NEW YORK ALGEBRA TABLE OF CONTENTS

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1 NEW YORK ALGEBRA TABLE OF CONTENTS CHAPTER 1 NUMBER SENSE & OPERATIONS TOPIC A: Number Theory: Properties of Real Numbers {A.N.1} PART 1: Closure...1 PART 2: Commutative Property...2 PART 3: Associative Property...3 PART 4: Distributive Property...4 PART 5: Identity Element...5 PART 6: Inverse Property...7 TOPIC B: Meanings of Operations and Procedures PART 1: Simplifying Radical Terms (no variable in the radicand) {A.N.2}...9 PART 2: Operations on Radicals {A.N.3} Section a: Addition and Subtraction of Radicals...10 Section b: Multiplication of Radicals...13 Section c: Division of Radicals...16 PART 3: Scientific Notation {A.N.4} Section a: Evaluating Scientific Notation...18 Section b: Multiplying and Dividing Scientific Notation...20 PART 4: Solving Algebraic Problems {A.N.5} Section a: Algebraic Problems Involving Fractions Section 1: Addition...22 Section 2: Subtraction...25 Section 3: Multiplication...27 Section 4: Division...29 Section b: Algebraic Problems Involving Decimals...31 Section c: Algebraic Problems Involving Percents (Percent Decrease, Percent Increase, and Discount)...32 Section d: Ratio, Proportion, and Direct Variation Section 1: Proportion Equations...37 Section 2: Direct Variation...40 Section 3: Proportionality Constants...42 Section 4: Ratio and Proportion Word Problems (See Chapter 12A)...43 PART 5: Factorials, Absolute Values, and Exponential Expressions {A.N.6} Section a: Evaluating Factorial Expressions...46 Section b: Evaluating Absolute Value Expressions...47 Section c: Evaluating Exponential Expressions...49 PART 6: Fundamental Counting Principle {A.N.7}...52 PART 7: Permutations {A.N.8}...54 CHAPTER 2 ALGEBRAIC VARIABLES & EXPRESSIONS TOPIC A: Translating Verbal Phrases into Algebraic Expressions and Equations {A.A.1} PART 1: Literal Translations of Algebraic Expressions and Equations...59 PART 2: Determining Expressions for Algebraic Word Problems...60 TOPIC B: Translating Algebraic Expressions into Verbal Phrases {A.A.2}...63 TOPIC C: Operations on Monomial Expressions {A.A.12} PART 1: Multiplication of Monomials...64 PART 2: Division of Monomials...67 TOPIC D: Adding, Subtracting, and Multiplying Monomials and Polynomials {A.A.13} PART 1: Addition of Monomials and Polynomials Section a: Monomials...71 Section b: Polynomials...75 PART 2: Subtraction of Monomials and Polynomials Section a: Monomials...81 Section b: Polynomials...85

2 PART 3: Multiplication of Binomials and Polynomials Section a: Binomials or Polynomials by a Monomial...92 Section b: Binomials and Polynomials...95 TOPIC E: Dividing a Polynomial by a Monomial or Binomial {A.A.14} PART 1: Binomial or Polynomial by a Monomial PART 2: Binomial or Polynomial by a Binomial CHAPTER 3 FACTORING TOPIC A: Identifying and Factoring the Difference of Two Perfect Squares {A.A.19} PART 1: Different Types of Factoring PART 2: Factoring the Difference of Two Perfect Squares TOPIC B: Factoring Algebraic Expressions {A.A.20} PART 1: Factoring the Greatest Common Factor (GCF) PART 2: Factoring Trinomials PART 3: Factoring Completely CHAPTER 4 ALGEBRAIC FRACTIONS (Rational Expressions) TOPIC A: Undefined Algebraic Fractions {A.A.15} TOPIC B: Simplifying Algebraic Fractions {A.A.16} TOPIC C: Operations on Algebraic Fractions PART 1: Addition of Algebraic Fractions {A.A.17} PART 2: Subtraction of Algebraic Fractions {A.A.17} PART 3: Multiplication of Algebraic Fractions {A.A.18} PART 4: Division of Algebraic Fractions {A.A.18} CHAPTER 5 LINEAR EQUATIONS & INEQUALITIES TOPIC A: Identifying the Difference Between Algebraic Expressions and Algebraic Equations {A.A.3} TOPIC B: Solving Linear Equations in One Variable {A.A.22} PART 1: Single Operation PART 2: Two or More Operations PART 3: Using the Distributive Property TOPIC C: Solving Literal Equations for a Given Variable {A.A.23} TOPIC D: Solving Linear Inequalities in One Variable {A.A.24} TOPIC E: Solving Equations Involving Fractional Expressions {A.A.25} TOPIC F: Solving Algebraic Proportions in One Variable {A.A.26} TOPIC G: Translating Verbal Sentences {A.A.4} PART 1: Into Mathematical Equations PART 2: Into Mathematical Inequalities TOPIC H: Writing Algebraic Equations or Inequalities to Represent a Situation {A.A.5} PART 1: Equations PART 2: Inequalities TOPIC I: Analyzing and Solving Verbal Problems {A.A.6} PART 1: Linear Equations in One Variable PART 2: Linear Inequalities in One Variable TOPIC J: Verifying Solutions to Equations and Inequalities {A.A.21} PART 1: Linear Equations in One Variable PART 2: Linear Inequalities in One Variable CHAPTER 6 SOLVING QUADRATIC, EXPONENTIAL, & SYSTEMS OF EQUATIONS TOPIC A: Solving Systems of Linear Equations Algebraically {A.A.10} (See Chapter 11E) PART 1: Using Addition or Subtraction PART 2: Using Substitution PART 3: Using Any Method TOPIC B: Using Systems of Linear Equations to Solve Verbal Problems {A.A.7} TOPIC C: Using the Multiplication Property of Zero to Solve Quadratic Equations {A.A.27} TOPIC D: Using Quadratic Equations to Solve Verbal Problems {A.A.8} TOPIC E: Verbal Problems Involving Exponential Growth and Decay {A.A.9} TOPIC F: Solving Systems of One Linear and One Quadratic Equation {A.A.11} PART 1: Algebraic Solutions PART 2: Graphic Solutions...214

3 TOPIC G: Solving Algebraic Proportions Resulting in Quadratic Equations {A.A.26} TOPIC H: Roots of Quadratic Equations and Factors of Quadratic Expressions {A.A.28} PART 1: Factoring Quadratic Expressions and Finding the Roots PART 2: Determining the x-intercepts of Quadratic Equations PART 3: Writing Quadratic Equations Given the Roots CHAPTER 7 PATTERNS, RELATIONS, & FUNCTIONS TOPIC A: Elements of a Set {A.A.29} PART 1: Set-builder Notation PART 2: Inequality and Interval Notation TOPIC B: Finding the Complement of a Subset {A.A.30} TOPIC C: Finding the Intersection and Union of Sets {A.A.31} PART 1: Intersection of Sets PART 2: Union of Sets PART 3: Venn Diagrams CHAPTER 8 COORDINATE GEOMETRY -- PROPERTIES OF EQUATIONS TOPIC A: Understanding Slope as a Rate of Change Between Dependent and Independent Variables {A.A.32}..243 TOPIC B: Determining the Slope of a Line Given Two Points on the Line {A.A.33} TOPIC C: Finding a Point Given a Point and Slope (edification) TOPIC D: Writing Equations of Lines PART 1: Given Slope and a Point on the Line {A.A.34} PART 2: Given Two Points on the Line {A.A.35} PART 3: Parallel to the Axes {A.A.36} TOPIC E: Determining the Slope of a Line From its Equation {A.A.37} TOPIC F: Determining the y-intercept of a Line From its Equation (edification) TOPIC G: Determining the Slope, y-intercept, and Equation of Graphed Lines (edification) TOPIC H: Identifying Equations of Parallel and Perpendicular Lines {A.A.38} TOPIC I: Determining Whether a Point is on the Equation of a Line {A.A.39} TOPIC J: Determining Whether a Point is in the Solution Set of a System of Linear Inequalities {A.A.40} TOPIC K: Determining the Vertex and Axis of Symmetry of a Parabola From its Equation {A.A.41} (See Chapter 11H) PART 1: Vertex (Turning Point) PART 2: Axis of Symmetry CHAPTER 9 TRIGONOMETRIC FUNCTIONS & THE PYTHAGOREAN THEOREM TOPIC A: Finding Sine, Cosine, and Tangent Ratios {A.A.42} TOPIC B: Evaluating Trigonometric Ratios {A.A.42} PART 1: Using the Table of Trigonometric Values PART 2: Using a Calculator PART 3: Using Any Method TOPIC C: Determining the Measure of an Angle of a Right Triangle Given Two Side Measures {A.A.43} TOPIC D: Finding the Measure of a Side of a Right Triangle Given an Angle and a Side Measure {A.A.44} TOPIC E: Trigonometry Word Problems {A.A.44} PART 1: Sine Problems PART 2: Cosine Problems PART 3: Tangent Problems PART 4: Multi-step Problems TOPIC F: Determining the Measure of a Third Side of a Right Triangle Using the Pythagorean Theorem {A.A.45} PART 1: Pythagorean Theorem PART 2: Converse of the Pythagorean Theorem CHAPTER 10 GEOMETRY TOPIC A: Finding the Area of 2-Dimensional Figures {A.G.1} PART 1: Area of Squares PART 2: Area of Rectangles PART 3: Area of Triangles PART 4: Area of Parallelograms PART 5: Area of Circles...330

4 PART 6: Area of Polygons PART 7: Area of Sectors of Circles TOPIC B: Finding the Perimeter or Circumference of 2-Dimensional Figures {A.G.1} PART 1: Perimeter of Squares PART 2: Perimeter of Rectangles PART 3: Perimeter of Triangles PART 4: Perimeter of Parallelograms PART 5: Circumference of Circles PART 6: Perimeter of Regular Polygons TOPIC C: Perimeter, Circumference, and Area Combination Problems {A.G.1} TOPIC D: Calculating Volume of 3-Dimensional Figures {A.G.2} PART 1: Volume of Cubes PART 2: Volume of Rectangular Solids PART 3: Volume of Cylinders TOPIC E: Calculating Surface Area of 3-Dimensional Figures {A.G.2} PART 1: Surface Area of Cubes PART 2: Surface Area of Rectangular Solids PART 3: Surface Area of Cylinders CHAPTER 11 COORDINATE GEOMETRY -- GRAPHS OF EQUATIONS TOPIC A: Determining if a Relation is a Function {A.G.3} PART 1: Using Ordered Pairs PART 2: Using Graphs TOPIC B: Graphing Linear, Quadratic (Parabolic), Absolute Value, and Exponential Functions {A.G.4} PART 1: Types of Functions PART 2: Graphs of Functions Section a: Linear Functions Section b: Quadratic Functions Section c: Absolute Value Functions Section d: Exponential Functions TOPIC C: Affect of Changing the Coefficients of a Function on its Graph {A.G.5} PART 1: Linear Functions PART 2: Quadratic Functions PART 3: Absolute Value Functions PART 4: Exponential Functions TOPIC D: Graphing Linear Inequalities {A.G.6} PART 1: Linear Inequalities in Two Variables PART 2: Inequalities on a Coordinate Grid TOPIC E: Graphing and Solving Systems of Linear Equations and Inequalities {A.G.7} (See Chapter 6A) PART 1: Systems of Linear Equations with Rational Coefficients in Two Variables PART 2: Systems of Linear Inequalities with Rational Coefficients in Two Variables TOPIC F: Solving Systems of Linear and Quadratic Equations Graphically {A.G.9} TOPIC G: Finding the Roots of a Parabolic Function Graphically {A.G.8} TOPIC H: Determining the Vertex and Axis of Symmetry of a Parabola From its Graph {A.G.10} (See Chapter 8J) CHAPTER 12 UNITS OF MEASUREMENT TOPIC A: Calculating Rates Using Appropriate Units {A.M.1} TOPIC B: Converting Between Measurements {A.M.2} TOPIC C: Calculating the Relative Error in Measuring Square and Cubic Units (A.M.3} CHAPTER 13 COLLECTING, ORGANIZING, DISPLAYING, & ANALYZING STATISTICAL DATA TOPIC A: Organizing and Displaying Statistical Data PART 1: Qualitative or Quantitative Data {A.S.1} PART 2: Univariate or Bivariate Data {A.S.2} PART 3: Biased Collections or Displays of Data {A.S.3&15} PART 4: Measures of Central Tendency {A.S.4} Section a: Mean Section b: Median Section c: Mode...461

5 Section d: Comparisons of Central Tendency PART 5: Statistical Graphs -- Histograms, Cumulative Frequency Histograms, and Box-and-Whisker Plots (A.S.5) Section a: Frequency Tables and Histograms Section b: Cumulative Frequency Tables and Histograms Section c: Box-and-Whisker Plots PART 6: Box-and-Whisker Plots Constructed From the Five Statistical Summaries {A.S.6} PART 7: Scatter Plots of Bivariate Data {A.S.7} PART 8: Scatter Plots -- Lines of Best Fit and Their Equations {A.S.8} TOPIC B: Analyzing Statistical Data PART 1: Frequency and Cumulative Frequency Tables or Histograms and Box-and-Whisker Plots {A.S.9} Section a: Frequency Distribution Tables or Histograms Section b: Cumulative Frequency Distribution Tables or Histograms Section c: Box-and-Whisker Plots PART 2: Published Statistical Reports and Graphs {A.S.10} PART 3: Percentile Ranks of Items in Data Sets {A.S.11} PART 4: Relationships Between Independent and Dependent Variables in Scatter Plots {A.S.12} PART 5: Relationship Between Correlation and Causation {A.S.13&14} TOPIC C: Making Predictions From Data PART 1: Recognizing the Effect of Linear Transformations of One-Variable on Statistical Data {A.S.16} PART 2: Predictions Based on Interpolations or Extrapolations of Lines of Best Fit {A.S.17} CHAPTER 14 PROBABILITY TOPIC A: Understanding Conditional Probability {A.S.18} TOPIC B: Determining Numbers of Elements in Sample Spaces and Numbers of Favorable Events (A.S.19) PART 1: Numbers of Elements in Sample Spaces PART 2: Numbers of Favorable Events TOPIC C: Calculating the Probability of an Event and its Complement {A.S.20} PART 1: Probability of an Event PART 2: Complement of an Event TOPIC D: Determining Empirical Probabilities of Specific Sample Data {A.S.21} TOPIC E: Calculating the Probability of a Set of Events {A.S.22} PART 1: Probability of Events that are More, Less, or Equally Likely to Occur PART 2: Probability of Certain and Uncertain Events TOPIC F: Calculating the Probability of Compound Events {A.S.23} PART 1: Probability of Independent Events PART 2: Probability of Dependent Events PART 3: Probability of Two Mutually Exclusive Events PART 4: Probability of Two Non-Mutually Exclusive Events APPENDIX HOW TO ADD MATH GRIDS & TABLES TO AN EXAM...555

Number Sense and Operations Strand

Number Sense and Operations Strand Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems. Number Theory NY A.N.1 Identify and apply the