Quiz Maths Terminale : Testez vos connaissances en analyse et algèbre

Question 1 sur 10 10:00

[{"id":62752,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x - 5","option_d":"2x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62753,"question":"L'intégrale de 0 à 1 de x² dx est égale à :","option_a":"1\/3","option_b":"1","option_c":"0","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de x² entre 0 et 1 est [x³\/3]₀¹ = 1\/3 - 0 = 1\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62754,"question":"Une suite géométrique de raison q = -2 et de premier terme u₀ = 3 est-elle convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite géométrique est convergente si et seulement si |q| \u003C 1. Ici, |q| = 2 \u003E 1, donc elle diverge.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62755,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"x = e²","option_b":"x = 2","option_c":"x = 100","option_d":"x = √2","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation ln(x) = 2 équivaut à x = e² (car ln(e²) = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62756,"question":"La fonction f(x) = x³ - 3x² + 4 admet-elle un extremum local en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"f'(x) = 3x² - 6x. En x = 1, f'(1) = -3 ≠ 0, donc pas d'extremum local. Cependant, f''(1) = 0, il faut vérifier avec le signe de f' autour de 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62757,"question":"Quelle est la limite de (2x² + 3x - 1)\/(x² + 1) quand x tend vers +∞ ?","option_a":"2","option_b":"1","option_c":"0","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient (2 + 3\/x - 1\/x²)\/(1 + 1\/x²) → 2\/1 = 2 quand x → +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62758,"question":"Un dé à 6 faces est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le chiffre 6 ?","option_a":"1\/6","option_b":"1\/36","option_c":"1\/12","option_d":"1\/18","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'obtenir un 6 est 1\/6. Pour deux lancers indépendants, c'est (1\/6) × (1\/6) = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62759,"question":"La fonction f(x) = e^x est-elle toujours positive sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel (e^x \u003E 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62760,"question":"Quelle est l'intégrale de 1\/(1+x²) entre -∞ et +∞ ?","option_a":"π","option_b":"0","option_c":"1","option_d":"+∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 1\/(1+x²) est arctan(x). Entre -∞ et +∞, arctan(+∞) - arctan(-∞) = π\/2 - (-π\/2) = π.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":62761,"question":"Un nombre complexe z = 3 + 4i a pour module :","option_a":"5","option_b":"7","option_c":"1","option_d":"12","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module de z = a + bi est √(a² + b²) = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]