Quiz : Maîtrisez les fonctions dérivées, intégrales et probabilités en Terminale

Question 1 sur 10 10:00

[{"id":80202,"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 + 1","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":80203,"question":"L’intégrale ∫(2x + 3) dx entre 0 et 2 est égale à :","option_a":"8","option_b":"10","option_c":"12","option_d":"14","option_e":"","option_f":"","bonne_reponse":"B","explication":"Calculez la primitive F(x) = x² + 3x, puis évaluez F(2) - F(0) = (4 + 6) - 0 = 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80204,"question":"La fonction f(x) = e^x est 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.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80205,"question":"Quelle est l’espérance d’une variable aléatoire suivant une loi binomiale B(n=10, p=0.3) ?","option_a":"3","option_b":"3.3","option_c":"3.5","option_d":"4","option_e":"","option_f":"","bonne_reponse":"B","explication":"L’espérance d’une loi binomiale B(n,p) est E(X) = n*p = 10*0.3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80206,"question":"L’intégrale ∫(1\/x) dx est égale à :","option_a":"ln|x| + C","option_b":"1\/x² + C","option_c":"e^x + C","option_d":"x²\/2 + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 1\/x est ln|x| + C, à condition que x ≠ 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80207,"question":"La dérivée de la fonction f(x) = ln(x) est f'(x) = 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est bien 1\/x pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80208,"question":"Quelle est la probabilité d’obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc P = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80209,"question":"L’intégrale ∫(sin(x)) dx est égale à :","option_a":"-cos(x) + C","option_b":"cos(x) + C","option_c":"tan(x) + C","option_d":"sec(x) + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de sin(x) est -cos(x) + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80210,"question":"Si X suit une loi normale N(μ=5, σ=2), alors P(X ≤ 5) est égale à :","option_a":"0.25","option_b":"0.5","option_c":"0.75","option_d":"0.95","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour une loi normale, la probabilité que X soit inférieure ou égale à la moyenne μ est de 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80211,"question":"La dérivée seconde d’une fonction constante est toujours nulle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée première d’une fonction constante est nulle, donc sa dérivée seconde l’est aussi.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]