -4\/3","option_b":"x \u003E -4\/3","option_c":"x \u003C 4\/3","option_d":"x \u003E 4\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant 2x - 3 \u003E 5x + 1, on obtient -3x \u003E 4, soit x \u003C -4\/3 (en divisant par -3, on inverse le sens de l'inégalité).","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 \u003C -4\/3\", \"b\": \"x \u003E -4\/3\", \"c\": \"x \u003C 4\/3\", \"d\": \"x \u003E 4\/3\"}}","_debug_options_count":4},{"id":128,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour trouver la limite d'une fonction rationnelle en l'infini, on compare les termes de plus haut degré. Ici, f(x) ≈ 2x²\/x² = 2 lorsque x tend vers l'infini.","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\/2\", \"d\": \"1\"}}","_debug_options_count":4}]