Mathématiques Terminale : Testez vos connaissances en exercices corrigés

Question 1 sur 10 10:00

[{"id":49051,"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) = x² - 2x + 5","option_c":"f'(x) = 3x² - 4x + 1","option_d":"f'(x) = x³ - 4x + 5","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":49052,"question":"La fonction f(x) = x² est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est convexe si sa dérivée seconde est positive. Ici, f''(x) = 2 \u003E 0, donc f est convexe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49053,"question":"Quelle est la limite de la suite u_n = (2n² + 3n) \/ (n² + 1) quand n tend vers l’infini ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant le numérateur et le dénominateur par n², on obtient u_n = (2 + 3\/n) \/ (1 + 1\/n²). Quand n → ∞, u_n → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49054,"question":"Soit une fonction f dérivable sur ℝ. Si f'(x) \u003E 0 pour tout x ∈ ℝ, alors f est strictement croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si la dérivée est strictement positive sur un intervalle, la fonction est strictement croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49055,"question":"Quelle est la valeur de la somme S = 1 + 2 + 3 + ... + n ?","option_a":"n(n+1)\/2","option_b":"n²","option_c":"(n+1)²\/2","option_d":"n(n-1)\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme des n premiers entiers naturels est donnée par la formule S = n(n+1)\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49056,"question":"La fonction f(x) = e^x est sa propre dérivée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de e^x est e^x, donc f(x) = e^x est bien sa propre dérivée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49057,"question":"Quelle est la primitive de f(x) = 3x² - 4x + 1 ?","option_a":"F(x) = x³ - 2x² + x + C","option_b":"F(x) = x³ - 4x² + x + C","option_c":"F(x) = 6x - 4 + C","option_d":"F(x) = x³ - 2x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive s’obtient en intégrant terme à terme : ∫3x² dx = x³, ∫-4x dx = -2x², ∫1 dx = x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49058,"question":"Si une suite u_n est croissante et majorée, alors elle converge.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C’est le théorème de convergence monotone : une suite croissante et majorée converge vers sa borne supérieure.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49059,"question":"Quelle est la valeur de l’intégrale ∫(2x + 1) dx entre 0 et 2 ?","option_a":"6","option_b":"4","option_c":"8","option_d":"10","option_e":"","option_f":"","bonne_reponse":"A","explication":"L’intégrale s’obtient en calculant [x² + x] entre 0 et 2, soit (4 + 2) - (0 + 0) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49060,"question":"La fonction f(x) = ln(x) est définie pour tout x ∈ ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]