Tips for Writing the Gauss, Pascal, Cayley, and Fermat Contests

Here are some tips for writing the Gauss, Pascal, Cayley, and Fermat contests, published by the Centre for Excellence in Mathematics and Computing at the University of Waterloo (formerly known as the Canadian Mathematics Competitions):

• These contests are multiple-choice, so read the tips on the multiple choice test tips page. There are several useful strategies listed there that can be applied to the Gauss, Pascal, Cayley, and Fermat tests.
• Set realistic goals for yourself, and don't be worried about doing "badly". These contests are designed so that the average person writing the contest scores half of the available points. Since most people that write the contest are above-average in math, even a modest score is still a very creditable performance. If you aren't sure what would be a realistic goal, you can find an old copy of the contest you plan to write (see below for links), write it in your spare time, check the answers and tally your score. This should give you a rough idea.
• You don't have to study for the the Gauss, Pascal, Cayley, or Fermat contest; however, if your results are important to you, some form of preparation is a good idea. Probably the best way to do so is to solve problems from past contests; you can find several at CEMC past contests. Also available are several books in the Problems Problems Problems series with problems from previous contests (the books can be hard to find, but you can find a few volumes on Amazon—volume 3, volume 5—or you can check the University of Waterloo bookstore).
• While the mathematical concepts required to solve the questions are all taught in your classes, many questions also require insight and originality to solve. It can help to study problem solving skills as well as strategies for discovering how to solve problems.
• Ensure that you bring all allowable aids (calculator, ruler, compasses). Drawing diagrams is an important part of solving problems, and having these aids can help with this.
• You only have 60 minutes to answer 25 questions, which isn't a lot of time since many of the later problems in the test are designed to be challenging. Depending on your proficiency in mathematics, you might find that you get the best results if you don't attempt every question; for the majority of students, it's probably a better idea to ignore most of the questions in part C and focus on part A and on the questions in part B that they have a good chance of answering.
• Some tips about guessing:
  • You get two points for each unanswered question up to a maximum of 20 points, so you don't get extra marks for leaving more than 10 questions unanswered. So, if you've left (10 + x) questions unanswered (where x > 0), be sure to guess on x questions. Since the questions in part C are worth the most, guess on those questions first.
  • If you've left no more than 10 questions unanswered, the way that the test is scored means that you are penalized fairly heavily for guessing, especially in parts A and B, so you should avoid guessing randomly. However, if you can eliminate several answers, educated guessing (especially in parts B and C) may be beneficial.
• Diagrams and other figures are not necessarily drawn to scale, but using your ruler to measure them may give you at least a rough idea of what the answer might be, or it might provide other insight into the problem.