HOW TO PREPARE FOR MATH CONTESTS
Noetic
The Noetic Learning Math Contest (NLMC), commonly known as the Noetic Contest, is a mathematics competition designed for elementary and middle school students.
Here are some key details about the Noetic Contest:
Who can take the Noetic?:
The Noetic Contest is open to students in grades 2 through 8. It is designed to challenge and engage students in mathematical problem-solving.
Where can you take the Noetic?:
The Noetic Contest can be administered at participating schools or other educational institutions that choose to register for the competition. Students generally take the contest at their own schools under the supervision of teachers or coordinators.
How to score high on the Noetic?:
Regular Practice: Consistent practice with math problems is essential. Familiarity with a variety of mathematical concepts helps students feel more comfortable tackling problems during the contest.
Understand Problem Types: Reviewing past Noetic Contest problems can help students understand the types of questions that may be asked. Pay attention to problem-solving strategies.
Critical Thinking: The Noetic Contest often involves problems that require creative and critical thinking. Encourage students to think beyond rote memorization and apply their understanding to novel situations.
Time Management: Practice with time constraints to ensure students can manage their time effectively during the actual contest.
Best resources to prepare for the Noetic contest:
Noetic Learning Website: The official Noetic Learning website provides sample problems, solutions, and other resources that can help students prepare.
Math Contest Preparation Books: There are several math contest preparation books available that cover a range of problem-solving strategies. Look for books that focus on the types of problems featured in the Noetic Contest.
Practice Contests & Mocks for Noetic:
Noetic Learning Math Contest Practice Tests: The official website may offer practice tests that students can use for preparation. These tests are designed to simulate the conditions of the actual contest.
Online Platforms: Some educational platforms offer practice contests and mock exams for the Noetic Contest. These resources can be valuable for students to gauge their readiness.
Materials allowed on the Noetic contest:
The Noetic Contest is usually conducted in a supervised setting, and students are generally not allowed to use any external materials such as calculators, books, or notes.
Math Olympiad
The Math Olympiad (MOEMS), officially known as the Mathematical Olympiads for Elementary and Middle Schools, is a series of contests designed to stimulate enthusiasm and a love for mathematics among elementary and middle school students.
Here are some key details about MOEMS:
Who can take the Math Olympiad?:
MOEMS is typically open to students in grades 4 through 8. There are two divisions: Division E (grades 4-6) and Division M (grades 6-8). Students from around the world can participate in the contest.
Where can you take the Math Olympiad?:
MOEMS contests are often administered at participating schools. Schools can register to participate in the program, and students take the exams at their respective schools under the supervision of teachers or contest coordinators.
How to score high on the Math Olympiad?:
Understand Problem Solving Techniques: MOEMS problems often require creative and strategic problem-solving approaches. Practice various problem-solving techniques, including drawing diagrams, making tables, and looking for patterns.
Familiarize Yourself with Past Problems: Solve past MOEMS contest problems to get a sense of the types of questions that may be asked. Understanding the format and difficulty level is essential.
Build a Strong Foundation: Ensure a solid understanding of fundamental mathematical concepts in arithmetic, algebra, geometry, and number theory. MOEMS problems cover a broad range of topics.
Practice Regularly: Regular practice is key to improving mathematical skills. Work on solving problems from various sources to enhance your problem-solving abilities.
Best resources to prepare for the Math Olympiad contest:
MOEMS Official Website: The official MOEMS website (https://www.moems.org/) provides information about the contest, sample problems, and details on how to participate.
Problem-Solving Books: Books that focus on elementary and middle school mathematical problem-solving can be valuable. Some recommended titles include "Math Olympiad Contest Problems" by Richard Kalman and "Math Olympiad Contest Problems for Elementary and Middle Schools" by George Lenchner.
Math Enrichment Programs: Consider participating in math enrichment programs that provide additional problem-solving challenges and exposure to advanced mathematical concepts.
Practice Contests & Mocks for Math Olympiad:
Official MOEMS Contests: Work through past official MOEMS contests to gain familiarity with the format and difficulty level of the problems.
Math Olympiad Training Programs: Some organizations and online platforms offer training programs with practice contests and mock exams designed to prepare students for MOEMS.
Materials allowed on the Math Olympiad contest:
The specific rules regarding materials allowed during the MOEMS contest may vary, and it's essential to check the official guidelines provided by MOEMS. In general, calculators and other reference materials are not allowed, and students are expected to solve problems using their mathematical knowledge and problem-solving skills. Always refer to the most recent official rules for accurate information.
AMC 12
The AMC 12, or the "American Mathematics Competitions 12," is a nationwide high school mathematics competition in the United States.
Here are key details about the AMC 12:
Who can take the AMC 12?:
The AMC 12 is typically intended for high school students in the United States and around the world. It is often taken by students in grades 11 and 12, although some advanced students in lower grades may also choose to participate.
Where can you take the AMC 12?:
The AMC 12 is administered at various testing centers across the United States and internationally. Many high schools, colleges, and other institutions serve as host locations for the exam. Students need to register with a designated host institution to participate.
How to score high on the AMC 12?:
Understand the Format: Familiarize yourself with the format of the AMC 12, which consists of 25 multiple-choice questions to be solved in 75 minutes.
Master Content Areas: The AMC 12 covers a range of topics, including algebra, geometry, number theory, and combinatorics. Ensure you have a solid understanding of these areas.
Practice Regularly: Solve problems from past AMC 12 exams to get a sense of the types of questions that may be asked. This helps you become comfortable with the exam format and time constraints.
Time Management: Practice time management to ensure that you can allocate the right amount of time to each question. Don't spend too much time on any single problem.
Review Mistakes: Analyze your mistakes and understand the solutions to problems you may have missed. This helps in improving your problem-solving skills.
Best resources to prepare for the AMC 12 contest:
Art of Problem Solving (AoPS): AoPS offers a variety of resources, including textbooks, online classes, and an active online community. Their "Introduction to Algebra," "Introduction to Geometry," and other books are often recommended.
AMC 12 Problem Books: Books specifically designed for AMC 12 preparation, such as "The Art of Problem Solving Volume 2" by Richard Rusczyk and Sandor Lehoczky, can be valuable resources.
Previous AMC 12 Exams: Solve past AMC 12 exams to understand the style and difficulty level of the questions. Official AMC problems and solutions are available on the official MAA website.
Khan Academy: Khan Academy provides free online resources covering various mathematical topics that may be useful for AMC 12 preparation.
How to prepare for the AMC 12 contest
Step I: Reviewing the Basics
If you are new to competition math or taking the AMC 12 for the first time, you need to ensure that you have a good understanding of the fundamental mathematical concepts. You can use the following resources to get started:
1. Free AMC 10/12 Fundamentals Course: A free course that covers the most basic concepts for the AMC 12 like Expected Value, Modular Arithmetic, Diophantine Equations, Power of a Point, etc.
2. Volume 1 book by AoPS: The Volume 1 essentially provides a summary of the Introduction Series by AoPS, covering many important concepts.
Step II (If time): Build Strong Fundamentals
To solidify your fundamentals, it is highly recommended that you work through the AoPS Introductory series books. They are quite comprehensive, but they take a long time to complete.
3. Introduction Series books by AoPS (In order of importance)
a. Introduction to Counting & Probabhttps://amzn.to/3GKosRAility
d. Introduction to Number Theory
You can also use Alcumus for extra practice along with these books.
In addition, you can also check out paid classes from organizations like Alphastar Academy, Art of Problem Solving, and others.
Step III: Mastering AMC 12 Concepts
4. Volume 2 book by AoPS: Volume 2 is appropriate for students who have mastered the problem solving fundamentals presented in Volume 1 and are ready for a greater challenge.
5. Intermediate Series books by AoPS
a. Intermediate Counting & Probability
6. PreCalculus by AoPS (Chapters 1-8): Precalculus covers trigonometry, complex numbers, vectors, and matrices. It includes nearly 1000 problems, ranging from routine exercises to extremely challenging problems drawn from major mathematics competitions
In the last 1-2 months before the contest, it is important to review and refresh all the concepts that are important for the AMC 12 test.
7. Mastering AMC 10/12: This free book will help you learn and practice advanced concepts useful for AMC 12 problems such as Linearity of Expectation, Markov Chains, Cyclic Quadrilaterals, etc.
Step 4: Practice Contests & Mocks
In order to practice speed and accuracy, it's important to take full AMC 12 tests.
Some tips when mocking AMC 12:
1. Don't brush off silly mistakes: Rather than treating a silly as something that's not a big deal, analyze why you made that silly and what you will do not to make that mistake again. Here is a video with tips to avoid sillies.
2. Peek but not read: For problems that you are not able to solve, don't just "read the solution". Rather, try to look at a few lines of the solution and then solve the rest of the problem on your own.
3. Build speed gradually: At first, try to work at a pace that you can achieve high accuracy with. Then, try to gradually increase your speed while still maintaining high accuracy. Never rush or work carelessly to increase speed as this will only reduce your accuracy significantly.
List of Mock Contests
Official AMC 12 from previous years with solutions: Use these tests with a 75 minute timer to simulate test taking situations. The AMC's are increasing in difficulty every year, so only AMC 12 contests from 2021 Fall and after are representative of the difficulty of recent AMC 12.
AoPS Created AMC 12 Mock Contest 2023: A high quality mock contest created by Art of Problem Solving problem writers
AoPS Created AMC 12 Mock Contest 2022: A high quality mock contest created by Art of Problem Solving problem writers
AoPS Created AMC 12 Mock Contest 2021: Another high quality mock created by Art of Problem Solving problem writers
AoPS User created AMC 12 Mock Contests: These mock contests are created by users on the AoPS forums and are of varying quality and difficulty levels. Still a good practice if you have completed all the previous year’s AMC 12 contests.
CMC Mock Contests: Nearly all of the tests created by CMC (even the ones from 2017) are extremely high quality and close in difficulty to AMC's nowadays.
AoPS Online Resources: AoPS provides mock exams and practice problems for the AMC 12 on their website.
Local Math Clubs and Organizations: Many local math clubs and organizations organize mock AMC exams or practice sessions. Check with your school or local community for such opportunities.
Materials allowed on the AMC 12 contest:
Writing Utensils: Pencils are typically allowed for marking answers on the answer sheet.
Scratch Paper: AMC 12 participants are often provided with scratch paper for rough work.
No Calculators: Calculators are not allowed on the AMC 12, so students must rely on their mathematical skills for problem-solving.
AMC 10
The AMC 10, or the American Mathematics Competitions 10, is a mathematics competition for high school students in the United States. It is part of the series of contests organized by the Mathematical Association of America (MAA).
Here are some key details about the AMC 10:
Who can take the AMC 10?:
The AMC 10 is intended for students in grades 9 and 10 (or below) who are 15.5 years of age or younger on the day of the competition. It is designed to provide younger students with an opportunity to participate in a challenging math contest.
Where can you take the AMC 10?:
The AMC 10 is offered at various testing centers across the United States and internationally. Schools, math clubs, and other educational institutions may register to host the AMC 10, and eligible students at these locations can take the exam.
How to score high on the AMC 10?:
Understand the Format: Familiarize yourself with the format of the exam, which consists of 25 multiple-choice questions to be answered in 75 minutes.
Review Basic Concepts: Ensure a strong understanding of fundamental mathematical concepts in algebra, geometry, number theory, and combinatorics.
Practice Regularly: Solve problems from previous AMC 10 exams and other math competitions. Regular practice will help you develop problem-solving strategies and improve your speed.
Time Management: Practice time management during your preparation and mock exams. The AMC 10 requires efficient use of time to complete all the questions.
Learn from Mistakes: Analyze your mistakes in practice exams and understand the solutions to problems you find challenging. This helps identify areas for improvement.
Best resources to prepare for the AMC 10 contest:
Art of Problem Solving (AoPS) Books: The AoPS series, including books like "Introduction to Algebra," "Introduction to Geometry," and others, provides in-depth coverage of topics commonly tested on the AMC 10.
AoPS Online Resources: The AoPS website offers an online community, forums, and resources for practicing problems, discussing solutions, and getting help.
Previous AMC 10 Exams: Solve past AMC 10 exams to get a sense of the types of problems that may appear and to gauge your readiness.
Khan Academy: Khan Academy provides free online resources covering a wide range of mathematical topics, making it a useful supplement to your preparation.
Practice Contests & Mocks for AMC 10:
AoPS Mock Contests: The AoPS website often provides mock contests designed to simulate the AMC 10. Participating in these can be valuable for preparation.
Local Math Clubs or Schools: Check if local math clubs or schools organize mock AMC 10 contests. Participating in such events can help you become more comfortable with the exam format.
Official AMC 10 from previous years with solutions: Use these tests with a 75 minute timer to simulate test taking situations. The AMC's are increasing in difficulty every year, so only AMC 10 contests from 2021 Fall and after are representative of the difficulty of recent AMC 10.
AoPS Created AMC 10 Mock Contest 2023: A high quality mock contest created by Art of Problem Solving problem writers
AoPS Created AMC 10 Mock Contest 2022: A high quality mock contest created by Art of Problem Solving problem writers
AoPS Created AMC 10 Mock Contest 2021: Another high quality mock created by Art of Problem Solving problem writers
AoPS User created AMC 10 Mock Contests: These mock contests are created by users on the AoPS forums and are of varying quality and difficulty levels. Still a good practice if you have completed all the previous year’s AMC 10 contests.
AlphaStar AMC 10 Practice Tests Book: A book with some high quality mock contests created by the problem writing team at AlphaStar Academy.
CMC Mock Contests: Nearly all of the tests created by CMC (even the ones from 2017) are extremely high quality and close in difficulty to AMC's nowadays.
DMC Mock Contests: Another site with high quality mock AMC 10s.
OMC Mock Contest: A good AMC 10 mock from 2023.
Materials allowed on the AMC 10 contest:
No Calculators: The AMC 10 is a no-calculator competition, so participants are not allowed to use calculators during the exam.
Pencils and Scratch Paper: Participants are typically provided with pencils and scratch paper for working out solutions.
AMC 8
The AMC 8, or the "American Mathematics Competitions 8," is a middle school mathematics competition in the United States.
Here are some key details about the AMC 8:
Who can take the AMC 8?:
The AMC 8 is typically open to middle school students, typically those in grades 8 and below. However, eligibility can vary by location, and some students in higher grades may also be eligible to participate.
Where can you take the AMC 8?:
The AMC 8 is administered at various testing centers across the United States and around the world. Schools, math clubs, and other educational institutions often host the exam.
How to score high on the AMC 8?:
Study Math Fundamentals: Ensure a solid understanding of basic mathematical concepts in algebra, geometry, number theory, and combinatorics.
Review AMC 8 Problems: Familiarize yourself with the types of problems that commonly appear on the AMC 8 by reviewing past exams and understanding the solutions.
Practice Regularly: Solve a variety of math problems regularly to build problem-solving skills. Use resources that cover a range of difficulty levels.
Time Management: The AMC 8 is a timed test, so practice working under time constraints. Develop a strategy to manage your time effectively during the exam.
Best resources to prepare for the AMC 8 contest:
AoPS (Art of Problem Solving) Books: AoPS offers textbooks that cover various topics tested in the AMC 8. Books like "Introduction to Algebra," "Introduction to Geometry," and "Introduction to Number Theory" are helpful.
Past AMC 8 Exams: Access and solve previous years' AMC 8 exams to get a sense of the question formats and difficulty levels. These are available on the official AMC website.
Online Platforms: Websites like Khan Academy, Brilliant.org, and others provide interactive lessons and practice problems that can supplement your preparation.
Practice Contests & Mocks for AMC 8:
AoPS Online Resources: The AoPS website offers online practice problems, contests, and forums for discussing solutions. They also provide mock contests to simulate the AMC 8 experience.
Local Math Clubs and Schools: Check with local math clubs, schools, or educational organizations for any mock contests or practice sessions they may offer.
Official AMC 8's from previous years with solutions: Use these tests with a 40 minute timer to simulate test taking situations.
AoPS Created Mock Contest 2022: A high quality mock contest created by Art of Problem Solving problem writers
AoPS Created Mock Contest 2021: Another high quality mock created by Art of Problem Solving problem writers
AoPS User created Mock Contests: These mock contests are created by users on the AoPS forums and are of varying quality and difficulty levels. Still a good practice if you have completed all the previous year’s AMC 8 contests.
AlphaStar AMC 8 Practice Tests Book: A book with some high quality mock contests created by the problem writing team at AlphaStar Academy.
Challenging Problems in Middle School Math: This is a good book for preparing for middle school competitions
Materials allowed on the AMC 8 contest:
The AMC 8 is a paper-and-pencil exam, and participants are typically provided with the necessary materials (such as scratch paper and pencils) by the testing center.
Calculators are not allowed on the AMC 8, and participants should rely on their problem-solving skills without the aid of electronic devices.
AIME
The AIME, or the "American Invitational Mathematics Examination," is a math competition in the United States organized by the Mathematical Association of America (MAA).
Here are some key details about the AIME:
Who can take the AIME?
The AIME is typically open to high school students in the United States and Canada who perform exceptionally well on the AMC 10 or AMC 12 exams. These students, often in grades 10 through 12, are invited to participate in the AIME based on their performance in the earlier rounds.
Where can you take the AIME?
The AIME is administered at various testing centers across the United States and Canada. Invited students usually take the exam at their respective schools or designated testing locations.
How to prepare for the AIME contest?
Solid Foundation: Ensure a strong understanding of fundamental mathematical concepts in algebra, geometry, number theory, and combinatorics.
Review AMC Exams: Since AIME qualification is based on performance in the AMC 10 or AMC 12, reviewing the problems from these exams is crucial to understand the types of questions that may appear on the AIME.
Practice Problem Solving: Solve challenging math problems from various sources, including past AIME exams, to hone your problem-solving skills.
Study Materials: Use textbooks and resources that cover advanced topics in algebra, geometry, number theory, and combinatorics. Art of Problem Solving (AoPS) books are often recommended.
Mock Exams and Practice Contests: Simulate test conditions by taking timed practice exams and mock contests. This helps improve time management and builds stamina for the three-hour AIME.
Practice Contests & Mocks
In order to practice speed and accuracy, it's important to take full AIME tests for timed practice.
List of Mock Contests
Official AIME from previous years with solutions: Use these tests with a 75 minute timer to simulate test taking situations. The AMC's are increasing in difficulty every year, so only AMC 12 contests from 2021 Fall and after are representative of the difficulty of recent AMC 12.
AIME problems (till 2014) Sorted By Topic: This is a great resource to practice AIME problems topic by topic. For each topic, the problems are sorted roughly in increasing order of difficulty. A strategy you can consider is use this handout to practice topic by topic problems and do the AIME's 2015 onwards as practice tests.
CIME Mock Contests: Nearly all of the tests created by CMC (even the ones from 2017) are extremely high quality and close in difficulty to AMC's nowadays.
AIME Practice Tests Book by AlphaStar Academy: This book contains four AIME practice exams with new problems not used in any past competitions and with insightful solutions.
AoPS Forum with Many Mocks: This forum has many mocks created by AoPS users. Most of them are great quality and good to practice with but they can often be hard. Some ones I recommend are DIME, EIME, and XYZIME but there are probably many other great mocks you can find here
List of AIME mocks on AoPS: Long list of user created mocks
More mocks from AoPS forum: Another list of mocks from AoPS.
Problem Trainers
For even more practice, there are some useful websites which help you practice specific topics and improve problem solving speed.
1. Alcumus: Free resource by AoPS to practice problems from specific topics.
2. AMC Trivial: This site generates problems from past contests. You can even make custom mocks from older questions and it can give problems from specific topics or difficulty levels.
3. MAATester: This site makes it easy to search for problems related to any topic from various contests.
MATHCOUNTS
MATHCOUNTS is a national middle school mathematics competition program in the United States. It aims to promote mathematics achievement through a series of fun and engaging contests. The competition is designed to foster mathematical skills and interest among middle school students.
Here are some key points about MATHCOUNTS
When is MATHCOUNTS?
MATHCOUNTS competitions typically occur at different levels throughout the school year. School-level competitions are held first, followed by chapter, state, and finally, the national competition.
Who can take MATHCOUNTS?
MATHCOUNTS is open to students in grades 6-8 in the United States. The competition is divided into different rounds, including school, chapter, state, and national levels.
How to score high on MATHCOUNTS?
Scoring high in MATHCOUNTS involves a combination of mathematical knowledge, problem-solving skills, and efficient time management. Regular practice, exposure to various types of mathematical problems, and familiarity with the format of the competition are crucial for success.
Best resources to prepare for MATHCOUNTS:
AoPS (Art of Problem Solving): AoPS provides a variety of resources, including textbooks, online classes, and a vibrant online community. Their "Introduction to Algebra," "Introduction to Counting & Probability," and other books are popular choices.
MATHCOUNTS Trainer: The MATHCOUNTS Trainer is an online tool provided by AoPS that allows students to practice problems from past MATHCOUNTS competitions, categorized by topic and difficulty.
Previous MATHCOUNTS Competitions: Studying past competition problems is an excellent way to familiarize yourself with the types of questions asked. You can find these on the official MATHCOUNTS website.
Competition Math for Middle School by Jason Batterson: This book is often recommended for MATHCOUNTS preparation and covers various topics tested in the competition.
The Art of Problem Solving Volume 1 and 2 by Richard Rusczyk: These books cover a broad range of topics and provide in-depth explanations of problem-solving strategies.
Practice Material/Books from MATHCOUNTS with links?
MATHCOUNTS provides official practice materials on their website, including past competition problems and solutions. Visit the official MATHCOUNTS website at www.mathcounts.org for access to these resources.
Materials allowed on the MATHCOUNTS contest
The materials allowed during the contest may vary, so it's essential to check the official MATHCOUNTS rules for the specific year. Typically, students are only allowed to use certain types of calculators, and additional aids like books, notes, or electronic devices are not permitted.