Algebra Help

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
Basic Algebra Terms - Constants, Variables, Coefficients, Terms, Expressions, Equations, Quadratic Equations
Number Properties - Commutative property, Associative property, Distributive property

Algebraic Expressions
Writing 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 Multiply

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 the Variables on Both Sides
Solving Algebra Equations by Distributive Property

Solving Two-Step Equations
Solving Muti-Step Equations

Systems of Linear Equations, or Simultaneous Equations

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

Inequalities

Inequalities and the Number Line
Operations on Inequalities

Solving Single-Step Inequalities by Addition or Subtraction
Solving Single-Step Inequalities by Multiplication
Solving Single-Step Inequalities by Division

Solving Inequalities
Graphing Linear Inequalities
Compound Inequalities

Solving Systems of Linear Inequalities / Simultaneous Linear Inequalities
Absolute Value Inequalities
Solving Quadratic Inequalities

Quadratic Equations

Difference of Squares
Square of Sum or Perfect Square Trinomials

Completing the Square
Quadratic Formula or Quadratic Equation

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

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 Word Problems
Consecutive Integer 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 Problems
With 2 Objects and With more than 2 Objects

Money Word Problems
Money Word Problems

Motion Word Problems
Motion Problems

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

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 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

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 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 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 Sens:e 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 lines: Given 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

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

What 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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