Quiz : Testez vos connaissances en Maths pour le Bac !

Question 1 sur 10 10:00

[{"id":22828,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"A : 2x + 3","option_b":"B : x² + 3","option_c":"C : 2x - 5","option_d":"D : 2x + 3x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22829,"question":"La limite de (sin x)\/x quand x tend vers 0 est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une limite fondamentale en analyse : lim (x→0) sin x \/ x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22830,"question":"Soit une suite définie par Uₙ₊₁ = 2Uₙ + 1 avec U₀ = 0. Quelle est la valeur de U₃ ?","option_a":"A : 3","option_b":"B : 7","option_c":"C : 15","option_d":"D : 31","option_e":"","option_f":"","bonne_reponse":"C","explication":"Calculons pas à pas : U₁ = 1, U₂ = 3, U₃ = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22831,"question":"Dans une expérience aléatoire, la probabilité d'un événement A est P(A) = 0.4. Quelle est la probabilité de l'événement contraire ?","option_a":"A : 0.4","option_b":"B : 0.6","option_c":"C : 0.8","option_d":"D : 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité de l'événement contraire est P(A̅) = 1 - P(A) = 0.6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22832,"question":"L'équation différentielle y' = y admet pour solution générale y = Ceˣ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une équation différentielle classique dont la solution est bien y = Ceˣ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22833,"question":"Quelle est la valeur de l'intégrale ∫₀¹ (3x² + 2x) dx ?","option_a":"A : 1","option_b":"B : 2","option_c":"C : 3","option_d":"D : 4","option_e":"","option_f":"","bonne_reponse":"C","explication":"Calculons : [x³ + x²]₀¹ = 1 + 1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22834,"question":"Dans un repère orthonormé, la distance entre les points A(1;2) et B(4;6) est :","option_a":"A : 5","option_b":"B : √13","option_c":"C : √25","option_d":"D : 7","option_e":"","option_f":"","bonne_reponse":"A","explication":"La distance est √[(4-1)² + (6-2)²] = √(9 + 16) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22835,"question":"La fonction f(x) = x³ - 3x est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Sa dérivée f'(x) = 3x² - 3 s'annule en x = ±1, donc la fonction n'est pas croissante sur tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22836,"question":"Soit une variable aléatoire X suivant une loi normale N(0;1). Quelle est la probabilité P(X ≤ 1) ?","option_a":"A : 0.68","option_b":"B : 0.84","option_c":"C : 0.95","option_d":"D : 0.99","option_e":"","option_f":"","bonne_reponse":"B","explication":"D'après la table de la loi normale, P(X ≤ 1) ≈ 0.8413.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22837,"question":"L'équation de la tangente à la courbe y = x² au point d'abscisse x = 1 est :","option_a":"A : y = 2x - 1","option_b":"B : y = x + 1","option_c":"C : y = 2x","option_d":"D : y = x²","option_e":"","option_f":"","bonne_reponse":"A","explication":"La tangente a pour équation y = f'(1)(x-1) + f(1) = 2(x-1) + 1 = 2x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]