Need some algebra help? Or just wanting to review some key concepts
in algebra? Here are some lessons to get you started on this
important branch of math. With these lessons, algebra will no longer
be a mystery reserved for the selected few.
An overview of algebra
word problems (includes video)
covers the common types of word problems in high school and college
prep math and the various techniques for solving them.
Free Algebra Worksheets are available to provide practice on some of the following topics, for example solving of equations.
Basic Algebra An introduction to
Algebra

Basic Algebra Terms Constants,
Variables, Coefficients, Terms, Expressions, Equations,
Quadratic Equations

Number Properties Commutative
property, Associative property, Distributive property


Algebraic ExpressionsVariables,
constants, terms, expressions, and coefficients

Writing Algebraic Expressions
Translate from words to algebraic expressions

Adding and Subtracting Expressions  Multiplying and Dividing Expressions 
Simplifying Expressions  Multiplying Expressions or Expanding Expressions 
FOIL Method used to distribute two binomials  
Isolate the Variable (Transposition)  Combine Like Terms 
Cross Multiplication  Solving Linear Equations 
Solving Equations by Addition or
Subtraction

Solving Equations by Division,
Multiplication or taking the Reciprocal

Solving Equations by Combining Like
Terms

Solving Equations with
Variables on Both Sides

Solving Algebra
Equations by Distributive Property


Solving MutiStep Equations  Solving Equations with Absolute Values 
Solving for a Variable in a Formula  
Solve Systems of
Equations by Substitution

Solve Systems of
Equations by Addition Method (OppositeCoefficients
Method)

Solve Systems of Equations
Graphically


Factoring Quadratic Equations  Finding Common Factors 
Square of Sum  Square of Difference 
Difference of Two Squares  Coefficient of x^{2} is 1 
Coefficient of x^{2} is greater than 1  Difference of Squares 
Square of Sum or Perfect Square Trinomials  Completing the Square 
Graphical Solutions of Quadratic
Equations How the solutions of a quadratic
equation is related to the graph of the quadratic
function, how to use the graphical method to solve
quadratic equations.

Simplifying Rational Expressions  Adding Rational Expressions 
Subtracting Rational Expressions  Multiplying Rational Expressions 
Dividing Rational Expressions  Partial Fraction Decomposition 
Relations and Functions  Function Notation 
Domain and Range of a Function  Arithmetic Operations on Functions 
Composite Functions  Functions & Composite Functions 
Inverse of a Function  
Adding and Subtracting Real Numbers  Multiplying and Dividing Real Numbers 
Properties of Real Numbers  Identity Property of 1 and 0 
Order of Operations for Real Numbers  
Translating Words to Equations
The following examples, solutions and videos will show you how to solve the types of algebra word problems that are commonly found in algebra assignments, homework and tests. We hope that these examples will help you learn how to approach the different types of algebra word problems.
Coordinate Geometry Coordinate
plane, Slope Formula, Equation of a Line, Slopes of
parallel lines, Slope of perpendicular lines, Midpoint
Formula, Distance Formula

Coordinate Plane Coordinate plane
or Cartesian plane, points on the Cartesian Plane,
quadrants

Slope of a Line Slope of line from
the graph (rise over run), using the slope formula,
negative slope, yintercept

Equation of a Line Slopeintercept
form for the equation of a line, how to write equations
in slopeintercept form, how to write equations of
horizontal and vertical lines, how to get the equation
of a line given two points on the line.

Forms of Linear
EquationsSlopeintercept form, the pointslope
form, the general form, the standard form, how to
convert between the different forms of linear equations.

Graphing Linear
Equations How to graph linear equations by
plotting points, how to graph linear equations by
finding the xintercept and yintercept,
how to graph linear equations using the slope and yintercept.

Slope and Intercept
of a Linear Equation How to graph a linear
equation when the equation is given in slopeintercept
form or when the equation is given in general form.

Explore the straight line graph
Activity to investigate how the change of the slope and
yintercept can affect the straight line graph.

Slopes of Parallel and Perpendicular
Lines How to determine if two lines are parallel
or perpendicular when given their slopes, how to find
the equation of a line given a point on the line and a
line that is parallel or perpendicular to it, how to
find parallel or perpendicular lines using Standard
Form.


Midpoint FormulaMidpoint formula,
how to find the midpoint given two endpoints, how to
find one endpoint given the midpoint and another
endpoint, how to proof the midpoint formula.

Distance FormulaHow to derive the
distance formula from the Pythagorean Theorem, how to
use the distance formula.

Graphing Linear
Inequalities Graph of linear inequalities, how to
graph linear inequalities, how to graph systems of
linear inequalities.


Linear Programming
Linear programming, how to use linear programming to
solve word problems.

Quadratic Functions
Different forms of quadratic functions, general form,
factored form, vertex form, convert from general form to
factored form, convert from the general form to the
vertex form using the vertex formula, convert from the
general form to the vertex form using completing the
square.

Graphing Quadratic Functions How
to graph of quadratic functions by plotting points, how
to graph quadratic function of the form y = ax^{2,
}the properties of the graph y = ax^{2},
how to graph a quadratic function given in general form,
how to graph a quadratic function given in factored
form, how to graph a quadratic function given in vertex
form.

Graphical Solutions of Quadratic
Equations How the solutions of a quadratic
equation is related to the graph of the quadratic
function, how to use the graphical method to solve
quadratic equations.

Graphing Cubic Functions How to
graph of cubic functions by plotting points, how to
graph cubic functions of the form y = a(x
− h)^{3} + k.

Graphing Exponential Functions
How to graph exponential functions by plotting points,
the characteristics of exponential functions, how to use
transformations to graph an exponential function.

Graphing Reciprocal Functions
How to graph reciprocal functions by plotting points,
the characteristics of graphs of reciprocal functions,
how to use transformations to graph a reciprocal
function, how to get the equation of a reciprocal
function when given its graph.

Sketching the Graphs of some Functions
How to graph functions of the form y = ax^{n} + c,
how to sketch some basic or common graphs.

Introduction
to Algebraic Expressions: What is an algebraic expression?
The vocabulary of algebraic expressions
The geometry of algebraic expressions, Combining like terms
Simplifying Algebraic Expressions using the distributive
property
An introduction to equations
Why do we write equations? What is an equation?
What is a solution to an equation? Different types of equations
Introduction to linear equations
Solving
Linear Equations: Properties of equality Equations that
involve simplification, Equations containing fractions.
A general strategy for solving linear equations
Solution Sets:
Solutions vs solution sets ? graphing solution sets
Identity equations and inconsistent equations; the empty set;
the set of real numbers Solution sets for linear equations
Solutions and solution sets to inequalities; set builder
notation
Solving linear inequalities that have only one variable
Solution sets to inequalities, The addition property of
inequalities
The positive and negative property of inequalities
The negative multiplication property of inequalities
Literal
Equations ? Definition, Solving for a variable Modelling
and solving word problems using algebra
Word problems with one unknown
Word problems with more than one unknown
An alternative strategy for thinking through the problem
Working
with percents Percents, fractions and decimals
A basic blueprint for percent questions
A bonafide application involving percents
Problem
solving Mixtures and solutions
The fundamental concept of mixing it up in mixture problems,
Examples
Ratio,
proportions and rates Ratio, rates and rational numbers,
Proportions
Problem Solving with Proportions
Direct proportions, Inverse or reciprocal proportions
Proportions in geometry
2dimensional
geometry Introduction to perimeter and area
Perimeter, circumference and linear units
Threedimensional geometry
Introduction to volume and surface area
Volume and surface area formulas
Equations
with two variablesSolutions sets to equations with one
variable
Solution sets to linear inequalities with one variable
Solution sets to equations with two variables
Plotting
solutions from a table Table of values, Application
Slope between two points, Slope of a line
Positive slope, negative slope, zero slope
Determining slope from tables: Computing ?rise over run? given a
table of data Determining whether a table of data describes a
linear relationship
Generating a table of data from a verbal description
Slope
Sense Sign on slope, Magnitude of slope, Parallel lines
Comparing slopes: Perpendicular lines, Vertical lines,
Horizontal lines
Summary of slopes
Graphing Linear Equations With Two Variables using intercepts
Three forms of the equation for a line Intercepts
Standard Form, Slopeintercept form
Matters of scale: Slippery slope, Broken scale
Finding
equations of linesGiven slope and vertical intercept
Given both intercepts, Applications
Slopeintercept form:
Find the equation of a line given the slope and a point on the
line
Applications of linear equations
Pointslope form of a linear equation:
Pointslope form, Finding a linear equation given two points on
a line
Finding a linear equation given a graph of a line
Applications of Linear Equations
Linear
Inequalities in two variables
Applications of Linear Inequalities in two variables
Course Review and Summary: Linear Equations
Linear Modelling
Solving
Systems of Linear Equations
What is a solution to a Systems of Linear Equations in Two
Variables?
Solving Systems of Linear Equations in Two Variables by
Substitution
When is Substitution the best method?
Special Cases, Three Common Solution Methods
Applications
involving Systems of Linear Equations in Two Variables A
Word Problem, Applications involving money
Linear Systems based in Geometry
Using Substitution to find new formulas from old
ExponentsThree
important rules of exponents
Two important definitions of exponents
An alternate definition of a polynomial
Examples, Find a strategy that will work for you
One last exponent rule
PolynomialsWhat
is a polynomial? Definitions
Evaluating polynomials
Multiplying monomials, The distributive property, Multiplying
binomials
Multivariable Product: Multiplying polynomials by monomials,
FOIL
Special products, Products involving polynomials with more than
two terms
The geometry of polynomial multiplication:, examples and
applications
Perfect square trinomials
Scientific
Notation Powers of ten and place value
Computations using scientific notation, Astronomical
Calculations
An
introduction to factoring What is factoring?
The greatest common factor, Factoring out the greatest common
factor
Factoring Binomials of the form x^{2} + bx + c
Recognizing patterns that emerge from FOIL
Guess and check, Factoring binomials
Factoring Trinomials by grouping
Factoring seconddegree trinomial expressions
Factoring multivariable trinomial expressions
Special
form factorization Perfect Square Trinomials
Difference of Squares, Sum or difference of cubes
Discuss what went wrong in the following ?factorizations?
Solving
Quadratic Equations by Factoring What is a quadratic
equation?
The zeroproduct principle
Finding
square roots Simplifying Square Roots Rationalizing the
denominator
Solving Quadratic Equations using the square root property
Solution sets to quadratic equations
Solving Quadratic Equations Using the Quadratic Formula
What is the quickest method to solve a quadratic equation?
Applications
of Quadratic Equations Working with formulas
Modeling with quadratic equations
Graphs of Parabolas
The axis of symmetry and the vertex
Modelling
with Quadratic Equations
The Graphing Form of Quadratic Equations in Two Variables
Applications involving maxima and minima
Functions
Relations, Domain, Range
Definition of a Function, Function Notation
Numerical and Graphical Representation of Functions
Course
Review Systems of Equations, Exponents and Square Roots
Polynomials, Quadratic Equations, Functions
Questions on Systems of Equations, exponents, square roots,
scientific notation, quadratics