• The Road Map
    • Functions and Relations
      • Discrete vs continuous
      • Relation representations
      • Relations vs functions
      • Injective, surjective, and bijective
      • Domain, range, function test
      • One-to-one functions
      • Decreasing and increasing intervals
      • Inverse of relations
      • Function symmetry
      • Function notation
      • Average rate of change
      • Function intercepts
    • Cartesian Plane and Graphs of Equations
      • The Cartesian plane
        • Plotting points
        • Coordinates of points
        • Distance between 2 points
        • Verifying a right triangle
        • Midpoint of a line segment
      • Graphs of equations
        • Coordinate table filling
        • Find x- and y-intercepts of a graph
    • Linear Functions
      • Linear versus nonlinear
      • Slope and y-intercept
      • Slope-intercept form
      • Point-slope form
      • Standard form
      • Parallel and perpendicular
      • Word problems
    • Linear Equations
      • Solve linear equations
      • Linear equation applications
    • Quadratic Functions
      • Function evaluation
      • Vertex form
      • Intercept form
      • General form
      • Maximum/minimum
      • Completing the square
      • Perfect square
      • Quadratic properties
      • Quadratic factoring
      • Quadratic identification
    • Monomials
      • Identify a monomial
      • Degree of a monomial
      • Simplify a monomial
      • Restrictions
      • Determine if two monomials are similar
      • Combine monomials
    • Polynomials
      • Evaluate polynomials
        • Single-variable polynomials
        • Multi-variable polynomials
      • Polynomial division
        • Long division
        • Long division calculator
        • Synthetic division
        • Synthetic division calculator
      • Polynomial properties
        • Identify a polynomial
        • Degree/leading coefficient/constant of a polynomial
        • End behaivor
        • Zeros and multiplicities
        • Determine multiplicities from a graph
        • Intervals of increasing and decreasing
        • Possible number of turns
        • Possible number of real roots
        • Find function given zeros and a point
      • Simplify polynomials
        • Add/subtract polynomials
        • Multiply polynomials
      • The Remainder theorem
        • Find the remainder
        • Determine k given the remainder
        • Determine k and m given the remainders
      • The Factor theorem
        • Check if (x - a) is a factor
        • Check if a real number is a zero or root
        • Determine k given (x - a) is a factor
      • The Rational Root theorem
        • List all possible rational roots
        • Find all rational zeros and multiplicities
        • Complete factorization of a polynomial
      • Solve polynomial equations by factoring
      • Polynomial applications
        • Word problems
      • Polynomial Miscellaneous
        • Find a polynomial given zeros and a point
        • Identify a polynomial
        • Match polynomials
        • Polynomial inequality
    • Quadratic Trinomal Expressions
      • Quadratic trinomial factoring I
      • Quadratic trinomial factoring II
      • Quadratic trinomial factoring III
      • Quadratic trinomial factoring IV
      • Quadratic trinomial factoring V
      • Quadratic trinomial factoring VI
      • Completing the squares
      • Perfect square trinomial
    • Quadratic Equations
      • The discrimiant
      • Solve by factoring
      • Solve by extracting square roots
      • Solve by completing the square
      • Solve by quadratic formula
      • Applications
    • Radical Expressions
      • Restrictions
      • Mixed vs entire radical
      • Convert to mixed radical
      • Convert to entire radical
      • Convert radical to exponential form
      • Conver exponential to radical form
      • Simplify (mixed radical)
      • Radical and exponential form conversions
    • Radical Functions
      • Domain and range
      • Transformations
    • Radical Equations, Inequalities, and Applications
      • Radical equations
      • Radical inequalities
      • Word problems
    • Inverse Functions
      • Find the inverse of a function
      • Inverse as a function or ralation
      • Domain restrictions
      • Applications
    • Reciprocals
      • Reciprocal Functions
        • Identifying Functions
        • Domain and Range
        • Asymptotes
        • Intercepts
        • Invariant Points
        • Equation from Graph
        • Matching Graphs
    • Exponentials
      • Exponential Functions
        • Equations: From Asymptote & Points
        • Equations: From Graphs
        • Key Features & Properties
        • Identifying Functions
        • Graph Matching
        • Transformations
      • Exponential Expressions
        • Product of powers
        • Quotient of powers
        • Power of power
        • Power of a product
        • Power of a quotient
        • Mixed operations with exponents
      • Exponential Equations
        • Solving: Linear (No Logs)
        • Solving: Quadratic (No Logs)
        • Solving: Using Logarithms
    • Absolute Values
      • Absolute Values Functions
        • Abs. Inequality: from Graphs
        • Addition and Subtraction
        • Multiplication and Division
        • Mixed Operations
      • Absolute Value Expressions
        • Key Features & Properties
        • Identifying Functions from Graphs
        • Transforming Functions
        • Finding Transformations from Graphs
        • as Piecewise Functions
      • Absolute Value Word Problems
        • Distance: from a Point
        • Distance: Between & Beyond
        • Cumulative Change
      • Absolute Value Equations
        • Single Absolute Value (Linear)
        • Single Absolute Value (Quadratic)
        • Double Absolute Values (Linear)
      • Absolute Value Inequalities
        • Single Absolute Value Inequality (Less than or Equal to)
        • Single Absolute Value Inequality (Greater than or Equal to)
        • Double Absolute Value Inequalities
    • Rationals
      • Rational Functions
        • Check: Rational or Not?
        • Identify: Function Type
        • Identify: from Graphs
        • Match: Equation to Graph
        • Find: Domain
        • Find: Range
        • Find: Vertical Asymptotes & Holes
        • Find: Horizontal & Oblique Asymptotes
        • Find: X & Y-Intercepts
        • Find: End Behavior
      • Rational Expressions
        • Non-permissible values
        • Simplify: Single Rational Expression
        • Simplify: Multiply & Divide
        • Simplify: Add/Subtract
        • Simplify: Complex Rational Expressions
      • Rational Equations
        • Rational Linear
        • Rational Quadratic
      • Rational Inequalities
        • Solving Inequalities: Single-Term
        • Solving Inequalities: Double-Term
      • Rational Word Problems
        • Work Rate Problems
        • Movement Problems
        • Number Problems
        • Pricing Problems
    • Logarithms
      • Convert to exponential form
      • Convert to logarithmic form
      • Evaluate logarithmic expression manually
      • Properties of logarithms
      • Simplify logarithmic expressions
      • Solve logarithmic equations
    • System of Equations
      • Linear and linear
        • Nature of solutions
        • Solve by substitutions
        • Solve by elimination
        • Applications
      • Linear and quadratic
        • Nature of solutions
        • Solve by substitutions
        • Applications
    • Transformations
      • Base or parent functions
        • The identity function
        • The squaring function
        • The cubic function
        • The absolute value function
        • The square root function
        • The reciprocal function
    • Trigonometry I
      • Angles
        • Standard position angles
          • Which one is not a standard position angle?
          • Which one is a standard position angle?
          • Which one is a negative standard position angle?
          • Match angles to diagrams
          • Find the standard position angle from diagram
          • Find in which quadrant a terminal lies
          • Find the angle in standard position after reflection
        • Reference angles
          • Find a reference angle given a standard position angle
          • Find 4 standard position angles given a reference angle
          • Find the reference angle from diagram
      • Trigonometric ratios of any angle
        • The Pythagorean Theorem
          • Determine the length of the hypothenus
          • Determine the length of a leg
          • Distance between two points
        • The sine ratio
          • Calculate the sine of an angle
          • Calculate the measure of an angle using sine inverse
        • The cosine ratio
          • Calculate the cosine of an angle
          • Calculate the measure of an angle using cosine inverse
        • The tangent ratio
          • Calculate the tangent of an angle
          • Calculate the measure of an angle using tangent inverse
      • The Sine Law
      • The Cosine Law
      • Word problems