Quiz — 65f02ad15bb4a__série 26 ( devoir de synthèse 2).pdf

Question 1 sur 10 20:00

[{"id":17229,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5 ?","option_a":"3x² - 4x","option_b":"3x² - 4x + 5","option_c":"x² - 2x","option_d":"3x² - 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction 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\": \"3x² - 4x\", \"b\": \"3x² - 4x + 5\", \"c\": \"x² - 2x\", \"d\": \"3x² - 2","_debug_options_count":4},{"id":17230,"question":"Dans un repère orthonormé, l'équation x² + y² = 25 représente :","option_a":"Une droite","option_b":"Un cercle de centre O et de rayon 5","option_c":"Une parabole","option_d":"Une hyperbole","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation x² + y² = r² représente un cercle de centre l'origine et de rayon r.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Une droite\", \"b\": \"Un cercle de centre O et de rayon 5\", \"c\": \"Un","_debug_options_count":4},{"id":17231,"question":"La probabilité d'un événement impossible est égale à :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La probabilité d'un événement impossible est toujours égale à 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":17232,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"b","explication":"sin(π\/6) = 1\/2, valeur à connaître par cœur dans le cercle trigonométrique.","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\", \"b\": \"1\/2\", \"c\": \"√2\/2\", \"d\": \"1\"}}","_debug_options_count":4},{"id":17233,"question":"La fonction f(x) = 1\/x est définie pour :","option_a":"x ∈ ℝ","option_b":"x ∈ ℝ*","option_c":"x \u003E 0","option_d":"x ≠ 0","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction inverse f(x) = 1\/x est définie pour tout réel x sauf x = 0 (ℝ*).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x ∈ ℝ\", \"b\": \"x ∈ ℝ*\", \"c\": \"x \u003E 0\", \"d\": \"x ≠ 0\"}}","_debug_options_count":4},{"id":17234,"question":"Dans une série statistique, la médiane est toujours égale à la moyenne.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane et la moyenne sont deux indicateurs différents qui ne sont égaux que dans des cas particuliers (série symétrique).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":17235,"question":"Quelle est l'équation réduite de la droite passant par les points A(1,2) et B(3,4) ?","option_a":"y = x + 1","option_b":"y = 2x - 1","option_c":"y = x","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1. L'équation est y = x + 1 (car 2 = 1*1 + 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\": \"y = x + 1\", \"b\": \"y = 2x - 1\", \"c\": \"y = x\", \"d\": \"y = 2x + 1\"}}","_debug_options_count":4},{"id":17236,"question":"La fonction exponentielle f(x) = e^x est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour tout x réel, e^x \u003E 0. C'est une propriété fondamentale de la fonction exponentielle.","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":17237,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4. La solution est x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x \u003E 4\", \"b\": \"x \u003C 4\", \"c\": \"x \u003E 1\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4},{"id":17238,"question":"Le volume d'une sphère de rayon r est donné par la formule :","option_a":"4\/3πr²","option_b":"4πr²","option_c":"4\/3πr³","option_d":"πr³","option_e":"","option_f":"","bonne_reponse":"c","explication":"La formule du volume d'une sphère est V = (4\/3)πr³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"4\/3πr²\", \"b\": \"4πr²\", \"c\": \"4\/3πr³\", \"d\": \"πr³\"}}","_debug_options_count":4}]