Maths 4ème : Fonctions, Équations et Probabilités

Question 1 sur 5 10:00

[{"id":1183,"question":"Quelle est la dérivée de la fonction f(x) = x³ + 2x² - 5x + 1 ?","option_a":"3x² + 4x - 5","option_b":"x² + 2x - 5","option_c":"3x² + 4x + 1","option_d":"x³ + 2x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynomiale se calcule en appliquant la règle : (x^n)' = n*x^(n-1). Ainsi, f'(x) = 3x² + 4x - 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1184,"question":"Résolvez l'équation : 2x² - 5x + 2 = 0.","option_a":"x = 1 ou x = 2","option_b":"x = -1 ou x = -2","option_c":"x = 0.5 ou x = 2","option_d":"x = -0.5 ou x = 2","option_e":"","option_f":"","bonne_reponse":"C","explication":"En utilisant la formule des racines d'une équation du second degré (Δ = b² - 4ac), on trouve x = 0.5 ou x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1185,"question":"Soit une urne contenant 3 boules rouges et 2 boules bleues. Quelle est la probabilité de tirer une boule rouge ?","option_a":"0.3","option_b":"0.4","option_c":"0.5","option_d":"0.6","option_e":"","option_f":"","bonne_reponse":"D","explication":"La probabilité est le rapport du nombre de cas favorables sur le nombre total de cas. Ici, 3 boules rouges sur 5 boules au total donne 3\/5 = 0.6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1186,"question":"Quelle est la solution de l'inéquation : 3x - 7 \u003E 2x + 1 ?","option_a":"x \u003E 8","option_b":"x \u003C 8","option_c":"x \u003E 6","option_d":"x \u003C 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 3x - 2x \u003E 1 + 7, soit x \u003E 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1187,"question":"Quelle est la formule de la probabilité conditionnelle P(A|B) ?","option_a":"P(A) + P(B)","option_b":"P(A ∩ B) \/ P(B)","option_c":"P(A) * P(B)","option_d":"P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité conditionnelle P(A|B) se calcule par le rapport de la probabilité de l'intersection de A et B sur la probabilité de B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]