Réviser les maths pour le Bac : quiz interactif

Question 1 sur 10 10:00

[{"id":71892,"question":"Quelle est la limite de la fonction f(x) = (x² - 4)\/(x - 2) lorsque x tend vers 2 ?","option_a":"A. 0","option_b":"B. 4","option_c":"C. Indéterminée","option_d":"D. +∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction se simplifie en f(x) = x + 2 pour x ≠ 2. Ainsi, la limite est 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71893,"question":"La dérivée de la fonction f(x) = x³ - 3x² + 2x est f'(x) = 3x² - 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée correcte est f'(x) = 3x² - 6x + 2. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71894,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"A. x = e","option_b":"B. x = e²","option_c":"C. x = 2","option_d":"D. x = 1\/e²","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation ln(x) = 2 équivaut à x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71895,"question":"La fonction f(x) = x² est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée seconde f''(x) = 2 \u003E 0, donc la fonction est convexe sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71896,"question":"Quelle est l'intégrale de f(x) = 3x² entre 0 et 1 ?","option_a":"A. 0","option_b":"B. 1","option_c":"C. 3","option_d":"D. 1\/3","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale de 3x² est x³. Entre 0 et 1, cela donne 1 - 0 = 1. L'option C (3) est incorrecte, la bonne réponse est 1 (option B). Correction : la bonne réponse est B (1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71897,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule du discriminant est bien Δ = b² - 4ac.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71898,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 \u003C 0 ?","option_a":"A. x ∈ ]2; 3[","option_b":"B. x ∈ ]-∞; 2[ ∪ ]3; +∞[","option_c":"C. x ∈ ]-∞; +∞[","option_d":"D. x ∈ ∅","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines sont x = 2 et x = 3. Le polynôme est négatif entre ces deux racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71899,"question":"La fonction exponentielle est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, eˣ \u003E 0. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71900,"question":"Quelle est la dérivée de la fonction f(x) = sin(2x) ?","option_a":"A. cos(2x)","option_b":"B. 2cos(2x)","option_c":"C. -2cos(2x)","option_d":"D. sin(2x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de sin(u) est u'cos(u). Ici, u = 2x, donc u' = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71901,"question":"La probabilité d'un événement impossible est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, la probabilité d'un événement impossible est 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]