Algebra lessons

Find here a great variety of algebra lessons that will help you learn algebra in no time.

Prerequisites

  1. Introduction to integers
  2. Comparing integers
  3. Adding integers
  4. subtracting integers
  5. Modeling the addition/subtraction of integers
  6. Multiplying integers
  7. Modeling the multiplication of integers
  8. Dividing integers
  9. Why multiply before adding
  10. Order of operations
  11. Variables in algebra
  12. Writing an algebraic expression
  13. Evaluate an algebraic expression
  14. How to write an inequality 
  15. Linear equations
  16. Important academic words in math
  17. Interval notation
  18. Math problem solving strategies
  19. Common mistakes in math

Solving one, two, or multi steps equations

  1. Solving equations using addition 
  2. Solving equations using subtraction 
  3. Solving multiplication equations 
  4. Solving two-step equations
  5. Solving an equation with a variable on both sides
  6. Solve an equation using the distributive property
  7. Solving literal equations

Exponents, scientific notation, square root, and rational numbers

  1. Exponents
  2. Laws of exponents
  3. Properties of exponents
  4. Scientific notation
  5. Compute with scientific notation
  6. Rational numbers
  7. Irrational numbers
  8. Square root of a number
  9. Estimate the square root of a number

Graphing equalities, inequalities, linear equations, and linear inequalities

  1. Graphing equalities
  2. Cartesian coordinate system
  3. Graphing points in three dimensions
  4. Graphing equations in three dimensions
  5. Graphing inequalities
  6. Solve and graph inequalities
  7. Inequalities with no solutions
  8. Inequalities with all real numbers as solutions
  9. Compound inequalities
  10. Graphing linear equations
  11. Graphing linear inequalities

Solving absolute value equations

  1. Definition of absolute value
  2. Properties of absolute value
  3. Solving absolute value equations
  4. Solving multi-step absolute value equations
  5. Solving absolute value inequalities
  6. Absolute value word problems
  7. Solve tough absolute value equations

Solving system of linear equations  

  1. System of linear equations
  2. Solutions of systems of linear equations with two variables
  3. Solve a system with two variables with infinitely many solutions
  4. Solutions of systems of equations with three variables
  5. Elimination method
  6. Substitution method
  7. Solve a system of linear equations by making a table
  8. Solve a system of equations with three variables by elimination
  9. Solve a system of equations with three variables by substitution

Polynomials

  1. Definition of a polynomial
  2. Degree of a polynomial
  3. Properties for simplifying algebraic expressions
  4. Simplifying algebraic expressions
  5. Adding polynomials
  6. Subtracting polynomials
  7. Multiplying polynomials
  8. Factoring polynomials using the sum and difference of cubes
  9. Polynomial long division
  10. Divide polynomials with synthetic division
  11. Solve a polynomial equation by graphing

Factoring

  1. What is factoring
  2. Factoring integers
  3. Finding the greatest common factor
  4. Multiplying binomials using FOIL
  5. Multiplying binomials geometrically
  6. Factoring algebraic expressions
  7. Factoring trinomials
  8. Factoring by grouping
  9. Factoring perfect square trinomials
  10. Factoring using the quadratic formula
  11. Factoring a trinomial by getting rid of the impostor
  12. Factoring a trinomial using the box method
  13. Factoring formulas
  14. Factoring strategy and tricks

Radicals

  1. Radical expressions
  2. Factoring radicals
  3. Simplifying radicals containing variables
  4. Adding and subtracting radicals
  5. Conjugates
  6. Multiplying radical expressions
  7. Rationalizing the denominator of a radical expression
  8. Solve radical equations

Solve quadratic equations

  1. Zero product property
  2. Ways to solve quadratic equations
  3. Solve quadratic equation by factoring
  4. Solve quadratic equations by completing the square
  5. Solve quadratic equations using the quadratic formula
  6. Quadratic equations word problems
  7. Quadratic equation solver
  8. Find complex solutions of a quadratic equation
  9. Discriminant of a quadratic equation

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

Sequences and patterns

  1. Sequences and patterns
  2. Arithmetic sequence
  3. Sum of arithmetic sequences
  4. Geometric sequence
  5. Fibonacci sequence

Functions

  1.  How to identify a function
  2.  Vertical line test
  3.  Horizontal line test
  4.  Function rule
  5.  Find function values
  6.  Function notation
  7.  Linear parent function
  8.  Difference between discrete and continuous data 
  9.  Ways to represent domain and range
  10.  Domain of a function
  11.  Range of a function
  12.  Greatest integer function
  13.  Operations on functions
  14.  Composite function

Absolute value functions

  1.  Absolute value function
  2.  Graph an absolute value function
  3.  Graph of the parent absolute value function
  4.  The family of absolute value functions

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.  How to write the equation of a parabola
  7.  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

Useful algebra calculators

Quadratic equation calculator

Linear equations calculator

Order of operations calculator

Factoring calculator

System of linear equations solver

Matrix calculator

Scientific notation calculator

Goal of these algebra lessons

The goal of these algebra lessons is help you become very familiar with the following topics:

  • Learn to add, subtract, multiply, and divide integers
  • Learn the difference between rational numbers and irrational numbers
  • Learn to solve linear equations, absolute value equations, and system of linear equations
  • Learn to add, subtract, and multiply polynomials
  • Learn to factor and solve quadratic equations
  • Learn to add, subtract, and multiply matrices
  • Explore sequences and patterns
  • Find the probability of events
  • Explore some important algebra proofs
  • Learn to find the mean, mean, mode,  standard deviation, and others
  • And much more!

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