Quiz — serie 25 p2.pdf

Question 1 sur 5 10:00

[{"id":951,"question":"Quelle est la dérivée de la fonction f(x) = (3x² + 2x - 1)³ ?","option_a":"f'(x) = 3(3x² + 2x - 1)²","option_b":"f'(x) = (6x + 2)(3x² + 2x - 1)²","option_c":"f'(x) = 3(6x + 2)(3x² + 2x - 1)²","option_d":"f'(x) = (6x + 2)³(3x² + 2x - 1)","option_e":"","option_f":"","bonne_reponse":"c","explication":"On applique la formule de dérivation d'une fonction composée : (u³)' = 3u² × u'. Ici, u = 3x² + 2x - 1, donc u' = 6x + 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\": \"f'(x) = 3(3x² + 2x - 1)²\", \"b\": \"f'(x) = (6x + 2)(3x² + 2x - 1","_debug_options_count":4},{"id":952,"question":"Dans l'espace, l'équation x + 2y - z + 3 = 0 représente :","option_a":"Un point","option_b":"Une droite","option_c":"Un plan","option_d":"Une sphère","option_e":"","option_f":"","bonne_reponse":"c","explication":"L'équation générale d'un plan dans l'espace est ax + by + cz + d = 0. Ici, les coefficients (1, 2, -1) définissent un plan.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Un point\", \"b\": \"Une droite\", \"c\": \"Un plan\", \"d\": \"Une sphère\"}","_debug_options_count":4},{"id":953,"question":"Soit une suite géométrique de premier terme u₀ = 5 et de raison q = 2. Quelle est la valeur de u₃ ?","option_a":"10","option_b":"20","option_c":"40","option_d":"80","option_e":"","option_f":"","bonne_reponse":"d","explication":"La formule d'une suite géométrique est uₙ = u₀ × qⁿ. Donc u₃ = 5 × 2³ = 5 × 8 = 40.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"10\", \"b\": \"20\", \"c\": \"40\", \"d\": \"80\"}}","_debug_options_count":4},{"id":954,"question":"On lance un dé équilibré à 6 faces. Quelle est la probabilité d'obtenir un nombre pair ?","option_a":"1\/6","option_b":"1\/3","option_c":"1\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"c","explication":"Les nombres pairs sur un dé sont 2, 4 et 6, soit 3 issues 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\": \"c\", \"options\": {\"a\": \"1\/6\", \"b\": \"1\/3\", \"c\": \"1\/2\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":955,"question":"Quel est le module du nombre complexe z = 3 + 4i ?","option_a":"5","option_b":"7","option_c":"√7","option_d":"√12","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe z = a + bi est donné par |z| = √(a² + b²). Ici, |z| = √(3² + 4²) = √(9 + 16) = √25 = 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\": \"5\", \"b\": \"7\", \"c\": \"√7\", \"d\": \"√12\"}}","_debug_options_count":4}]