Maths BAC : Testez vos connaissances en analyse et géométrie

Question 1 sur 10 10:00

[{"id":11998,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"3","option_b":"2","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x tendant vers l'infini, on compare les termes de plus haut degré. Ici, 3x²\/x² = 3, donc la limite est 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11999,"question":"La fonction f(x) = x³ - 3x + 2 est-elle strictement 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 - 3 s'annule en x = ±1. La fonction n'est donc pas strictement croissante sur tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12000,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² + 2x en x = 1 ?","option_a":"2","option_b":"3","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"D","explication":"Le coefficient directeur est f'(1) = 2*1 + 2 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12001,"question":"L'équation x² - 5x + 6 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 25 - 24 = 1 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12002,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"2\/(2x + 1)","option_b":"1\/(2x + 1)","option_c":"2x\/(2x + 1)","option_d":"1\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 2x + 1, donc u' = 2. Ainsi, f'(x) = 2\/(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12003,"question":"La suite définie par uₙ = (n² + 1)\/n est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"uₙ = n + 1\/n. Lorsque n tend vers l'infini, uₙ tend vers l'infini, donc la suite diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12004,"question":"Quel est le résultat de l'intégrale ∫(3x² - 2x + 1) dx ?","option_a":"x³ - x² + x + C","option_b":"x³ - x² + 2x + C","option_c":"3x³ - x² + x + C","option_d":"x³ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 3x² est x³, celle de -2x est -x², et celle de 1 est x. On ajoute la constante C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12005,"question":"L'aire sous la courbe de f(x) = x² entre x = 0 et x = 2 est-elle égale à 8\/3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire est donnée par ∫₀² x² dx = [x³\/3]₀² = 8\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12006,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 5 \u003E 3x + 1 ⇒ -5 - 1 \u003E 3x - 2x ⇒ -6 \u003E x ⇒ x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12007,"question":"La fonction f(x) = e^(2x) est-elle toujours positive sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle e^u est toujours positive, donc e^(2x) \u003E 0 pour tout x ∈ ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]