Quiz Mathématiques Terminale : Algèbre, Analyse et Géométrie

Question 1 sur 10 10:00

[{"id":25148,"question":"Quelle est la limite de la fonction f(x) = (3x² - 2x + 1)\/(x² + 1) lorsque x tend vers l'infini ?","option_a":"A) 0","option_b":"B) 1","option_c":"C) 3","option_d":"D) +∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"La limite est obtenue en divisant chaque terme par x² : (3 - 2\/x + 1\/x²)\/(1 + 1\/x²) → 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25149,"question":"L'équation x² + 4x + 5 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0, donc l'équation n'a pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25150,"question":"Quelle est la dérivée de la fonction f(x) = ln(2x + 1) ?","option_a":"A) 1\/(2x + 1)","option_b":"B) 2\/(2x + 1)","option_c":"C) 1\/(x + 1)","option_d":"D) 2\/(x + 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de ln(u) est u'\/u, donc ici u = 2x + 1 → u' = 2 → f'(x) = 2\/(2x + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25151,"question":"La fonction f(x) = x³ - 3x² + 4 est-elle 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). Sur [0, 2], f'(x) ≤ 0, donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25152,"question":"Quelle est l'intégrale de la fonction f(x) = 2x + 1 entre 0 et 2 ?","option_a":"A) 4","option_b":"B) 5","option_c":"C) 6","option_d":"D) 7","option_e":"","option_f":"","bonne_reponse":"D","explication":"L'intégrale est [x² + x] entre 0 et 2 = (4 + 2) - (0 + 0) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25153,"question":"La suite définie par uₙ = (n² + 1)\/n converge-t-elle vers 0 lorsque n tend vers l'infini ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite converge vers +∞, car uₙ = n + 1\/n → +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25154,"question":"Quelle est la solution de l'équation différentielle y' + 2y = 0 avec y(0) = 1 ?","option_a":"A) y = e^(-2x)","option_b":"B) y = e^(2x)","option_c":"C) y = e^(-x\/2)","option_d":"D) y = 2e^(-x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution générale est y = Ce^(-2x). Avec y(0) = 1 → C = 1 → y = e^(-2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25155,"question":"Le produit scalaire de deux vecteurs orthogonaux est-il toujours nul ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire égal à 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25156,"question":"Quelle est la probabilité d'obtenir un double 6 en lançant deux dés équilibrés ?","option_a":"A) 1\/6","option_b":"B) 1\/12","option_c":"C) 1\/18","option_d":"D) 1\/36","option_e":"","option_f":"","bonne_reponse":"D","explication":"Il y a 36 combinaisons possibles, dont une seule donne un double 6 → probabilité = 1\/36.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":25157,"question":"La fonction f(x) = e^(-x²) est-elle 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}]