There is much apprehension from students taking Calculus. It seems that for many people, "Calculus" is synonymous with "difficult." However, any teacher of Calculus will tell you that the reason that students are not successful in Calculus is not because of the Calculus, it's because their algebra and trigonometry skills are weak. You see, Calculus is really just one additional step beyond algebra and trig. Calculus is algebra and trigonometry with limits and limits aren't really that hard once you figure them out. There is often only one step in the problem that actually involves calculus, the rest is simplifying using algebra and trigonometry. That's why it is crucial that you have a good background in those subjects to be successful in calculus.GOOD NEWS:
More good news about calculus is that we live in the real world, we don't deal with imaginary numbers (except for section: complex number). Also, in Calculus 1, we don't deal with logarithmic or exponential functions, which seem to give some people great difficulty. The purpose of this post is to help identify some of those areas where you will need good algebra and trigonometry skills so that your calculus experience can be successful, pleasant, and rewarding.ALGEBRA SKILLS NEEDED
- Factoring - You need to be able to factor expressions and equations like it was second nature to you. Many of the problems in calculus will involve finding the roots of a function and for the most part that means factoring. Don't just concentrate on polynomial factoring, either; you need to be able to factor expressions with rational exponents. Here is an example of factoring out the greatest common factor, which is involves taking the smallest exponent on all of the common terms.Know how to recognize and factor the special patterns of the difference of two squares, the difference of two cubes, and the sum of two cubes. Know that the sum of two squares usually doesn't factor in the real world.
- Completing the Square - Another task that you will be called on to perform occasionally is completing the square. You need to be able to do this with both an equation and an expression. Examples of both are shown below.
- Simplifying Expressions - Much of your time in this course will be spent simplifying the results of an expression that you obtained. Know how to combine similar or like terms and know the properties of exponents like adding exponents when multiplying factors that have the same base or multiplying exponents when raising to a power.
