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Intermediate Algebra

Intermediate Algebra

This is the rung after Elementary Algebra: a second course that carries the core skills forward into the language of functions. It opens by consolidating the foundations — real numbers and their properties — then moves through solving linear equations, graphs and functions, systems, polynomials, factoring, rational and radical expressions, quadratics, exponential and logarithmic functions, conics, and finally sequences and series.

Prerequisites: Elementary Algebra, or comfort with solving linear equations, graphing lines, and working with polynomials and factoring. This is advisory, not a gate — start here if the earlier material already feels familiar.

Chapters

This book is organized into twelve chapters, each broken into short sections you can work through in order.

  • Foundations — the language of algebra, integers, fractions, decimals, and the properties of real numbers.
  • Solving Linear Equations — a general strategy, problem solving, formulas, mixture and uniform motion applications, and linear, compound, and absolute value inequalities.
  • Graphs and Functions — the rectangular coordinate system, slope, finding equations of lines, graphing linear inequalities, and relations and functions.
  • Systems of Linear Equations — solving systems in two and three variables, applications, and solving systems using matrices and determinants.
  • Polynomials and Polynomial Functions — adding, subtracting, and multiplying polynomials, exponent properties, polynomial functions, dividing, and factoring by greatest common factor and grouping.
  • Factoring — factoring trinomials, special products, a general strategy, and solving quadratic equations by factoring.
  • Rational Expressions and Functions — simplifying, operating on, and solving rational expressions and equations, rational functions, and variation.
  • Roots and Radicals — simplifying and operating on radicals, rational exponents, solving radical equations, and complex numbers.
  • Quadratic Equations and Functions — the square root property, completing the square, the quadratic formula, quadratic form, graphing, and quadratic inequalities.
  • Exponential and Logarithmic Functions — inverse functions, exponential and logarithmic functions, the properties of logarithms, and solving exponential and logarithmic equations.
  • Conics — distance and midpoint, circles, parabolas, ellipses, hyperbolas, and solving systems of nonlinear equations.
  • Sequences, Series and Binomial Theorem — sequences, arithmetic and geometric sequences and series, and the Binomial Theorem.

About this edition

This book is adapted from OpenStax Intermediate Algebra 2e, used under the terms of its Creative Commons Attribution-NonCommercial-ShareAlike (CC BY-NC-SA 4.0) license. Reviewers who vet or adapt this material are credited in the reviewed_by field of each page.

Foundations