Quiz interactif : Les incontournables des maths en Terminale Scientifique

Question 1 sur 10 10:00

[{"id":68852,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 3","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite d'un rapport de polynômes de même degré est égale au rapport des coefficients dominants. Ici, 3x²\/x² = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68853,"question":"Soit f une fonction dérivable sur ℝ telle que f'(x) = 2x - 3. Si f(1) = 4, quelle est l'expression de f(x) ?","option_a":"A. f(x) = x² - 3x + 6","option_b":"B. f(x) = x² - 3x + 4","option_c":"C. f(x) = 2x² - 3x + 4","option_d":"D. f(x) = x² - 3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En intégrant f'(x), on obtient f(x) = x² - 3x + C. Avec f(1) = 4, on trouve C = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68854,"question":"Vrai ou Faux ? La fonction f(x) = x³ - 3x² + 2 est croissante sur l'intervalle [0, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² - 6x = 3x(x - 2) est négative sur [0, 2], donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68855,"question":"Quelle est la valeur de l'intégrale ∫(de 0 à 1) (2x + 1) dx ?","option_a":"A. 1","option_b":"B. 2","option_c":"C. 3","option_d":"D. 4","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale d'une fonction affine se calcule comme l'aire d'un trapèze : (2*1 + 1)*1\/2 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68856,"question":"Soit (O, i, j) un repère orthonormé. Les droites d'équations y = 2x + 3 et y = -0.5x + 1 sont-elles perpendiculaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit des coefficients directeurs est 2 * (-0.5) = -1, donc les droites sont perpendiculaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68857,"question":"Quelle est la solution de l'équation 2^(x-1) = 8 ?","option_a":"A. x = 2","option_b":"B. x = 3","option_c":"C. x = 4","option_d":"D. x = 5","option_e":"","option_f":"","bonne_reponse":"D","explication":"8 = 2³, donc 2^(x-1) = 2³ ⇒ x - 1 = 3 ⇒ x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68858,"question":"Vrai ou Faux ? La suite définie par uₙ = n²\/(n+1) est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant par n, uₙ = n\/(1 + 1\/n) → +∞ lorsque n → +∞, donc la suite diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68859,"question":"Soit f(x) = ln(x² + 1). Quelle est la dérivée de f ?","option_a":"A. f'(x) = 2x\/(x² + 1)","option_b":"B. f'(x) = 2x","option_c":"C. f'(x) = 1\/(x² + 1)","option_d":"D. f'(x) = x\/(x² + 1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la dérivée d'une fonction composée : f'(x) = (2x)\/(x² + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68860,"question":"Quelle est l'équation du plan passant par les points A(1,0,0), B(0,1,0) et C(0,0,1) ?","option_a":"A. x + y + z = 1","option_b":"B. x - y + z = 1","option_c":"C. x + y - z = 1","option_d":"D. x - y - z = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le plan a pour équation x + y + z = 1, car il passe par les trois points donnés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":68861,"question":"Vrai ou Faux ? La fonction f(x) = e^(-x²) est paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"f(-x) = e^(-(-x)²) = e^(-x²) = f(x), donc la fonction est paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]