Algebra Help



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.

Algebra Topics

Introduction

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


Techniques to Solve Equations

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 Muti-Step Equations Solving Equations with Absolute Values
Solving for a Variable in a Formula

Systems of Linear Equations, or Simultaneous Equations

Solve Systems of Equations by Addition Method (Opposite-Coefficients Method)




Inequalities

Inequalities and the Number Line Operations on Inequalities
Solving Single-Step Inequalities by Addition or Subtraction
Graphing Linear Inequalities Compound Inequalities
Solving Systems of Linear Inequalities / Simultaneous Linear Inequalities Absolute Value Inequalities
Solving Quadratic Inequalities

Factoring and Solving Quadratic Equations

Factoring Quadratic Equations Finding Common Factors
Square of Sum Square of Difference
Difference of Two Squares Coefficient of x2 is 1
Coefficient of x2 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.

Factoring Trinomials

Factoring Trinomials Factoring Trinomials by GCF
Factoring Perfect Square Trinomials Factoring Trinomials by Grouping
Factoring Trinomials by Trail and Error - Unfoiling Factoring Trinomials with Two Variables

Polynomials

Adding and Subtracting Polynomials FOIL method used to multiply two binomials
Multiplying Polynomials Dividing Polynomials by Monomials
Dividing Polynomials by Long Division Synthetic Division
Factoring by Grouping Remainder Theorem
Factor Theorem Solving Cubic Equations
Binomial Theoerm





Rational Expressions

Simplifying Rational Expressions Adding Rational Expressions
Subtracting Rational Expressions Multiplying Rational Expressions
Dividing Rational Expressions Partial Fraction Decomposition

Logarithms

Introduction to Logarithms Solving Logarithmic Functions
Common and Natural Logarithms Logarithm Rules or Properties of Logarithms
Proof for the Properties of Logarithms Solving Logarithmic Equations
Graphs of Logarithmic Functions

Functions

Relations and Functions Function Notation
Domain and Range of a Function Arithmetic Operations on Functions
Composite Functions Functions & Composite Functions
Inverse of a Function

Real Number Videos

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





Types Of Algebra Word Problems

Translating Words to Equations

Age Word Problems

Age Problems Age Problems involving a Single Person
Age Problems Involving More Than One Person

Average Word Problems

Average Problems Arithmetic Mean
Weighted Average Average Speed

Coin Word Problems

Problems involving Coins Stamp problems
Ticket problems Consecutive Integer Problems

Consecutive Integer Word Problems

Consecutive Integer Consecutive Odd Integer
Consecutive Even Integer

Digit Word Problems

Simple Digit Problems Convert Digits to Numbers and Interchanging Digits

Distance Word Problems

Distance Problems Travel at Different Rates
Travel in Different Directions Given Total Time

Fraction Word Problems


Fraction Problems
Geometry Word Problems

Geometry Word Problems Involving Perimeters
Involving Areas Involving Angles

Integer Word Problems

Involving 2 Unknowns Involving More Than 2 Unknowns

Interest Word Problems


Interest Problems
Lever Word Problems

Lever Word problems with 2 objects and more than 2 objects
Mixture Word Problems

Mixture Problems Adding to a Solution
Remove from a Solution Replace a Solution
Mix Items of Different Values

Money Word Problems

Money Word Problems
Motion Word Problems

Motion Problems
Number Sequence Word Problems

Number Sequence Problems Value of a Particular Term
Pattern of a Sequence

Proportion Word Problems

Proportion Problems Directly Proportional
Inversely Proportional

Ratio Word Problems

Ratio Problems Two-Term Ratios
Three-Term Ratios

Symbol Word Problems

Symbol Problems

Variation Word Problems

Direct Variation Problems Inverse Variation Problems
Joint and Combined Variation Problems

Work Word Problems

Work Problems Two Persons
More Than Two Persons Pipes Filling up a Tank





Algebra Word Problems Videos

Age Word Problems I Age Word Problems II
Coin Word Problems I Coin Word Problems II
Digits Word Problems Integer Word Problems I
Integer Word Problems II Perimeter Word Problems I
Perimeter Word Problems II Area Word Problems
Volume Word Problems Angle Word Problems
Proportion Word Problems Ratio Word Problems
Rate, Time, Distance Problems I Rate, Time, Distance Problems II
Rate, Time, Distance Problems III Simple Interest Word Problems
Compound Interest Word Problems I Compound Interest Word Problems II
Investment Word Problems
Algebra Work Problems I Algebra Work Problems II
Algebra Mixture Problems I Algebra Mixture Problems II
Algebra Mixture Problems III


Coordinate Geometry and Graphs

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 and vertical lines, how to get the equation of a line given two points on the line.
Forms of Linear EquationsSlope-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 and y-intercept, how to graph linear equations using the slope and y-intercept.
Slope and 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.
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 = ax2, the properties of the graph y = ax2, 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(xh)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 = axn c, how to sketch some basic or common graphs.




A series of Mathematics Lessons given in videos by Portland Community College - Algebra Review

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 bona-fide 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

2-dimensional geometry Introduction to perimeter and area
Perimeter, circumference and linear units
Three-dimensional 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, Slope-intercept form
Matters of scale: Slippery slope, Broken scale

Finding equations of linesGiven slope and vertical intercept
Given both intercepts, Applications
Slope-intercept form:
Find the equation of a line given the slope and 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 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 x2 + bx + c
Recognizing patterns that emerge from FOIL
Guess and check, Factoring binomials
Factoring Trinomials by grouping
Factoring second-degree 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 zero-product 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
Modelling 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



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