My younger cousin has to take the Comprehensive Assessment Program for Junior High School Students (CAP), which is the so-called United Examination in Chinese, and consequentially I pay more attentions on the relative news about this examination. I knew the non-selective questions of mathematics are very difficult from the newspaper, and I couldn't find the reference answer about them on the website of the entrance examination. The 1st question is very simple, and examinees just need to calculate the boundary and space to find the answer. The 2nd question is a proof question of geometry, which I liked it and chose Computational Geometry as the topic as my master thesis especially, so that I intent to solve it as a reference for examinees.
How do examinees think about it? All of the given proof conditions can be thought about the answer by the reverse logic, and consequently examinees just need to choose the reverse order of the given proof conditions. The target answer is △CDE = △ABC / 2, and therefore |CM = |MB, which is △CMA = △AMB, can be adopted as the 1st given condition. The next adopted given condition may choose |AE // |DM, so that the given condition lets △EDM and △ADM have the same perpendicular height to obtain △EDM = △ADM. Combined the 1st derived equation with the 2nd derived equation, the intersectional area △CDM is the same area for △CMA and △CDE to build the relationship between the two derived equations. That's all, and you can make it.
References
  
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How do examinees think about it? All of the given proof conditions can be thought about the answer by the reverse logic, and consequently examinees just need to choose the reverse order of the given proof conditions. The target answer is △CDE = △ABC / 2, and therefore |CM = |MB, which is △CMA = △AMB, can be adopted as the 1st given condition. The next adopted given condition may choose |AE // |DM, so that the given condition lets △EDM and △ADM have the same perpendicular height to obtain △EDM = △ADM. Combined the 1st derived equation with the 2nd derived equation, the intersectional area △CDM is the same area for △CMA and △CDE to build the relationship between the two derived equations. That's all, and you can make it.
References
- 國立臺灣師範大學心理與教育測驗研究發展中心（2013）國中教育會考，http://cap.ntnu.edu.tw/
- 林曉雲（2013.04.20）《國中會考》數學非選題超難 51%考生抱鴨蛋，自由時報，http://www.libertytimes.com.tw/2013/new/apr/20/today-life7.htm
- C. M. Huang（2004）Delaunay triangulation for quality assessment in two dimensions and Sliver investigation in three dimensions, Supervisor: C. S. Chen, Master Thesis, Department of Civil Engineering, National Taiwan University, Taipei, Taiwan, R.O.C.
- Wikipedia, Computational geometry, http://en.wikipedia.org/wiki/Computational_geometry
