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