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Topic overview in Mathematics
Why learn math?
If you ask a hundred people why math is important, you might get a hundred different answers. Ask a thousand or ten thousand people and the answers may vary, but only by a bit. Ask your parents and they might be able to tell you why, but then might not be able to help you if you have questions about your homework. Ask a teacher and you might get a vague answer in the form of a cliché to the effect of, “Math is all around you,” or, “You use math everyday.” And some teachers might even give you a tongue-in-cheek answer like, “...because you have a test in a few weeks.”
The truth is, the reasons to learn math are just as varied as the answers to the question ‘why learn math’. Math is one of the few school subjects that constantly and consistently builds on previously learned material.
Overview of High School Math
Algebra 1 introduces students to the basic tools needed to begin solving rational equations. You will build a familiarity with real numbers and their properties such as additive and multiplicative identities, inverse operations and the distributive and commutative properties, just to name a few. In this level, you will also be exposed to polynomials and be expected to carry out already-familiar calculations like area, perimeter and volume with more complex expressions instead of given numbers. Functions will also be investigated in detail and you will be able to find the x- and y-intercepts with and without the use of a graph.
The next subject, Geometry, focuses on shapes (of course) and investigating the properties of geometric shapes: perimeter, area, surface area and volume. You will also spend a considerable amount of time learning the special properties of right triangles such as sine, cosine, tangent and their inverses. Additionally, your teacher might also ask you to prove certain concepts in geometry using theorems and postulates.
Algebra 2 builds on the knowledge acquired in Algebra I and Geometry. Additionally, you will be shown how to manipulate and graph quadratic functions with the help of the quadratic formula. Concepts such as factoring polynomials that were first presented in Algebra I will be expanded to include techniques like completing the square. You will be introduced to the idea of imaginary numbers as well as one of the most beautiful numbers in the world: Euler’s constant, e.
Pre-Calculus takes the algebraic and geometric topics presented in the first few years of high school and begins to form some of the concepts needed to succeed in Calculus. Some of the most important topics addressed in Pre-Calculus are: the unit circle, complex numbers, vectors and matrices.
Calculus. Just hearing the word incites fear in many students. To put it simply, limits lead to the idea of derivatives; finding derivatives needs an opposing operation, so integrals are taught next. Then you will start to learn a lot of techniques that people named after themselves such as L’Hôpital’s rule, Taylor’s theorem, and the General Leibniz rule. Maclaurin, Fourier, Green, Stokes and Simpson (no, not those Simpsons…) are also famous mathematicians that discovered new techniques for calculation. All this talk of math may seem like an insurmountable task, but don’t worry. We will be your safety net at every step along the way.
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