Algebra 1: Summary of Coursework

Essential Information

Algebra 1 is referred to by a variety of titles, such as elementary algebra, introductory algebra or college algebra. It may be completed as part of an undergraduate program, and it is usually a prerequisite for more advanced math classes such as trigonometry and calculus. Some schools require that students complete a prerequisite math course or pass a placement test to enroll in this course.

Here is an outline of common concepts taught in Algebra 1 courses:

  • Linear equations
  • Single properties
  • Word problems
  • Algebraic expression
  • Polynomial equations
  • Quadratic formula
  • Functions
  • Point-slope
  • Slope-intercept

List of Common Topics

Linear Equations

This topic area teaches students about the relationship between linear equations, proportional relationships and lines. Students learn to solve linear equations involving a single property, integer coefficients, rational expressions (fractions) and decimals.


In this segment, students learn how to translate word problems into algebraic expression and interpret expression structure. Other info includes use of the order of operation, distributive property, and rules for radicals and exponents used in simplifying expressions. Additional topics include how to evaluate and simplify expressions that involve absolute value.


The polynomials course topic presents a thorough explanation of the characteristics of polynomial equations and how to solve them. Students learn how to solve higher order equations. Rules relating to multiplication, subtraction and addition operations in factoring polynomials are included. Students also learn the zero factor property.

Quadratic Equations

This section focuses on solving applied problems and quadratic equations using a variety of methods, including use of factoring, the square root property and the quadratic formula, as well as through completing the square.


Function as a course topic teaches students to recognize, interpret and evaluate different types of functions. Students also learn how to determine the intercepts, domain and range. How to determine the equation of a quadratic function using a graph is also covered.


Students will learn how to determine a line's slope and sketch a line given a single point and its slope. The concepts of x- and y-intercepts are covered. Information presented in this topic includes finding a line's equation using both the point-slope and slope-intercept form. Parallel and perpendicular lines are introduced along with how to find their equations. Students learn to determine whether lines are perpendicular, parallel or neither.

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