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Common Algebra courses and concepts

Pre-Algebra (middle school)

This course is typically taught in middle school ranging from grades 6-8.  It requires strong skills in addition - subtraction - multiplication - division of whole numbers, fractions, and decimals.

Early pre-algebra concepts may include: positive/negative numbers; order of operations; exponents/square roots; absolute value; proportions; ratios; percent; evaluating expressions; distributive property; bar/line graph analysis; scientific notation; and graphing points on a coordinate plane.

Advanced pre-algebra concepts may include: solving multi-step linear equations and inequalities; graphing linear equations and inequalities; understanding linear functions; domain and range; using slope-intercept form, distance formula, midpoint formula; Pythagorean theorem; area and volume of various polygons; adding/subtracting/multiplying/dividing monomials; and factoring polynomials.

Algebra 1 (middle school or high school)

This course is typically taught freshman year of high school.  However, some students who master pre-algebra concepts in 6/7 grade may be eligible to take this course in middle school.

Early Algebra 1 concepts may include: solving multi-step equations; solving and graphing linear equations and inequalities; using point-slope, slope-intercept, standard form; and functions/relations of functions.

Advanced Algebra 1 concepts may include: solving systems of equations/inequalities; adding/subtracting/multiplying/dividing polynomials; factoring techniques of polynomials; simplifying and solving rational expressions; solving methods for quadratic equations; graphing quadratic equations; and solving rate/time/distance/mixture story problems.

Algebra 2 (high school)

This course is typically taught sophomore or junior year of high school.  Although Algebra 1 is a pre-requisite for Algebra 2, many students often take geometry in between these two courses.  It is recommended students review the major concepts of Algebra 1 prior to beginning course work in Algebra 2.

Early Algebra 2 concepts may include: solving, graphing, and differentiating between linear, exponential, quadratic, and absolute value functions; solving 3 variable functions using matrices and determinants; advanced factoring of quadratic functions; simplifying rational expressions; and solving rational equations.

Advanced Algebra 2 concepts may include: solving/graphing cubic functions; understanding conic sections; using function notation; composition of functions; inverse functions; simplifying radicals; operations of radicals; rational exponents; complex numbers; solving quadratic systems; exponential/logarithmic functions; arithmetic/geometric sequences and series; and binomial theorem.

College Algebra (post high-school)

This course is offered at the collegiate level, and often mirrors the concepts taught in Algebra 2 and Trigonometry.  It usually consists of more complex equations and functions, and usually moves at a more accelerated pace.

Applications and Career Opportunities with Algebra

Most people utilize the core fundamentals of algebra when calculating best rates, percentages, discounts/profit, time and distance, etc.  However, some professions heavily rely on algebra and advanced mathematics.  Students with a high level of mastery in these courses may excel in a profession as a: civil or mechanical engineer; software developer; research analyst; medical scientist; financial advisor; economist; physicist; or computer programmer.