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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