Pre Algebra & Beginning Algebra
Numbers, arithmetic, and the language of algebra. Equations, inequalities, expression manipulation, and the coordinate plane.

81
Video
Lessons 
133
Embedded Video
Questions 
656
Practice
Problems
Table of Contents
The Sets of Numbers
 Know the definitions of the sets of numbers
 Determine which set or sets a number belongs to
Graphing Real Numbers
 Graph a fraction or mixed number on a number line
 Graph a decimal number on a number line
 Graph an irrational number on a number line
Properties of Real Numbers
 Know the closure properties of the real numbers
 Know the commutative, associative, and distributive properties
 Know what additive and multiplicative identity elements and inverses are
 Know the multiplication and division properties of zero
Adding Integers Using a Number Line
 Represent positive addends using a rightfacing arrow
 Represent negative addends using a leftfacing arrow
 Add integers using a number line
Multiplying Integers 1
 Multiply signed numbers
 Multiply integers using long multiplication
Multiplying Integers 2
 Multiply integers using the table method
Dividing Integers
 Divide integers
 Division by zero
Order of Operations
 You should know the order in which mathematical operations are followed
 Use the order of operations in the context of simplifying expressions
Fraction Multiplication Part 1
 Multiply two or more fractions together
 Multiply positive and negative fractions
Fraction Multiplication Part 2
 Multiply a fraction by a mixed number
 Simplify after finding the product of two fractions
 Simplify before finding the product of two fractions
Fraction Division Part 1
 Divide a whole number or fraction by a fraction
Fraction Division Part 2
 Divide with negative fractions
 Divide with fractions and mixed numbers
Adding Fractions Part 1
 Add fractions that have the same denominator
 Add negative fractions
Adding Fractions Part 2
 Add fractions with different denominators
 Add mixed numbers
Subtracting Fractions Part 1
 Subtract fractions that have the same denominator
 Subtract fractions with negative signs
Subtracting Fractions Part 2
 Subtract fractions with different denominators
 Subtract mixed numbers
Simplifying Fractions
 Reduce fractions by division
 Reduce fractions by writing the prime factorization and canceling
 Reduce fractions with one variable
Reading and Writing Decimals
 Identify the names of the place values
 Write decimals in standard form
 Write decimals in expanded form
 Write decimals in words
Adding and Subtracting Decimals
 Add two decimals
 Add multiple decimals
 Subtract decimals
 Evaluate sums and differences involving negative decimals
Multiplying Decimals
 Multiply decimals as fractions
 Multiply decimals using vertical multiplication
 Multiply positive and negative decimals
Dividing Decimals
 Divide decimals using long divisions
 Divide decimals and round to a given place value
Absolute Value
 Define absolute value
 Find the absolute value of integers
Converting Decimals to Fractions
 Convert a terminating decimal to a fraction
Repeating Decimals
 Define a repeating decimal
 Convert a fraction to a repeating decimal
Converting Fractions to Decimals 1
 Convert a fraction to a terminating decimal
Converting Fractions to Decimals 2
 Convert a mixed number to a decimal
Percents
 Write percents as fractions
 Write percents as decimals
 Write decimals as percents
 Write fractions as percents
Additive Property of Equality
 Know the additive property of equality
 Understand and use the additive property of equality to isolate variables in equations
Multiplicative Property of Equality
 Know the multiplicative property of equality
 Understand and use the multiplicative property to isolate a variable in an equation
Solving Equations
 Know when to use the properties of equality
 Know how to use the distributive property
 Employ the properties of equality
 Employ the distributive property
 Solve equations involving properties together
Using Formulas to Fina Area
 Find the area of common shapes using formulas
Percent Equations 1
 Identify the base in percent equations
 Set up percent equations
 Solve percent equations
Percent Equations 2
 Formulate problems as percent equations
 Solve the resulting percent equations
Percent Increase and Decrease
 Set up and solve percent increase problems
 Set up and solve percent decrease problems
Markup and Discount
 Formulate markup and discount problems as percent increase and decrease problems
 Solve markup and discount problems
Simple Interest
 Use the simple interest formula to find simple interest due
 Find the maturity value of a simple interest loan
Linear Equations Application: Ladder Problem
 Solving equations
 Adding and Subtracting Polynomials
Introduction to Inequalities
 Know the meaning of a solution set
 Represent the solution set of an inequality on a number line
Manipulating Inequalities
 Manipulate inequalities to isolate a variable and represent the solution set on a number line
Linear Inequalities Application: Exercise
 Average of a set of numbers
 Solving a linear equation
Word Problems with Inequalities
 Write an inequality from a situation
 Solve word problems involving linear inequalities
The Cartesian Plane
 Plot a point on the Cartesian plane if given its coordinates
 Find the coordinates of a point on the Cartesian plane
Tables of Values for Linear Equations
 Construct a table of values given a formula
 Graph a linear equation by constructing a table of values
x and yIntercepts of a Line
 Know what the x and yintercepts of a line are
 Find the xintercept of a line
 Find the y intercept of a line
 Graph a line once you know the x and yintercepts
The Slope of a Line
 Know what the slope of a line is
 Find the slope of a line if given two points
 Find the slope of a line from a graph
 Graph a line that goes through a point and has a given slope
SlopeIntercept Form of a Line
 Know the slopeintercept form of a line
 Find the equation of a line in slope intercept form if given the graph
 Find the equation of a line in slopeintercept form if given two points
 Graph a line if its equation is in slopeintercept form
PointSlope Form of a Line
 Know the pointslope form of a line
 Find the equation of a line in pointslope form if given a graph
 Find the equation of a line in pointslope form if given two points
 Graph a line if its equation is in pointslope form
Parallel and Perpendicular Lines
 Know the definition of parallel lines
 Know the definition of perpendicular lines
 Determine if two lines are parallel from their equations
 Determine if two lines are perpendicular from their equations
Arithmetic Properties of Exponents
 Know the rules for exponents
 Manipulate and simplify expressions with positive exponents
Negative and Fractional Exponents
 Know the rules dictating how to deal with fractional and negative exponents
 Manipulate expressions with fractional and negative exponents
Scientific Notation
 Express numbers in scientific notation
 Convert numbers from scientific notation to decimal form
 Perform calculations with numbers expressed in scientific notation
Square Roots of Perfect Squares
 Understand what a perfect square is
 Find square roots of perfect squares
 Understand why there is no square root of a negative number (in the real numbers)
Pythagorean theorem
 Know the Pythagorean Theorem and its converse
 Know some Pythagorean triples
 Use the Pythagorean Theorem to find the sides of a right triangle
Trigonometry application: Docked boat
 Pythagorean theorem
Algabraic Expressions
 Identify the terms in an algebraic expression
 Identify the factors of a term
 Identify the coefficient of a term
 Identify the degree of an algebraic expression
Polynomial Vocabulary
 Determine whether an expression is a polynomial
 Classify a polynomial as a monomial, binomial, or trinomial
 Find the degree of a polynomial
Simplifying Exponent Expressions
 Simplify exponent expressions without variables
 Evaluate exponent expressions using substitution
Adding and Subtracting Polynomials
 Know the definition of "like terms"
 Identify like terms in an expression
 Combine like terms correctly
 Be able to add and subtract polynomial expressions by identifying like terms
Multiplying Polynomials
 Know the distributive property of multiplication
 Use the distributive property to multiply polynomials with polynomials
 Be able to multiply polynomials of any length
Factoring a Common Term
 Know the definition of "greatest common factor"
 Find the greatest common factor among terms of an expression
 Factor a common term out of a polynomial expression
Factoring by Grouping
 Use the grouping technique to factor certain polynomials
Factoring Trinomials with Lead Coefficient 1
 Factor trinomials with a leading coefficient of 1 into two binomials
Factoring Trinomials with Lead Coefficient a
 Factor trinomials with a leading coefficient of a into two binomials
Factoring Perfect Square Trinomials
 Identify a trinomial as being a perfect square
 Factor a perfect square into two binomials
Factoring Differences of Squares
 Identify a difference of two squares
 Factor a difference of two squares into two binomials
Simplifying Rational Expressions
 Use factoring to simplify rational expressions
Polynomial Long Division
 Divide polynomials using long division
Finding the Intersection of Lines
 Determine the intersection point of two lines by using a graph
 Determine the intersection point of two lines using algebraic methods
Systems of Equations: Substitution Method
 Know how to isolate a variable
 Know how to use the isolated variable to make a substitution
 Know how to solve for a variable after substitution
 Use the substitution method to solve a system of equations
Systems of Equations: Linear Combination Method
 Know the method of elimination
 Know the idea behind using linear combinations of equations to eliminate a variable
 Use the linear combination method to solve a system of equations
 Be able to recognize a solution of "all real numbers" or "no solution"
Systems of Equations Application: Fruit Prices
 Substitution method
Systems of Equations Application: Guitars
 Substitution method
Systems of Equations Application: Video Game Points
 Linear combination method
Systems of Equations Applications: Trip to the Movies
 Linear combination method
What is a Function?
 The definition of a function
 Describe a function using a formula
 Describe a function using a table
 Recognize if a given relation is a function or not
Evaluating Functions
 Evaluate a function on numerical input
 Evaluate a function on variable input
Graph of a Function
 Understand the definition of the graph of a function
 Know how to determine if a given plot represents a function
 Plot the graph of a function
 Use a graph to evaluate a function
Domain of a Function
 Know the definition of the domain of a function
 Find the domain of a function using a graph
 Find the domain of a function if given a formula
Range of a Function
 Know the definition of the range of a function
 Find the range of a function using a graph
 Find the range of a function if given a formula
Linear Equations Application: Graphing Population
 Solving Equations
 Solving Systems of Equations
Linear Equations Application: Economic Theory
 Solving Equations
 Inverse Functions