关于"动词不定式"的补充说明：
1) 前面讲到："动词不定式"的完成式表示过去时，它常在以下句型中出现：
(主语)+ be said / reported / believed / supposed to have (been) done
(主语)+ seem to have (been) done
(主语)+ be likely to have (been) done
当考试时看到这样的句型出现，首先要考虑是否是"动词不定式"的完成式
2) 注意"动词不定式" to与介词to的区别，即：是to + 动词，还是to + 名词或动名词(-ing)。"第二讲五个基本句型"中已经提到：object to / look forward to / be (get) accustomed (used) to / be subjected to / subject to / be subjected to / be opposed to / agree to等中的to是介词。
当考试时看到这样的表达方式出现，首先要考虑选择-ing形式(一般不会给纯名词形式)
关于on + ing 形式和with (without) + 分词独立主格结构
1)on + ing 形式：一般将介词on + -ing形式理解为"分词"(要有行为主体)而不是"动名词"，意为 "当…时"，"一…就…"，相当于when 或as soon as，例如：
On hearing the news， she burst into tears. (一听到这个消息，她一下子哭了起来。)
错：On arriving in Beijing， it began to rain heavily. (一到北京，就开始下起大雨来了。)
由于句子的主语it并不是arriving的行为主体，该句语法不成立。可以改为：
No sooner had we arrived in Beijing than it began to rain heavily.
2) with (without) + 分词独立主格结构
She fell asleep with the lamp burning. (她开着灯谁着了。)
Almost every day the kids returned home with their hands and faces covered with mud and sweat.(孩子们几乎每天回家时手上脸上都是泥和汗。)
当这样的独立主格结构中的动词为 "be" 动词时，往往省略，例如：
Every day the old teacher entered the classroom， with a poor bag under his arm. (每天，这位老教师夹着个破包走进教室。= with a poor bag being under his arm)