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Algebra 1 is great fun – you get to solve puzzles!
You play some computer games by running, jumping or finding secret doors. Well, with Algebra you play with letters, numbers and symbols. And once you learn some of the “tricks”, it becomes a fun challenge to work out how to use your skills in solving each “puzzle”.
Algebra 2 is really fun, interesting, and challenging because it required the knowledge and skills of algebra 1 and geometry. In fact, I’ve taught both Honors and regular Algebra 2 for a decade and I’d enjoyed every moment of it. I have many short cuts and tricks to help students to memorize formula, know how to graph different types of functions, and solve certain equations as well as solve word problems effectively.
In general, I loved to figure out math problems, especially calculus problems. I guess because there is always a right answer and there can be many ways of going about getting that answer. Unlike English, an essay can never be perfect, it can never be completed—there is always something more that can be done.
I told my calculus students that math skills are like muscles in your body, if you don’t work out you won’t go anywhere. Therefore, you just practice, practice, and practice in order to do well in calculus.
Geometry was totally a different playing field for me when I first took it in high school because I used to have hard time in grasping the concepts of proofs and know how applied the definitions and theorems.
Geometry is more of a visual subject—requires more abstract thinking in analyzing shapes and figures. But now, after teaching Geometry classes for ten years, I’d really like the subject and I personally think it is easier than Algebra since it doesn’t involve with solving complex equations. Despite the fact that Geometry is not as hard as algebra, I still suggest that students must know the definitions, axioms or postulates, theorems, and formula to in order to do well.
Many students find algebra to be a very interesting subject. However, some students find algebra to be very difficult. Often the reason for this is that they have not yet mastered the concepts of pre-algebra. This is why it’s so important to for students to learn pre-algebra thoroughly before moving on to higher levels of math. If students start doing various kinds of math problems early in their studies, they are less likely to encounter problems further down the road.
Exponents, arithmetic equations and basic graphing are other primary topics in pre-algebra. These are the pre-algebraic concepts with the widest applications in everyday life. Their applications are almost countless. These concepts of pre- algebra are used in almost every field in business and the sciences. From small-scale business to huge engineering projects, algebra plays a central role in solving problems. If the student wants to have a career in business or the sciences, it’s important that he/she learn pre-algebra as a stepping stone to higher mathematics.
Precalculus prepares students for calculus the same ways as pre-algebra prepares students for Algebra I. While pre-algebra teaches students many different fundamental algebra topics, precalculus does not involve calculus, but explores topic that will be applied in calculus. Precalculus was a fun challenging course that I went through in last year of high school. There are three main components of precalculus that are so vital that I suggest students must know:
1. Know how to represent functions. There are many different ways you can describe a functions, the most popular are algebraic and graphical.
2. Know the basic function library. Knowing the basic properties of common will save you a lot of time in your calculus studies. Basic functions include trigonometry functions, exponential function, polynomials, and many more. Each set of functions has unique properties that make them useful in different ways.
3. Know how to transform functions. Basically this is taking one function and turning it into another through a set of manipulations—shifts, stretches, and compressions.
Trigonometry is one of my favorite math concepts due to the fact it has many real-life applications. Trigonometry is really isn’t hard. If it seems hard, then that’s because you were taught in a manner that doesn’t work for you. Different people learn different ways, but teachers sometimes only teach one way, whereas the way you are taught needs to be the way you learn.
There are only three important definitions in trigonometry. Everything else is based on those three. If you can understand these three definitions, you should have no trouble understanding any other part of trig.
The three most important definitions are:
Sine of the angle = opposite/hypotenuse
Cosine of the angle = adjacent/hypotenuse
Tangent of the angle = opposite/hypotenuse
Yes, trigonometry finds itself enmeshed within our world. The three trigonometric functions do more than tell us the ratio of sides of a right triangle; they help tell us about life itself. Keep this in mind next time you run into the sine, cosine, or tangent.