Quiz : Les incontournables de Maths en Terminale

Question 1 sur 10 10:00

[{"id":40145,"question":"Quelle est la limite de la suite définie par uₙ = (2n + 1)\/(n - 3) quand n tend vers l'infini ?","option_a":"A) 0","option_b":"B) 2","option_c":"C) +∞","option_d":"D) -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La limite d'une suite rationnelle est le rapport des coefficients des termes de plus haut degré. Ici, 2n\/n = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40146,"question":"La fonction f(x) = x³ - 3x² + 2 est-elle dérivable en x = 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction polynôme est dérivable sur ℝ. Sa dérivée f'(x) = 3x² - 6x existe donc en x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40147,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"A) 1","option_b":"B) 25","option_c":"C) 1","option_d":"D) -1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40148,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est-elle de 1\/2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé équilibré a 3 nombres pairs (2, 4, 6) sur 6 faces possibles. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40149,"question":"Quelle est la forme algébrique de z = (3 + 2i)\/(1 - i) ?","option_a":"A) 0.5 + 2.5i","option_b":"B) 2.5 + 0.5i","option_c":"C) 1 + 3i","option_d":"D) 3 + 2i","option_e":"","option_f":"","bonne_reponse":"A","explication":"En multipliant par le conjugué du dénominateur : z = (3+2i)(1+i)\/2 = (3+3i+2i+2i²)\/2 = (1+5i)\/2 = 0.5 + 2.5i.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40150,"question":"L'équation différentielle y' + 2y = 0 a pour solution générale y = Ce^(-2x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une équation différentielle linéaire du premier ordre. Sa solution générale est bien y = Ce^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40151,"question":"Quel est le coefficient directeur de la tangente à la courbe de f(x) = x² - 4x + 3 au point d'abscisse x = 2 ?","option_a":"A) -4","option_b":"B) 0","option_c":"C) 2","option_d":"D) -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur est f'(2) = 2(2) - 4 = 0. La tangente est donc horizontale en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40152,"question":"La variance d'une série statistique est-elle toujours positive ou nulle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La variance mesure la dispersion des données autour de la moyenne. Elle est toujours positive ou nulle (cas d'une série constante).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40153,"question":"Quelle est la dérivée de f(x) = e^(3x) ?","option_a":"A) e^(3x)","option_b":"B) 3e^(3x)","option_c":"C) e^(x)","option_d":"D) 3e^(x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de e^(u(x)) est u'(x)e^(u(x)). Ici, u(x) = 3x, donc u'(x) = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40154,"question":"L'intégrale de 0 à 1 de x² dx est-elle égale à 1\/3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de x² est x³\/3. Évaluée entre 0 et 1, cela donne (1³\/3) - (0³\/3) = 1\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]