ModelCourses/CollegeAlgebra

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General Description

• Freshman level college algebra course
• Pre-requisite: Intermediate algebra or 2 years of high school algebra.

Possible textbooks include, but are not limited to:

• Michael Sullivan and Michael Sullivan III. College Algebra—Enhanced with Graphing Utilities, Fifth Edition. Upper Saddle River, NJ: Prentice-Hall, Inc., 2009.

Topics Covered

• Lines and Circles and their graphs
• Functions and Their Graphs
• Inverse Functions
• Linear Functions, Their Properties, and Linear Models
• Quadratic Functions and Their Properties
• Inequalities Involving Quadratic Functions
• Polynomial and Rational Functions
• Exponential Functions
• Logarithmic Functions
• Exponential Growth and Decay Models
• Conics: Parabola, Ellipse and Hyperbola
• Systems of Equations and Inequalities

Problem sets

Review

• Set 01 Real numbers, essential algebra rules
  
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Students will be able to

• • evaluate algebraic expressions
  • domain of a variable
  • laws of exponents
  • square roots
  • scientific notation

• Set 02 Formulas
  
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Students will be able to

• • Formulas

• Set 03 Polynomials
  
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Students will be able to

• • Polynomials
  • Multiplication formulas

• Set 04 Factoring polynomials
  
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  • Factoring polynomials
  • Long division

• Set 05 Synthetic Division
  
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• Synthetic Division

• Set 06 Rational Expressions
  
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  • Rational Expressions

• Set 07 Roots and rational exponents
  
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  • Roots and rational exponents

College algebra problem sets

• Set 01 Linear Equations
  
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  • Linear equations (populated)

• Set 02 Quadratic Equations
  
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  • Quadratic Equations (populated)

• Set 03 Quadratic Equations with Complex Roots
  
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  • Complex numbers and quadratic equations (populated)

• Set 04 Equations with Quadratic form and Radicals
  
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Students will be able to

• • Use Quadratic form equations
  • Solve Factorable equations
  • Solve Equations with radicals (populated)

• Set 05 Inequalities
  
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Students will be able to

• • Solve very simple inequalities
  • Solve compound inequalities (populated, needs more)

Unit 6 - Linear Equations

Problem set for this unit

• Absolute value equations and inequalities (populated)

Unit 7 - Linear Equations

Problem set for this unit

• Word problems: interest, mixture, motion, constant rate jobs (populated)

Unit 8 - Linear Equations

Problem set for this unit

• Coordinate system. Distance and midpoint formula (populated)

Unit 9 - Linear Equations

Problem set for this unit

• Graphs of equations in two variables, intercepts, symmetry (populated)

Unit 10 - Linear Equations

Problem set for this unit

• Lines

Unit 11 - Linear Equations

Problem set for this unit

• Circles

Unit 12 - Linear Equations

Problem set for this unit

• Variation (formulas for science laws, say)

Unit 13 - Linear Equations

Problem set for this unit

• Functions

Unit 14 - Linear Equations

Problem set for this unit

• Graph of functions

Unit 15 - Linear Equations

Problem set for this unit

• Properties of functions

Unit 16 - Linear Equations

Problem set for this unit

• Library of functions, piecewise-defined functions

Unit 17 - Linear Equations

Problem set for this unit

• Graphing techniques, transformations

Unit 18 - Linear Equations

Problem set for this unit

• Math models: building functions

Unit 19 - Linear Equations

Problem set for this unit

• Linear functions and their properties (populated)

Unit 20 - Linear Equations

Problem set for this unit

• Linear models

Unit 21 - Linear Equations

Problem set for this unit

• Quadratic functions and their properties

Unit 22 - Linear Equations

Problem set for this unit

• Quadratic models from ‘word problems’

Unit 23 - Linear Equations

Problem set for this unit

• Inequalities with quadratic functions Audrey

Unit 24 - Linear Equations

Problem set for this unit

• Polynomial functions and models

Unit 25 - Linear Equations

Problem set for this unit

• Properties of rational functions?

Unit 26 - Linear Equations

Problem set for this unit

• Graph of a rational function?

Unit 27 - Linear Equations

Problem set for this unit

• Polynomial and Rational Inequalities: Audrey

Unit 28 - Linear Equations

Problem set for this unit

• Real zeros of polynomials

Unit 29 - Linear Equations

Problem set for this unit

• Complex zeros, fundamental theorem of algebra

Unit 30 - Linear Equations

Problem set for this unit

• Composite functions

Unit 31 - More about Functions

Problem set for this unit

• One-to-one functions
• Inverse functions

Unit 32 - Conic sections

Problem set for this unit

• Conic sections