Algebra II Course Outline

Algebra II expands on the topics of Algebra I in both depth and complexity. Students will be introduced to conic sections including ellipses and hyperbolas. The course will also explore some of the properties of complex numbers and systems of equations. This course uses Algebra and Trigonometry: Functions and Applications by P. Foerster.

Semester I

Chapter 2: Functions and Relations

  • graphs of equations with two variables
  • graphs of functions
  • functions and relations

Chapter 3: Linear Functions

  • properties of linear functions
  • graphs of linear functions
  • linear functions as mathematical models

Chapter 4: Systems of Linear Equations and Inequalities

  • solutions of linear equations
  • systems of equations
  • second order determinants
  • linear equations with three or more variables
  • systems of linear inequalities

Chapter 5: Quadratic Functions and Complex Numbers

  • graphs of quadratic functions
  • x-intercepts and the quadratic formula
  • imaginary and complex numbers
  • evaluating quadratic functions
  • quadratic functions as models

Chapter 6: Exponential and Logarithmic Functions

  • exponential functions
  • properties of exponentiation
  • rational exponents
  • scientific notation

Semester II

Chapter 6: Exponential and Logarithmic Functions

  • logarithms
  • logarithms and other bases
  • logarithm properties
  • inverses of functions
  • add-multiply property

Chapter 7: Rational Algebraic Functions

  • discontinuities and asymptotes
  • special products and factoring
  • long division of polynomials
  • factoring higher-degree polynomials
  • products and quotients of rational expressions
  • sums and differences of rational expressions
  • fractional equations and extraneous solutions
  • variation functions

Chapter 8: Irrational Algebraic Functions

  • graphs of irrational functions
  • radicals and simple radical form
  • radical equations
  • variation functions with non-integer variable

Chapter 9: Quadratic Relations and Systems

  • circles, ellipses, hyperbolas, and parabolas
  • graphs of conics
  • system of quadratics

Chapter 10: Higher Degree Functions and Complex Numbers

  • complex numbers
  • graphs of higher degree functions
  • mathematical models

Chapter 11: Sequences and Series

  • arithmetic and geometric sequences
  • arithmetic and geometric means
  • arithmetic and geometric series
  • convert geometric series
  • factorials
  • binomial series and the binomial formulas

Chapter 12: Probability, Data Analysis, and Functions of Random Variable (as time allows)

  • counting principles
  • permutations and combinations
  • properties of probability
  • random variables
  • mathematical expectation

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