Some concepts that come under Algebra 1 are linear equations, inequalities, graphing functions, exponents, and quadratic equations.
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Algebra 1 is the foundation of algebraic skills and is a required course for high school graduation. It includes a variety of topics that focus on building students’ understanding of mathematical concepts. Some of the core concepts under Algebra 1 are:

Linear Equations: One of the fundamental topic in Algebra 1 is solving for linear equations. A linear equation can be described as an equation that involves variables raised to the first power, and the variables in these equations are usually limited to one or two. The formulas used to solve linear equations help students build their problemsolving abilities.

Inequalities: Inequality is another important topic in Algebra 1, which involves solving equations that have a range of possible answers. Students learn to determine which values of variables make the equation true with the help of inequalities.

Graphing Functions: Graphing functions is a graphical representation of a function that provides a quick view of its properties represented by its graph. Graphing functions is a way for students to visually represent equations and make comparisons between different functions.

Exponents: Exponents in Algebra 1 are used to represent repeated multiplication. They are used to solve equations that involve repeated multiplication or long multiplication problems.

Quadratic Equations: Quadratic equations are equations with variables raised to the second power, and it usually takes the form of ax² + bx + c = 0. Solving quadratic equations requires students to apply the quadratic formula that has positive and negative solutions.
According to Norton Juster,
“Algebra is the language through which we describe patterns.”
Here are some interesting facts about Algebra:
 Algebra originated in the Middle East, India, and China around the 9th century.
 The word Algebra comes from the Arabic word “aljabr,” which means reunion of broken parts.
 Algebra was used during ancient times in Egypt, Babylonia, Greece, and Rome for commerce, legal work, and building projects.
 The first book on Algebra was written by Diophantus in the 3rd century.
 Algebra is a field of mathematics that deals with solving mathematical equations with letters or symbols representing numbers.
Table:
Algebra Concepts  Description 

Linear Equations  Solving equations with variables raised to the power of 1. 
Inequalities  Solving equations that have a range of possible answers. 
Graphing Functions  A graphical representation of a function that provides a quick view of its properties by graph. 
Exponents  Used to represent repeated multiplication in equations. 
Quadratic Equations  Equations with variables raised to the second power. Typically takes the form of ax²+bx+c = 0. 
In conclusion, Algebra 1 plays a critical role in building student’s understanding of mathematical concepts. Through learning the core concepts, students will be equipped with the tools needed to solve multistep equations, build problem solving abilities, and lay a strong foundation for further mathematical theory.
Video answer to your question
The Algebra 1 Full Course covers variables and expressions, algebraic terms and coefficients, the distributive property and combining like terms, equations and solving equations. The video explains that an equation is a statement showing that two algebraic expressions are equal, and to solve an equation, we need to find the value or values that make the equation true when we substitute them in for the variable. The video also introduces three properties that are used to solve equations including the additive inverse, the additive identity, and the addition property of equality, which tells us that we can add the same value to both sides of an equation without changing the solution.
https://www.youtube.com/watch?v=GANjgzYsIo
Many additional responses to your query
Some of the overarching elements of the Algebra I course include the notion of function, solving equations, rates of change and growth patterns, graphs as representations of functions, and modeling.
The concepts that come under algebra 1 or elementary algebra include variables, evaluating expressions and equations, properties of equalities and inequalities, solving the algebraic equations and linear equations which have one or two variables, and so on.
Algebra 1 typically includes evaluating expressions, writing equations, graphing functions, solving quadratics, and understanding inequalities.
I’ve TAed Calc 1 a number of times and while there are more things than just these, here are some of the things I wish students had better command of coming in:
1. The unit circle. As much as I am against memorizing things in math, this is one that won’t take much time or occupy a ton of mental space and will make your life much easier when you take calc. (Note: radians are better, stop thinking in degrees if you can.)
2. Familiarity with basic properties and identities of sin and cos (periodicity, transformations and translations of them, what the graphs look like, bounded by +/ 1, the relationships between them…).
3. Factoring. Especially with quadratics. Many of the examples you’ll do in calc will be made much simpler if you factor. Being able to do this quickly is a must.
4. Polynomial long division. You see this less often in calc, but if you haven’t seen it before, learning how to do it at the same time as mastering some element of calculus may be a lot to handle at the same ti…