Top 5 things I have learned in Precalc 11

1. Graphing: Is the number one thing that I learned. This semester, I found graphing straightforward and eyeopening.  I learned that once you find the vertex, you just have to follow the 1,3,5.. pattern and multiply the pattern if it has a stretch or compressed value (number in front of the ). I learned that you could find the number of solutions which is also the x-intercepts, as well as the vertex which is a key component to graphing. This made graphing absolute values easy as well as reciprocal graphs. It was really cool to see I could graph all these different types of graphs with just some information given.

2.  Substitution: Solving systems with substitution was another thing I learned in precalc instead of drawing the graphs out. I finally knew how to solve systems algebraically which made me feel more knowledgeable about solving systems and it became a useful tool if I didn’t have graph paper to graph out the systems.

 

3. Completing the squares: I never realized how important completing the squares was. We used it a lot during this course such as changing general form into standard form to get the vertex, to find the axis of symmetry, and to solve an equation. It does take awhile when it comes to solving an equation, however, it still is a useful tool when it’s an equation is unfactorable and I found myself using it a lot when I had to find the vertex.

4. Trigonometry: The most important lessons I got out of this chapter is the Sine Law and Cosine Law. They were very useful when it came to scalene triangles and I found solving sides and angles a lot easier than I thought it would. I am now able to tell when to use Cosine Law and Sine Law (Cosine – when three sides are given or two sides and a contained angle are known; Sine – when two angles and one side are known or two sides and a non-contained angle are known).

5.  Square roots : Whenever we were solving an equation and we had to square root both sides to get the variable by itself, there was both a positive and negative sign in front. Before, I always treated a square root as having one answer but now I realized that there are both positive and negative values (only when I add in a square root but if there is already a square root, you take the positive roof of it). Even though it is a simple concept, this was a big eye opener for me.