math6blog

[math6blog]

Fourth Quarter Synthesis and School Life Synthesis

First I would start with the required questions.

Fourth quarter was fun. For the last short quarter of my Pisay Life, I guess this is the most fun I had in math, primarily because this was the last quarter of PSHS math I would sit in. The lessons were also not that difficult and I was able to enjoy the company of my classmates without the stress of not understanding the lesson.

The topics also was one thing that contributed to my enjoyment. For the most enjoyable one it was 3D, because of the extensive background in 2D and the use of my imagination. My mind wanders sometimes and with the use of my imagination it was able to stay in place this time.

For the most difficult topic, it was Polar equations, because I never got the handle of sin cos and tan. Although, the use of the calculator was helpful, the lack of experience using polar coordinates didn't help one bit.

And from the answers above I think it is obvious 3D was the easiest to learn because of the background in 2D and my imagination. Polar was inspiring because of the art it could create. I thought of doing polar art for the project but I am not artistic enough for it nor am I smart enough in math for me to find equations for it.

When it comes to mastery, it would also be 3D. I mastered it the most because of it being 2d plus Z which is just 1 step more than 2D.

For what I have masted the least, I think it is polar equations, I still had difficulties describing the figure and resorted to graphing them in the Long Test which may have contributed to my low score.

And finally notes. For my classmates, I hope you succeed in the future and continue being yourselves don't change because it is what some people want change because you want it and it makes you better. I also hope to meet you sometime in the future and share stories.

For sir Dex, thank you for sharing your knowledge with us for the past academic year. I though of going to Level 1 at the start but knowing you were going to be my teacher I shockingly chose to stay, good reviews from other batches. Thank you for being patient with me, especially in times where I seem to not understand anything, although most of those times I slightly understand it but forget during the exams.

And for myself, keep your head held high. Confidence in what you do is important to succeed, no matter what you have stored in your brain if you don't share it you will never know if your right or wrong, if it could help someone or not, if it is useful or not. Life is too short to keep things to yourself, if you think it is right, or if you need help don't be scared to speak up.

In my six years, I failed to realize to that at some point you have to put yourself out there, the opportunities I missed, the people I could have interacted with, all just a what if. Maybe it wasn't the right time, maybe faith doesn't exist, but who knows maybe we all have a predestined path. I hope to handle the sails of my life as I exit high school, and control where I want to go. Like my favorite line from the poem Invictus: "I am the master of my faith, I am the captain of my soul". I hope to live by it some day.

Cheers to a fruitful six years!

Polar Exercises

3D Exercises

[math6blog]

Week 3 and 4 and Exam: Three-Dimensional coordinate system

Its like cartesian system plus z. Which is easier than polar because circles have pi in them which is not fun. For some unknown reason even to myself I actually was able to imagine the 3D figures which helped in my highest scoring LT so far. More than 100% woooo. But it was like a quiz so I don't know if it counts.

The other parts of this lesson is distance formula, which is different because it has z and the sphere, which was confusing until I actually remembered the working equation for a sphere in 2D and added z. In all this lesson was 2D plus Z.

The last exam was memorable, maybe for all of the wrong reasons. 1 because I actually was able to write because I used a table instead of an armchair, being left handed sucks sometimes. 2 the fire alarm went off in the middle of the exam. It didn't affect me because I was just contemplating my life choices after I finished my paper and refused to pass it, but still it broke me out of my thoughts of my future and college.

It was a good six years, could have been better if it wasn't online for 2 years.

[math6blog]

Week 2? I think: Polar equations and Graphs and First LT

This was an extension to the first topic. Using desmos helped in this especially with the ability to copy paste and edit the value inside without removing the equation. Although, the graphing was a bit difficult especially with my drawing skills, the graphs were still understandable enough.

It was a bit difficult to apply, because my brain gets fried most of the time, and thinking about stuff in polar after years of using cartesian is confusing sometimes. Entering the wrong values in the calc is sometimes an issue.

This was also the last lesson for the first LT that I partially failed. Some people call it pasang awa while I call it, my stupidity. Anyways, I don't like taking exams in the physics lab never really passed in any exam I took in there. Which results to low scores for the first LT for the whole year. The mental block from physics 1 is insane.

I could have also prepared better for the exam, but juggling things is not my cup of tea and with conditioning for mt. pulag on going, of course I would choose to put time in the thing that requires less brain power. Which has been a mistake i have been doing for six years, but what is life without fun. College. Which is why I am having the most fun now because the future looks dull, which is what I say to myself to cope for my stupidity and lack of effort.

[math6blog]

Week 1: Polar Coordinates

To start the fourth quarter we learned about polar coordinates. Although the template is not new to me, the system is. It didn't take much time to understand, especially with a background in using the circle template thing from grade 10.

Funnily enough, I forgot how to use it, especially the distance between the lines, I clearly did not do well in radians. But with face to face classes I understood it better, especially with the calc.

Desmos was very helpful, didn't need to change the whole equation every time.

[math6blog]

Quarter Synthesis

This third quarter learning journey was like a roller coaster full of ups and downs. The ups were mainly due to me understanding the lesson and how the forms worked and the downs were most of the time due to me realizing that my grade this quarter will be decided by my algebra and arithmetic, both questionable. I guess I need more practice and better stress management when doing exams.

The lesson I found most enjoyable was center of mass of a plane region, I guess because it was more simple compared to center of mass of a rod and it doesn't involve pi like the disks, washers, and shells.

Although, the lessons in this quarter were easy to understand, the lesson I found most challenging was center of mass of a rod, because in some questions we would have to find the linear density and the function representing it, and it was more difficult than I expected.

The easiest was the disks, because it was one simple equation and plug the function in it. The fact that it was one equation made it easier, although if the function is hard to integrate i give up sometimes. The hardest is the center of mass of a rod, especially if the linear density is not given. If the linear density is given it is easy to solve but that doesn't happen most of the time so it was difficult.

I mastered the disks and washers the most. Because the disks and washers are just 1 equation and larger- smaller. the equations were also easy to remember.

While I mastered the center of mass of a plane the least, probably because I am bad at graphing and sometimes my writing is confusing. Although the lesson is enjoyable the sheer amound of equation memorization is difficult for me especially in times that nothing really is entering my brain nad staying there.

For myself, practice algebra nad arithmetic, and even simple integration. In most of hte long tests this is where I made mistakes and writing. Write properly next time. Use your time wisely as well, stop and think if you have time it will save ou rushing if you notice the mistake early.

For my classmates, thanks for helping me through third quarter, I don't know where I would be without you guys.

And for my teacher, thank you for noticing if I am spacing out in class to return my focus back to the subject at hand.

Finally, what have I learned, I need practice in algebra and arithmetic, which is funny because I have been doing it for years, overconfidence bites back sometimes, most of the time, and at random times, What am I saying? Anyways, stay humble, stay focused, and stop spacing out. Also be sure to fix your writing, we can't repeat mistakes.

Gubye,

Jusip

[math6blog]

Long Test 2

I failed, my writing is bad. I got the proper limits for the last question but my one looked like 2 so instead of -1 to 2, I solved for -2 to 2. And everything was wrong, I realised it in the last 3 mins and I couldn't change it, so I accept my faith to fail this lt. May the Gods have mercy on me.

[math6blog]

3.4 Center of mass of a rod and 3.5 Centroid of a plane region

Another plug and play, although I had difficulties finding the function for center of mass for a rod, I think with proper practice and going back to the lessons of FYP I think I can remmeber it. The center of the plan region is also plug and play, its weird to say plug and play, but with two derivatives there is more room for error. The lessons were easy to understand although to execute them is another question because mistakes in algebra and arithmetic can make the answer wrong some way or another. I also learned that if the figure is symmetric solving one can give both the answers. that the blog Gubye!

p.s. I forgot how to solve for the power with fractions, but before the test I got reminded of it.

[math6blog]

3.3 Arc Length

Another summation. I guess this quarter really is based on skills on how to get derivatives. Although, the lesson was fine, I still need more practice doing simple integration, especially IBS and IBP. Also, I should remember how to integrate roots because sometimes the arithmetic gets me in the end.

P.S. I relly need to practice my arithmetic and algebra

[math6blog]

Long Test 1

I failed according to my standards. 22/30 and I failed because I couldn't do integrals properly. Also my arithmetic caught up to me I guess. I need more practice especially in trigonometric sub, and some simple arithmetic. I hope to do better on the next long test. p.s. I think I didn't I like saving these in drafts then add pictures at the end of the quarter but after that second lt I don't know if I did well in math this quarter.

[math6blog]

3.1 Volume of solids by slicing, washers, and disks and 3.2 Volume of a solid of revolution by cylindrical shells

Fist lessons this quarter, I don't know how to feel I guess mga grade in math is mid but compared to my classmates is low. Although, I have the ability to underperform most of the times when I don't put my mind to it. Anyways firsts lesson, which is purely plug and play. The lesson although "easy" relies on the fact that I should be able to get derivatives properly which is sometimes questionable. I guess I need more practice. Although I liked the first lesson more because it had more simple derivatives the second lesson was by far faster if the functions were easy enough. I had this habit of forgetting dx and dy so I had bars on my scrap paper showing me what was dx and dy. Overall, the first two weeks were fine but I need more general practice.

P.S. I learned that I have deficiencies on Algebra and arithmetic when under pressure

[math6blog]

Quarter Synthesis

This quarter was a rollercoaster and I hope that the high was not the first quarter and it is all downhill from there. There were small victories, big defeats, but the ride still goes on.

The most enjoyable lesson was the first lesson because it was the easiest so far. The second lesson was also fun, uvdvu, that is the only thing I remember from that.

I found trigonometric Identities most challenging, I guess I can't memorize much. There are also a lot of rules to follow and to remember so it was hard and I still don't fully understand it.

The easiest to learn was Inverse circular functions and trigonometric substritution. It was purely memorization and with the creative mnemonics some batchmates made it was easier to remember. It being the most easiest to learn it is also the lesson/s I have mastered the most, although when trigo identities are involved everything is thrown out the window. I may do inverse circular functions and trigo substitution right, when trigo identities are involved in the end I fail to get it right most of the time.

And lastly trigo identities, is the lesson I have mastered the least. I guess with all the brainpower it needs I lack most of it.

Quick notes:

For myself - meditate, self-care, practice, practice, practice, you let yourself slip a lot this quarter and it affected your grade by a lot. Also stop putting the blogs in the drafts. I just noticed it earlier. Don't be ashamed to ask for help

For teacher - Sir, I promise I learned a lot, it may not seem like it but I actually did.

For classmates - Math wouldn't be as fun as it is without you guys <3

Skadoooosh

Gubye!!!!!!

[math6blog]

Quarter 2: Lesson 6: Partial fractions

Partial fractions, this lesson was filled with rules but if you understand the rules then I guess it would be easy. I worry over my skills on doing systems of equations though. It was a weakspot back then and probably now. I guess I need practice.

[math6blog]

Quarter 2: Lesson : Inverse Circular Functions

This lesson was similar to the last one. And like the last one, it relies heavily on memorization. Practice will help a lot for the second long test but I hope I remember needed trigonometric identities.

Anyways this along with the last lesson was fun and easy to learn. We also had a thought experiment and solved the same problem using this and the last lesson and we got the same answer, well one solution took 2 minutes more but it works.

*I set up the scanner wrong.

[math6blog]

Quarter 2: Lesson 4: Trigonometric Substitution

I don't like triangles and trigonometry. This lesson is filled with a lot of cancellations. Although it is slightly easier due to memorization of forms and thats it. Although remembering trigonometric identities still is a big part of the lesson. And I forgot half of them. This was one of the easier lesson and a bit of practice will help especially with the memorization.

[math6blog]

Quarter 2: Lesson 3: Trigonometric Identities and Long Test

Trigonometric Identites, back to memorizing. I can only hope for these identities to be in the cheatsheet but that is a piper dream. So what I have learned tan^2x = 1 - sec^2x and sin^2x + cos^2x = 1. That is all I remember but I hope I don't forget in the long test. I think I can solve trigonometric identities, I can only hope. I still don't get sec^6x thought. I lose braincells after ^5. Its easier if there is both tan and sec or sin and cos in the same equation, having only one surprisingly complicates things.

Post Note: I failed the long test and I refuse to look at it. I want to learn from my mistakes but thinking about it I knew my mistakes the moment I left the room and I got the answers from my friends and I still don't understand Trigo Identities with pressure. Without pressure though I guess it is easier. I have to relearn that skill again sometime, working under pressure.

I think what made it hard was lack of practice, this quarter has been a downtrend for me, maybe holiday blues or something but I hope to get over it sometime. I realized I perform based on my mood, when I am feeling great I perform okay but when I am down everything is affected. We live and we learn, I mean failure is not the end of the world. I am still alive and kicking so I'll do better next time I hope.

[math6blog]

Quarter 2: Lesson 2: Integration by Parts(IBP)

I don't know what to say. I don't understand what was happening but anyways; uv-dvu I guess? U derivative and v antiderivative. Pick what is easier for you. Its just dividing the equation to make it simpler, if simple exists in math. And that is all I remember, I guess this is important for the next lesson, if I survive til the next lesson.

It is simple once I internalized it and I hope to pass the long test. After the next lesson.

Why am I in level 2? I don't know

[math6blog]

Quarter 2: Lesson 1: Integration by Substitution(IBS)

I hope the whole quarter was this easy. It's just U substitution all over again. I guess I have to know derivatives and basic algebra but that is easy, I hope, I guess. Well it was enjoyable at least especially with the cheat sheet and not really needing to memorize antiderivatives.

I had some difficulties with ln, I always have difficulties with ln, but with the cheat sheet it is fine.