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ALGEBRA REVIEW AND STUDY GUIDE
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The Algebra Review and Study Guide provides the essential material to excel in Algebra. The guide contains all the fundamental equations, formulas and procedures needed for algebra I high school and college courses. .
Complete with over 100 illustrations and examples
Ove 50 equations and formulas
Over 100 algebra definitions and facts
Algebra I Review and Study Guide was designed for high school and college algebra students as well as teachers and tutors who teach Algebra I, and those that need to review basic algebra for high school exit exams, college entrance exams, SAT tests, state teacher certification tests such as the CBEST and CSET as well as those studying for the GRE, ACT, GMAT and AVSBE.
Chapter 1: Algebra Fundamentals
 Algebra Cheat Sheet (Formula and Equation Summary
 Number Sets
 Algebra Laws and Properties
 Order of Operations (PEMDAS
 Prime Numbers and Prime Factorizations
 Prime Factorizations and Factor Trees
 Least Common Multiple: Definitions and Solutions Methods
 Least Common Multiple: Prime Factorization Method
 Least Common Multiple: Subproducts Methods
 Fraction Operations
 Fraction Properties and Ratios
Chapter 2: Exponents, Roots and Radicals
 Exponent Formula and Fact Review Sheet
 Integer Exponents Defined
 Zero Power, 1st Power, Multiplication, Division
 Power Rules
 Inverse Identity
 Fractional Exponents Defined
 Radicals and Roots
 Radical Properties
 Radical to Exponent Conversion
CHAPTER 3: Algebraic Expressions and Procedures
 Equations of One Variable
 Like Terms
 Solving Equations of One Variable
Chapter 4: Polynomials
 Monomials: Definition, Types and Degree
 Polynomials: Definition, Type and Degree
Chapter 5: The Cartesian Coordinate System
 Cartesian Coordinate System Defined
 Cartesian Coordinate System Graph
Chapter 6: Functions
 Function Types
 Function Definition
 Functions and Relations: Vertical Line Test
 Functions: Domain and Range
Chapter 7: The Line  Polynomials of the First Degree
 Study Guide and Review Sheet: Line Formulas and Facts
 Line Equation Forms
 Slope, XIntercepts, YIntercepts
 Horizontal and Vertical Lines
 Line Graphing Procedures: Slope Intercept Form
 Standard Form
 Line Midpoint Formula
 Line Distance Formula
 Parallel Lines Test
 Parallel Lines Test Case Examples
 Perpendicular Lines Test
 Identical Lines Test
 Line Translation
Chapter 8: Absolute Value Function
 Absolute Value Formula and Fact Study Guide
 Absolutue Value of One Variable: Number Line Graphs
 Absolutle Value Inequalities of One Variable Number Line Graphs
 Examples
 Special Cases Examples
 Inequality Examples
 Absolute Value Function of Two Variables
 Definition and Rules, Base Form Function
 General Form Function
 Compression and Expansion
 Vertical and Horizontal Translation
Chapter 9: Linear System of Equations
 Linear Systems Formula and Fact Review Sheet
 Linear Systems and Solutions Defined
 Solving Graphically
 Solving Through Elimination
 Solving Through Substitution
 Solving with Kramer's Rule Solution
Chapter 10: Linear Inequatlities of One and Two Variables
 Linear Inequalities Formula and Fact Review Sheet
 Linear Inequalities of One Variable
 Linear Inequalities of Two Variables: Vertical Lines
 Linear Inequalites of Two Variables: Shading Methods
Chapter 11: Linear System of Inequalities
 Linear System of Inequalities and Solutions Defined
 Shading Method
 Test Point Method
Chapter 12: Parabolas  Polynomials of the Second Degree
 Parabola Review and Study Guide
 Equation Forms
 Convavity: Sign of Leading Coefficient Test
 Compression and Expansion
 Standard Equation Form: Parameters and Graphing
 Vertex Equation Form: Parameters and Graphing
 XIntercept Equation Form: Parameters and Graphing
Chapter 13: Second Degree Factoring Methods
 Second Degree Factoring Review and Study Guide
 FactorSum Table Methods (a =1)
 FactorSum Table Method (a not =1)
 Quadratic Formula Factor Method
 Completing the Square Factoring
 Second Degree Polynomial Identities
Chapter 14: Cubics  Polynomials of the Third Degree
 Cubic Review and Study Guide
 3rd Degree Polynomial Functions: Definition and Parameters
 Polynomials of Higher Degrees
Chapter 15: Third Degree Factoring Methods
 Third Degree Review and Study Guide
 Greatest Common Factor Method
 Grouping Method
 Third Degree Polynomial Identities
Chapter 16: Polynomial Algebra
 Polynomial Review and Study Guide (Facts and Formulas)
 Rational Expressions
 Polynomial Addition and Subtraction
 Polynomial Multiplication
 Polynomial Division
Chapter 17: Inverse Variation Functions
 Inverse Variation Review and Study Guide
 Definition, Rules, Graphing
 Origin and Asymptotes
 Translation
 Compression and Expansion
Chapter 18: Word Problems
 Formula and Fact Review Sheet
 Algebraic Translation
 Types
 Engineering: Area, Quadratic Formula
 Business: Rate of Work Equations
 Business: Sales / Price Equations
 Chemistry: Mixture Equations
 Physics: Projectile Height
 Physics: Vehicle, Wind and Current Speed
Chapter 19: Probability
 Formula and Fact Summary Sheet
 Sets and Venn Diagrams
 Sample Space
 Addition and Multiplication Rules
 Factorials, Permutations, Combinations
Chapter 20: Statistics
 Median
 Mode
 Measures of Dispersions: Range and Standard Deviation
 Normal Distribution
 Standard Deviation
 Mean
Algebra I Review and Study Guide
Chapter 1: Algebra Fundamentals
 Algebra Fundamentals Formula and Fact Review Sheet
 Number Sets
 Algebra Laws and Properties
 Order of Operations (PEMDAS
 Prime Numbers and Prime Factorizations
 Prime Factorizations and Factor Trees
 Least Common Multiple: Definitions and Solutions Methods
 Least Common Multiple: Prime Factorization Method
 Least Common Multiple: Subproducts Methods
 Fraction Operations
 Fraction Properties and Ratios
All reals except rational numbers. Spacing between Algebra operations, a double equal sign, maybe incude prime factorizations and factor trees. Order of operations:
LCM (3, 7) = 21 without a remainder. GCF ( 9, 12, 18) = 3
Algebra I Review and Study Guide
Chapter 2: Algebraic Fraction Operations
Fraction Operations
Fraction Proportions, Ratios and Percentages
Algebra I Review and Study Guide
Chapter 5: The Cartesian Coordinate System
 Cartesian Coordinate System Defined
 Cartesian Coordinate System Graph
Algebra I Review and Study Guide
Deductive and Inductive Reasoning
Algebra I Review and Study Guide
Chapter 2: Exponents, Roots and Radicals
 Exponent Formula and Fact Review Sheet
 Integer Exponents Defined
 Zero Power, 1st Power, Multiplication, Division
 Power Rules
 Inverse Identity
 Fractional Exponents Defined
 Radicals and Roots
 Radical Properties
 Radical to Exponent Conversion
Include Fractional Exponents and radicals
A number or variable. is often expessed as 3 to the fourth power.
always equal to 1.
Algebra I Review and Study Guide
CHAPTER 3: Algebraic Expressions and Procedures
 Equations of One Variable
 Like Terms
 Solving Equations of One Variable
Algebra I Review and Study Guide
Move the fourth paragraph to the third paragraph. include the same exact variables raised to the same exact power. EX: 5x + 2 consists of the terms 5x and 2,
EQUATIONS OF ONE VARIABLE
Like Terms
Solving for X: Onv Variable Equation Solutions
Algebra I Review and Study Guide
Chapter 4: Polynomials
 Monomials: Definition, Types and Degree
 Polynomials: Definition, Type and Degree
(WITH ONLY NONNEGATIVE INTEGERS) Add
Chapter 6: Functions




Algebra I Review and Study Guide
FUNCTIONS
Function Summary Sheet
Function Definiton
Function Domain and Range
Function Examples and Solutions
Chapter 7: Lines  Polynomials of the First Degree
 Study Guide and Review Sheet: Line Formulas and Facts
 Line Equation Forms
 Slope, XIntercepts, YIntercepts
 Horizontal and Vertical Lines
 Line Graphing Procedures: Slope Intercept Form
 Standard Form
 Line Midpoint Formula
 Line Distance Formula
 Parallel Lines Test
 Parallel Lines Test Case Examples
 Perpendicular Lines Test
 Identical Lines Test
 Line Translation
Algebra I Review and Study Guide
Notation for a line. l1, range and domain of a line
Base Function y = x (m =1, b = 0), The function f(x) = x
Example
From the slope intercept form of the line equaion the slope and the yintecept can be determine directly.
Horizontal lines with different yintercepts are parallel. Vertical lines with different xintercepts are always parallel.
Algebra I Review and Study Guide
The Absolute Value Function
Chapter 8: Absolute Value Function
 Absolute Value Formula and Fact Study Guide
 Absolutue Value of One Variable: Number Line Graphs
 Absolutle Value Inequalities of One Variable Number Line Graphs
 Examples
 Special Cases Examples
 Inequality Examples
 Absolute Value Function of Two Variables
 Definition and Rules, Base Form Function
 General Form Function
 Compression and Expansion
 Vertical and Horizontal Translation
h controls the Change Range to if a All Reals > K (if a >0) All Reals < K (a < 0)
The graph of y = !x!
Algebra I Review and Study Guide
Chapter 9: Linear Systems of Equations
 Linear Systems Formula and Fact Review Sheet
 Linear Systems and Solutions Defined
 Solving Graphically
 Solving Through Elimination
 Solving Through Substitution
 Solving with Kramer's Rule Solution
Stirke Graphically, Substitution Colon, plot the lines of the system and
Algebra I Review and Study Guide
Chapter 10: Linear Inequatlities of One and Two Variables
 Linear Inequalities Formula and Fact Review Sheet
 Linear Inequalities of One Variable
 Linear Inequalities of Two Variables: Vertical Lines
 Linear Inequalites of Two Variables: Shading Methods
Stike Sign in second paragrah, compound inequalities of one variable
Compound inequalities
INEQUALITIES OF TWO VARIABLES
Vertical Line Graphical Shading Method
Slope Intercept Form Graphical Shading Method
Test Point Method
Algebra I Review and Study Guide
graphed line space on y=2x + 3 (either inclusive or exclusive of the line itself)
SYSTEM OF LINEAR INEQUALITIES
Graphical Shading Method
Test Point Method
Algebra I Review and Study Guide
Chapter 11: Linear System of Inequalities
 Linear System of Inequalities and Solutions Defined
 Shading Method
 Test Point Method
highlight true in the last paragraph.
Spacing between equations, which of the bounded regions, for which all the inequalities are true.
third line, than a test point "be" selected.
Algebra I Review and Study Guide
Chapter 12: Parabolas  Polynomials of the Second Degree
 Parabola Review and Study Guide
 Equation Forms
 Convavity: Sign of Leading Coefficient Test
 Compression and Expansion
 Standard Equation Form: Parameters and Graphing
 Vertex Equation Form: Parameters and Graphing
 XIntercept Equation Form: Parameters and Graphing
The base parabola function f(x) = x2 is obtained by setting b=0 and c=0
Make table for b2  4ac Add Domain and Range, Base Function,
Vertex Form
Vertex, Axis of Symmetry, Direction
Horizontal and Vertical Translation
Discriminant
XIntercepts
XIntercept Caclulations
Algebra I Review and Study Guide
Chapter 13: Second Degree Factoring Methods
 Second Degree Factoring Review and Study Guide
 FactorSum Table Methods (a =1)
 FactorSum Table Method (a not =1)
 Quadratic Formula Factor Method
 Completing the Square Factoring
 Second Degree Polynomial Identities
Factoring Formations (x + f)(x + g) = 0
(dx + f)
Algebra I Review and Study Guide
Chapter 17: The Inverse Variation Function
 Inverse Variation Review and Study Guide
 Definition, Rules, Graphing
 Origin and Asymptotes
 Translation
 Compression and Expansion
y = x + K  h, and y = x  K + h
Base Form 1/x, the base form, axis of symbetrry x  K and x+ K NOT Quite
is the xaxis, is the yaxis, vertical aysmptote x=0, yaxis, domain: all reals except x=0, is
obtained when
CUBICS: POLYNOMIALS OF THE THIRD DEGREE
3RD Degree Polynomial Formula and Fact Review Sheet
Greatest Common Factor
Grouping Method
3rd Degree Factoring Identities
Rational Expressions
Polynomial Addition
Polynomial Multiplication
Polynomial Division
Algebra I Review and Study Guide
Chapter 14: Cubics  Polynomials of the Third Degree
 Cubic Review and Study Guide
 3rd Degree Polynomial Functions: Definition and Parameters
 Polynomials of Higher Degrees
strike degree in the first sentence, cubics in third paragraph, redraw graph
Chapter 15: Third Degree Factoring Methods
 Third Degree Review and Study Guide
 Greatest Common Factor Method
 Grouping Method
 Third Degree Polynomial Identities
as the GCF the 3rd and 2nd degrrr terms are grouped and the GCF factored out.
Chapter 16: Polynomial Algebra
 Polynomial Review and Study Guide (Facts and Formulas)
 Rational Expressions
 Polynomial Addition and Subtraction
 Polynomial Multiplication
 Polynomial Division
multiplied in the second sentence
WORD PROBLEMS
Word Problem Formula and Fact Review Sheet
Algebraic Translation
Engineering: Areas
Business: Rate of Work
Business: Sales and Price
Chemistry: Solutions
Physics: Projectiles
Physics: Vehicle Velocity
Algebra I Review and Study Guide
Chapter 18: Word Problems
 Formula and Fact Review Sheet
 Algebraic Translation
 Types
 Engineering: Area, Quadratic Formula
 Business: Rate of Work Equations
 Business: Sales / Price Equations
 Chemistry: Mixture Equations
 Physics: Projectile Height
 Physics: Vehicle, Wind and Current Speed
the number of each of two items sold, require linear system of equations.
Algebra I Review and Study Guide
Chapter 19: Probability
 Formula and Fact Summary Sheet
 Sets and Venn Diagrams
 Sample Space
 Addition and Multiplication Rules
 Factorials, Permutations, Combinations
null set if all nonunique ordered sequences are excluded. of n objects for combinations. eliminated is included.
There is no condition for factorials
Add a few examples
Algebra I Review and Study Guide
Chapter 20: Statistics
 Median
 Mode
 Measures of Dispersions: Range and Standard Deviation
 Normal Distribution
 Standard Deviation
 Mean
2nd P, if there is "an" even. The number in the middle posittion of a numerical data set, (ordered ascendingly) the median is the number in the center position of the data set.
Algebra I Review and Study Guide
Appendexes
 Algebraic Notation and Abbreviations
 Common
Squares, Cubes and Higher Powers
 Perfect Square Trinomials
 Geometric Relations in Algebra
 Word Problem Algebraic Translation
 Common Errors
 Factoring, Exponents and Radicals
 Lines, Parabolas, Absolute Value and Indiret Variations
COMMON ERRORS
Factoring, Exponents and Radicals
Lines, Parabolas, Absolute Value and Indiret Variations