RoadMap – Project 2205

Tree View

The Road Map
- Functions and relations
- 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 equations
  - Solve linear equations
  - Linear equation applications
- 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
  - Solve radical equations
  - Solve equations with a rational exponent
  - Applications
- Rational Expressions
  - Simplify rational expressions
    
    With integral positive exponents
    
    With fractional positive exponents
    
    With power groups
    
    With binomials and quadratic trinomials
  - Rational expression non-permissible values
  - Multiply/divide and simplify rational expressions
    
    With multiple variables
    
    With binomials and quadratic trinomials
  - Add/subtract and simplify rational expressions
  - Complex (rational within) rational expressions
  - Rational inequalities
- Rational equations
  - Solving rational equations
- Rational functions
  - Identify/Match rational functions
  - Rational function properties
    
    Domain and range
    
    Vertical asymptotes and holes
    
    Horizontal and oblique asymptotes
    
    x and y intercepts
  - Rational applications
    
    Work rate
    
    Moving with or against
    
    Reciprocals of numbers
    
    Pricing
- Absolute values
  - Evaluation
- Absolute Expressions
- Absolute functions
  - Domain and range
  - Transformations
- Absolute value equations
  - Single absolute value
  - Double absolute values
  - Applications
- Absolute value inequalities
  - Solve absolute value inequalites
- Inverse functions
  - Find the inverse of a function
  - Inverse as a function or ralation
  - Domain restrictions
  - Applications
- Reciprocal functions
  - Domain and range
  - Invariant points
  - Horizontal asymptote
  - Applications
- Exponential functions
  - Domain and range
  - Compound interest
  - Growth and decay
  - Applications
- Logarithm
  - 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

The Road Map