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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

  1. Algebra Cheat Sheet (Formula and Equation Summary
  2. Number Sets
  3. Algebra Laws and Properties
  4. Order of Operations (PEMDAS
  5. Prime Numbers and Prime Factorizations
  6. Prime Factorizations and Factor Trees
  7. Least Common Multiple: Definitions and Solutions Methods
  8. Least Common Multiple: Prime Factorization Method
  9. Least Common Multiple: Subproducts Methods
  10. Fraction Operations
  11. Fraction Properties and Ratios

Chapter 2: Exponents, Roots and Radicals

  1. Exponent Formula and Fact Review Sheet
  2. Integer Exponents Defined
  3. Zero Power, 1st Power, Multiplication, Division
  4. Power Rules
  5. Inverse Identity
  6. Fractional Exponents Defined
  7. Radicals and Roots
  8. Radical Properties
  9. Radical to Exponent Conversion

 

CHAPTER 3: Algebraic Expressions and Procedures

  1. Equations of One Variable
  2. Like Terms
  3. Solving Equations of One Variable

Chapter 4: Polynomials

  1. Monomials: Definition, Types and Degree
  2. Polynomials: Definition, Type and Degree

Chapter 5: The Cartesian Coordinate System

  1. Cartesian Coordinate System Defined
  2. Cartesian Coordinate System Graph

Chapter 6: Functions

  1. Function Types
  2. Function Definition
  3. Functions and Relations: Vertical Line Test
  4. Functions: Domain and Range

Chapter 7: The Line - Polynomials of the First Degree

  1. Study Guide and Review Sheet: Line Formulas and Facts
  2. Line Equation Forms
  3. Slope, X-Intercepts, Y-Intercepts
  4. Horizontal and Vertical Lines
  5. Line Graphing Procedures: Slope Intercept Form
  6. Standard Form
  7. Line Midpoint Formula
  8. Line Distance Formula
  9. Parallel Lines Test
  10. Parallel Lines Test Case Examples
  11. Perpendicular Lines Test
  12. Identical Lines Test
  13. Line Translation

Chapter 8: Absolute Value Function

  1. Absolute Value Formula and Fact Study Guide
  2. Absolutue Value of One Variable: Number Line Graphs
  3. Absolutle Value Inequalities of One Variable Number Line Graphs
  4. Examples
  5. Special Cases Examples
  6. Inequality Examples
  7. Absolute Value Function of Two Variables
  8. Definition and Rules, Base Form Function
  9. General Form Function
  10. Compression and Expansion
  11. Vertical and Horizontal Translation

Chapter 9: Linear System of Equations

  1. Linear Systems Formula and Fact Review Sheet
  2. Linear Systems and Solutions Defined
  3. Solving Graphically
  4. Solving Through Elimination
  5. Solving Through Substitution
  6. Solving with Kramer's Rule Solution

Chapter 10: Linear Inequatlities of One and Two Variables

  1. Linear Inequalities Formula and Fact Review Sheet
  2. Linear Inequalities of One Variable
  3. Linear Inequalities of Two Variables: Vertical Lines
  4. Linear Inequalites of Two Variables: Shading Methods

Chapter 11: Linear System of Inequalities

  1. Linear System of Inequalities and Solutions Defined
  2. Shading Method
  3. Test Point Method

Chapter 12: Parabolas - Polynomials of the Second Degree

  1. Parabola Review and Study Guide
  2. Equation Forms
  3. Convavity: Sign of Leading Coefficient Test
  4. Compression and Expansion
  5. Standard Equation Form: Parameters and Graphing
  6. Vertex Equation Form: Parameters and Graphing
  7. X-Intercept Equation Form: Parameters and Graphing

 

Chapter 13: Second Degree Factoring Methods

  1. Second Degree Factoring Review and Study Guide
  2. Factor-Sum Table Methods (a =1)
  3. Factor-Sum Table Method (a not =1)
  4. Quadratic Formula Factor Method
  5. Completing the Square Factoring
  6. Second Degree Polynomial Identities

Chapter 14: Cubics - Polynomials of the Third Degree

  1. Cubic Review and Study Guide
  2. 3rd Degree Polynomial Functions: Definition and Parameters
  3. Polynomials of Higher Degrees

Chapter 15: Third Degree Factoring Methods

  1. Third Degree Review and Study Guide
  2. Greatest Common Factor Method
  3. Grouping Method
  4. Third Degree Polynomial Identities

Chapter 16: Polynomial Algebra

  1. Polynomial Review and Study Guide (Facts and Formulas)
  2. Rational Expressions
  3. Polynomial Addition and Subtraction
  4. Polynomial Multiplication
  5. Polynomial Division

Chapter 17: Inverse Variation Functions

  1. Inverse Variation Review and Study Guide
  2. Definition, Rules, Graphing
  3. Origin and Asymptotes
  4. Translation
  5. Compression and Expansion

Chapter 18: Word Problems

  1. Formula and Fact Review Sheet
  2. Algebraic Translation
  3. Types
  4. Engineering: Area, Quadratic Formula
  5. Business: Rate of Work Equations
  6. Business: Sales / Price Equations
  7. Chemistry: Mixture Equations
  8. Physics: Projectile Height
  9. Physics: Vehicle, Wind and Current Speed

Chapter 19: Probability

  1. Formula and Fact Summary Sheet
  2. Sets and Venn Diagrams
  3. Sample Space
  4. Addition and Multiplication Rules
  5. Factorials, Permutations, Combinations

Chapter 20: Statistics

  1. Median
  2. Mode
  3. Measures of Dispersions: Range and Standard Deviation
  4. Normal Distribution
  5. Standard Deviation
  6. Mean


 

Algebra I Review and Study Guide

Chapter 1: Algebra Fundamentals

  1. Algebra Fundamentals Formula and Fact Review Sheet
  2. Number Sets
  3. Algebra Laws and Properties
  4. Order of Operations (PEMDAS
  5. Prime Numbers and Prime Factorizations
  6. Prime Factorizations and Factor Trees
  7. Least Common Multiple: Definitions and Solutions Methods
  8. Least Common Multiple: Prime Factorization Method
  9. Least Common Multiple: Subproducts Methods
  10. Fraction Operations
  11. Fraction Properties and Ratios
Algebra Reveiw Sheet Numbers Algebra Operations Prime Natural Whole Irrational Rational

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

 

Least Common Multiple Determination Problem Solution Example Product Subset Method

 

 

Algebra I Review and Study Guide

Chapter 2: Algebraic Fraction Operations


Fraction Operations
Fraction Proportions, Ratios and Percentages

Fractions Operations Review Sheet Cross Multiplication Recprocol Repricol Multiplication


 


Algebra I Review and Study Guide

Chapter 5: The Cartesian Coordinate System

  1. Cartesian Coordinate System Defined
  2. 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

  1. Exponent Formula and Fact Review Sheet
  2. Integer Exponents Defined
  3. Zero Power, 1st Power, Multiplication, Division
  4. Power Rules
  5. Inverse Identity
  6. Fractional Exponents Defined
  7. Radicals and Roots
  8. Radical Properties
  9. 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 fractional exponents roots radicals topic review

 

Algebra I Review and Study Guide

CHAPTER 3: Algebraic Expressions and Procedures

  1. Equations of One Variable
  2. Like Terms
  3. Solving Equations of One Variable

 

 

 

 

 

Algebra I Review and Study Guide

Algebra Equations of One Variable Review Sheet, Cheat Sheet Simplifying Expressions and Equations Varaible Definitions Like Term Defintion Equation Solution Rules

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

  1. Monomials: Definition, Types and Degree
  2. Polynomials: Definition, Type and Degree

    3.

 

 

 

algebra, polynomial topic review, polynomial defintion, monomial definition, trinomial definition, binomial definition, polynomial equation, polynomial degree, monomial degree

 

 

(WITH ONLY NON-NEGATIVE INTEGERS) Add

 

 

Chapter 6: Functions

  1. Function Types

  2. Function Definition

  3. Functions and Relations: Vertical Line Test

  4. Functions: Domain and Range

 

 

 

 

Algebra I Review and Study Guide

FUNCTIONS

Function Summary Sheet
Function Definiton
Function Domain and Range
Function Examples and Solutions

algebra function review sheet cheet sheet study guide parabola line inverse variation cubic domain range vertical line test

 


 

Chapter 7: Lines - Polynomials of the First Degree

  1. Study Guide and Review Sheet: Line Formulas and Facts
  2. Line Equation Forms
  3. Slope, X-Intercepts, Y-Intercepts
  4. Horizontal and Vertical Lines
  5. Line Graphing Procedures: Slope Intercept Form
  6. Standard Form
  7. Line Midpoint Formula
  8. Line Distance Formula
  9. Parallel Lines Test
  10. Parallel Lines Test Case Examples
  11. Perpendicular Lines Test
  12. Identical Lines Test
  13. 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 y-intecept can be determine directly.

Horizontal lines with different y-intercepts are parallel. Vertical lines with different x-intercepts are always parallel.

Figure: Graph Line Translation and the Y-Intercept

 

 

Algebra I Review and Study Guide

The Absolute Value Function

Chapter 8: Absolute Value Function

  1. Absolute Value Formula and Fact Study Guide
  2. Absolutue Value of One Variable: Number Line Graphs
  3. Absolutle Value Inequalities of One Variable Number Line Graphs
  4. Examples
  5. Special Cases Examples
  6. Inequality Examples
  7. Absolute Value Function of Two Variables
  8. Definition and Rules, Base Form Function
  9. General Form Function
  10. Compression and Expansion
  11. 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

  1. Linear Systems Formula and Fact Review Sheet
  2. Linear Systems and Solutions Defined
  3. Solving Graphically
  4. Solving Through Elimination
  5. Solving Through Substitution
  6. Solving with Kramer's Rule Solution

algebra topic review sheet system of linear equations graphical, substitution elimination kramers graph of linear system of equations figure

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

  1. Linear Inequalities Formula and Fact Review Sheet
  2. Linear Inequalities of One Variable
  3. Linear Inequalities of Two Variables: Vertical Lines
  4. Linear Inequalites of Two Variables: Shading Methods

 

algebra linear inequalities of one variable review sheet cheat sheet formula sheet

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

topic review sheet inequalities of two variables cheat sheet, forumula sheet, steps, method

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

  1. Linear System of Inequalities and Solutions Defined
  2. Shading Method
  3. Test Point Method

 

algebra linear system of inequalities topic review solution methods graph figure

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

  1. Parabola Review and Study Guide
  2. Equation Forms
  3. Convavity: Sign of Leading Coefficient Test
  4. Compression and Expansion
  5. Standard Equation Form: Parameters and Graphing
  6. Vertex Equation Form: Parameters and Graphing
  7. X-Intercept 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
X-Intercepts
X-Intercept Caclulations

 

 

 

 

 

 

 

Algebra I Review and Study Guide

Chapter 13: Second Degree Factoring Methods

  1. Second Degree Factoring Review and Study Guide
  2. Factor-Sum Table Methods (a =1)
  3. Factor-Sum Table Method (a not =1)
  4. Quadratic Formula Factor Method
  5. Completing the Square Factoring
  6. Second Degree Polynomial Identities

algebra topic review sheet second degree factoring methods sum table, a equal 1, a not equal 1, quadratic equation, GCF, completing the square, second degree factoring identities

Factoring Formations (x + f)(x + g) = 0
(dx + f)




 

 

 

 

 

Algebra I Review and Study Guide

 

Chapter 17: The Inverse Variation Function

  1. Inverse Variation Review and Study Guide
  2. Definition, Rules, Graphing
  3. Origin and Asymptotes
  4. Translation
  5. 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 x-axis, is the y-axis, vertical aysmptote x=0, y-axis, 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

  1. Cubic Review and Study Guide
  2. 3rd Degree Polynomial Functions: Definition and Parameters
  3. Polynomials of Higher Degrees


strike degree in the first sentence, cubics in third paragraph, redraw graph

Chapter 15: Third Degree Factoring Methods

  1. Third Degree Review and Study Guide
  2. Greatest Common Factor Method
  3. Grouping Method
  4. Third Degree Polynomial Identities

 

algebra third degree factoring methods topic review sheet cheat sheet GCF grouping polynomial identities

as the GCF the 3rd and 2nd degrrr terms are grouped and the GCF factored out.

algebra third degree greatest common factor, factoring

Chapter 16: Polynomial Algebra

  1. Polynomial Review and Study Guide (Facts and Formulas)
  2. Rational Expressions
  3. Polynomial Addition and Subtraction
  4. Polynomial Multiplication
  5. Polynomial Division

 

polynomial algebra, polynomial addition, polynomial subtraction, polynomial division, polynomial multiplication, rational expressions, review sheet, cheat cheat

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

  1. Formula and Fact Review Sheet
  2. Algebraic Translation
  3. Types
  4. Engineering: Area, Quadratic Formula
  5. Business: Rate of Work Equations
  6. Business: Sales / Price Equations
  7. Chemistry: Mixture Equations
  8. Physics: Projectile Height
  9. Physics: Vehicle, Wind and Current Speed

 

algebra word problems, mixtures, rates, sales price equations, velocity, projectile, work rate

the number of each of two items sold, require linear system of equations.

 

 

 

 

 

Algebra I Review and Study Guide

Chapter 19: Probability

  1. Formula and Fact Summary Sheet
  2. Sets and Venn Diagrams
  3. Sample Space
  4. Addition and Multiplication Rules
  5. Factorials, Permutations, Combinations

 

algebra topic review probabiity, sets, factorials, combinations, permutations, sets, sample space

null set if all non-unique 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

  1. Median
  2. Mode
  3. Measures of Dispersions: Range and Standard Deviation
  4. Normal Distribution
  5. Standard Deviation
  6. Mean

 

algebra statistics topic review sheet median, mode, mean, standard deviation, formulas, empirical rule, normal distribution curve

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

  1. Algebraic Notation and Abbreviations
  2. Common Squares, Cubes and Higher Powers
  3. Perfect Square Trinomials
  4. Geometric Relations in Algebra
  5. Word Problem Algebraic Translation
  6. Common Errors
  7. Factoring, Exponents and Radicals
  8. Lines, Parabolas, Absolute Value and Indiret Variations

COMMON ERRORS
Factoring, Exponents and Radicals
Lines, Parabolas, Absolute Value and Indiret Variations