Math Olympiad
This page is a place for you to boost your critical thinking skills by challenging yourself with a wide range of tricky problems in Algebra, Geometry, Trigonometry, Probability, Statistics, Pre-Calculus, Calculus posted in each subpage. All challenging problems were collected from a variety of exams for Gifted and Talented students ranging from Middle School to High School levels all over the world. This is the most challenging part ever. Questions in this test are far more difficult than those in ISEE, PSAT, SAT, ACT, AMC, and MATHCOUNT tests.
Math Olympiad competitions are designed to be tough, and often students who are used to getting perfect scores on math tests find themselves getting only half or even less correct. This is normal since tests like Gifted and Talented exam measure your ability to solve challenging problems creatively and independently, not just memorize information; so be positive. These problems will really challenge your mathematical thinking and will result in so much growth.
I aimed for clear, concise explanations and a conversational approach that would encourage you to read the solutions. You can learn a lot by reading my solutions, but you will develop deeper understanding by doing those problems on your own, and answering the unsolved questions along the way.
Before challenging yourself, please give yourself a try to explore the techniques how to approach the solutions to the problems and go back to compare your answers with my solutions. Please be minded that there is always more than 1 method to arrive at the solutions. My solution is just suggested for your reference. The best way to learn advanced math is to ask yourself if you can figure out the solutions without any help and if you will be able to approach the difficult problems with many different ways using the following variation of Polya’s problem-solving process:
understand the problem,
develop a mathematical model,
solve the mathematical model and support or confirm the solutions, and
interpret the solution.
Now, let's explore each challenging problem and enjoy the art of problem solving by clicking NEXT. I also solve all Math Olympiad problems on my YouTube channel. Please check it out.