Maths BAC : Testez vos connaissances en 10 questions clés

Question 1 sur 10 10:00

[{"id":48721,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2x","option_c":"6x - 5","option_d":"x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48722,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0. Une seule solution réelle double : x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48723,"question":"Quelle est la limite de (3x² + 2x) \/ (x² - 1) quand x tend vers l'infini ?","option_a":"3","option_b":"0","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x) \/ (1 - 1\/x²). Quand x→∞, les termes en 1\/x tendent vers 0, donc la limite est 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48724,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = (-x)³ = -x³ ≠ f(x). Donc elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48725,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4. L'inéquation est vérifiée pour x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48726,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'un événement impossible est 0. Un événement certain a une probabilité de 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48727,"question":"Quelle est la valeur de ∫(2x + 1) dx entre 0 et 2 ?","option_a":"6","option_b":"4","option_c":"8","option_d":"2","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x + 1 est x² + x. Entre 0 et 2 : (4 + 2) - (0 + 0) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48728,"question":"La fonction f(x) = 1\/x est-elle continue sur ℝ* ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction 1\/x est continue sur son domaine de définition ℝ* (tous les réels sauf 0), car elle n'y présente aucune discontinuité.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48729,"question":"Quelle est la solution de l'équation e^(2x) = 5 ?","option_a":"x = ln(5)\/2","option_b":"x = 2ln(5)","option_c":"x = 5\/2","option_d":"x = ln(2)\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"e^(2x) = 5 ⇒ 2x = ln(5) ⇒ x = ln(5)\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48730,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]