Week 18: Top 5 things I have learnt in Pre Calculus 11

The most important things in Pre Calculus 11 for me have been:

1. Factoring: Reviewing and adding on to previous knowledge. This one was super important throughout the semester because it showed up in pretty much every chapter, and you had to be able to factor immediately or find a way to the simplified version.  For me, the 4 square chart was very useful. As well we learnt how to complete the square and use the quadratic formula when dealing with quadratic equations, which was huge when an equation to factor nicely.

4 square chart:  

 

(3x+2)(x+4) and from here you can use the zero product law to find the solutions. So, (3x+2) x=  and (x+4) x=-4.

Adding on to factoring, the hint CDPEU (Can divers pee easily underwater) helped to remember the steps.

C= is there anything common

D= Is it a difference of squares

P= Does it have the regular pattern

E= Is it easy

U= Is it ugly.

2. When factoring does not work, we learnt two new ways to find the solutions which is very helpful, completing the square and the quadratic formula. Both of these are used for quadratic equations and need to be in Where y = 0. I thought these were important because they were different ways to get to the solutions or x intercept values. And these x values have been super important throughout the year as they were mainly what we would be looking for, whether they were defined as x intercepts, solutions, and roots.

Quadratic Formula:

Completing the square:

 

3. Graphing: Lines and Parabolas. This was also a huge part of the year, as we needed to be able to graph lines as soon as we saw the equation and learning to graph parabolas was a big part of the year and related to multiple chapters afterwards.

Linear Line Form: y=mx+b. Where m is the slope and b is the y intercept.

Standard Form: The best form for graphing a parabola. y= a(x – p)2 + q, where (p,q) is the vertex of the parabola.

 

4. A helpful tool we used this year was finding the discriminant to know how many roots or solutions there are in a equation. To do this you take part of the quadratic formula, and input the correct numbers. If your answer comes out negative there are no solutions, if it comes out as 0 it has one solution, and if it is positive it has 2 solutions. TO do this you need the equation to be in general form.

 

5. Reciprocal Functions: These were new and interesting and pretty difficult for myself, but once I understood them, they were very interesting and I was kept being told I will see this next year in Pre. Calc 12 and I want to be able to understand this to do well next year, so I worked hard at this for that reason.

When graphing Reciprocal Functions. There are 4 steps to graphing them,

1. Graph the Function. Linear or Quadratic
2. Find the invariant points. The 1 and -1 on on the y axis
3. Draw in the asymptotes. The horizontal one where y=0 and the vertical one which is the x intercept.
4. And lastly, you draw the hyperbola, in which you start the in the invariant and draw as close to the asymptotes as you can but never touch as the lines are converging.