PRECALCULUS/DMACC MAT 129
Urbandale High School Syllabus
Description of Course
Precalculus is a course designed to match the AP (College Board) goals and objectives. The goal is to provide students with the good critical-thinking skills needed to succeed in any endeavor. Algebraic, numerical, and graphical representations are emphasized throughout the course.
Five hours of DMACC credit is available for Precalculus because the course is taught to meet the DMACC curriculum/competencies. This will be offered in the second semester.
Textbook and Supplementary Material
Precalculus – Graphical, Numerical, Algebraic – Seventh Edition - 2007
ISBN 0-13-227650-X
Demana, Waits, Foley, Kennedy
Pearson/Addison Wesley
Student Practice Workbook
ISBN 0-13-198580-9
Graphing Calculators – Students are encouraged to have their own graphing calculatorto use daily to explore, discover and reinforce the concepts of precalculus.Urbandale High School will provide any students with TI-84 Plus if they are unable to provide their own. Students may use the graphing calculators on some but not all assessments.
Technology Resources
• InterAct Math Tutorial Web site , – gives students practice and tutorial help.
• Web site, - provides resources for students including TI graphing calculator downloads, online quizzing, and study tips.
Grading Scale
A – 93-100B+– 87-89C+– 77-79D+– 67-69F– 0-59
A- – 90-92B – 83-86C – 73-76D – 63-66
B-– 80-82C-– 70-72D-– 60-62
Timeline
This is a full year course (2 semesters – 36 weeks).
PPrerequisites
This unit is to be completed as an independent study. The student has 4 weeks for each of the seven major topics (28 weeks). A unit exam will be given for each major topic at the end of each 4 weeks.
IFunctions and Graphs – 5 weeks – Mid-unit and Unit Exams
IIPolynomial, Power and Rational Functions – 6 weeks – 2 Mid-unit and Unit Exams
IIIExponential, Logistic and Logarithmic Functions – 6 weeks – 2 Mid-unit and Unit Exams
First Semester Exam
IVApplications of Trigonometry – 5 weeks – 2 Mid-unit and Unit Exams
VSystems and Matrices – 4 weeks – 2 Mid-unit and Unit Exams
VIAnalytic Geometry – 5 weeks – 2 Mid-unit and Unit Exams
VIIIntroduction to Calculus: Limits, Derivatives, and Integrals – 3 weeks – Unit Exam
Second Semester Exam
Unit Information
Major Topics
PPrerequisites
P.1Real Numbers
• Representing Real Numbers • Order and Interval Notation • Basic Properties of Algebra • Integer Exponents • Scientific Notation
P.2Cartesian Coordinate System
• Cartesian Plane • Absolute Value • Distance Formulas • Midpoint Formulas • Equations of Circles • Applications
P.3Linear Equations and Inequalities
• Equations • Solving Equations • Linear Equations in One Variable • Linear Inequalities in One Variable
P.4Lines in a Plane
• Slope of a Line • Point-Slope Form • Slope-Intercept Form • Graphing • Parallel and Perpendicular Lines • Applications
P.5Solving Equations
• Solving Equations Graphically • Solving Quadratic Equations • Approximating Solutions Graphically and Numerically with Tables
P.6Complex Numbers
• Complex Numbers • Basic Operations • Conjugates and Division • Complex Solutions of Quadratic Equations
P.7Solving Inequalities
• Absolute Value • Quadratic • Approximating • Projectile Motion
IFunctions and Graphs
1.1Modeling and Equation Solving
• Numerical Models • Algebraic Models • Graphical Models • Zero Factor Property • Problem Solving • Grapher Failure and Hidden Behavior • A Word about Proof
1.2Functions and Their Properties
• Function Definition and Notation • Domain and Range • Continuity • Increasing and Decreasing Functions • Boundedness • Local and Absolute Extremes • Symmetry • Asymptotes • End Behavior
1.3Twelve Basic Functions
• What Graphs Can Tell Us • Twelve Basic Functions • Analyzing Functions Graphically
1.4Building Functions from Functions
• Combining Functions Algebraically • Compositions • Relations and Implicitly Defined Functions
1.5Parametric Relations and Inverses
• Relations Defined Parametrically • Inverses Relations and Inverse Functions
1.6Graphical Transformations
• Transformations • Vertical and Horizontal Translations • Reflections Across Axes • Vertical and Horizontal Stretches and Shrinks • Combining Translations
1.7Modeling with Functions
• Functions from Formulas • Functions from Graphs • Functions from Verbal Descriptions • Functions from Data
IIPolynomial, Power and Rational Functions
2.1Linear and Quadratic Functions and Modeling
• Polynomial Functions • Linear Functions and Their Graphs • Average Rate of Change • Linear Correlation and Modeling • Quadratic Functions and Their Graphs • Applications of Quadratic Functions
2.2Power Functions and Modeling
• Power Functions and Variation • Monomial Functions and Their Graphs • Graphs of Power Functions • Modeling with Power Functions
2.3Polynomial Functions of Higher Degree with Modeling
• Graphs • End Behaviors • Zeros • Intermediate Value Theorem • Modeling
2.4Real Zeros of Polynomial Functions
• Long Division and the Division Algorithm • Remainder and Factor Theorems • Synthetic Division • Rational Zeros Theorem • Upper and Lower Bounds
2.5Complex Zeros and the Fundamental Theorem of Algebra
• Two Major Theorems • Complex Conjugate Zeros • Factoring with Real Number Coefficients
2.6Graphs of Rational Functions
• Rational Functions • Transformations of the Reciprocal Function • Limits and Asymptotes • Analyzing Graphs • Exploring Relative Humidity
2.7Solving Equations in One Variable
• Solving Rational Equations • Extraneous Solutions • Applications
2.8Solving Inequalities in One Variable
• Polynomial Inequalities • Rational Inequalities • Other Inequalities • Applications
IIIExponential, Logistic and Logarithmic Functions
3.1Exponential and Logistic Functions
• Exponential Functions and Their Graphs • The Natural Base e • Logistic Functions and Their Graphs • Populations Models
3.2Exponential and Logistic Modeling
• Constant Percentage Rate and Exponential Functions • Exponential Growth and Decay Models • Using Regression to Model Population • Other Logistic Models
3.3Logarithmic Functions and Their Graphs
• Inverse of Exponential Functions • Common Logarithms • Natural Logarithms • Graphs • Measuring Sound Using Decibels
3.4Properties of Logarithmic Functions
• Properties of Logarithms • Change of Base • Graphs • Re-expression Data
3.5Equation Solving and Modeling
• Solving Exponential Equations • Solving Logarithmic Equations • Orders of Magnitude and Logarithmic Models • Newton’s Law of Cooling • Logarithmic Re-expression
3.6Mathematics of Finance
• Interest Compounded Annually • Interest Compounded k Times per Year • Interest Compounded Continuously • Annual Percentage Yield • Annuities-Future Value • Loans and Mortgages-Present Value
IVApplications of Trigonometry
4.1The Law of Sines
• Deriving the Law of Sines • Solving Triangles (AAS, ASA) • The Ambiguous Case (SSA) • Applications
4.2The Law of Cosines
• Deriving the Law of Cosines • Solving Triangles (SAS, SSS) • Triangle Area and Heron’s Formula • Applications
4.3Vectors in the Plane
• Two-Dimensional Vectors • Vector Operations • Unit Vectors • Direction Angles • Applications of Vectors
4.4Dot Product of Vectors
• The Dot Product • Angle between Vectors • Projecting One Vector onto Another • Work
4.5Polar Coordinates
• Polar Coordinate System • Coordinate Conversion • Equation Conversion • Finding Distance Using Polar Coordinates
4.6Graphs of Polar Equations
• Polar Curves and Parametric Curves • Symmetry • Analyzing Polar Graphs • Rose Curves • Limaçon Curves • Other Polar Curves
4.7De Moivre’s Theorem and nth Roots
• The Complex Plane • Trigonometric Form of Complex Numbers • Multiplication and Division of Complex Numbers • Powers of Complex Numbers • Roots of Complex Numbers
VSystems and Matrices
5.1Solving Systems of Two Equations
• Substitution • Graphing • Elimination • Applications
5.2Matrix Algebra
• Matrices • Matrix Addition and Subtraction • Matrix Multiplication • Identity and Inverse Matrices • Determinant of a Square Matrix • Applications
5.3Multivariate Linear Systems and Row Operations
• Triangular Form • Gaussian Elimination • Elementary Row Operations and Row Echelon Form • Reduced Row Echelon Form • Inverse Matrix
5.4Partial Fractions
• Decomposition
VIAnalytic Geometry in Two and Three Dimensions
6.1Conic Sections and Parabolas
• Conic Sections • Geometry of a Parabola • Translations of Parabolas • Reflective Property of a Parabola
6.2Ellipses
• Geometry of an Ellipse • Translations of Ellipses • Orbits and Eccentricity • Reflective Property of an Ellipse
6.3Hyperbolas
• Geometry of a Hyperbola • Translations of Hyperbolas • Eccentricity and Orbits • Reflective Property of a Hyperbola
6.4Polar Equations of Conics
• Writing Polar Equations for Conics • Analyzing Polar Equations of Conics
6.5Three-Dimensional Cartesian Coordinate System
• Three-Dimensional Coordinate System • Distance and Midpoint Formulas • Equation of a Sphere • Vectors in Space • Lines in Space
VIIAn Introduction to Calculus: Limits, Derivatives, and Integrals
7.1Limits and Motion: A Tangent Problem
• Limits Revisited • The Connection to Tangent Lines • The Derivative
7.2Limits and Motion: The Area Problem
• Limits at Infinity • The Connection to Areas
Daniel Mueller
Department of Mathematics
Urbandale High School
Urbandale, Iowa