Quiz de révision — Mathématiques Terminale

Question 1 sur 10 10:00

[{"id":30598,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 5x - 2 ?","option_a":"6x + 5","option_b":"6x² + 5","option_c":"3x + 5","option_d":"6x + 5x - 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (5x)' = 5 et (-2)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30599,"question":"La fonction f(x) = x³ est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = x³ est f'(x) = 3x², qui est toujours positive ou nulle. Donc la fonction est croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30600,"question":"Quelle est la limite de (2x + 1)\/(x - 3) 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":"En divisant numérateur et dénominateur par x, on obtient (2 + 1\/x)\/(1 - 3\/x), qui tend vers 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30601,"question":"L'équation x² - 4x + 4 = 0 a-t-elle deux solutions distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = (-4)² - 4*1*4 = 0, donc l'équation a une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30602,"question":"Quelle est la primitive de f(x) = 4x³ ?","option_a":"x⁴ + C","option_b":"12x² + C","option_c":"x⁴\/4 + C","option_d":"4x⁴ + C","option_e":"","option_f":"","bonne_reponse":"C","explication":"La primitive de xⁿ est x^(n+1)\/(n+1) + C. Ici, n = 3, donc la primitive est x⁴\/4 + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30603,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction 1\/x n'est pas définie en x = 0 car le dénominateur devient nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30604,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"√2\/2","option_b":"1\/2","option_c":"√3\/2","option_d":"0","option_e":"","option_f":"","bonne_reponse":"B","explication":"sin(π\/6) = 1\/2, valeur à connaître par cœur dans le cercle trigonométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30605,"question":"L'intégrale de 0 à 1 de x² dx est-elle égale à 1\/3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de x² de 0 à 1 est [x³\/3]₀¹ = 1\/3 - 0 = 1\/3. Donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30606,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"e²","option_b":"2","option_c":"1\/e²","option_d":"ln(2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"ln(x) = 2 ⇒ x = e², car la fonction exponentielle est la réciproque du logarithme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30607,"question":"La suite uₙ = n\/(n+1) converge-t-elle vers 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En calculant la limite de uₙ lorsque n tend vers l'infini, on obtient 1. Donc la suite converge vers 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]