Pre-Calculus

Course Syllabus

Generally, the class content will be covered as follows:

Chapter 1, 2, & 4:  Functions

• Interval Notation
• Increasing or decreasing intervals
• Find the maximum/minimum value of a function
• Find the rate of change & difference quotient of a function
• Identify when the function is positive or negative
• Identify even and odd function
• Domain & Range
• Graphing families of functions through Transformations
• Inverse Functions
• Composition of Functions 

Chapter 5:  Trigonometric Functions

• Convert between degrees and radians and understand their relationship
• Find the exact values of trigonometric functions given a point on the unit circle, the value of one trigonometric ratio, or a special angle
• Graph trigonometric functions using amplitude, period, and phase shift

Chapter 6:  Analytic Trigonometry

• Evaluate inverse trig functions
• Establish (prove) trigonometric identities
• Evaluate trig functions using Sum & Difference Formulas
• Evaluate trig functions using Double- & Half-Angle Formulas
• Evaluate using Product-to-Sum or Sum-to-Product Formulas
• Solve trigonometric equations

Chapter 7:  Application of Trigonometric Functions

• Solving problems through right triangle trigonometry
• Solving triangles using the Law of Sines
• Solving triangles using the Law of Cosines
• Finding the area of a triangle using trigonometry and Heron's Formula 

Chapter 3:  Polynomial & Rational Functions

• Domain & Range of polynomial & rational functions
• Zeros of a polynomial function; real and complex
• Turning points, local maxima/minima
• End behavior 
• Asymptotic behavior
• Multiplicity
• Using intervals to solve inequalities involving polynomial or rational functions

Chapter 4:  Exponential & Logarithmic Functions

• Equations and Inequalities
• Distance
• Constant Increasing and Decreasing Examples – Flight Plans, etc.
• Domain and Range

Chapter 11:  Sequences & Series

• Students will understand interest and the time-value of money
• Simple and Compound Interest
• Present and Future Value of Annuities
• Mortgages
• Financing (APR)

Chapter 13:  Limits

• Compare and Contrast Permutations and Combinations
• Calculate the number of permutation of n objects taken r at a time.
• Calculate the number of combinations of n objects taken r at a time.
• Define and five contextual examples of complementary, dependent, independent, and/or mutually exclusive
• Given two or more events in a problem setting, determine if the events are complementary, dependent,
• independent, and/or mutually exclusive.
• Find Conditional Probabilities for Dependent, Independent, and Mutually exclusive events
• Represent and Calculate probabilities using Venn diagrams and probability tress.