Quiz — 659971e9ced7f_énoncé_SerieSD.pdf

Question 1 sur 5 10:00

[{"id":26309,"question":"Quelle est la dérivée de la fonction f(x) = 3x² - 5x + 2 ?","option_a":"6x - 5","option_b":"6x² - 5x","option_c":"3x - 5","option_d":"6x - 5x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x - 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\": \"6x - 5\", \"b\": \"6x² - 5x\", \"c\": \"3x - 5\", \"d\": \"6x - 5x\"}}","_debug_options_count":4},{"id":26310,"question":"Dans une classe de 30 élèves, 18 ont réussi leur contrôle de maths. Quelle est la probabilité qu'un élève choisi au hasard ait réussi ?","option_a":"0,4","option_b":"0,6","option_c":"0,3","option_d":"0,5","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est le rapport du nombre de cas favorables sur le nombre total de cas. Ici, P = 18\/30 = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,4\", \"b\": \"0,6\", \"c\": \"0,3\", \"d\": \"0,5\"}}","_debug_options_count":4},{"id":26311,"question":"Quelle est l'équation cartésienne de la droite passant par les points A(2,3) et B(-1,5) ?","option_a":"2x + 3y - 13 = 0","option_b":"x - y + 1 = 0","option_c":"3x - 2y + 5 = 0","option_d":"y = -2\/3x + 13\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La droite a pour coefficient directeur m = (5-3)\/(-1-2) = -2\/3. Son équation est y = -2\/3x + b. En remplaçant par A(2,3), on trouve b = 13\/3. L'équation cartésienne est 2x + 3y - 13 = 0.","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 + 3y - 13 = 0\", \"b\": \"x - y + 1 = 0\", \"c\": \"3x - 2y + 5 = 0\", ","_debug_options_count":4},{"id":26312,"question":"Soit une suite géométrique de premier terme u₀ = 4 et de raison q = 1\/2. Quelle est la valeur de u₃ ?","option_a":"0,5","option_b":"1","option_c":"2","option_d":"0,25","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule d'une suite géométrique est uₙ = u₀ * qⁿ. Ici, u₃ = 4 * (1\/2)³ = 4 * 1\/8 = 0,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0,5\", \"b\": \"1\", \"c\": \"2\", \"d\": \"0,25\"}}","_debug_options_count":4},{"id":26313,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"+∞","option_d":"-∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour les fonctions rationnelles, la limite en l'infini est le rapport des coefficients des termes de plus haut degré. Ici, lim(x→∞) f(x) = 2x²\/x² = 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\": \"2\", \"b\": \"0\", \"c\": \"+∞\", \"d\": \"-∞\"}}","_debug_options_count":4}]