Algebraic thinking is important in real life to predict trends, set up Excel spreadsheet formulas, write computer programs, etc. Being able to describe a situation with and equation and a variable means that you can solve similar problems, even if the numbers are different. This is a powerful skill to develop for school and work. Success in algebra is key to doing well on SAT, and in other high school and college math classes.
Depending on your school, you may take this course before or after you have taken Geometry.
In New York State the second course in algebra is part of the Algebra 2/Trig Regents course.
This involves more work with functions, imaginary numbers, polynomials, exponents, and logarithms.
Calculus is the mathematics of change and motion. You need calculus to make predictions with non-linear functions, irregular shapes, motion in a gravity field, maximum/minimum problems, etc.
Geometry is more than just triangles and circles. It is the course where students learn to think in a different way. Beginning with a few basic axioms, relationships and patterns are proven to be theorems, which can be used to prove or disprove new conjectures. This math skill helps students to construct logical arguments in their technical courses or even in their humanities essays!
Physics is the branch of science devoted to understanding how the universe works at all scales of size. Physics combines the scientific method with applied mathematics to create experimental and theoretical investigations into phenomena of the world and the universe.
To do well in physics, you must take time to understand what is going on, which math represents this, and use the math to solve problems.
Prealgebra mathematics in middle school is about becoming comfortable using the math operations you have been learning your whole life. Using fractions to solve proportions, getting used to solving for variables, and a lot of good experience with numbers are crucial background for getting reading for Algebra in 8th or 9th grade.
Precalculus is all about the behavior of functions. Students will be able to see an equation and visualize its graph. They will be able to see a graph and predict its equation. They will understand how to change an equation to shift a graph up, down, left, right, etc. Precalculus studies the conic sections of lines, circles, ellipses, parabolas, and hyperbolas.
This study of the likelihood that certain events will or will not happen is not as straightforward as it may seem. Often the correct answers to a probability problem go against our common sense, which is why we must always carefully read what is asked, and carefully apply the definitions and step by step procedures to logically set up and calculate the solution.
Most SAT problems are just Algebra and Geometry. You can solve them systematically, or you can try each of the four possible answers to see which one works. As always the key is to read the question carefully and not fall for the gotcha trick in that problem.
Statistics is about taking, interpreting, and presenting data. Usually we are trying to learn something about a population by taking a sample. We learn how to find our margin of error and our confidence level of our conclusion. Statistics is also about proving or disproving a hypothesis. This is an important skill to have for any student who will do research, or for any educated consumer of information.
Basic trigonometry is often introduced in the Algebra I course. This course reviews sine, cosine, and tangent, and applies them to more difficult triangle problems. We then look at the behavior of the three trigonometric functions on a graph, as well as there related functions of secant, cosecant, and cotangent. The relationships of the six functions are described in many identity formulas, which help to simplify complex trigonometric expressions. The Law of Sines and Law of Cosines are also applied.