Quiz — 63c52dff048dc__corrigé 15-01-2023.pdf

Question 1 sur 5 10:00

[{"id":1221,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x - 2)(x - 3) = 0. Les solutions sont donc 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\": \"x = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":1222,"question":"Soit f(x) = x³ - 3x² + 2. Quelle est la dérivée f'(x) ?","option_a":"f'(x) = 3x² - 6x","option_b":"f'(x) = 3x² - 3x","option_c":"f'(x) = x² - 6x","option_d":"f'(x) = 3x - 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = x³ - 3x² + 2 est f'(x) = 3x² - 6x, obtenue en appliquant la règle de dérivation des puissances.","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\", \"b\": \"f'(x) = 3x² - 3x\", \"c\": \"f'(x) = x² -","_debug_options_count":4},{"id":1223,"question":"Quelle est la limite de (2x² - 3x + 1)\/(x² + 1) lorsque x tend vers l'infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"b","explication":"En divisant le numérateur et le dénominateur par x², on obtient (2 - 3\/x + 1\/x²)\/(1 + 1\/x²). Lorsque x tend vers l'infini, les termes en 1\/x et 1\/x² tendent vers 0, donc la limite est 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\": \"2\", \"b\": \"1\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":1224,"question":"Un sac contient 3 boules rouges et 2 boules bleues. Quelle est la probabilité de tirer une boule rouge ?","option_a":"3\/5","option_b":"2\/5","option_c":"1\/5","option_d":"5\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 3 boules rouges sur un total de 5 boules. La probabilité de tirer une boule rouge est donc 3\/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\": \"3\/5\", \"b\": \"2\/5\", \"c\": \"1\/5\", \"d\": \"5\/3\"}}","_debug_options_count":4},{"id":1225,"question":"Quelle est la valeur de la suite définie par uₙ = 2n + 1 pour n = 4 ?","option_a":"u₄ = 9","option_b":"u₄ = 8","option_c":"u₄ = 10","option_d":"u₄ = 7","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant n par 4 dans la formule uₙ = 2n + 1, on obtient u₄ = 2*4 + 1 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"u₄ = 9\", \"b\": \"u₄ = 8\", \"c\": \"u₄ = 10\", \"d\": \"u₄ = 7\"}}","_debug_options_count":4}]