Pre-Calculus Pre-AP Syllabus

Mrs. M. Knobel                                                                          Room # 417


Course Description:


              In Pre-Calculus, students continue to build on the k-8, Algebra I, Algebra II and Geometry foundations as they expand their understanding of mathematics. Students will use functions, as well as, symbolic reasoning to represent and connect ideas in geometry, probability, statistics, trigonometry and calculus to model physical situations. Finally, students will use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools and technology (including, but not limited to calculators with graphing capabilities, data collection devices and computers) to model functions and equations and solve Real-Life problems.


Course Objective: Pre-Calculus students will acquire and demonstrate knowledge of concepts, definitions, properties and applications of topics listed below. The main goal of Pre-Calculus is to help students obtain critical thinking and decision making skills that will allow them to connect concepts, develop computational skills and learn strategies needed to solve mathematical problems.


Course Assessment:

             60% Exams

             40% Other Assignments


               Chapter 1 Graphs

    1. The Distance and Midpoint formula; Graphing

    2. Intercepts; symmetry; Graphing Key Equations

    3. Solving Equations Using a Graphing Utility

    4. Lines

    5. Circles



      Chapter 2   Functions and Their Graphs

                2.1 Functions

                2.2 The Graph of a Function

                2.3 Properties of Functions

                2.4 Library of Functions: piecewise-defined Functions

                2.5 Graphing Techniques: Transformations

                2.6 Mathematical Models: Building Functions



      Chapter 3   Linear and Quadratic Functions

                3.1 Linear Functions and Their Properties

                3.2 Linear Models: Building Linear Functions from Data

                3.3 Quadratic Functions and Their Properties

                3.4 Build Quadratic Models from Verbal Descriptions and from Data

                3.5 Inequalities Involving Quadratic Functions


      Chapter 4   Polynomial and Rational Functions

                4.1 Polynomial Functions and models

                4.2 The Real Zeros of a Polynomial Function

                4.3 Complex Zeros: Fundamental Theorem of Algebra

                4.4 Properties of Rational Functions

                4.5 The Graph of a Rational Function

                4.6 Polynomial and Rational Inequalities



      Mid Term Exams


      Chapter 5 Exponential and logarithmic Functions

                5.1 Composite Functions

                5.2 One-to-One Functions: Inverse Functions

                5.3 Exponential Functions

                5.4 Logarithmic Functions

                5.5 Properties of Logarithms

                5.6 Logarithmic and Exponential Equations

                5.7 Financial Models

                5.8 Exponential Growth and Decay Models

                5.9 Building Exponential, Logarithmic, and Logistic Models


      Chapter 6 Trigonometry Functions

                6.1 Angles and Their Measure

                6.2 Trigonometric Functions: Unit Circle Approach

                6.3 Properties of the Trigonometric Functions

                6.4 Graphs of Sine and Cosine Functions

                6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

                6.6 Phase Shift: Sinusoidal Curve Fitting


      Chapter 7   Analytic Trigonometry

                7.1 The inverse Sine, Cosine, and Tangent Functions

                7.2 The Inverse Trigonometric Functions (Continued)

                7.3 Trigonometric Equations

                7.4 Trigonometric Identities


      Chapter 8 Applications of Trigonometric Functions

                8.1 Right Triangle Trigonometry: Applications

                8.2 The Law of Sines

                8.3 The Law of Cosines

                8.4 Area of Triangle

                8.5 Simple Harmonic Motion; Damped Motion: Combining Waves



      ***If time permits, then the following lessons will be cover***



      Chapter 9 Polar Coordinates; Vectors

                 9.1 Lines

                 9.2 Polar Equations and Graphs

                 9.3 The Complex Plane; De Moivre’s Theorem


      Chapter 12 Sequences; Induction; the Binomial Theorem

                12.1 Sequences

                12.2 Arithmetic Sequences: Geometric Series

                12.3 Geometric Sequences; Geometric Series


      Chapter 14 A Preview of Calculus: The Limit, Derivative, and Integrals

                 14.1 Finding Limits Using Tables and Graphs

                 14.2 Algebra Techniques for Finding Limits

                 14.3 One-Sided Limits; Continuous Functions

                 14.4 The Area Problem; The Derivative

                 14.5 The Area Problem; The Integral






      Learn and Have Fun