1.A
go through 表示“仔细检查”时,目的是为了找出某样东西或者把东西归类,你看它的英文释义就知道了：If you go through a lot of things such as papers or clothes,you look at them,usually in order to sort them into groups or to search for a particular item.
在第一道题中,她仔细搜查他的夹克是为了寻找钥匙.所以用 go through.
2.C
go over 通常表示“检查（文件、文字）”等书面材料,达到检查、校对、仔细分析的目的.它的英文释义是：If you go over a document,incident,or problem,you examine,discuss,or think about it very carefully.
在第二道题中,她检查的是papers,是文件,目的是从文件里归纳出所需信息,因此用 go over.