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    PRE-CALCULUS HONORS  (DCC MAT 185 – 4 credits)

    Code:  M661 Full Year         (11,12)   (1 credit)

    Prerequisite: Algebra 2 Honors, Algebra 2 with 95% Average

    (rank weight 1.10)

    Note:  This course is intended primarily for students planning to take calculus. Topics include a review of the fundamental operations; polynomial, rational, trigonometric, exponential, logarithmic, and inverse functions; modeling and data analysis.

     

    Areas of Study Include:

    • Functions and Graphs                                                                                    
    • Determine the domain and range of a function.
    • Evaluate piecewise-defined and greatest integer functions.
    • Analyze graphs to determine domain and range, local maxima and minima, intercepts, and intervals where they are increasing and decreasing.
    • Transform graphs of parent functions.
    • Determine whether a graph is symmetric with respect to the x-axis, y-axis, and/or origin.
    • Perform addition, subtraction, multiplication, division, and composition of functions.
    • Define inverse relations and functions and determine whether an inverse relation is a function.
    • Verify inverses using composition.

     

    • Polynomial, Power, and Rational Functions                                                 
    • Divide polynomials.
    • Apply the Remainder and Factor Theorems.
    • Determine the maximum number of zeros of a polynomial.
    • Find all rational zeros of a polynomial.
    • Simplify and perform operations on complex numbers.
    • Solve for the complex zeros of a polynomial.
    • Analyze and sketch polynomial functions using continuity, end behavior, intercepts, local extrema, and points of inflections.
    • Use polynomial functions to model and solve real-world problems.
    • Find the domain of a rational function.
    • Identify intercepts, holes, vertical, horizontal, and slant asymptotes in order to sketch graphs of rational functions.

     

    • Exponential and Logarithmic Functions                                           
    • Simplify expressions containing radicals or rational exponents.
    • Graph and identify transformations of exponential functions, including the number.
    • Use exponential functions to model and solve real-world problems.
    • Graph and identify transformations of logarithmic functions.
    • Evaluate logarithms to any base with and without a calculator.
    • Apply properties and laws of logarithms to simplify and evaluate expressions.
    • Solve exponential and logarithmic equations.
    • Use exponential and logarithmic models to solve real-world problems.
    • Trigonometry
    • Define and evaluate the six trigonometric ratios.
    • Solve triangles using trigonometric ratios.
    • Define radian measure and convert angle measures between degrees and radians.
    • Define the trigonometric functions in terms of the unit circle.
    • Develop basic trigonometric identities.
    • Use trigonometric functions to model and solve real-world problems, including right triangle relations, arc length, and speed.
    • Trigonometric Graphs                                                                                   
    • Graph the sine, cosine, and tangent functions.
    • Identify the domain and range of a basic trigonometric function.
    • Graph transformations of the sine, cosine, and tangent graphs.
    • Graph the cosecant, secant, and cotangent functions and their transformations.
    • Identify and sketch the period, amplitude (if any), and phase shift of the cosine, sine, and tangent functions.
    • Use trigonometric graphs to model and solve real-world problems.
    • Trigonometric Equations and Identities                                                         
    • Solve trigonometric equations graphically and algebraically.
    • Define the domain and range of the inverse trigonometric functions.
    • Write a trigonometric function to model and solve real-world problems.
    • Apply strategies to prove identities.
    • Use the addition and subtraction identities for sine, cosine, and tangent functions.
    • Use the double-angle and half-angle identities.
    • Use identities to solve trigonometric equations.
    • Solve triangles using the Law of Cosines.
    • Solve triangles using the Law of Sines.
    • Applications of Laws of Cosines and Sines
    • Applications of Trigonometry                      
    • Vectors in the Plane
    • 2 Dimentional Vectors
    • Vector Operations
    • Unit Vectors
    • Direction Angles
    • Applications of Vectors
    • Dot Product of Vectors
      • Angle between Vectors
    • Parametric Equations and Motion
      • Parametric Equations
      • Parametric Curves
      • Eliminating the Parameter
    • Polar Coordinates
      • Coordinate Conversions
      • Coordinate Equations
    • Graphs of Polar Equations
    • DeMoivre’s Theorem and nth Roots
      • The Complex Plane
      • Polar Form of Complex Numbers
      • Operations on Complex Polar Numbers 
    • Matrices                    
    • Identifying Matrices
    • Matrix Addition and Scalar Multiplication
    • Matrix Multiplication
    • Identity and Inverse Matrices
    • Applying Matrices to Linear Systems
    • Applications:
        • Communication Matrices
        • Transition Matrices
        • Transformation Matrices        
    • Analytic Geometry                                                                    
    • Eccentricity
    • Define a circle and write its equation.
    • Analyze and sketch the graph of a circle.
    • Define an ellipse and write its equation.
    • Analyze and sketch the graph of an ellipse.
    • Define a hyperbola and write its equation.
    • Analyze and sketch the graph of a hyperbola.
    • Define a parabola and write its equation.
    • Analyze and sketch the graph of a parabola.
    • Write the equation of and graph a translated conic section.
    • Use conic sections to model and solve real-world problems.

     Limits                                                       

    • Use the informal definition of limit.
    • Use and apply the properties of limits to find the limit of various functions.
    • Find one-sided limits.
    • Determine if a function is continuous at a point or an interval.
    • Find the limit as x approaches infinity

    Derivatives - as time allows

     

    Optional Topics, if Time:       

    • An Introduction to Calculus   
    • The Slope of a Curve
    • Using Derivatives in Curve Sketching
    • Extreme Value Problems
    • Velocity and Acceleration

         

     

     

    Assessment(s):  Pre-Calculus Honors students will take a district-wide final exam in June in addition to a DCC final exam in the 3rdquarter.

     

    Textbook:  Functions Modeling Change: A Preparation for Calculus, 4thEdition, published by John Wiley & Sons, Inc, ©2011