the art of problem solving amc 10

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Amc resources.

AMC Resources consists of material for teachers , parents and students to help with mathematical problem solving and to prepare for the MAA American Mathematics Competitions (AMC).

AMC Preparation Materials For Purchase

AMC Preparation Materials for Purchase  consists of flash drives of past AMC 8/10/12, AIME and USAMO contests as well as AMC 8 and 10/12 Math Club Packages. 

Student and Educator Resources

Amc m-powered.

With inquiry-driven instruction and projects highlighting comprehension, retention, and critical thinking, the AMC M-Powered site promotes learning by doing.  Prepare for competitions, attend virtual events, and access lesson plans. Whether you are an educator, student, parent, or a member of our greater AMC community, we invite you to connect! 

CURRICULUM INSPIRATIONS

Developed by james tanton ,  curriculum inspirations  is a collection of resources for middle and high school math teachers that demonstrate practical ways to engage students in the lively exploration of mathematics and mathematical thinking using problems from amc 8/10/12 contests — america’s longest-running and most prestigious mathematics competitions. now featured on m-powered., the art of problem solving.

The Art of Problem Solving  (AoPS) develops educational materials for the nation's top students in grades 2-12. The AoPS online community includes over 360,000 members from around the world, and the AoPS online school helps thousands of students each year develop tools needed for success in top-tier colleges and in prestigious math competitions.

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In this summer course, advanced high school students develop the problem-solving skills and strategies they’ll need to succeed in major high school math contests.

Students grades 9-12 prepare for the American Mathematics Competitions, the American Invitational Math Exam, and more.

AMC 10/12 Prep Camp is designed for students in grades 9 through 12 who want to excel at math competitions such as the American Mathematics Competitions 10 and 12 (AMC 10/12), the American Invitational Math Exam (AIME), and other major high school contests.

Our expert instructors use content developed by the Art of Problem Solving curriculum team to teach High School Math Contests. As a deep exploration of challenging mathematics, AoPS curriculum prepares students for success at top universities, and competitive careers. No books are required for this class.

In this course, students study and practice successful strategies for the American Mathematics Competitions 10 and 12 (AMC 10/12) and other major high school contests. Students also participate in practice competitions to build both mathematical skills and test-taking experience to prepare them for the upcoming school year.

Since 1993, high school students have relied on AoPS for contest preparation. Composed entirely of AoPS students, the USA Mathematical Olympiad Team has won the International Math Olympiad 4 out of the last 6 years — after not winning for the previous 20 years.

Our instructors hold classes virtually, in a small-sized (10-16 students) videoconferencing classroom.

There is no required homework for AMC 10/12 Prep Camp. However, we've prepared more materials than we can cover during class and many students continue working on them after class for extra practice.

If you drop a summer course before the start of your first class session, we'll issue a full refund for the course tuition. No refunds will be issued for withdrawing from a summer course after the start of your first class session.

Our summer course offerings meet five days a week, Monday through Friday. We offer this course in two timing formats. Both cover the same course material.

• The two-week course meets for 3 hours each day.
• The four-week course meets for 1.5 hours each day.

2018 AMC 10B Problems/Problem 20

• 2 Solution 1 (Algebra)
• 3 Solution 2 (Algebra)
• 4 Solution 3 (Finite Differences)
• 5 Solution 4 (Pattern)
• 6 Solution 5 (Pattern)
• 7 Solution 6
• 8 Solution 7
• 9 Video Solution
• 10 See Also

Solution 1 (Algebra)

Solution 2 (Algebra)

~AopsUser101 ~MRENTHUSIASM

Solution 3 (Finite Differences)

Now, there are two ways to finish.

~Professor-Mom

Solution 4 (Pattern)

Solution 5 (Pattern)

~CharmaineMa07292010

Video Solution

https://www.youtube.com/watch?v=aubDsjVFFTc

https://youtu.be/ub6CdxulWfc

~savannahsolver

• Introductory Algebra Problems

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Top Resources for AMC Preparation: Books, Courses, and More

The AMC (American Mathematics Competitions) exams are renowned for their challenging math problems that require deep mathematical insight and problem-solving skills. To excel in AMC competitions like the AMC 10/12, AIME, and USA(J)MO, it's essential to have access to quality resources that can help you prepare effectively. Here's a list of top resources, including books, courses, websites, and practice materials, to enhance your AMC preparation:

1. "Art of Problem Solving" (AoPS) Series: This series of books, including "Introduction to Algebra," "Introduction to Counting & Probability," and others, provides comprehensive coverage of topics frequently tested in AMC exams.

2. "Competition Math for Middle School" by Jason Batterson: A great resource for students preparing for the AMC 8 and 10. It covers various topics in a clear and engaging manner.

3. "AMC 10/12 Preparation Books" by AoPS: AoPS offers books specifically tailored for AMC 10 and AMC 12 preparation. These books contain a collection of challenging problems with detailed solutions.

4. "The Art and Craft of Problem Solving" by Paul Zeitz: This book offers a broader perspective on mathematical problem-solving and is suitable for students looking to improve their problem-solving skills beyond the AMC exams.

5. "Volume 1: The Basics" and "Volume 2: And Beyond" by AoPS: These books are excellent for building a strong mathematical foundation and contain numerous problems that are helpful for AMC preparation.

 Online Courses and Classes:

1. AoPS Online: The Art of Problem Solving website offers online classes specifically designed for AMC preparation. They cover various topics and are taught by experienced instructors.

2. Khan Academy: Khan Academy provides a range of free math courses that can help you build a solid mathematical foundation. While not focused solely on AMC topics, it's a valuable resource for strengthening your math skills.

3. Brilliant.org: Brilliant offers interactive courses in math and science, including a specific section for competition math. It provides a platform to practice solving challenging problems.

4. MATHCOUNTS Trainer: While primarily designed for MATHCOUNTS, this resource is excellent for AMC preparation, especially for the AMC 8 and 10.

 Websites and Online Resources:

1. AoPS Community: The AoPS online community features discussion forums where you can interact with other students, ask questions, and gain insights into problem-solving techniques.

2. Art of Problem Solving Wiki: AoPS's wiki is a valuable resource for finding detailed solutions and explanations to AMC and AIME problems.

3. Alcumus: This free online resource from AoPS offers a wide range of problems with varying levels of difficulty. It's an excellent tool for practicing problem-solving skills.

4. AMC's Official Website: The official AMC website provides information about exam dates, registration, and past AMC problems, including solutions and statistics.

5. MIT OpenCourseWare: MIT offers free online courses that cover advanced math topics that can be beneficial for AMC preparation.

 Practice Tests and Problems:

1. AMC Past Papers: Access past AMC exams on the official AMC website. These are invaluable for practicing under timed conditions.

2. AoPS Contests and Mock Tests: AoPS offers a collection of practice contests and mock tests that closely resemble the format and difficulty of AMC exams.

3. Mathematics Stack Exchange: While not specific to AMC exams, this Q&A platform is a great place to ask math-related questions and learn from the community.

4. Online Problem-Solving Platforms: Websites like Project Euler, Codeforces, and LeetCode offer challenging math and programming problems that can improve your problem-solving skills.

 Additional Resources:

1. Math Clubs and Competitions: Join or start a math club at your school or participate in local and regional math competitions to gain experience and exposure to challenging problems.

2. Math Olympiad Training Books: Books like "USA Mathematical Olympiads" and "Mathematical Olympiad Challenges" provide a wealth of challenging problems that are excellent for AMC preparation.

3. Math Circles: Look for local math circles or online math communities where you can discuss math problems and exchange ideas with like-minded students.

4. Educational YouTube Channels: Channels like Numberphile, 3Blue1Brown, and MindYourDecisions offer engaging math content that can deepen your understanding of mathematical concepts.

Remember that consistent practice, active problem-solving, and a commitment to learning are key to success in AMC competitions. Utilize these resources to tailor your preparation strategy, and adapt it to your strengths and weaknesses. Good luck with your AMC preparation journey!

Conclusion 

In conclusion, effective preparation for AMC (American Mathematics Competitions) exams requires access to high-quality resources that enhance your mathematical skills, problem-solving abilities, and overall understanding of advanced math concepts. The recommended books, online courses, websites, and practice materials listed in this guide serve as valuable tools to aid your AMC preparation.

Remember that success in AMC competitions, whether it's the AMC 10/12, AIME, or USA(J)MO, is not solely about memorizing formulas but about developing a deep understanding of mathematical principles and honing your problem-solving skills. Make the most of these resources by actively engaging with the material, practicing regularly, and seeking support from online communities, teachers, or mentors when needed.

Your dedication, consistent effort, and effective utilization of these resources will greatly contribute to your performance in AMC exams and help you achieve your mathematical goals. Keep a positive mindset, embrace challenges, and enjoy the journey of mathematical exploration and discovery. Good luck with your AMC preparation!

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