Quiz — corrigé 22 aout 2022.pdf

Question 1 sur 5 10:00

[{"id":619,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"2x² + 3","option_c":"x² + 3","option_d":"2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (x^n)' = n*x^(n-1). Ainsi, f'(x) = 2x + 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\": \"2x + 3\", \"b\": \"2x² + 3\", \"c\": \"x² + 3\", \"d\": \"2x - 5\"}}","_debug_options_count":4},{"id":620,"question":"Résoudre 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":"En utilisant la formule des racines d'un polynôme du second degré ax² + bx + c, on trouve x = [5 ± √(25-16)]\/4 = [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":621,"question":"Quelle est l'intégrale indéfinie de la fonction f(x) = 3x² + 2x ?","option_a":"x³ + x² + C","option_b":"x³ + x + C","option_c":"3x³ + x² + C","option_d":"x³ + 2x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale d'une fonction polynôme s'obtient en augmentant l'exposant de 1 et en divisant par le nouvel exposant. Ainsi, ∫(3x² + 2x)dx = x³ + x² + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x³ + x² + C\", \"b\": \"x³ + x + C\", \"c\": \"3x³ + x² + C\", \"d\": \"","_debug_options_count":4},{"id":622,"question":"Dans un repère orthonormé, quelle est l'équation de la droite passant par les points A(1;2) et B(3;6) ?","option_a":"y = 2x","option_b":"y = 3x - 1","option_c":"y = x + 1","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"d","explication":"Le coefficient directeur est (6-2)\/(3-1) = 2. En utilisant l'équation y = mx + p et le point A, on trouve p = 0. D'où y = 2x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"y = 2x\", \"b\": \"y = 3x - 1\", \"c\": \"y = x + 1\", \"d\": \"y = 2x + 1\"}}","_debug_options_count":4},{"id":623,"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 a 6 faces (1,2,3,4,5,6). Les nombres pairs sont 2,4,6, 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}]