The Board shall prepare and submit to the Mayor of the District of Columbia an annual budget itemizing the appropriations necessary for the performance of its functions and duties under this chapter, including appropriations necessary for the purchase of books, literature, newspapers, periodicals, technical reference material, trophies, and medals, and as provided in § 10-224, the Board’s share of the cost of improvement, maintenance, and upkeep of the buildings and grounds used by the Board and which are under the jurisdiction of the Board of Education, the Mayor, or the National Park Service.