Most of us assume that pre-calculus is simply the study or understanding of what calculus really is. Most of you could be right, but this definition doesn't mean anything without having some knowledge of what calculus is.
Students learn mathematics by doing mathematics. To be precise, you can learn math by active involvement; it is very strange for someone to learn the subject by merely watching their mentor perform on Tuesday, Wednesday, and Thursdays. Therefore, the homework is the core of the subject and above all, study time is the key to success in Math. In modern science mathematics has become a “basic language”, commencing with precalculus, moving into calculus and continuing into more advanced math.
Calculus is a theoretical outline that provides organized methods for solving problems. These problems are aptly valid to logical geometry and algebra. Hence pre-calculus gives an experience for the mathematical theories, problems, issues, concepts and methods that appear in calculus, including functions, matrices, complex numbers, trigonometry, vectors, and others.
Basic math is truly a sequential process. Students must learn skills in a particular order and it is imperative that they don’t move on to another skill until the previous skill is mastered. This process will also give the student confidence in his or her ability to apply these skills to higher level math.
The problem solving process can be easily summarized. You start with a depiction of a problem that is presented mainly in the form of words. Instead of trying to directly go from words to symbols, you can consider going from words to pictures. Once you get a clear picture, you jump from pictures to symbols. Students generally need to rely on mathematical definitions as they interpret the words of the problem; and, on algebra skills while formulating the equations one needs to solve your problem.
Words $\Rightarrow$ Pictures $\Rightarrow$ Symbols or Symbols $\Rightarrow$ Pictures $\Rightarrow$ Words
Important points to keep in mind while solving a Math problem:
- Prior to a given class, ensure you have looked over the reading assigned.
- If you can’t finish it, at least look it over and get the basic idea of the topic that’s to be discussed.
- Having looked over the study topic ahead of time, you will get far more out of the lecture.
- Then, after the lecture, you will be ready to complete the homework.
- Once this is followed, it will lessen the number of times you leave in a daze.
- Extend your study time evenly over the week, rather than waiting until the day before an assignment is due.
To understand calculus have a background that allows you to use numbers and variables in the background of algebra, equations and functions algebraically, and "real world" applications that use functions to communicate the quantities involved.
The sensible approach to prepare for calculus is:
- Review and restart your understanding of numbers and variables as used in algebra.
- Evaluate and reintroduce your understanding of equations both algebraically and visually.
- Review, renew, and expand your understanding of functions.
- Connect "real world" applications to the equations and functions introduced.
- Introduce problems in calculus when pre-calculus methods can be used for solution.
- Introduce methods from current expertise that will make pre-calculus analysis easier.