If you’re an advanced high school student in math, the Continental Math League (CML) competition is a great opportunity to strengthen and demonstrate your skills at high-level math and creative problem-solving techniques.
If you’re hoping to use the CML competition to show strong performance in mathematics beyond what’s offered in your curriculum or to hone your skills for college-level coursework, this guide offers key tips for giving your best performance and scoring high.
We have also covered a host of other math competitions and comprehensive guides, a few of them being the Harvard/MIT Mathematics Tournament, the American Regions Mathematics League Competition, and the Math Prize for Girls
What is the Continental Math League?
Founded in 1980, the Continental Math League competition is designed to increase student engagement and excitement in math and to supplement existing mathematics education where students can collaborate with school peers and compete with others both regionally and nationally.
The CML offers competitions open to students from second grade through high school. The CML competition is split into three levels, organized by level of difficulty. The Pythagorean and Euclidean levels are designed for students in late-elementary and middle school, while the Calculus League is geared towards advanced high school students, drawing from mathematical concepts at the AP Calculus levels and beyond.
What are the advantages of competing in the CML?
High achievement in CML can be strategic for high-achieving students looking to show above-grade-level mathematical competency in college admissions.
The problems in the CML Calculus League competitions are designed to be challenging, requiring students to think critically and apply their mathematical knowledge in innovative ways. You’ll have the chance to prove your abilities to apply methods in calculus, statistics, number theory, and college-level math to novel contexts ranging from real-world situations to physics.
The CML notes that the competition problems anticipate a level of mathematical knowledge above a student’s grade level. Participating in the CML competition has the potential to enhance your college applications and demonstrate your dedication and aptitude in mathematics through high rankings at regional and national levels.
Participating in math competitions can further demonstrate your dedication and motivation to dive deeper into a particular academic subject, and that you have the skills necessary to ace college-level coursework.
If you’re considering further studies or a career in STEM, the experience gained from solving challenging math problems and working collaboratively can be a valuable opportunity to gain early expertise in these academic contexts.
How is the CML Calculus League Structured?
The CML Calculus League consists of four rounds of competitions, or “meets”, throughout the academic year. Though there are set dates for each meeting — typically in November, February, March, and April, you’ll complete the competition exam at your high school.
Within your school, which will need to register as a member of the League in order to administer the competition, you may form a team of any size to compete.
Each meeting consists of eight challenging math problems, which will test your problem-solving skills, mathematical reasoning, and creativity. The problems cover a wide range of mathematical topics, including algebra, geometry, number theory, combinatorics, and calculus. You’ll be given a total of 40 minutes to complete the eight problems.
Solutions are submitted by the teams, and the scores are determined based on the accuracy of the answers and the problem-solving techniques employed. Though you’ll need to complete the problems individually, your team score is the sum of the top 6 scores of any student on any problem from your school team.
Scores are tabulated after each contest round, and the results are posted on the CML website. Participating schools can see how their teams performed relative to other schools in their division and region. At the end of the competition year, awards and certificates are given to the top-performing teams and individuals, calculated on both the regional and national level.
7 Tips to Ace the Continental Math League (CML)
1. Solidify Your Foundation Across Levels of Mathematics
CML problems often cover various mathematical topics. As a high school student competing in the Calculus League, you’ll be expected to have competence at the AP Calculus AB level or above. Participating can aid you in strengthening your existing academic skills through cross-applying mathematical concepts to other disciplines, preparing you for interdisciplinary college coursework and advanced courses such as physics, economics, and statistics.
If your coursework has been primarily focused on calculus or higher-level mathematical concepts, you may be out of practice with quickly solving advanced problems in algebra and geometry even if you have a strong background. Though these subjects may not be the focus of the CML competition, you will be expected to integrate these concepts into your work. So, brush up on solving problems from earlier coursework in Algebra 2 and Pre-Calculus. Consider reviewing coursework from courses you’ve already taken or accessing online practice tests from resources such as recommended Pre-Calculus work from the College Board or instructional lessons and practice problems from Khan Academy.
2. Prepare for the Competition Time Pressure
Time is limited during the competition, so work on improving your speed while maintaining accuracy. As you’ll have 40 minutes to complete a total of eight problems, make sure during practice that you can not only solve problems correctly, but can do so within a limited amount of time. It is strategic to divide time evenly between questions, which puts you at five minutes per question.
When you first begin practicing for the competition, working through problems slowly will be helpful to confirm your understanding and approach to the problem and ensure your highest level of accuracy.
Once you become more comfortable with the competition structure, practice solving problems under the competition time constraints to develop a good sense of pacing and build confidence in your ability to solve problems quickly. If you’re not used to solving these higher-level problems on a fast timeline, you may feel rushed and make avoidable mistakes due to the time pressure.
3. Be Prepared to Move On if Timing is Tight
Transitioning from practicing to competing can be stressful, and you might find yourself struggling to complete a particularly tricky question. However, with an average of 5 minutes per question, spending extra time on a challenging question can lead to you falling behind on subsequent problems. If you’ve spent 5 minutes on a problem but are still unable to find a solution, move on to the next question.
Remember, you can always come back to questions you skip. Don’t waste limited time pushing through a confusing problem --- this will lead to frustration and increased stress when completing the following questions with tighter time constraints. And don’t forget --- you are eligible for partial credit even if you do not find the full solution.
4. Strategize with your Team
Form study groups or join math clubs at your school to collaborate with like-minded peers. Discussing problems, sharing approaches, and explaining solutions to each other can deepen your understanding and provide different perspectives.
Your teammates might have specialties in different areas --- share your expertise with one another. When you’re working on practice problems, compare answers and methods. If any team members struggle with a particular problem, make sure they are given guidance by someone with a successful solution.
5. Learn from Previous CML Competitions
Familiarize yourself with previous CML contests to get a sense of the types of problems that may be asked. Study the solutions and strategies employed by successful participants. This can give you valuable insights and help you prepare effectively.
Make use of any official resources provided by CML, such as sample problems, practice tests, or study guides. These resources are designed to give you an idea of what to expect and can help you prepare more effectively. Unfortunately, the CML offers very limited free practice problems. More comprehensive preparation resources are available at a cost.
If you’re in need of additional resources, searching for online resources in advanced calculus, asking for recommendations from past competition participants or mathematics instructors at your school may provide useful preparation.
6. Memorize Essential Formulas
As you practice, pinpoint mathematical identities that pop up frequently across problems. Remember, due to the relevance of speed as well as accuracy, you’ll need to think quickly about how to approach the problem at hand. Though you might be skilled in applying essential formulas and identities to math problems, being able to recall them quickly is just as important. If you’re able to memorize essential identities and solutions, this will reduce the time you spend on computation, meaning that you’ll be able to focus more deeply on developing an accurate and creative approach to questions with challenging theoretical components. Some of the most essential formulas and identities to internalize are squares, cubes, powers of three and five, calculus identities, and key derivatives and integrals.
7. Carefully Review Solutions to Sample Problems
Though this tip is most critical for questions you may have answered incorrectly, looking over the provided solutions for practice problems is always a strategic choice. Remember, though you may have arrived at the correct answer, this does not mean that you used the ideal technique in doing so. There may be a more efficient method that can be applied across similar problems, and it is always possible to arrive at a correct solution through incorrect calculations. Your score on the CML can be affected by your problem-solving technique — you don’t want to miss out on full-credit for a correct solution because of missteps in your work. Reviewing provided solutions will give you a clear sense of the approach that the CML recommends for solving problems that require a creative approach to critical thinking in mathematics.
If you are looking to do cutting-edge research in math, then you should consider applying to the Lumiere Research Scholar Program, a selective online high school program for students that I founded with researchers at Harvard and Oxford. Last year, we had over 4000 students apply for 500 spots in the program! You can find the application form here.
Stephen is one of the founders of Lumiere and a Harvard College graduate. He founded Lumiere as a Ph.D. student at Harvard Business School. Lumiere is a selective research program where students work 1-1 with a research mentor to develop an independent research paper.
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