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Question 1 sur 10 10:00

[{"id":70852,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x - 5","option_d":"6x² + 2","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 + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":70853,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc la suite est bien arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":70854,"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":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour les fonctions rationnelles, la limite en l'infini est égale au rapport des coefficients dominants. Ici, lim(x→∞) f(x) = 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":70855,"question":"La fonction exponentielle est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle, notée exp(x) ou e^x, est strictement positive pour tout réel x. Elle est définie sur ℝ et son image est ]0, +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":70856,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"1\/6","option_b":"1\/12","option_c":"1\/36","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"C","explication":"Il y a 6 faces sur chaque dé, donc 6×6 = 36 issues possibles. Un seul cas favorable (6 et 6), donc la probabilité est 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":70857,"question":"La fonction f(x) = x³ - 3x est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = (-x)³ - 3(-x) = -x³ + 3x ≠ f(x), donc la fonction n'est pas paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":70858,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = e²","option_b":"x = 2","option_c":"x = ln(2)","option_d":"x = 100","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation ln(x) = a a pour solution x = e^a. Ici, x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":70859,"question":"Un événement certain a une probabilité de :","option_a":"0","option_b":"0.5","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"Par définition, la probabilité d'un événement certain est égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":70860,"question":"La dérivée de la fonction f(x) = sin(2x) est :","option_a":"cos(2x)","option_b":"2cos(2x)","option_c":"cos(x)","option_d":"2sin(x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule de dérivation des fonctions composées, (sin(u))' = u'cos(u). Ici, u = 2x, donc u' = 2 et f'(x) = 2cos(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":70861,"question":"La suite géométrique de premier terme u₀ = 3 et de raison q = 2 a pour terme général :","option_a":"uₙ = 3×2ⁿ","option_b":"uₙ = 3×n²","option_c":"uₙ = 2×3ⁿ","option_d":"uₙ = 3 + 2n","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une suite géométrique, uₙ = u₀ × qⁿ. Ici, uₙ = 3 × 2ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]