
PRECALCULUS 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 piecewisedefined 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 xaxis, yaxis, 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 realworld 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 realworld 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 realworld 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 realworld 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 realworld 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 realworld problems.
 Apply strategies to prove identities.
 Use the addition and subtraction identities for sine, cosine, and tangent functions.
 Use the doubleangle and halfangle 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 realworld problems.
Limits
 Use the informal definition of limit.
 Use and apply the properties of limits to find the limit of various functions.
 Find onesided 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): PreCalculus Honors students will take a districtwide final exam in June in addition to a DCC final exam in the 3^{rd}quarter.
Textbook: Functions Modeling Change: A Preparation for Calculus, 4^{th}Edition, published by John Wiley & Sons, Inc, ©2011