Welcome to Compete Math
This website and each curriculum is intended to help you prepare for math competitions. We believe that students learn best when they are taught to understand how and why things work. We also believe that the best way to cement a deep understanding of concepts into the mind of students is by having them work on problems. The problems in this website are challenging and are meant to help students learn to solve problems as well as learning the concepts. Thus, each concept taught will start with sample problems to introduce it as well as problems at the end for further practice. In addition, for any student using this curriculum, we highly recommend that they attempt all of the sample problems on their own before reading the given solution.
We currently have the following curricula: AMC 10 |
Hard Problems |
Teaching Through Problems |
The practice problems at the end of each section are meant to be hard and thought provoking. These problems shouldn't be easy, and just finding out the correct answer isn't enough. We encourage you to find a full proof and write it up for yourself. By having you do full proofs, we hope that you will explore the concepts for yourself in order to more thoroughly understand them. Full solutions to these problems will be provided, but do not look at these solutions before you have done as much as you can to try to solve a problem; you are only cheating yourself if you look.
Understanding Why Things WorkWhen learning a concept or doing a problem, we believe that just as important as finding the right answer, if not more important, is to understand how to get to a solution and why each step works. If students are merely taught facts without proofs, they might as well not be being taught those facts at all, for they do not truly understand the fact. An understanding of how things work is also critical to to develop a deeper mathematical intuition. Not only will this help student establish an understanding of how mathematical ideas are developed in the real world, but, by understanding why things work, students get a deeper understanding of the concept and how to apply it.
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We believe that the best method to help students understand how concepts are used, and how to apply them in other problems where they aren't explicitly told to do so, is to introduce concepts through problems. Nearly all of our curricula will be taught by showing how a hard problem can lead to the development of an idea that the students are taught. Some concepts, of course, will not be taught this way, but we aim to teach the majority of the curriculum through problems. Not only will this improve students' understanding, but it will also teach import problem solving skills.
Exploring ConceptsWe encourage students to explore concepts further on their own. If students discover an interesting idea or notice an interesting pattern while doing practice problems or reading a sample, we highly encourage them to look further into it on their own. If students do this, they will not only gain a much better comprehension of what they learn, but they will likely discover useful facts by themselves, perhaps even concepts that will be taught later. By having students discover this themselves, it will stay in their memory much better, and they will be able to feel the joy of what it is like to solve mathematics problems in the real world or Olympiad level math, and how to discover new conjectures on their own.
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Learning without
thought is labor lost;
thought without
learning is perilous.
-Confucius
A Foundation for Competitive Math
The courses on the website are intended to give students the majority of the tools, concept-wise, that they need to do well in mathematics competitions. There will definitely be concepts that are not included in the curricula that could be of help to students taking the competition a curriculum is designed for. There are too many concepts that are useful to thoroughly enumerate all of them in a curriculum. However, the aim of this site is to give students a basis off of which they can succeed on an AMC 10 test.
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These courses are intended to give students an introduction to critical thinking used in every math contest. However, we do not claim that after these courses someone will be able to solve an problem that appears on a contest. We are merely attempting to add on to and develop the student's critical thinking in a way that will develop them on all contests they take in the future. Ultimately, to master this skill students must spend times on their own doing more problems.
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