Quiz — DS2.4.12.pdf

Question 1 sur 10 20:00

[{"id":40010,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = -1 ou x = -6","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (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 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":40011,"question":"La fonction f(x) = 2x + 3 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction affine f(x) = 2x + 3 a un coefficient directeur positif (2 \u003E 0), donc elle est croissante sur ℝ.","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":40012,"question":"Quelle est la moyenne d'une série statistique de 5 valeurs : 10, 12, 14, 16, 18 ?","option_a":"14","option_b":"15","option_c":"16","option_d":"13","option_e":"","option_f":"","bonne_reponse":"b","explication":"La moyenne se calcule par (10+12+14+16+18)\/5 = 70\/5 = 14.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"14\", \"b\": \"15\", \"c\": \"16\", \"d\": \"13\"}}","_debug_options_count":4},{"id":40013,"question":"L'équation 3x - 7 = 2x + 5 a pour solution :","option_a":"x = 12","option_b":"x = -12","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x, on obtient 3x - 2x = 5 + 7, soit x = 12.","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 = 12\", \"b\": \"x = -12\", \"c\": \"x = 2\", \"d\": \"x = -2\"}}","_debug_options_count":4},{"id":40014,"question":"La médiane d'une série de 7 valeurs est toujours la 4ème valeur triée.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une série de 7 valeurs, la médiane est bien la 4ème valeur triée.","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":40015,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + x ?","option_a":"f'(x) = 3x² - 4x + 1","option_b":"f'(x) = x² - 2x + 1","option_c":"f'(x) = 3x² - 4x","option_d":"f'(x) = 3x² - 2x + 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant les règles de dérivation, f'(x) = 3x² - 4x + 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 + 1\", \"b\": \"f'(x) = x² - 2x + 1\", \"c\": \"f'(x) ","_debug_options_count":4},{"id":40016,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est l'énoncé du théorème de Pythagore, une propriété fondamentale en géométrie.","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":40017,"question":"Quelle est la solution de l'inéquation 2x + 5 \u003E 11 ?","option_a":"x \u003E 3","option_b":"x \u003C 3","option_c":"x \u003E -3","option_d":"x \u003C -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En isolant x, on obtient 2x \u003E 6, soit x \u003E 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 \u003E 3\", \"b\": \"x \u003C 3\", \"c\": \"x \u003E -3\", \"d\": \"x \u003C -3\"}}","_debug_options_count":4},{"id":40018,"question":"La fonction g(x) = -x² + 4x - 3 admet-elle un maximum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction est une parabole tournée vers le bas (coefficient de x² négatif), donc elle admet un maximum.","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":40019,"question":"Quel est l'écart-type d'une série de valeurs : 2, 4, 6, 8, 10 ?","option_a":"2,83","option_b":"3,16","option_c":"2,45","option_d":"3,50","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'écart-type se calcule après avoir trouvé la moyenne (6) et la variance (8), soit √8 ≈ 2,83.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2,83\", \"b\": \"3,16\", \"c\": \"2,45\", \"d\": \"3,50\"}}","_debug_options_count":4}]