Optimal Strategies to Solve Hard AMC Geometry Problems

Henry Wan, Ph.D.

The AMC 10 is a 25-question, multiple choice contest. The questions are arranged from the easiest to the hardest. The scoring will be 6 points for a correct answer, 1.5 point for a blank answer, and 0 points for an incorrect answer. The key to doing well on the AMC 10 is not to get the most difficult questions (usually question #21 – #25) right; rather, it is to correctly answer the first 20 problems without error. However, the last five problems of the AMC 10 almost always contain at least two geometry problems that can be solved using a ruler, protractor and compass. Getting these two problems correct can give a student even more points, so they can get at least 120 points on the AMC 10 and advance to the next level, the AIME.

Although the rules of AMC state that no calculators are allowed, students are permitted to use scratch paper, graph paper, rulers, compass, protractors, and erasers. We must use these tools to our advantage. Even if you do not know to solve a problem mathematically, you can always use these tools to solve it.
For example, 2014 AMC 10 Problem #22 is a very difficult problem to solve mathematically. But by simply using a ruler and a protractor, one can easily solve this problem.

2014 AMC 10A #22

In rectangle ABCD, AB = 20 and BC = 10. Let E be a point on CD such that . What is AE?

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