Notes and Videos for College Algebra Final

Practice Problems for College Algebra Final

Notes and Videos from Spring '25 Final.
- Spring '25 Solutions for Final - Made During the Recording of the Videos.
- Spring '25 Solutions - These were made prior to grading the Final.
- Videos
  - #1 - Graph a System of Inequalities
  - #2 - Corner Points for #1
  - #3 - Absolute-Value Inequalities
  - #3 - Method 2 - Factoring a "- 1" out of the absolute value
  - #4 - Operations on Functions and Domain
  - #5 - EFFICIENT Equations of Lines, Parallel Lines, Perpendicular Lines/a>
  - #6 - Quadratic Functions, Quadratic Formula, Completing the Square, and Graphing
  - #s 7 and 8 - An Equation and Related Inequality Involving Rational Functions.Sign Patterns are essential. They're not that hard, either.
  - #9 - Theory of Polynomials. Find all zeros of a Quartic Polynomial, using Rational Zeros, Synthetic Division, and Depressed Polynomial.
  - #10 - Sketch the Graph of a Pretty Basic Rational Function.
  - #11 - Sketch the Graph of a Rational Function with a Slant (Oblique) Asymptote.
  - #12 - Domain of the Square Root of a Rational Function. - This is an exercise in Sign Patterns. Easy if you get it. Impossible if you don't. Not much middle ground
  - #13 - Sketch an Exponential Function by Transforming a Basic Exponential Function.
  - #14 - Find the Inverse of the Exponential Function in #13
  - #15 - Sketch the Graph of the Logarithmic Function in #14
  - #16 - Sketch a Parabola. Show its Focus and Directrix.
  - #17 - Graph Hyperbola. Show Center, Foci, Vertices and Asymptotes
  - #18 - Complete the Square to Write Ellipse in Standard Form.
  - #19 - Sketch the Graph of the Ellipse in #18. Show Endpoints of its Major and Minor Axes and its Foci
  - #20 - Label the Endpoints of the Latera Recti of the Ellipse in #19
  - #21 - Use Pascal's Triangle to Expand a Binomial to the 5th Power
  - #22 - Pluck out one of the Coefficients of the 12th Power of a Binomial
  - #23 - Combinations Word Problem.
  - #24 - Permutations Word Problem.
  - #25 - Solve a System of 3 Linear Equations in 3 Variables, if a Solution Exists.
- Notes for the Week 12 Videos
  - #1 - Solve a System of 2 linear equations in 2 variables
  - #2 - Solve an independent system of 3 linear equations in 3 variables by elimination.
  - #3 - Solve a dependent system of 3 linear equations in 3 variables, with infinitely-many solutions
  - #4 - Show that the dependent system of 3 linear equations in 3 variables given has no solutions.
- Notes for the Week 14 Videos - These are similar to the Week 14 solutions, but they are board work from the videos, rather than straight-up solutions that I released, previously. Also, the system of linear inequalities is a brand-new system, for more practice.
  - #1 - Partial Fractions
  - #2 - Graph a system of linear inequalities
  - #3 - Parabolas: Vertex, Focus and Directrix
  - #4 - Ellipses: Center, Vertices and Foci. "The box."
    - #4a - Center at the origin
    - #4b - Center NOT at the origin
  - #5 - Hyperbolas: Center, Vertices, Asymptotes, and Foci. Also "the box."
    - #5a - Hyperbola with vertex at the origin
    - #5b - Hyperbola with vertex NOT at the origin
  - #6 - Binomial Theorem and Binomial Coefficients
    - #6a - Pascal's Triangle
    - #6b - Full-blown Binomial Theorem
  - #7 - Permutations: Choose and Arrange.
  - #8 - Combinations: Choose!