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### Tips for Succeeding in Calculus

The key steps that students sometimes miss when learning a new subject are:

• Building a strong base.
• Multiple exposures to each new concept.
• Using the homework to help you learn instead of just trying to get it done.

#### Building a strong base

It is often said that the most difficult thing about calculus is the algebra. Calculus builds heavily off of algebra and it is important that you have these skills mastered so that you can succeed in calculus. Some key algebra topics include:

• Manipulation of fractions including multiplying by a conjugate
• Factoring
• Long division with polynomials
• The unit circle and trig function properties
• Solving absolute value inequalities
• Solving rational inequalities
To help you review these skills the Math Department has created some documents and practice quizzes to refresh your memory which are available HERE.

#### Multiple exposures to each concept

Your goal is to put each calculus concept to memory so that you can recall it on quizzes/exams/final/life as need be. To do this successfully it is recommended that you get multiple exposures to each concept to really help them stick. For each section you please consider trying:

1. Try a WeBWorK problem or two to get motivated to learn the material. Having a problem in mind that you want to be able to solve helps to see purpose behind what you are about to learn.
2. Watch a video or two provided on the resource page to see the material once before going to class.
3. Go to class to gain a more in depth understanding of the material.
4. Try the rest of you WeBWorK problems.
5. Go to the Math Learning Center or your professor's office hours if you get stuck.
Before a quiz or exam you should make it your goal to be exposed to each concept on at least 4 different occasions.

#### Using the Homework to help you learn instead of just trying to get it done.

Too often students are focus on getting the homework done when in reality it is meant to be a learning tool. Try to take away something from each problem. If you solve the problem correctly try to summerize what you learned from it. If you can't solve a problem try to pin point exactly where you get stuck so you can study that topic more. For instance:

Example: Suppose I have the problem: $\displaystyle\lim_{x\to2}\left(\dfrac{x^2-4}{x-2}\right)$.

• I try plugging in $2$ on top and bottom but that just gives me $\, \dfrac{0}{0}\,$.
• A question I could write down is: How can I cancel the 0's on top and bottom to get a real number answer?
• After seeing some more problems and reading in the book I find out the factoring is the key.
Notice that I didnt even bring up the answer (it's 4 by the way). The answer won't help me solve the next problem or the problem after that. Its the lessons I learn like "factoring is the key" that will really help!

This example is maybe too easy but it's the idea that is powerful. By determining exactly what it is that you don't know you can fix it! The key is to make the homework work for you so that you can be extra prepared for your quizzes/exams/final/life.