CLEP College Algebra: Study Guide & Free Lessons
Short lessons, worked examples, and practice that connects.
Powers, roots and equivalent forms
Exponent notation records repeated multiplication, and its rules depend on the operation connecting the terms. A product, a quotient and a power of a power are different structures.
Read and combine polynomial structure
A polynomial organizes terms by powers of its variable. Coefficients, degree and evaluation describe different aspects of that structure and should not be confused.
Factor to expose a useful feature
Factoring rewrites a sum as a product. The new form is useful when a problem asks for roots, common factors or a cancellation that must respect domain restrictions.
Rational expressions and excluded inputs
A rational expression is a quotient of polynomials. Its denominator determines excluded inputs before any cancellation is performed.
Linear equations, systems and boundaries
Linear equations and inequalities can be solved by reversible operations, but an inequality changes direction when multiplied or divided by a negative number.
Quadratic equations and discriminants
The coefficients of a quadratic encode its roots and graph. Factoring, completing the square and the quadratic formula provide different ways to reveal that information.
Absolute value as a distance
Absolute value measures distance from zero. An equation |x − a| = r asks for points r units away from a, while an inequality describes an interval or its exterior.
Functions, composition and inverse inputs
A function assigns one output to each allowed input. Composition feeds one function output into another, and an inverse reverses an input-output relationship when that reversal is itself a function.
Transformations and graph features
A graph connects algebraic form to coordinates. Shifts inside a function affect input positions, while shifts outside affect output values.
Exponential and logarithmic relationships
An exponential function describes repeated multiplication by a fixed positive base different from one. A logarithm asks which exponent produces a given positive number from that base.
Complex numbers without losing the sign
A complex number has a real part and an imaginary coefficient. The defining relation i² = −1 determines how products and powers simplify.
Sequences, factorials and binomial choices
An arithmetic sequence adds a constant difference, whereas a geometric sequence multiplies by a constant ratio. Factorials count ordered arrangements and build binomial coefficients.
Radical structure and rationalization
An exponent with a denominator describes a root, while its numerator describes a power.
Polynomial factors, division and multiplicity
A polynomial can be organized by coefficients, factors or graph behavior, and each representation reveals different information.
Combine rational expressions and preserve holes
A fraction whose numerator or denominator contains fractions still follows the ordinary division rule.
Inequalities through signs and feasible sets
A product can be positive when both factors are positive or when both are negative.
Transform equations, then test the candidates
An algebraic transformation may produce candidates rather than equivalent solutions.
Absolute value with nonlinear and exterior conditions
Absolute value encodes a nonnegative distance, but the expression inside the bars can be nonlinear.
Nonlinear inverses and combined domains
An inverse reverses a function’s input-output pairing, so the original range becomes the inverse domain.
Transform points, symmetry and asymptotes
A graph transformation acts on input and output coordinates differently.
Logarithm laws with domain checks
Logarithm rules translate products into sums and quotients into differences only for valid positive arguments.
Recover parameters from exponential evidence
Exponential change uses a fixed multiplicative factor for equal input increments.
Complex division and nonreal roots
Complex division can be converted into multiplication by a conjugate over a real denominator.
Binomial terms and constrained counting
A binomial coefficient counts the ways to choose which factors contribute a particular term in a product.
Foundation pilot: selected college-algebra skills, not complete syllabus coverage.
A clear route through the material
Follow the topics in order or use the prerequisites to choose a starting point. Read the worked example before focused practice, then use review cards to revisit the idea.
Continue your preparation
Scope: College Algebra foundations