Quiz Maths Terminale : Testez vos connaissances en algèbre et analyse

Question 1 sur 10 10:00

[{"id":21828,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0.5 ou x = 2","option_c":"x = 1 ou x = -2","option_d":"x = -0.5 ou x = 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvons l'équation 2x² - 5x + 2 = 0. Le discriminant Δ = (-5)² - 4*2*2 = 25 - 16 = 9. Les solutions sont x = (5 ± √9)\/4, soit x = 2 ou x = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21829,"question":"La fonction f(x) = x³ - 3x + 1 est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction n'est donc pas strictement croissante sur tout ℝ (elle décroît entre -1 et 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21830,"question":"Quelle est la limite de (sin x)\/x lorsque x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n'existe pas","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est un résultat fondamental en analyse : lim(x→0) (sin x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21831,"question":"L'intégrale de 0 à π de sin(x) dx vaut :","option_a":"0","option_b":"1","option_c":"2","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale de sin(x) est -cos(x). Évaluée entre 0 et π, on obtient -cos(π) - (-cos(0)) = 1 - (-1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21832,"question":"Pour toute fonction dérivable f, (f²)' = 2f * f'.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par la règle de dérivation des fonctions composées, (f²)' = 2f * f' est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21833,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003C 0 ?","option_a":"x ∈ ]1, 3[","option_b":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_c":"x ∈ ]-∞, +∞[","option_d":"x ∈ ∅","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines de x² - 4x + 3 = 0 sont x = 1 et x = 3. Le polynôme est négatif entre les racines, donc x ∈ ]1, 3[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21834,"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":"Pour tout x réel, e^x \u003E 0. La fonction exponentielle est donc toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21835,"question":"Quelle est la dérivée de f(x) = ln(3x + 2) ?","option_a":"f'(x) = 1\/(3x + 2)","option_b":"f'(x) = 3\/(3x + 2)","option_c":"f'(x) = 1\/(x + 2)","option_d":"f'(x) = 3x\/(3x + 2)","option_e":"","option_f":"","bonne_reponse":"B","explication":"Par la règle de dérivation des fonctions composées, f'(x) = (3)\/(3x + 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21836,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce^(-2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une équation différentielle linéaire du premier ordre. La solution générale est bien y = Ce^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21837,"question":"Quelle est la valeur de l'intégrale de 0 à 1 de e^(-x) dx ?","option_a":"1 - 1\/e","option_b":"e - 1","option_c":"1\/e","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de e^(-x) est -e^(-x). Évaluée entre 0 et 1, on obtient -e^(-1) - (-e^0) = 1 - 1\/e.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]