# Week 18 – Top 5 things

Over the course of this semester, I have come to learn a lot. I learned that math isn’t always just numbers and finding an answer, sometimes it’s looking deeper at the question and finding solutions to certain areas, not necessarily the end. I (re) learned that mnemonics are so helpful in math and different ones can be used across all units. I learned that I love some units in math and absolutely hate other units. And finally I learned that one bad test score isn’t the end of the world, what’s more, important is how you get back up, wipe yourself off and what you do to improve on the next one. So in honor of the end of the semester and math 11, here is a list of the top 5 things we learned.

1. Converting between Standard, Vertex and Factored Form

Due to the heavy emphasis on graphing in this class, knowing how to convert between the different forms is definitely useful. All the forms have a different purpose, some more helpful than the others. Standard Form is probably the most useless and only really tells us if it opens up and what the y-intercept is, but it’s still important to know. Vertex Form is definitely helpful because as stated in its name, it helps to find the vertex. And Factored Form is helpful because you can find the x-intercepts. And all these different forms help you draw the most accurate graphs.

2. Factoring

I swear knowing how to factor is probably one of the most useful things to have in math 11. So many units use it, so it is necessary to understand. It’ll be used in basically all units and will come up often when trying to find the solutions/roots/x-intercepts/etc. Practice is key to being great and factoring and being sure to know the little helpful hints. The mnemonic “Can Divers Pee Easily Underwater” which stands for common, a difference of squares, pattern, easy, ugly are all things to look for when factoring. Ask yourself is there anything in common? Is it a difference of square? Is there the $x^2$ + x + #? Is it easy (no coefficients)? Is it ugly? If it is ugly it will most likely have a coefficient other than 1 and it will be helpful to use the window/box method to factor.

3. Adding / Subtracting Rational Expressions

This one I put down not necessarily because it’s the most important thing to know in math 11, but because it was important to me. This unit was one that I probably struggled with the most. To me, it was somewhat of a complicated unit, or at least for me. Knowing how to add and subtract rational expressions is a good skill to have, may only be used for one unit but it comes in handy because it’s different than other chapters.

4. Sine and Cosine Law

Trigonometry is definitely one of my favorite units this year and last. And this being one of the only units that you’re allowed a calculator is a huge plus. The sine and cosine laws are very important in this unit and actually very helpful. They’re both in easy to read formats and all you have to do is plug in the numbers that go in the spots. They’re such helpful laws to have and made my life so much easier when solving in the trig unit. Use the laws and you save so much time and extra effort.

5. Rationalizing Denominators

Rationalizing denominators is a weirdly useful thing to know in math 11. It is so important to realize that a radical cannot be left in the denominator spot. And getting rid of a binomial denominator with a radical, you must multiply it using the opposite sign. It’s a bit confusing at first but once you get the hang of it, it’ll help you think more clearly in other units.

In the end, I learned a lot of things in my math 11 class. I hope that they will be useful to me next year when I’m taking precalculus 12. Had a great semester and can’t wait for my next math experience where I can continue to learn.