Beginning and intermediate algebra together, in course order.
The arithmetic and number-system groundwork every algebra course assumes: fractions, order of operations, and the transition from arithmetic to symbolic algebra.
Rules for manipulating exponents, negative and zero exponents, and scientific notation. Most texts fold these rules into the polynomial chapter; DCM (and the P.O.W.E.R. sequence) introduce them first.
Solving linear equations, translating and solving applications, and solving and graphing linear and compound inequalities on the number line.
The coordinate plane, graphing lines, slope, and the several equivalent forms for the equation of a line.
Solving systems of linear equations by graphing, substitution, and elimination; applications; three-variable systems; and graphing linear inequalities in two variables.
Introduction to polynomials and the operations of adding, subtracting, multiplying, and dividing them.
The standard factoring toolkit — GCF and grouping, trinomials, and special forms — plus solving quadratic equations by factoring and their applications. Includes the Intermediate-Algebra comprehensive factoring review.
Simplifying and operating with rational expressions, complex fractions, solving rational equations, applications, and variation.
Solving equations and inequalities involving absolute value.
Radicals and roots, rational exponents, simplifying and operating with radical expressions, rationalizing, radical equations, and imaginary/complex numbers.
A complete set of methods for solving quadratic equations, quadratics in other forms, and their applications.
The function concept, basic parent graphs and transformations, and a focused treatment of quadratic functions and their applications.
One-to-one and inverse functions, exponential functions, and logarithms — the capstone of the developmental sequence and the bridge to college algebra and precalculus.
A self-contained placement and review track (DCM ALEKS class): 54 short videos re-teaching the developmental-algebra arc from fractions through logarithms, grouped by ALEKS module. Distinct from the topic lessons above; kept together as a series for placement prep.