There's no simple solution          this problem.

of

for

to 

about

考查介词。句意：这个问题没有什么简单的解决方法。此处是短语“

the solution to....的解决方法”，应用介词to。故选C项。

Suddenly a good idea occurred to her, but she couldn't find any paper           .

 to write

to write on

written

writing on

考查了非谓语动词。句意：她突然有了一个好主意，但是她找不到纸来写下它。根据句意可知，这里用不定式表目的，而且固定搭配是write sth on the paper。故选B项。

---what shall we do tonight then?

---              whatever you want.

Help yourself

No problem

It's a deal

It's up to you

考查交际用语。句意：---我们今晚做什么。---由你决定，你想干什么都行。根据空格后的 whatever you want，以及句意可知空格处填It's up to you由你定。故选D项。

Mary and her friend          a plan and gathered forty people from my company to help the homeless people at the Christmas party.

came up with

put up with

caught up with

kept up with

考查动词短语辨析。句意：玛丽和她的朋友想出了一个计划，在圣诞节聚会上，从我的公司聚集了四十几个人来帮助无家可归的人。A. came up with 提出；B. put up with 忍耐；C. caught up with追上，赶上；D.kept up with 跟上。下文“聚集人帮助无家可归的人”是想出的计划。故选A项。

With a lot of difficult problems           ,he feels like a cat on  hot bricks.

to settle

being settled

settling

settled

考查非谓语动词。句意： 因为有一大堆难题要解决，他感觉像像热锅上的蚂蚁。本句with +名词+to do sth,动词不定式表示的动作尚未发生或当时看来尚未发生。本句表示“因为有一大堆难题要解决”。故选A项。