Quiz : Maîtrisez les Maths de la 3ème Année Secondaire !

Question 1 sur 10 10:00

[{"id":55151,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"On factorise l'équation : (x-2)(x-3)=0, donc les solutions sont x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55152,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle dérivable en x=1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction est un polynôme, donc dérivable sur ℝ. Sa dérivée f'(x)=3x²-6x+2 existe en x=1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55153,"question":"Quelle est la limite de (x² - 4)\/(x - 2) quand x tend vers 2 ?","option_a":"0","option_b":"4","option_c":"Indéterminée","option_d":"2","option_e":"","option_f":"","bonne_reponse":"C","explication":"On factorise : (x-2)(x+2)\/(x-2) = x+2 pour x≠2. La limite est donc 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55154,"question":"La dérivée de f(x) = e^(2x) est :","option_a":"f'(x) = e^(2x)","option_b":"f'(x) = 2e^(2x)","option_c":"f'(x) = e^(x)","option_d":"f'(x) = 2e^x","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^u est u'e^u. Ici u=2x, donc u'=2, d'où f'(x)=2e^(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55155,"question":"La fonction f(x) = 1\/x est-elle continue en x=0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction 1\/x n'est pas définie en x=0, donc elle n'est pas continue en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55156,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003E 0 ?","option_a":"x ∈ ]-∞;1[ ∪ ]3;+∞[","option_b":"x ∈ ]1;3[","option_c":"x ∈ ]-∞;+∞[","option_d":"x ∈ [1;3]","option_e":"","option_f":"","bonne_reponse":"A","explication":"On résout x²-4x+3=0 → x=1 ou x=3. Le polynôme est positif à l'extérieur des racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55157,"question":"La dérivée de f(x) = ln(x) est :","option_a":"f'(x) = 1\/x","option_b":"f'(x) = x","option_c":"f'(x) = 1","option_d":"f'(x) = ln(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x pour x\u003E0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55158,"question":"La fonction f(x) = x² - 4x + 5 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une fonction du second degré avec a=1\u003E0, donc elle admet un minimum en x=-b\/(2a)=2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55159,"question":"Quelle est la valeur de la limite de (sin(x))\/x quand x tend vers 0 ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"Indéterminée","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est une limite remarquable : lim(x→0) sin(x)\/x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55160,"question":"La fonction f(x) = |x| est-elle dérivable en x=0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction valeur absolue n'est pas dérivable en x=0 car elle présente un point anguleux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]