If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Not feeling ready for this? Check out Get ready for Precalculus.

The complex plane: Complex numbersDistance and midpoint of complex numbers: Complex numbersComplex conjugates and dividing complex numbers: Complex numbersIdentities with complex numbers: Complex numbers

Modulus (absolute value) and argument (angle) of complex numbers: Complex numbersPolar form of complex numbers: Complex numbersGraphically multiplying complex numbers: Complex numbersMultiplying and dividing complex numbers in polar form: Complex numbersThe fundamental theorem of algebra: Complex numbers

Introduction to matrices: MatricesUsing matrices to represent data: MatricesAdding and subtracting matrices: MatricesProperties of matrix addition & scalar multiplication: MatricesUsing matrices to manipulate data: MatricesMatrices as transformations of the plane: MatricesUsing matrices to transform the plane: Matrices

Transforming 3D and 4D vectors with matrices: MatricesMultiplying matrices by matrices: MatricesProperties of matrix multiplication: MatricesRepresenting systems of equations with matrices: MatricesIntroduction to matrix inverses: MatricesFinding inverses of 2x2 matrices: MatricesSolving linear systems with matrices: Matrices

Venn diagrams and the addition rule: Probability and combinatoricsMultiplication rule for probabilities: Probability and combinatoricsPermutations: Probability and combinatoricsCombinations: Probability and combinatorics

Probability using combinatorics: Probability and combinatoricsProbability distributions introduction: Probability and combinatoricsTheoretical & empirical probability distributions: Probability and combinatoricsDecisions with probability: Probability and combinatoricsExpected value: Probability and combinatorics

Mastery unavailable

Defining limits and using limit notation: Limits and continuityEstimating limit values from graphs: Limits and continuityEstimating limit values from tables: Limits and continuityDetermining limits using algebraic properties of limits: limit properties: Limits and continuityDetermining limits using algebraic properties of limits: direct substitution: Limits and continuityDetermining limits using algebraic manipulation: Limits and continuitySelecting procedures for determining limits: Limits and continuity

Determining limits using the squeeze theorem: Limits and continuityExploring types of discontinuities: Limits and continuityDefining continuity at a point: Limits and continuityConfirming continuity over an interval: Limits and continuityRemoving discontinuities: Limits and continuityConnecting infinite limits and vertical asymptotes: Limits and continuityConnecting limits at infinity and horizontal asymptotes: Limits and continuityWorking with the intermediate value theorem: Limits and continuity

Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what you need to review.