What are you going to learn?

Algebra I introduces students to variables, algebraic expressions, equations, inequalities, functions, and all their multiple representations. In this class, students will develop the ability to explore and solve real-world application problems, demonstrate the appropriate use of graphing calculators, and communicate mathematical ideas clearly. This course lays the foundation for mathematical literacy that will help students be successful in every subsequent course in mathematics.

Content

Chapter 1. An Introduction to Algebra

  • Whole and Integer Numbers. Operations
  • Fractions and Operations. Least CommonMultiple (LCM)
  • Prime Numbers and the Greatest Common Factor (GCF)
  • The Real Numbers, Operations and its Properties
  • Exponents and Order of Operations

Chapter 2. Expressions and Polynomials

  • Translating and Evaluating Algebraic Expressions
  • Introduction to Polynomials
  • Combining Like Terms
  • Addition and Subtraction of Polynomials
  • Exponent Rules. Multiplying Polynomials
  • Factoring Polynomials
  • Applications

Chapter 3. Identities, Equations, and Inequalities

  • Introduction
  • Linear Equations with one Variable and Their Solutions
  • Absolute Value Equations
  • The Addition Principle of Equalities
  • The Multiplication Principle of Equalities
  • Translating Word Problems Into Equations
  • Linear Inequalities and their Solutions
  • Applications

Chapter 4. Rational Expressions

  • Addition and Subtraction of Rational Expression. LCM
  • Multiplication and Division of Rational Expressions
  • Simplifying Complex Rational Expressions
  • Order of Operations
  • Solving Equations with Rational Expressions
  • Applications

Chapter 5. Exponential and Logarithmic Functions

  • Composite Functions and Inverse Functions
  • Exponential Functions
  • Logarithmic Functions
  • Common Logarithms and Natural Logarithms
  • Exponential and Logarithmic Equations
  • Applications

Chapter 6. Conic Sections and More Graphing

  • Conic Sections: Parabola, Circles, and Ellipses
  • Conic Sections: Hyperbolas
  • The focus, Directrix properties of Conics
  • The Conics in Polar Coordinates
  • Rotation of Axis

Chapter 7. Systems of Equations and Inequalities with Three Variables

  • Introduction
  • Linear Equations in Three Variables
  • Solving System of Linear Equations by Matrix Methods
  • Nonlinear Systems of Equations
  • Compound and Absolute Values Inequalities

Chapter 8. Sequences and Series.The Binomial Theorem

  • Sequences and Series
  • Arithmetic Sequences and Series
  • Geometric Sequences and Series
  • The Binomial Theorem

Bibliography

  • Tussy, A., and R. David Gustafson(2009). Elementary & Intermediate Algebra. 4th Ed. Engage Learning. Belmont, USA.
  • Lial, M. et al (2012). Beginning Algebra. 9th Ed. Pearson Education, Inc. Boston, USA.
  • Lial, Hornsby, Schneider, Daniels. Beginning and Intermediate Algebra and College Algebra: a Corequisite Solution.1st ed.; Pearson

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