Quiz — DEVOIR PROBA+ALGEBRE.pdf

Question 1 sur 10 20:00

[{"id":21739,"question":"Quelle est la probabilité de tirer un as dans un jeu de 32 cartes ?","option_a":"1\/8","option_b":"1\/13","option_c":"1\/32","option_d":"4\/32","option_e":"","option_f":"","bonne_reponse":"d","explication":"Un jeu de 32 cartes contient 4 as. La probabilité est donc de 4\/32, soit 1\/8 après simplification.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"1\/8\", \"b\": \"1\/13\", \"c\": \"1\/32\", \"d\": \"4\/32\"}}","_debug_options_count":4},{"id":21740,"question":"Soit l'équation x² - 5x + 6 = 0. Les solutions sont :","option_a":"x = 2 et x = 3","option_b":"x = -2 et x = -3","option_c":"x = 1 et x = 6","option_d":"x = 0 et x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"En factorisant, on obtient (x-2)(x-3)=0, donc les solutions sont x=2 et x=3.","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 = 2 et x = 3\", \"b\": \"x = -2 et x = -3\", \"c\": \"x = 1 et x = 6\", ","_debug_options_count":4},{"id":21741,"question":"Vrai ou Faux ? La probabilité conditionnelle P(A|B) est toujours supérieure à P(A).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité conditionnelle P(A|B) peut être inférieure, égale ou supérieure à P(A), selon la relation entre A et B.","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":21742,"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":"En résolvant l'inéquation, on obtient 2x \u003E 8, donc 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":21743,"question":"Dans une classe de 30 élèves, 12 sont des filles. Quelle est la probabilité de choisir une fille au hasard ?","option_a":"0,4","option_b":"0,3","option_c":"0,6","option_d":"0,25","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité est le rapport du nombre de filles sur le nombre total d'élèves : 12\/30 = 0,4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,4\", \"b\": \"0,3\", \"c\": \"0,6\", \"d\": \"0,25\"}}","_debug_options_count":4},{"id":21744,"question":"Vrai ou Faux ? Une fonction affine est toujours croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Une fonction affine f(x) = ax + b est croissante si a \u003E 0 et décroissante si a \u003C 0.","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":21745,"question":"Quelle est la forme canonique de l'équation x² - 6x + 5 = 0 ?","option_a":"(x-3)² - 4","option_b":"(x-2)² - 1","option_c":"(x-1)² - 4","option_d":"(x-3)² + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"En complétant le carré, on obtient (x-3)² - 9 + 5 = (x-3)² - 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-3)² - 4\", \"b\": \"(x-2)² - 1\", \"c\": \"(x-1)² - 4\", \"d\": \"(x-3)","_debug_options_count":4},{"id":21746,"question":"Si A et B sont deux événements incompatibles, alors P(A ∪ B) = ...","option_a":"P(A) + P(B)","option_b":"P(A) * P(B)","option_c":"P(A) - P(B)","option_d":"P(A) \/ P(B)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour des événements incompatibles, la probabilité de leur union est la somme de leurs probabilités individuelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"P(A) + P(B)\", \"b\": \"P(A) * P(B)\", \"c\": \"P(A) - P(B)\", \"d\": \"P(A) ","_debug_options_count":4},{"id":21747,"question":"Quelle est la représentation graphique d'une fonction affine ?","option_a":"Une droite","option_b":"Une parabole","option_c":"Un cercle","option_d":"Une hyperbole","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine f(x) = ax + b est représentée par une droite dans un repère orthonormé.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Une droite\", \"b\": \"Une parabole\", \"c\": \"Un cercle\", \"d\": \"Une hyp","_debug_options_count":4},{"id":21748,"question":"Vrai ou Faux ? La loi binomiale s'applique uniquement à des expériences à deux issues.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La loi binomiale modélise une expérience aléatoire avec exactement deux issues possibles (succès\/échec) répétée n fois de manière indépendante.","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}]