1.①There exists a good way to solve the existing problem in maths.(exist)
②As is known to us, the Republic of China came into existence (exist) as an independent country in 1949.
2.①Doing small things well contributes to building(build) up our confidence and helping us meet bigger challenges in the future.
②The contributor contributed a lot of money to the project; that is to say, his contribution was great.(contribute)
3.①(北京卷)I borrowed the book Sherlock Holmes from the library last week, which my classmates recommended to me.
②(2019·四川雅安期末)My English teacher recommended to take(take) part in an English speech competition the other day.
③a. We strongly recommend that schools(should) provide(provide) students with more time for sports.
b. It is strongly recommended that schools (should) provide(provide) students with more time for sports.
