Advanced Summer Program for students age 11-14
who show high promise and love mathematics


Questions & Answers

The Qualifying Test

1. May I write a computer program that solves a Test problem? I would include the program with my answer.

A. A computer program that answers a question by brute force is not welcome. For instance, a program that solves a counting problem by listing every possibility and then counting the total is brute force. On the other hand, it is unlikely that a test question would allow a straightforward count. Thus the program would have to have clever ideas about how to count. And once you discover the clever ideas to make such a program work, you can almost surely carry them out by hand anyway in a short amount of time, and thus should do so.

Computers definitely have a role in mathematics - many professional mathematicians use them for some calculations, especially if even the best way they see to do a computation is tedious. But we have chosen Qualifying Test questions for which computers are not necessary if you think about the questions the right way.

2. Should I sumit the answers printed or handwritten?

A. You can submit it either way. For most students it is less time-consuming to submit handwritten answers than to format mathematical symbolism on a computer. (The exception is if you already know a math-formatting language such as TeX throughly. All professional mathematicians know some version of TeX - we formatted the Test in Plain TeX - but now, when you are trying to think about our Test, is not the time to learn TeX!) Note that it is the correct reasoning that earns the score, not the beauty of the page layout. The only requirement about how your answers look is that the presentation be readable.

3. What is your scoring scheme for the answers?

A. This is the wrong question! You should be worrying about doing the best you can and not about how we score. Our Test is not a competition, where everyone must be assigned an exact score because someone will be declared a winner. In fact, there is no exact grading rubric, no exact cutoff for admission, and you will never be told your score. (If you are admitted to MathPath and come, you will learn whether you were basically right or not because all test questions will be discussed when we go over student work on it in our plenary writing sessions.)

Of course, we have rough grading guidelines. Generally problems are worth 10 points, divided among the parts of a problem depending on difficulty level. Sometimes a problem is worth more if there are many parts. Answers alone are worth little. What can gain points is reasoning, good intuition, elegance, and clear communication. It's actually infrequent for someone to get full credit on a problem, but there is lots of partial credit. Overall, we are looking to see if a student has the sort of interest and aptitude that can grow at MathPath. We also are checking whether students have the basic geometry and algebra skills needed as a starter. So the bottom line is: Try all the questions and do the best you can. If you are not sure (part of) one of your solutions is correct, say so, indicating what you are not sure of. Knowing when you don't know is an important mathematical skill, and sometimes gains points.

4. I have answered four questions on the Qualfying Test and I am on the brink of solving the fifth. I am absolutely sure that the answers to the problems I did are correct, but I am just a tiny bit worried about the fifth. Do you suggest I try another question just to be safe?

A. See the answer to the previous question. Do as many questions as well as you can, first because we want to see as much of your thinking as we can, and second because you never know how your work will be evaluated or what quality of work you need to be admitted.

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