The NCC Partnership Program - For the Student
As stated in Functions Modeling Change: A Preparation for Calculus:
"Mathematics has the extraordinary power to reduce complicated problems to simple rules and procedures. Therein lies the danger in teaching (and learning) mathematics: it is possible to teach (and learn) the subject as nothing but rules and procedures - thereby losing sight of both the mathematics and its practical value."
The final examinations on this site all stress conceptual understanding and multiple ways of representing the key ideas of precalculus. The course you have completed stresses that functions can be grouped into families, and they can be used to model real-world behavior.
Rather than testing a myriad of topics, none of which is taught in depth, the topics asked on these examinations are tested in depth. As you go through these three-hour examinations, notice how, for the most part, questions are not repeated. However, the same topics are tested in various ways: sometimes analytically, sometimes graphically, sometimes numerically and sometimes verbally. Also, simply because a particular topic was not asked in previous years does not guarantee that this topic will not be asked in future years.
As you begin to study for your final examination, do not try to memorize the solutions to questions. Rather, understand how to interpret questions and then understand the strategy for solving questions of a similar type. Also, ask yourself what the point of the question is and how this same point could be asked differently. An outline of topics and concepts for review can be found below. This outline is meant to be used only as a guide for the student. Additional topics could have been included.
Studying for the final examination should take place over several weeks. Many students have found that studying or reviewing with a partner or in a small study group is helpful. Studies have found that students who prepare in this way out score students who study alone.