Topics in Algebra II

These lessons use MathJax to get the beautiful mathematics.

Section 1:
Recursion, Sequences, and Applications
  1. introduction to recursion and sequences
  2. arithmetic and geometric sequences
  3. loans and investments
  4. the compound interest formula
Section 2:
Functions and their Graphs
  1. graphs of functions
  2. basic models you must know
  3. graphical interpretation of sentences like  f(x) = 0  and  f(x) > 0 
  4. graphical interpretation of sentences like  f(x) = g(x)  and  f(x) > g(x
  5. composition of functions
Section 3:
  1. advanced set concepts
  2. basic probability concepts
  3. more probability concepts
  4. probability tree diagrams
  5. choosing things: does order matter?
  6. factorial notation
  7. combinations and permutations
Section 4:
  1. summation notation
  2. mean, median, and mode
  3. measures of spread
Section 5:
Systems of Equations
  1. introduction to systems of equations
  2. solving systems using substitution
  3. solving systems using elimination
  4. simple word problems resulting in a system of equations
Section 6:
  1. introduction to matrices
  2. basic arithmetic with matrices
  3. multiplying matrices
Section 7:
Graphical Transformations
  1. vertical and horizontal translations (moving up, down, left, and right)
  2. vertical and horizontal scaling (stretching and shrinking)
  3. reflections and the absolute value transformation
  4. graphical transformations: all mixed up
Section 8:
Quadratic Functions and More
  1. parabolas
  2. equations of simple parabolas
  3. quadratic functions and the completing the square technique
  4. algebraic definition of absolute value
  5. the quadratic formula
  6. complex numbers
  7. arithmetic with complex numbers
  8. equations of circles
Section 9:
Exponential and Logarithmic Functions
  1. introduction to logarithms
  2. properties of logarithms
  3. change of base formula for logarithms
  4. introduction to logarithmic functions
  5. introduction to exponential functions
Section 10:
  1. introduction to polynomials