Freshman Year Math - Algebra 2
Fractal Cuts - Sequences and Series
Based off of our education of sequencies and series, we constructed fractal cuts. In order to construct a fractal cut, you basically just have to cut and fold paper. The same pattern is reiterated in many generations at a fraction of the size. I was partnered with Sean and our pattern was to measure halfway into the cell and cut halfway up the height. Each generation's size was one quarter the size of the previous generation.
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Quote Reflection
"The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful." - J.H. Poincare
I agree with this quote. If you are someone who is going to study math your whole life, you better enjoy it and find it beautiful because you're going to be spending a lot of time with it. Personally, I think math is simply amazing. Math can be such a complicated subject to study, especially in the advanced level. The pure fact that individual people discovered the rules that I learn today is shocking to me. I think it would be extremely difficult to ever discover a mathematical rule that hasn't ever been thought about before. The study of Geometry is very beautiful to me. The shapes and angles that are required to make a simple design are amazing. I thought it was beautiful to figure out all of the rules to the lines and angles of the shapes that I see everyday without noticing it.
I agree with this quote. If you are someone who is going to study math your whole life, you better enjoy it and find it beautiful because you're going to be spending a lot of time with it. Personally, I think math is simply amazing. Math can be such a complicated subject to study, especially in the advanced level. The pure fact that individual people discovered the rules that I learn today is shocking to me. I think it would be extremely difficult to ever discover a mathematical rule that hasn't ever been thought about before. The study of Geometry is very beautiful to me. The shapes and angles that are required to make a simple design are amazing. I thought it was beautiful to figure out all of the rules to the lines and angles of the shapes that I see everyday without noticing it.
Temperature Lab
In this lab we tested the exponential decay of the temperature of hot water. First, we connected a probe to my calculator (TI-84). The first step was to find a constant room temperature. Then, we put the probe into a cup of hot water for one minute. Immediately following the one minute, the probe was taken out of the hot cup of water and allowed to cool down while the program that was preinstalled on the calculator graphed the data collected. Now that we had the data, we attempted to write a function to fit the data. Our equation was a little off from the actual data, but that was to be expected. We used the calculator to find the exponential regression to fit the data, using the room temperature as an asymptote for the graph. Overall, we found three equations to fit one set of data and we applied logarithmic functions to a real life situation.
Chapter 7 - Exponential and Logarithmic Functions
In this chapter we learned about exponential and logarithmic functions. We learned how to add, subtract, multiply and divide both exponential and logarithmic functions as well as graph both exponential and logarithmic functions. We also learned to convert logarithmic functions to exponential functions. This is my favorite chapter that I've learned so far this year. I liked this chapter because it was completely new information for me. I had never learned logarithms and it was interesting to see how it applies to real life.
Chapter 6 - Rational Exponents and Radical Functions
In Chapter 6 we learned about evaluating and simplifying radical functions and rational exponents. Also, we learned to graph cubic and squared functions. We also learned how to invert functions, graphs, and exponents. Finally, we pieced together all of the concepts we had learned to be able to solve radical equations.
Chapter 5 - Polynomials and Polynomial Functions
In Chapter 5 we learned about Polynomials and Polynomial Functions. We learned how to add, subtract, multiply, and divide polynomial functions. We learned two different versions of dividing polynomials and learned how they applied to real life and what the answers we were getting meant. Also, we learned how to analyze rational zeros and polynomial graphs and models.
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Updated on November 16, 2011