Unfortunately, I didn’t get through the course Algebra 2 by the end of April. That has been my goal for approximately the past 4 weeks and not achieving it is definitely a bit of a bummer. That being said, I’m 100% satisfied with the effort I put forward to try to finish the course by that deadline. I think I applied a strong amount of willpower to work as hard as I did over the past month. I likely put in close to 100 hours of work! Though I didn’t get through the course in time, the silver lining is that my bigger goal, to finish the following course, Trigonometry, by the end of May, should be achievable since it’s already 75% complete which I only just realized this past week! Wooo!

I’m also happy to report that the Corona virus doesn’t seem to be increasing exponentially any more. I haven’t been nearly as on top of the numbers as I was 4 weeks ago, but it sounds like the number of new cases per day (in Canada anyways) are beginning to stabilize. Apparently a number of the states in the U.S. are going to “re-open” their economies next week which could lead to a second, bigger wave of the virus. It seems there’s no right answer to the debate between what is worse for people, the potential of the virus getting worse or the economy being shut down, and it is impossible to come to the “right” answer. There is no right answer.  I think it’s possible to draw a correlation between unemployment and poverty levels and deaths per capita, but it’s impossible to foresee what correlation between the virus and deaths per capita will be if there’s a second wave. The virus’s affect on the health care system and, in turn, the economy, is impossible to predict, as well. Inevitably, people will look back in hindsight and say it was obvious that governments should have been handled this situation differently, however at this point no one can be sure what is the right thing to do. I’m happy that Canada is still in lock-down mode, however.

 This week started with the unit Modelling which was easy for the most part. The first ~40% of the unit was essentially review on how to manipulate variables in algebraic equations and then plugging certain values into parts of the equations to solve for certain unknown variables. I found this sections quite easy but at the same time satisfying in that I could essentially do it with my eyes closed. When I first started KA I would have struggled with these types of questions which is why it’s so satisfying now to be able to do them without any issues.

The next ~40% of the unit had me once again working through sinusoidal graphs. I was asked to look at graphs of periodic functions and determine the period or amplitude of the function based on the visual representation of it on a graph. I breezed through this section in 30 minutes or so.

I thought I was going to quickly finish the unit but found the last section to be quite challenging and which took me a lot longer to get through. This section of the unit had me work on word questions (my KA arch nemesis) which I always seem to struggle with, and these ones were particularly tough. A number of the questions were probability based which I don’t have much experience with and which I found very difficult. The key takeaways from this part of the unit were 1) always read through the questions slowly and multiple times and 2), before starting the question, always write down the values of each variable that are given as clearly as possible. I also found it helpful to draw out a visual representation of the question when it was possible.

I started the final unit of the course, Rational Functions, on Friday and managed to get through 40% of it by the end of the week. I learned that a rational function is a ratio (i.e. a fraction) of two polynomials. Examples of this would be:

• 1/x
• (x + 5)/(x^2 – 4x + 4)
• x(x + 1)(2x – 3)/(x-6)

The domain of a rational expression is all the Real numbers that can be used inside the function that don’t make the denominator equal to 0. When a Real number makes the denominator of a function equal to zero, it is said that the function is “undefined” for that value. It’s also worth noting that you can simplify rational expressions in the same way you can simplify regular fractions. For example:

• Standard Fraction:
  • 6/8
    • = (2 * 3)/(2 * 4)
    •  = (2 * 3)/(2 * 4)
    • = 3/4
• Rational Expression
  • (x^2 + 3x)/(x^2 + 5x)
    • = x(x + 3)/x(x + 5)
    • = x(x + 3)/x(x + 5)
    • = (x + 3)/(x +5) and x cannot = 0
  • Note: in order for the above rational expression to be true after simplifying, you literally must state that x cannot equal 0.

The last thing I learned about this past week are the definitions of Horizontal Asymptote, Vertical Asymptote, and Removable Discontinuity.

• Horizontal Asymptote
  • On a graph, this is a horizontal line which a function will approach but never actually touch no matter how far you go in the (-) or (+) directions on the X-axis.
  • You’re able to figure out where a horizontal asymptote occurs by inputting positive-infinity and negative-infinity into the highest degree terms in both the numerator and denominator which gives you a general idea of what number on the Y-axis the horizontal asymptote occurs.
• Vertical Asymptote
  • Similar to a horizontal asymptote, a vertical asymptote is a vertical line on a graph at a certain point on the X-axis that a function will approach but never actually touch no matter how far up or down the on Y-axis you go.
  • Occurs when a value in the denominator makes the function equal zero.
• Removable Discontinuity
  • A point on the line of a function where the function is considered undefined. Unlike a vertical aympotate however, the function will not increase or decrease exponentially when approaching a removable discontinuity.
  • When factoring a function, a removable discontinuity is when you have to state that x cannot = z because z would make the denominator equal to 0. It basically means that you’ve simplified a rational expression by factoring the numerator and denominator and then cancelled out an equal binomial in both the numerator and denominator.

The questions I worked through in this section had me looking at a function and picking between 4 graphs that could represent the function based on the functions equation. I had to pick the right graph based on the equation and the the graph’s horizontal and vertical asymptotes, and removable discontinuities. This was quite easy once I got the hang of it and understood what I needed to look for.

Unless the remainder of this unit turns out to be incredibly difficult, I don’t see any reason why I shouldn’t be able to get through Rational Functions (560/1400 M.P.) and Algebra 2 by the end of the week. I’m looking forward to getting through this course especially knowing that I have a truly good understanding of how and why the concepts that I’ve learned about work. Looking back on the past 35 weeks, I certainly feel like I’ve accomplished a lot. The main goal I had for myself when starting this endeavor was to learn calculus and after I finish this course I’ll only have a short trigonometry course and three statistics courses to get through before starting Precalculus. In a nerdy kind of way, I must admit it feels pretty good to know that I’ll soon be able to understand calculus! Which is definitely something I never thought I’d be able to say.