Quiz Mathématiques : Algèbre et Analyse pour Lycée Pilote

Question 1 sur 5 10:00

[{"id":1890,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 et x = 2","option_b":"x = 2 et x = 1\/2","option_c":"x = -1 et x = -2","option_d":"x = 1\/2 et x = 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"On utilise le discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 et x = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1891,"question":"Soit f(x) = (3x + 1)\/(x - 2). Quelle est l'équation de l'asymptote verticale ?","option_a":"x = 3","option_b":"x = -2","option_c":"x = 2","option_d":"x = 1\/3","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'asymptote verticale est obtenue en annulant le dénominateur : x - 2 = 0 ⇒ x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1892,"question":"Dans un espace vectoriel, quel est le résultat de 3u - 2v si u = (1, 2) et v = (4, -1) ?","option_a":"(-5, 8)","option_b":"(3, 6)","option_c":"(-5, 4)","option_d":"(5, 8)","option_e":"","option_f":"","bonne_reponse":"A","explication":"3u = (3, 6) et 2v = (8, -2). Donc 3u - 2v = (3-8, 6-(-2)) = (-5, 8).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1893,"question":"Calculez la limite : lim(x→+∞) (5x² - 3x + 1)\/(2x² + x - 4).","option_a":"5\/2","option_b":"0","option_c":"+∞","option_d":"2\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"On divise numérateur et dénominateur par x² : lim (5 - 3\/x + 1\/x²)\/(2 + 1\/x - 4\/x²) = 5\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":1894,"question":"Quelle est la dérivée de f(x) = x³ - 4x² + 5x - 2 ?","option_a":"3x² - 8x + 5","option_b":"x² - 4x + 5","option_c":"3x² - 8x + 5x","option_d":"x³ - 8x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x^n est nx^(n-1). Donc f'(x) = 3x² - 8x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]