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
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 right-facing arrow
• Represent negative addends using a left-facing 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
• Add fractions that have the same denominator
• Add fractions with different denominators
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
• Identify the names of the place values
• Write decimals in standard form
• Write decimals in expanded form
• Write decimals in words
• 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
• 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
• Solving equations
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 y-Intercepts of a Line
• Know what the x- and y-intercepts of a line are
• Find the x-intercept of a line
• Find the y- intercept of a line
• Graph a line once you know the x- and y-intercepts
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
Slope-Intercept Form of a Line
• Know the slope-intercept 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 slope-intercept form if given two points
• Graph a line if its equation is in slope-intercept form
Point-Slope Form of a Line
• Know the point-slope form of a line
• Find the equation of a line in point-slope form if given a graph
• Find the equation of a line in point-slope form if given two points
• Graph a line if its equation is in point-slope 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
• 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