Advanced algebra

Here, you can explore some advanced algebra lessons. These topics or lessons are usually covered in algebra 2 and include, among others, matrices, exponential and logarithmic functions, and some algebra proofs. 

A more comprehensive list is shown below. Do not forget to check the section about 100 tough algebra word problems.

Prerequisites

  1. Important academic words in math
  2. Common mistakes in math
  3. Math problem solving strategies
  4. Interval notation
  5. Consecutive integers

Graphing in three dimensions

  1. Graphing points in three dimensions
  2. Graphing equations in three dimensions

System of linear equations with three variables

  1. Solutions of systems of equations with three variables
  2. Solve a system of equations with three variables by elimination
  3. Solve a system of equations with three variables by substitution

Matrices

  1. Introduction to matrices
  2. Write the dimensions of a matrix
  3. Add and subtract matrices
  4. Properties of matrix addition
  5. Solve a matrix equation
  6. Multiply matrices

Quadratic functions

  1.  Definition of quadratic functions
  2.  How to convert a quadratic function from general form to vertex form
  3.  How to convert a quadratic function from vertex form to general form
  4.  Fit a quadratic function to 3 points
  5.  Graph of a quadratic function
  6.  The family of quadratic functions

Polynomial functions

  1.  Polynomial functions
  2.  How to write a polynomial from factored form to standard form
  3.  How to write a polynomial from standard form to factored form
  4.  How to write a polynomial function from its zeros
  5.  How to find the zeros of a polynomial function
  6.  Find the multiplicity of a zero
  7.  Remainder theorem
  8.  Rational root theorem
  9.  Irrational root theorem
  10.  Find rational roots using the rational root theorem
  11.  Evaluate a polynomial by synthetic division
  12.  Factor a higher-degree polynomial by using a quadratic pattern
  13.  Solve a higher-degree polynomial by using a quadratic pattern

Exponential and logarithmic functions

Exponential and logarithmic functions

Conic sections

  1. Equation of a circle
  2. Parabola
  3. Write the equation of a parabola
  4. Derive the equation of an ellipse

Complex numbers

  1. Complex numbers
  2. Graphing complex numbers
  3. Adding complex numbers
  4. Multiplying complex numbers
  5. Additive inverse of a complex number
  6. Powers of i
  7. Absolute value of a complex number
  8. Find complex solutions of a quadratic solution
  9. Complex conjugates

Algebra proofs

Examples of inductive reasoning

Proof by mathematical induction

Law of detachment

Algebra proofs

Proof that square root of five is irrational

How to prove that there is no rational number whose square is 2

How to prove that the sum of a rational number and an irrational number is an irrational number

Proof of the Pythagorean theorem
A proof of the Pythagorean theorem by president Garfield is clearly explained here. 

Proof of the quadratic formula
Here we prove the quadratic formula by completing the square. 

More interesting and challenging advanced algebra topics!

100 tough and tricky algebra word problems

Solve rational inequalities

Direct variation

Inverse variation

Topics covered in advanced algebra or algebra 2

The different branches of algebra are beginning algebra, advanced algebra, linear algebra, abstract algebra, and commutative algebra.

The goal of these advanced algebra lessons is to help you become very familiar with high school algebra taught in 11th grade or sometimes in 12th grade. We will teach you most of the following topics:

  • Graphing in three dimensions
  • Learn to add, subtract, and multiply matrices
  • Learn to graph quadratic equations
  • Write and graph polynomials functions
  • Solve polynomial equations
  • Use important theorems about the number of solutions to polynomial equations
  • Define, write, and evaluate exponential functions
  • Define exponential growth and decay
  • Modeling and graphing exponential growth and decay
  • Define, write, and evaluate logarithms
  • Simplify logarithms
  • Expanding logarithms
  • Properties of logarithms
  • Solve exponential and logarithmic functions
  • Learn how to prove things by induction
  • Learn how to prove the Pythagorean theorem
  • Learn how to prove the quadratic formula
  • Learn to add, multiply, and graph complex numbers
  • Use complex numbers to solve quadratic equations.

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Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

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