Quiz : Les Fondamentaux des Mathématiques en Terminale

Question 1 sur 10 10:00

[{"id":34633,"question":"Quelle est la dérivée de la fonction f(x) = x² + 3x - 5 ?","option_a":"2x + 3","option_b":"x² + 3","option_c":"2x + 5","option_d":"x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x² est 2x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 2x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34634,"question":"La suite définie par uₙ = (-1)ⁿ est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Cette suite oscille entre -1 et 1 et ne converge pas vers une limite unique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34635,"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":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 1\/x²)\/(1 - 4\/x²), qui tend vers 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34636,"question":"Soit une variable aléatoire X suivant une loi normale N(0,1). Quelle est la probabilité P(X ≤ 1) ?","option_a":"0.6826","option_b":"0.8413","option_c":"0.9544","option_d":"0.9974","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une loi normale centrée réduite, P(X ≤ 1) ≈ 0.8413 (valeur lue dans la table de la loi normale).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34637,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34638,"question":"Quelle est la primitive de la fonction f(x) = 5x⁴ ?","option_a":"x⁵ + C","option_b":"x⁵","option_c":"5x⁵ + C","option_d":"x⁴ + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de x⁴ est x⁵\/5, donc celle de 5x⁴ est x⁵ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34639,"question":"Soit une suite géométrique de premier terme u₀ = 2 et de raison q = 3. Quel est le terme u₃ ?","option_a":"18","option_b":"54","option_c":"162","option_d":"324","option_e":"","option_f":"","bonne_reponse":"A","explication":"u₃ = u₀ * q³ = 2 * 3³ = 2 * 27 = 54.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34640,"question":"La fonction f(x) = eˣ est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle eˣ est toujours strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34641,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 ?","option_a":"y = Ce⁻²ˣ","option_b":"y = Ce²ˣ","option_c":"y = C + e⁻²ˣ","option_d":"y = Cx","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation différentielle linéaire du premier ordre a pour solution générale y = Ce⁻²ˣ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34642,"question":"Soit deux événements A et B indépendants. Si P(A) = 0.4 et P(B) = 0.5, quelle est P(A ∩ B) ?","option_a":"0.2","option_b":"0.4","option_c":"0.5","option_d":"0.9","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements indépendants, P(A ∩ B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]