Quiz — 18.DOC

Question 1 sur 5 10:00

[{"id":26975,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1 ou x = -2","option_d":"x = 1\/2 ou x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation 2x² - 5x + 2 = 0 se résout en utilisant la formule des racines du second degré : 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\": \"b\", \"options\": {\"a\": \"x = 1 ou x = 2\", \"b\": \"x = 2 ou x = 1\/2\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":26976,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + 5 ?","option_a":"f'(x) = 9x² - 4x","option_b":"f'(x) = 6x² - 4x","option_c":"f'(x) = 9x² - 4","option_d":"f'(x) = 3x² - 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 9x² - 4x + 0, car la dérivée d'une constante est nulle.","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) = 9x² - 4x\", \"b\": \"f'(x) = 6x² - 4x\", \"c\": \"f'(x) = 9x² ","_debug_options_count":4},{"id":26977,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 5 cm et un côté mesure 3 cm, quelle est la longueur du troisième côté ?","option_a":"4 cm","option_b":"√34 cm","option_c":"√16 cm","option_d":"2 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore : hypoténuse² = côté1² + côté2². Donc côté2 = √(5² - 3²) = √(25 - 9) = √16 = 4 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\": \"4 cm\", \"b\": \"√34 cm\", \"c\": \"√16 cm\", \"d\": \"2 cm\"}}","_debug_options_count":4},{"id":26978,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction se simplifie en f(x) = (x - 1)(x + 1)\/(x - 1) = x + 1 pour x ≠ 1. Donc lim(x→1) f(x) = 1 + 1 = 2. Attention, la simplification est valable uniquement si x ≠ 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\": \"0\", \"b\": \"1\", \"c\": \"2\", \"d\": \"La limite n'existe pas\"}}","_debug_options_count":4},{"id":26979,"question":"Quelle est la somme des 5 premiers termes de la suite arithmétique de premier terme u₁ = 2 et de raison r = 3 ?","option_a":"40","option_b":"45","option_c":"50","option_d":"55","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des n premiers termes d'une suite arithmétique est donnée par Sₙ = n\/2 × (2u₁ + (n-1)r). Ici, S₅ = 5\/2 × (4 + 12) = 5\/2 × 16 = 40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"40\", \"b\": \"45\", \"c\": \"50\", \"d\": \"55\"}}","_debug_options_count":4}]