Week 24 – Feb. 10th to Feb. 16th

Did I make a “solid dent” in the unit Circles this week as I said I wanted to at the end of my last post? No. Am I happy with the effort I put in this week? For the most part, ya.

It took me much longer than I expected to get through Analytic Geometry than I expected. It took me 4 attempts to pass the unit test which I got through on Thursday. Looking back through my notebook however, I wrote out 21.5 pages of notes this week which I think is pretty respectable and a good indication of where my time went. As a heads up, having spent most of the week working through exercises and not watching videos/learning many new things this week means that this will be a relatively short post.

I picked up where I left off in Analytic Geometry working through questions involving the distance formula, i.e. the Pythagorean Theorem. After spending many hours working on these questions I became much more confident with the equation, recognizing when and where certain numbers should appear in the formula based on the graphs which made things much. The distance formula is d = {(x’2 – x’1)^2 + (y’2 – y’1)^2}. Similar to times in the past, I made most of my mistakes on these questions by not reading/writing down the correct X, Y coordinates, by incorrectly reading my own notes, getting simple addition/subtraction wrong that I tried to do in my head, or other “simple”, easily avoidable mistakes. I almost always did the “tough” math correctly (i.e. squaring numbers, taking the square roots of numbers, etc.). The lesson I need to take away from this is to slow down when I go through questions and make my notes neater.

The unit then got into parallel and perpendicular lines. For the most part, everything that came up in this section was review for me apart from learning that if line B is perpendicular to line A, line B will have the negative inverse slope of line A. In an equation, it is denoted as m vs -1/m. I’m unsure at this point if an “inverse” slope is the same thing as a slopes’ “reciprocal”. They seem to be the same thing as far as I can tell. 

I got through 6 videos and one exercise in the unit Circles. The videos I got through could have been considered a “glossary” for the different parts of a circle. I was already familiar with many of the terms/definitions but some new ones I learned included:

  • Tangent Line
    • A line which intersects a circle at only one point.
    • Imagine a ball sitting on the ground. Only one part of the ball is touching the ground. The ground could be considered the tangent line.
  • Secant Line
    • A line that goes through/intersects a circle at two points.
  • Chord
    • A line segment that runs across a circle connecting two points on the circle’s circumference.
  • Arcs
    • Minor Arc
      • Denoted with two letters with an arced line above them (ex. AB with an arced line above it).
      • The shortest distance between two points on the circumference of a circle (i.e. <180 degrees).
    • Major Arc
      • Denoted with three letters with an arced line above them (ex. CDE with an arced line above it).
      • The Longest distance between two points on the circumference of a circle (i.e. >180 degrees).
  • Unit Circle
    • A circle on a graph with a radius of one unit.
  • Central Angle
    • Any angle that’s created by going from one point on a circle, to the vertex of the circle, then to another point on the circle.
  • Arc Measure
    • The measure in degrees of any defined central angle.
  • Arc Length
    • The length of a section of the circumference between any two points on a given circle.
    • Calculated by using the arc measure of those two points and the size of the circle (I haven’t learned how to do this yet).

Week 26 is coming up quickly. Getting through Circles (80/1700 M.P.) before the half-year mark should be doable but will likely be a bit of a grind. There are 38 unwatched videos left in this unit and 16 exercises to get through, not to mention the unit test and then the course test to finish after that. I will be disappointed in myself if I don’t get through the High School Geometry course before Week 27. I think that potential disappointment will fuel me to work hard and get it all done in time. I just hope that I can get through everything first try and won’t have to CIRCLE-back on anything!!

…… I’m sorry.