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College Algebra

Free College Algebra study guide: 11 units with summaries, key ideas, flashcards and 305 practice questions with step-by-step solutions.

Lines up with: CLEP College Algebra; AP Precalculus Units 1-2 (partial).

Start studying College AlgebraFormula and fact sheet

Units

  1. UNIT 01

    Real numbers, exponents & radicals

    Everything in algebra rests on how numbers and exponents behave. This unit sets up the rules you'll use for the rest of the course.
  2. UNIT 02

    Polynomials & factoring

    Polynomials are sums of terms like axⁿ. Factoring them is the key skill for solving equations and simplifying rational expressions.
  3. UNIT 03

    Linear equations & inequalities

    Linear equations and inequalities are solved by undoing operations in reverse order. Absolute value adds a twist: it creates two cases.
  4. UNIT 04

    Quadratic equations

    Quadratic equations have the form ax² + bx + c = 0. You can always solve them with the quadratic formula, and the discriminant tells you what kind of solutions to expect.
  5. UNIT 05

    Functions & their properties

    A function assigns each input exactly one output. This unit covers how to read, evaluate and combine functions.
  6. UNIT 06

    Graphs & transformations

    Most graphs you'll meet are transformations of a small set of parent functions. Learn the parents, then learn how each change moves them.
  7. UNIT 07

    Inverse functions

    An inverse function undoes the original: if f sends a to b, then f⁻¹ sends b back to a.
  8. UNIT 08

    Polynomial & rational functions

    Polynomial and rational functions are the workhorses of algebra. Their zeros, end behavior and asymptotes tell you what the graph looks like.
  9. UNIT 09

    Exponential & logarithmic functions

    Exponential functions model repeated multiplication, like growth and decay. Logarithms are their inverses and let you solve for an exponent.
  10. UNIT 10

    Systems of equations

    A system is a set of equations solved together. The solution is the point (or points) that satisfies all of them at once.
  11. UNIT 11

    Sequences, series & binomial theorem

    Sequences are ordered lists of numbers; series add them up. The binomial theorem expands powers of a binomial without multiplying it out.