Quiz Maths Terminale : Fonctions, Suites et Géométrie

Question 1 sur 10 10:00

[{"id":73522,"question":"Quelle est la dérivée de la fonction f(x) = x³ + 2x² - 5x + 1 ?","option_a":"f'(x) = 3x² + 4x - 5","option_b":"f'(x) = 3x² + 4x + 5","option_c":"f'(x) = 3x² + 2x - 5","option_d":"f'(x) = 3x² + 4x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme s'obtient en appliquant la règle de dérivation terme à terme : (x^n)' = n*x^(n-1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73523,"question":"La suite définie par uₙ = (n² + 1)\/n a pour limite +∞ quand n tend vers +∞.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = n + 1\/n. Quand n→+∞, 1\/n→0, donc uₙ→+∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73524,"question":"Quel est le résultat de l'intégrale ∫(2x + 3) dx entre 0 et 2 ?","option_a":"8","option_b":"10","option_c":"12","option_d":"14","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'intégrale d'une fonction affine s'obtient en calculant [x² + 3x] entre 0 et 2, soit (4 + 6) - (0 + 0) = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73525,"question":"Dans un triangle ABC, si AB = 5, AC = 7 et BC = 8, alors l'angle BÂC est :","option_a":"aigu","option_b":"obtus","option_c":"droit","option_d":"plat","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la loi des cosinus : cos(BÂC) = (AB² + AC² - BC²)\/(2*AB*AC) = (25 + 49 - 64)\/70 = 10\/70 \u003E 0, donc l'angle est obtus.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73526,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, e^x \u003E 0. C'est une propriété fondamentale de la fonction exponentielle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73527,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = e²","option_b":"x = 2","option_c":"x = ln(2)","option_d":"x = e\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction logarithme est la bijection réciproque de l'exponentielle : ln(x) = 2 ⇔ x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73528,"question":"Un nombre complexe z = 3 + 4i a pour module :","option_a":"5","option_b":"7","option_c":"12","option_d":"√7","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module d'un nombre complexe z = a + bi est donné par |z| = √(a² + b²) = √(9 + 16) = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73529,"question":"La suite géométrique de premier terme u₀ = 2 et de raison q = 3 est croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite géométrique de raison q \u003E 1 et de premier terme positif est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73530,"question":"Quel est le résultat de la limite lim (x→0) (sin(x)\/x) ?","option_a":"0","option_b":"1","option_c":"∞","option_d":"n'existe pas","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est une limite fondamentale en analyse : lim (x→0) (sin(x)\/x) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73531,"question":"Dans un repère orthonormé, l'équation x² + y² - 4x + 6y - 3 = 0 représente :","option_a":"un cercle de centre (2, -3) et rayon 4","option_b":"un cercle de centre (2, -3) et rayon 16","option_c":"une droite","option_d":"une parabole","option_e":"","option_f":"","bonne_reponse":"A","explication":"En complétant les carrés : (x-2)² + (y+3)² = 16, donc c'est un cercle de centre (2, -3) et rayon 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]