Quiz — DS3-4M- 2021 (pilote nabel).pdf

Question 1 sur 5 10:00

[{"id":200,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = -0,5","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"Résolvons l'équation 2x² - 5x + 2 = 0 en utilisant le discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± √9)\/4, soit x = 2 ou x = 0,5.","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 ou x = 2\", \"b\": \"x = 0,5 ou x = 2\", \"c\": \"x = -1 ou x = -0,","_debug_options_count":4},{"id":201,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 3x² + 2x - 1 ?","option_a":"f'(x) = 3x² - 6x + 2","option_b":"f'(x) = 3x² - 6x + 1","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 formule (xⁿ)' = n·xⁿ⁻¹. Ainsi, 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 + 1\", \"c\": \"f'(x)","_debug_options_count":4},{"id":202,"question":"Dans un triangle ABC rectangle en A, si AB = 6 cm et BC = 10 cm, quelle est la longueur de AC ?","option_a":"8 cm","option_b":"4 cm","option_c":"√(100-36) cm","option_d":"6√3 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, AC² = BC² - AB² = 100 - 36 = 64. Donc AC = √64 = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"8 cm\", \"b\": \"4 cm\", \"c\": \"√(100-36) cm\", \"d\": \"6√3 cm\"}}","_debug_options_count":4},{"id":203,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 5)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"2","option_c":"∞","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"d","explication":"En x = 1, le dénominateur s'annule, tandis que le numérateur vaut 0. On a donc une forme indéterminée 0\/0. Après simplification, on obtient f(x) = (2x + 5)(x - 1)\/(x - 1) = 2x + 5 pour x ≠ 1. La limite est donc 2·1 + 5 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"0\", \"b\": \"2\", \"c\": \"∞\", \"d\": \"La limite n'existe pas\"}}","_debug_options_count":4},{"id":204,"question":"Quel est le volume d'un cône de rayon 3 cm et de hauteur 5 cm ?","option_a":"15π cm³","option_b":"45π cm³","option_c":"9π cm³","option_d":"30π cm³","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume d'un cône se calcule avec la formule V = (1\/3)·π·r²·h. Ici, V = (1\/3)·π·9·5 = 15π cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"15π cm³\", \"b\": \"45π cm³\", \"c\": \"9π cm³\", \"d\": \"30π cm³\"}}","_debug_options_count":4}]