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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 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
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 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
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

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