【知识点一】：语法结构辨析
1. 题目中的句子"The boy went in such an anxious rush when he left for school that he left his key inside the house."考察的是"such + a/an + 形容词 + 名词 + that..."与"so + 形容词 + a/an + 名词 + that..."的用法。正确答案是D．such an anxious rush，表示“如此急切匆忙以至于...”。
2. "The girl had hardly rung the bell before the door was opened suddenly..."使用了"hardly...when..."结构，意为“几乎还没有...就...”，表示两个动作几乎是同时发生。所以正确答案是A．before。
【知识点二】：动词短语搭配
4. "They stood there and opened their eyes wide, watching over what was happening."此句中"watch over"意为“监视，看护”，符合上下文语境。因此，正确答案是B．watching over。
【知识点三】：非谓语动词作状语
6. "With so many things to deal with, I have to work late into the night."这里使用了不定式"to deal with"作后置定语，表示将要处理的事情，故选A．to deal with。
【知识点四】：时态与语态
9. "With so many problems to solve, Jack looks like a cat on a hot tin roof."此处用不定式"to solve"表将来，表示杰克有待解决的问题。所以正确答案是B．to solve。
【知识点五】：固定短语搭配
10. "good manners arise from politeness and respect for others"使用了短语"arise from"，意为“源自于，由...产生”。所以正确答案是B．arise。
【知识点六】：副词辨析
11. "he was totally hopeless and killed himself."中"totally"意为“完全地，彻底地”，符合句意，表示他彻底绝望。
【知识点七】：名词辨析
13. "The new invention made last month would have a variety of applications in industry."中"applications"意为“应用”，表示新发明在工业中有多种用途。
【知识点八】：条件句
12. "A study shows that walking fast in your old age is a sign that you will live a long life."中"a sign that"引导同位语从句，表示“...的迹象”。
以上是题目中涉及的英语语法、词汇和表达方式的相关知识点。这些知识点对于英语学习者来说是非常重要的，它们涵盖了形容词副词的用法、动词短语、非谓语动词、时态语态、固定搭配以及名词辨析等多个方面，都是提高英语能力的关键点。
