Quiz — Lycée Pilote Monastir - DS 2 2021.pdf

Question 1 sur 10 20:00

[{"id":20109,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f'(x) = 3x² - 4x + 5\", \"b\": \"f'(x) = 3x² - 4x + 1\", \"c\": \"f'(x)","_debug_options_count":4},{"id":20110,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"8\", \"b\": \"10\", \"c\": \"12\", \"d\": \"14\"}}","_debug_options_count":4},{"id":20111,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":20112,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"3\", \"b\": \"3.3\", \"c\": \"3.5\", \"d\": \"4\"}}","_debug_options_count":4},{"id":20113,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"ln|x| + C\", \"b\": \"1\/x² + C\", \"c\": \"e^x + C\", \"d\": \"x²\/2 + C\"}}","_debug_options_count":4},{"id":20114,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":20115,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\/2\", \"b\": \"1\/3\", \"c\": \"1\/6\", \"d\": \"2\/3\"}}","_debug_options_count":4},{"id":20116,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-cos(x) + C\", \"b\": \"cos(x) + C\", \"c\": \"tan(x) + C\", \"d\": \"sec(x) ","_debug_options_count":4},{"id":20117,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.25\", \"b\": \"0.5\", \"c\": \"0.75\", \"d\": \"0.95\"}}","_debug_options_count":4},{"id":20118,"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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]