To My Future and Current Students,
I can't stress enough the IMPORTANCE of ALGEBRA! Of all the mathematics I have taken in my lifetime...BELIEVE ME IT'S BEEN A LOT, ALGEBRA is the only course that is WOVEN into every single course. I was lucky enough that my first mathematics teacher in High School (Mr. Large), turned me from a B student into an A student such that I graduated High School with a 4.0 in mathematics. The one piece of advice he gave me that I will share with you is that...I NEED TO CHECK, DOUBLE CHECK AND TRIPLE CHECK ALL OF MY ANSWERS!
Algebra is a required course (prerequisite) for many of your other math courses, but most importantly in your High School career it is MANDATORY in order to be successful in Algebra 2. It may seem silly to learn and master Algebra, however, it is an integral part of every math course you will take after that except some geometry courses. Algebra teaches you how to think, be organized and how to prove your answers by checking them. It makes use of all of those math principles you thought were useless before it like...adding, subtracting, multiplying and dividing signed numbers. It makes use of solving quadratic equations by solving single variable equations.
While taking your ALGEBRA course this year or next, focus on truly understanding the following concepts to be transferred into math you will later encounter:
1. Solving Single Variable Equations that require Combining Like Terms.
2. Understanding the how sign changes work with Addition, Subtraction, Multiplication and Division WITHOUT A CALCULATOR!
3. Factoring Polynomials by finding the Roots/Zeros.
b. Difference of Squares
c. Quadratic Formula
4. Completing the Square
5. Solving Systems of 2 equations
6. Performing Mathematical Operations on Polynomials
a. Multiplying and Dividing Monomials (e.g. x^2 * x^3 = x^5; (x^7) / (x^2) = x^5)
b. Multiplying Bionomials using FOIL.
c. Multiplying Polynomials (e.g. [(x + 7)(x^2 + 2x + 1)] = x^3 + 9x^2 + 15x + 7)
d. Dividing Monomials and Polynomials
e. Adding/Subtracting Monomials and Polynomials (e.g. x^2 + 2x = x^2 + 2x because the exponent on the variables are not the same though the variable is the same.
Each of these topics will be revisited in your remaining courses and thus should be MASTERED in Algebra if at all possible. Please note mastery does not mean you earned an A in the class. You can master a subject and have a B or even a C for a final grade. It takes some of us longer to learn material than others and that is all fine and well. Some teachers don't believe that your final exam grade if the exam is cumulative should trump your previous performance in the course. When I speak of MASTERY of a subject I am speaking of understanding the concepts and restrictions well enough to know when you can use the things you have learned and when you can not...MASTERY IS NOT PERFECTION, but it is the road that lead to NEAR PERFECTION.
Thanks for Reading!