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 videos and step-by-step solutions) 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 Expressions
Variables, constants, terms, expressions, & coefficients
Write Algebraic Expressions
Translate from words to algebraic expressions.
Add & Subtract Expressions
Multiply & Divide Expressions
Simplify Expressions
Multiply Expressions or Expand Expressions
FOIL Method used to distribute two binomials
Isolate the Variable (Transposition)
Combine Like Terms
Cross Multiplication
Solve Linear Equations
Solve Equations by Addition or Subtraction
Solve Equations by Division, Multiplication or taking the Reciprocal
Solve Equations by Combining Like Terms
Solve Equations with Variables on Both Sides
Solve Algebra Equations by Distributive Property
Solve Two-Step Equations
Solve Multi-Step Equations
Solve Equations with Absolute Values
Solve for a Variable in a Formula
Inequalities & the Number Line
Operations on Inequalities
Solve Single-Step Inequalities by Addition or Subtraction
Solve Single-Step Inequalities by Multiplication
Solve Single-Step Inequalities by Division
Solve Inequalities
Graphing Linear Inequalities
Compound Inequalities
Solve Systems of Linear Inequalities / Simultaneous Linear Inequalities
Absolute Value Inequalities
Solve Quadratic Inequalities
Factor 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
Quadratic Formula or Quadratic Equation
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.
How to Translate Words to Equations?
The following examples, solutions & videos will show you how to solve the types of algebra
word problems that are commonly found in algebra assignments, homework & 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, y-intercept
Equation of a Line
Slope-intercept form for the equation of a line, how to write equations in slope-intercept form, how to write equations of horizontal & vertical lines, how to get the equation of a line given two points on the line.
Forms of Linear Equations
Slope-intercept form, the point-slope 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 x-intercept & y-intercept, how to graph linear equations using the slope & y-intercept.
Slope & Intercept of a Linear Equation
How to graph a linear equation when the equation is given in slope-intercept 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 y-intercept can affect the straight line graph.
Equation of a Line Parallel to the X-axis or Y-axis
Equation of a Line Given its Slope and a Point on the Line
Equation of a Line Given Two Points on the Line
Slopes of Parallel & 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 & a line that is parallel or perpendicular to it, how to find parallel or perpendicular lines using Standard Form.
Midpoint Formula
Midpoint formula, how to find the midpoint given two endpoints, how to find one endpoint given the midpoint & another endpoint, how to proof the midpoint formula.
Distance Formula
How 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.
Graphing 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.
Expressions & Equations
Introduction To Algebraic Expressions:
- What is an algebraic expression?
- The vocabulary of algebraic expressions
- The geometry of algebraic expressions
- Combining like terms
- Simplify 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:
- What makes an equation linear?
- Using addition property and multiplication property of equality to solve linear equations.
- Checking solutions.
Equations & Inequalities
Solve 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 & inconsistent equations; the empty set; the set of real numbers
- Solution sets for linear equations
- Solutions & solution sets to inequalities; set builder notation
Solve Linear Inequalities That Have Only One Variable:
- Solution sets to inequalities.
- The addition property of inequalities
- The positive multiplication property of inequalities
- The negative multiplication property of inequalities
Word Problem, Percents, Mixtures
Literal Equations:
- Definition
- Solve for a variable
- Modeling & 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 & decimals
- A basic blueprint for percent questions
- A bona-fide application involving percents
Problem Solving Mixtures & solutions:
- The fundamental concept of mixing it up in mixture problems.
- Examples.
Ratio & Geometry
Ratio, Proportions & Rates:
- Ratio, rates & rational numbers, Proportions
Problem Solve With Proportions:
- Direct proportions
- Inverse or reciprocal proportions
- Proportions in geometry
2-Dimensional Geometry - Introduction To Perimeter & Area
- Perimeter, circumference & linear units
- Area & Square Units.
3-Dimensional Geometry:
- Introduction to volume & surface area
- Volume & surface area formulas
Equations & Slopes
Equations With Two Variables:
- Solutions 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:
- 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
Slopes & Lines
Slope Sense:
- Sign on slope
- Magnitude of slope
- Parallel lines
Comparing Slopes:
- Perpendicular lines
- Vertical lines, Horizontal lines
- Summary of slopes
Graphing Lines Using Intercepts:
- Three forms of the equation for a line Intercepts
- Standard Form
- Slope-intercept form
Matters Of Scale:
- Slippery slope
- Broken scale
Linear Equations
Finding Equations Of Lines:
- Given slope & vertical intercept
- Given both intercepts, Applications
Slope-Intercept Form:
- Find the equation of a line given the slope & a point on the line
- Applications of linear equations
Point-Slope Form Of A Linear Equation:
- Point-slope 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
Linear Inequalities In Two Variables:
- Linear inequalities of the form x > C
- Linear inequalities of the form y > C
- Linear inequalities of the form y > mx + b
- Applications of Linear Inequalities in two variables
Course Review & Summary:
- Linear Equations
- Linear Modeling
Systems Of Equations
Solve Systems Of Linear Equations:
- What is a solution to a Systems of Linear Equations in Two Variables?
- Solve Systems of Linear Equations by Graphing
- Solve Systems of Linear Equations in Two Variables by Substitution
- When is Substitution the best method?
- Special Cases
- Three Common Solution Methods
Systems Of Equations Applications
Applications Involving Systems Of Linear Equations In Two Variables:
- A Word Problem
- Applications involving money
Geometry, Systems & Substitutions:
- Linear Systems based in Geometry
- Using Substitution to find new formulas from old
Polynomials
Polynomials:
- What is a polynomial? Definitions
- Evaluating polynomials
Multiplying Polynomials:
- Multiply monomials
- The distributive property
- Multiply binomials
Multivariable Product:
- Multiply polynomials by monomials
- FOIL
- Special products, Products involving polynomials with more than two terms
The Geometry Of Polynomial Multiplication:
- Basic geometry examples & applications
- Perfect square trinomials
Exponents
Exponents:
- Three 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
Scientific Notation
- Powers of ten & place value
- Computations using scientific notation
- Astronomical Calculations
Factoring
- An introduction to factoring
- What is factoring?
- The greatest common factor
- Factor out the greatest common factor
- Factor Binomials of the form x^{2} + bx + c
- Recognizing patterns that emerge from FOIL
- Guess & check, Factor binomials
- Factor Trinomials by grouping
- Factor second-degree trinomial expressions
- Factor multivariable trinomial expressions
Factor Trinomials
- Special form factorization Perfect Square Trinomials
- Difference of Squares, Sum or difference of cubes
- Discuss what went wrong in the following ?factorizations?
- Solve Quadratic Equations by Factor
- What is a quadratic equation?
- The zero-product principle
Finding square roots
- Simplify Square Roots Rationalizing the denominator
- Solve Quadratic Equations using the square root property
- Solution sets to quadratic equations
- Solve 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 & the vertex
Modelling with Quadratic Equations
- The Graphing Form of Quadratic Equations in Two Variables
- Applications involving maxima & minima
Functions
- Relations, Domain, Range
- Definition of a Function, Function Notation
- Numerical & Graphical Representation of Functions
Course Review:
- Systems of Equations, Exponents & Square Roots
- Polynomials, Quadratic Equations, Functions
- Questions on Systems of Equations, exponents, square roots, scientific notation, quadratics
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