Quiz Mathématiques Terminale : Maîtrisez les fonctions et les suites !

Question 1 sur 10 10:00

[{"id":14238,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x² + 2","option_c":"f'(x) = 6x - 5","option_d":"f'(x) = 5x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14239,"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 uₙ₊₁ - uₙ est constant. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14240,"question":"Quelle est la limite de la suite uₙ = (3n + 1)\/(2n - 5) quand n tend vers l'infini ?","option_a":"1,5","option_b":"0","option_c":"3\/2","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par n, on obtient lim (3 + 1\/n)\/(2 - 5\/n) = 3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14241,"question":"L'équation différentielle y' = 2y admet-elle pour solution y = Ce^(2x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution générale de y' = ky est y = Ce^(kx). Ici, k=2, donc y = Ce^(2x) est bien une solution.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14242,"question":"Quel est le terme général d'une suite géométrique de premier terme u₀ = 4 et de raison q = 3 ?","option_a":"uₙ = 4 * 3ⁿ","option_b":"uₙ = 4 + 3n","option_c":"uₙ = 3 * 4ⁿ","option_d":"uₙ = 4 * n³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une suite géométrique, uₙ = u₀ * qⁿ. Ici, uₙ = 4 * 3ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14243,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x + 2 s'annule en x=1±√(1\/3), donc la fonction n'est pas toujours croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14244,"question":"Quelle est la solution de l'inéquation 2x - 5 ≤ 3x + 1 ?","option_a":"x ≥ -6","option_b":"x ≤ -6","option_c":"x ≥ 6","option_d":"x ≤ 6","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant 2x - 5 ≤ 3x + 1, on obtient -x ≤ 6, soit x ≥ -6. Mais attention à l'inversion du sens de l'inégalité lors de la division par un nombre négatif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14245,"question":"La probabilité d'un événement impossible est-elle égale à 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, la probabilité d'un événement impossible est bien égale à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14246,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² + 3x au point d'abscisse x=1 ?","option_a":"5","option_b":"3","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur de la tangente est f'(1). Ici, f'(x) = 2x + 3, donc f'(1) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14247,"question":"La suite uₙ = (-1)ⁿ est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite uₙ = (-1)ⁿ oscille entre -1 et 1, donc elle ne converge pas.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]