Quiz Maths Terminale : Testez vos connaissances en analyse, suites et probabilités !

Question 1 sur 10 10:00

[{"id":30738,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers +∞ ?","option_a":"A. 3","option_b":"B. 0","option_c":"C. +∞","option_d":"D. -3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour trouver la limite d'un quotient de polynômes en +∞, on compare les termes de plus haut degré. Ici, 3x²\/x² = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30739,"question":"La suite (uₙ) définie par uₙ = (2n + 1)\/(n + 3) est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La suite est convergente car elle tend vers 2 lorsque n tend vers +∞ (on divise numérateur et dénominateur par n).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30740,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"A. 1\/(2x + 1)","option_b":"B. 2\/(2x + 1)","option_c":"C. 2x\/(2x + 1)","option_d":"D. 1\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de ln(u) est u'\/u. Ici, u = 2x + 1, donc u' = 2. Ainsi, f'(x) = 2\/(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30741,"question":"Dans une classe de 30 élèves, la probabilité qu'un élève soit absent est de 0,1. Quelle est la probabilité qu'exactement 2 élèves soient absents ?","option_a":"A. 0,227","option_b":"B. 0,194","option_c":"C. 0,255","option_d":"D. 0,150","option_e":"","option_f":"","bonne_reponse":"B","explication":"On utilise la loi binomiale B(n=30, p=0,1). P(X=2) = C(30,2) * (0,1)² * (0,9)^28 ≈ 0,194.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30742,"question":"L'équation x² + 4x + 5 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0. L'équation n'a donc pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30743,"question":"Quelle est l'expression de la dérivée de la fonction f(x) = e^(3x² + 2x) ?","option_a":"A. e^(3x² + 2x)","option_b":"B. (6x + 2)e^(3x² + 2x)","option_c":"C. (3x² + 2x)e^(3x² + 2x)","option_d":"D. 6x * e^(3x² + 2x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^u est u' * e^u. Ici, u = 3x² + 2x, donc u' = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30744,"question":"Un dé équilibré est lancé 10 fois. Quelle est la probabilité d'obtenir exactement 3 fois le chiffre 6 ?","option_a":"A. 0,155","option_b":"B. 0,117","option_c":"C. 0,123","option_d":"D. 0,100","option_e":"","option_f":"","bonne_reponse":"A","explication":"On utilise la loi binomiale B(n=10, p=1\/6). P(X=3) = C(10,3) * (1\/6)^3 * (5\/6)^7 ≈ 0,155.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30745,"question":"La fonction f(x) = x³ - 3x² + 4 est-elle croissante sur l'intervalle ]-∞, 0[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 6x. Sur ]-∞, 0[, f'(x) \u003E 0 (ex: f'(-1) = 9 \u003E 0), donc la fonction est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30746,"question":"Quelle est la valeur de la somme S = Σ (k=1 à n) k² ?","option_a":"A. n(n + 1)\/2","option_b":"B. n(n + 1)(2n + 1)\/6","option_c":"C. n²(n + 1)²\/4","option_d":"D. n(n + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La formule de la somme des carrés est S = n(n + 1)(2n + 1)\/6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":30747,"question":"Dans un repère orthonormé, l'équation de la droite passant par A(1, 2) et B(3, 4) est :","option_a":"A. y = x + 1","option_b":"B. y = 2x - 1","option_c":"C. y = x","option_d":"D. y = 2x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1. L'équation est y = x + 1 (car 2 = 1*1 + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]