By Hunter, 9th Grader

Algebraic Concepts

Algebra is a branch of mathematics that deals with mathematical symbols and the rules (or algorithms) for using these symbols. So many symbols!

In Algebra 1, we start with the basics of algebraic expressions, equations, and inequalities. We learn about simplifying expressions, solving equations, and graphing lines and functions. In Algebra 2 we delve deeper into the subject, studying more advanced topics like parabolas, trigonometry, sequences, and logs.

One of the most important concepts in algebra is the idea of variables. A variable is a symbol that represents a quantity that can vary or change. That is why it is call a variable. In an algebraic expression or equation, variables can be used to represent unknowns that may change depending on the situation. For example, in the equation y = 2x + 3, x is a variable that can take on different values, and y is a dependent variable that changes depending on the value of x.

Another key concept in algebra is solving equations. An equation is a statement that two expressions are equal. So an equation will have something on each side of the equal sign. To solve an equation means to find the value(s) of the variable(s) that make the equation true. In Algebra 1, we start with solving linear equations, which have the form ax + b = c and are 1st degree.

Graphing is another essential skill in algebra. We use graphs to draw a picture of the equation. We can visualize the relationships between variables. A function is a rule that assigns each input value to a unique output value. We can represent functions using graphs, tables, or algebraic equations.

In conclusion, algebra is a powerful tool for solving problems and understanding the relationships between variables. By mastering the fundamental concepts and skills of Algebra 1 and 2, you will be equipped to tackle more advanced math subjects like calculus, physics, and engineering. Keep practicing and exploring the subject, and you’ll be amazed at what you can achieve!