This week I managed to get through two units, Foundations and Algebraic Equation. I’m happy to say I passed each unit test with 100% on the first try. I have six more units to go in the Algebraic Basics course.
The Foundations unit was about 60-70% complete before I began it. As mentioned in a previous post, the units/courses overlap which is why a good chunk of the Foundations unit had been completed before I opened it up. This unit reintroduced me to finding the area of both a triangle and a circle, as well as the circumference of a circle. Useful formulas to remember for those types of equations are:
- Circumference/Diameter = Pi
- C = Pi * D
- D = C/Pi
- C = 2 * Pi * r (radius)
- Area of circle = Pi * r^2
- Are of a triangle = Base * height/2
The Foundations unit also covered Order of Operations which was very helpful to go over. The acronym used in Order of Operations is PEDMAS which stands for 1) Parenthesis, 2) Exponents, 3) Division & Multiplication, and 4) Addition & Subtraction.
In Algebraic Expressions I worked on questions using variables. I practiced manipulating equations to solve for the variable, when possible, or simplify the equation. This included combining like terms (ex. -4q + 2q = -2q), using the distributive property (ex. 3(2x + 3y) = 6x + 9y), and simplifying or solving nested fractions (ex. (3 + 3/a)/(3/a) = a + 1). Nested fractions were tough but they were also the most satisfying once I started getting the hang of it. I also learned that if an equation has a negative sign in front of a set of parenthesis, it’s implied that there’s a negative one before the parenthesis (ex. 3 + -(2x * 4) = 3 + -1(2x * 4)).
On Friday I began the unit Linear Equations and Inequalities. This unit was also ~50% completed before I started it. Although I didn’t get through many new questions, one thing I already learned is that when you multiply an inequality by a negative number you must flip the greater-than/greater-or-equal-than or less-than/less-or-equal-than symbol (ex. 5x/-3 < 9 = 5x > 9*-3). Although I did watch a video about it, I don’t have a strong intuitive understanding of why this happens so I’ll need to watch more videos and practice more questions to get a better understanding of this concept.
My goal is to get through Algebraic Basics in the next 3 weeks. That would mean finishing 2 units per week which I think is doable. My minimum goal is to do 1 hour of KA each day, Monday to Friday but, in order to finish the course in 3 weeks, I think I may need to dedicate a few more hours on Fridays to get it done. Most people like to go out on Friday nights. I stay home and do math. Cool!