Algebra
The art of working with unknowns. Algebra introduces the symbols, equations, and structural moves that the rest of mathematics builds on — from balancing a single equation to manipulating whole families of curves.
Variables & Expressions
Letters as stand-ins for numbers, the syntax of expressions, and the difference between expressions and equations.
Linear Equations
Equations where each unknown appears to the first power. Solving, graphing, and the three forms — slope-intercept, point-slope, standard.
Systems of Linear Equations
Two or more lines, one answer (or none, or infinite). Substitution, elimination, and the geometric meaning of intersection.
Gaussian Elimination
The algorithm that mechanizes solving systems. Augmented matrices, the three row operations, row-echelon and reduced row-echelon form — and the gateway to matrices.
Inequalities
When the answer is a region, not a point. Solving linear inequalities and graphing solution sets.
Functions
From "rule that maps input to output" to domain, range, composition, and inverses.
Exponents & Radicals
Powers, roots, and the algebraic identities that let you move between them.
Exponential & Logarithmic Functions
f(x) = a·bˣ and its inverse. Growth, decay, the natural base e, log laws, and the equations that mix them.
Polynomials
Adding, multiplying, and factoring expressions with multiple terms. The bridge to higher-degree equations.
Factoring Techniques
The full toolbox: GCF, grouping, difference of squares, perfect-square trinomials, sum/difference of cubes, and the AC method.
Quadratic Equations
Equations of degree two. Factoring, completing the square, and the quadratic formula derived from first principles.
Rational Expressions
Fractions of polynomials. Domain restrictions, simplifying, common denominators, and the extraneous-solution trap.
Partial Fraction Decomposition
Un-adding fractions. The four cases — distinct linear, repeated linear, irreducible quadratic — and the cover-up shortcut. The on-ramp to integration tricks in calculus.
Sequences & Series
Arithmetic and geometric patterns, closed-form formulas, sigma notation, and a first encounter with infinite sums and convergence.
The Binomial Theorem
Pascal's triangle, binomial coefficients, and the formula that expands (a+b)ⁿ without multiplying n times. Where algebra and counting meet.