e to do something (formal)
a) used to talk about arrangements for the future 用作谈论未来的安排:
例：1. Audrey and Jimmy are to be married in June.
2. Two men are to appear in court on charges of armed robbery.
b) used to give an order or to tell someone about a rule(用来给命令或告诉某人一个规定) :
例：1. You are to wait here in this room until I return.
2. All staff are to wear uniforms.
c) used to say or ask what someone should do or what should happen (用来告诉某人应当做什么或会发生什么):
例：1. What am I to tell her?
2. He is not to be blamed.
d) used to ask how something can be done (用来问某事应当怎么做） :
例：How are we to get out of the present mess?
你的句子中的are to be covered应当属于b的情况,因为这是老师布置作业的一个规定.而且,主语句也是这种结构：The assignment for today is to write..., 你这个能够题解,也就能理解are to be covered (只是被动态而已).
至于这个in which就更简单,因为前面的summary在后面的定语从句中是作状语（如果把句子拆分的话就成了：The assignment for today is to write a summary. In the summary the major subjects in this chapter are to be covered.）,所以是in which (有时用where).如果在定语从句中是作主语或宾语的话就用which或that.