• College Algebra with Trig and Pre-Calculus
     
    FIRST SEMESTER
     
    Linear Equations and Inequalities
     
    1. Graphing lines
    2. Writing equations of lines
    3. Graphing Inequalities
    4. Review of absolute value, quadratic and rational inequalities
    4. Applications in one variable
    All word problem review
    Chapter Test
     
    Systems
     
    1. Solving linear systems algebraically, including 3 variables
    2. Classifying systems as consistent (dep or ind) or inconsistent
    3. Solving systems graphically
    4. Applications in two or more variables – all word problems
    5. Linear programming
    Chapter Test
     
    Matrices
     
    1. Size
    2. Operations
    3. Application with multiplication
    4. Determinants
    5. Inverses
    5. Solving systems using matrices
    a. calculator and inverse
    b. Cramer’s Rule
    Chapter Test
     
    Functions – deeper understanding and more rigor than Alg 2
     
    1. Relations and Functions
    2. Determining a Function
    Coordinates, vertical line test, mapping equations
    3. Domain and Range
    3. One-to-one, Many-to-one, Onto
    4. Function Notation
    5. The Algebra of Functions
    6. Composition of Functions and Domain
    7. Graphing using transformations (library of functions)
    8. Inverse Functions and Domain
    9. Piecewise, writing absolute value as a piecewise
    Chapter Test
     
    Quadratics
     
    1. Quick review
    2. Re-do with equations quadratic in form
    Chapter Test
    Rational Exponents
    1. Operations
    2. Evaluating
    2. Factoring
    3. Equations
    Chapter Test
     
    Exponentials and Logs
     
    Chapter Test
     
    Trig Review
     
    Chapter Test
    Fianl Examination for College Algebra with Trig
     
     
    SECOND SEMESTER
     
    Series and Sequences Review
     
    Chapter Test
     
    Higher Order Polynomials
     
    1. Classifying
    2. Leading term test and end behavior
    3. Intermediate Value thm
    4. Long division, synthetic division
    5. Factor thm and remainder thm
    6. Descartes rule of signs
    7. Rational roots thm
    8. Solving
    9. Graphing
    10. Writing equations given roots and multiplicity
    Chapter Test
     
    Analytic Geometry and Polar Coordinates
     
    1. rectangular coordinates into polar
    2. Polar coordinates into rectangular
    3. Writing complex into cis form
    4. Writing cis into complex
    5. Writing rectangular equations into polar
    6. Writing polar equations into rectangular
    7. Multiplying, dividing and power rules
    8. Finding nth roots
    9. Graphing polar coordinates
    10. Graphs
    Chapter Test
     
    Preview Calculus
     
    present two main ideas: tangent line and area under a curve
     
    Limits
     
    1. Understanding and notation
    2. Tables
    3. Graphically
    4. Algebraically
    5. at infinity
    6. Approaching infinity
    7. Involving trig
    Chapter Test
     
    Continuity
     
    1. Definitions and math jargon
    2. at a point
    3. Discontinuities
    4. Making a piecewise continuous at a point/over entire number line
    5. Intermediate Value thm
    Chapter Test
     
    Derivatives
     
    1. Definition of the Derivative, tangent line problem
    2. Finding derivatives using the limit process
    3. First rules
    Power rule, product rule, quotient rule, chain rule
    with equations of tangent/normal lines and horizontal tangent lines
    Quiz
    4. Abstract derivatives form graphs and tables
    Quiz
    5. Trig derivatives/equations of tangent lines
    Quiz
    7. ln u, eu, au, log au/equations of tangent lines
    Quiz
    Chapter Test