jamdoingmath

[jamdoingmath]

In which we enter the final revival of this blog.

How would you describe your math 6 learning journey?

-math 6 has been a rollercoaster throughout the years, however this quarter things have relatively settled down, from complex derivatives and integrals we enter a new dimension, (literally, the 3rd dimension!) we learn new concepts such as polar coordinates as well as adding a new axis to our regular cartesian graph, bringing us into the 3rd dimension as we learn distance formula all over again. while the concepts are new it brings a refreshing new scene into our math 6 journey.

Which topics did you enjoy the most?

Probably the introduction to polar coordinates, and even to 3d coordinates. Polar plotting and graphing is exciting to see the shapes take form on a new and interesting graphing system.

Like seen in this cheat sheet for polar graphs. The shapes formed by equations can be very visually striking.

What concepts did you find easy to learn?

-3d coordinates since i have had some experience with the 3d coordinate planes through video games and as well as 3d modelling programs like blender it was fairly easier to grasp, that although the classes alloted for the concept were few it was something i grasped quite quickly.

What concepts did you find most interesting?

-It would still be on 3d graphing and plotting. Since its something that i can apply more tangibly in my day to day life especially in my hobbies!

what concepts have you mastered the most?

polar graphing probably! It was something quite new but i had to learn properly, its quite tricky but also fun!

what concepts have you mastered the least?

Polar to cartesian and vice versa conversion in its the most challenging for someone as arithmetically challenged as me. While the formulas are not too hard to memorize its easily tricky and can get complicated at times. Especially with the presence of trigonometry

All in all i would say that my math 6 jourmey has been one full of learning. i am especially thankful for my teacher the one and only the man the myth the legend sir Jed de Leon!! As well as my fellow peers and classmates in math 6 who have helped me a lot throughout my journey. While its sad that this is the last blog of this account, the completion of this journey is definitely cause to celebrate! As well as the future that is to come in my mathematical misadventures!

[jamdoingmath]

Math Qt2 Project

In which i revive this old blog for the purposes of fulfilling my quarter 2 project for math 6.

(a) How would you describe your Math 6 second quarter learning journey?

                My math 6 learning journey can only be described as turbulent, while I would initially understand certain topics as it gets more complex the less likely I am to follow. While I do find math interesting I find myself struggling to retain a lot of information at times, leading to a lot of difficulty through my math journey. Surprisingly this quarter I scored quite well on the first LT, however I cannot say I am as confident for the second.

(b) Which topic did you find most enjoyable? What made it enjoyable for you? Provide clear images of solutions to sample problems or exercises on the topic.

                Integration of algebraic functions by trigonometric substitution was one of the topics that comes to mind. How it often comes together as terms are substituted and flipped around to cancel each other forming a much more simple and easy to solve problem. It feels as though it sort of reflects my thought process around problems sometimes, often taking a rather roundabout solution, substituting terms, and creating a seemingly more complicated process but one that, if familiar with, can be navigated easier, often ending up distilled into a simpler form.

 (c) Which topic did you find most challenging? What made it challenging for you? Provide clear images of solutions to sample problems or exercises on the topic.

                Integration of Rational Functions Using Partial Fractions. While trigonometry shall always give me difficulty, partial fractions in particular caused a bit of a problem especially during the second quarterly test wherein a problem relating to partial fractions appeared however I was not able to solve it due to a lack of mastery of the subject matter as it was a problem that I’ve never encountered before.

 (d) What concepts did you find easy to learn? What do you think made them easy for you?

                Integration by substitution. I find the substitution part interesting. Its sort of like focusing on a bigger picture before focusing on to smaller details, which can make a complex problem look simple. However, it comes with its own challenges as well which makes it all the more interesting to tackle especially in terms of its versatility as it can be used multiple times to solve a problem. Distillation as a problem-solving method is always interesting.

 (e) What concepts did you find most interesting/ inspiring? Why do you think so?

                Integration of Algebraic Functions Yielding Inverse Trigonometric Functions. Maybe it was because I was not present for one of the meetings wherein this was discussed and that’s why it alludes me. However I do really find the concept interesting. As well as the patterns that can be found within it.

(f) What concepts have you mastered the most? Why do you think so? Provide clear images of solutions to sample problems or exercises on the topic.

                Integration by Substitution, it is one of the core concepts that needed to be mastered in this quarter of math6 and the concept forms the guidelines for a lot of the concepts this quarter.

g) What concepts have you mastered the least? Why do you think so? Provide clear images of solutions to sample problems or exercises on the topic.

                Trigonometric integrals. The amount of memorization should prove a challenge on top of the given difficulty of trigonometry.x

(h) What quick notes do you have for:

i. your teacher.

                Thank you for your patience in instruction, I hope we can have more hands on and productive learning done together.

 ii. your classmates:

                Thank you to all my classmates and peers who have helped me get further in my journey.

 iii. yourself

                To do better next time, learn form your mistakes and to not put off practice.

[jamdoingmath]

WEEK 4.8

CONGRATULATIONS! CONGRATULATIONS!! CONGRATULATIONS!!!

important things must be said 3 times! you have reached the week of the final longtest and thus the finale of this math journey! Thank you to everyone who has helped me understand these topics that i ahve struggled with and special thank you to Sir Jed my math 5 teacher who made this all possible!

[jamdoingmath]

WEEK 4.7

The final week before the second long test and it expands on the past 2 lessons on functions and their first and second derivatives. this week we learn to sketch graphs of the functions from their derivatives!

rough (and inaccurate) illustration to demonstrate the relationships of the graphs of the function and the first and second order derivative:

[jamdoingmath]

WEEK 4.6

This week teaches us about concavity and determining concavity from the second derivative. and expands on the topics discussed in the previous lesson regarding gleaning information about a given function from its first and second derivatives.

mnemonic/assosciations to help remember second derivative meanings:

[jamdoingmath]

WEEK 4.5

This week sees to the extrema of functions using the first derivative test. in which we learn how to glean information about a given function through its derivative.

[jamdoingmath]

WEEK 4.4

LONGTEST WEEK!

LONGTEST WEEK!!

LONGTEST WEEK!!!

important things must be said three times. this week is a longtest week and it also marks the halfway point for the quarter

[jamdoingmath]

WEEK 4.3

in which it is the 3rd week. This week sees to lessons on related rates, an expansion of the previous week's lesson on rates of change, this weeks lesson talks about rates in relation to one another, such as how fast the distance between you and a moving object is increasing as it moves further away. this also continues on applications of derivatives and further expands on calculation of rates.

[jamdoingmath]

WEEK 4.2

Week 2 of 4th quarter This week tackles change in rates and rectilinear motion, this applies to many different subjects from physics, biology and even chemistry, for example one could calculate the rate at which an object moves through space or the growth rates of bacteria. This lesson is also an application of the lessons on derivatives from the previous quarter. (i struggled)

[jamdoingmath]

WEEK 4.1

The start of the 4th quarter! This week we learn about optimization. Optimization is the mathematical technique for finding the extremes of a given function. subject to several constraints. Put to use here are several tools such as colsed interval method, first derivative test, and second derivative test, fortunately the skills and lessons taught in the previous quarter will help greatly in this lesson.

[jamdoingmath]

Week 3.8

This week is the week in which longtest 2 is held, and is the culminative assessment of lessons learned in previous weeks.

[jamdoingmath]

Week 3.7

Higher Order Derivatives

This week Discusses higher order derivatives in which differentiation is applied to a function multiple times over.

[jamdoingmath]

Week 3.6

Implicit Differentiation

This week discusses implicit differentiation which discusses the relationships of each side of an equation by treating the variables as functions of the other. This also uses chain rule a lot which was discussed in depth week 3.4

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Week 3.5

Continuity and Differentiability and Common behaviors of graphs of non differentiable functions. This lesson allows further understanding of Differentiability and Continuity of functions in a graphic way and allows us to visualize differentiation of funtions through graphs.

This Week was also when long test 1 was held

[jamdoingmath]

Week 3.4

Week 3.4 Further discusses the Chain rule previously discussed in week 3.2 this is one of the most frequently used theorems in dealing with derivatives, thus deeper understanding and mastery allows easier time in evaluating derivatives,

[jamdoingmath]

Week 3.3

Week 3.3 is on the Derivatives of transcendental functions.

this teaches us how to evaluate derivatives of exponential, logarithmic, trigonometric and inverse trigonometric functions. the lessons in the previous weeks such as the rules of differentiation can help in this lesson.

[jamdoingmath]

Week 3.2

Rules of Differentiation

This week discusses the rules to be followed in differentiation.

such as the power rule, product rule, quotient rule, and chain rule. these continue to serve as fundamentals for the continuing lessons onward