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Foundational Mathematics with Assessments Understanding Whole Numbers 1 (with Assessments) Understanding Whole Numbers 1: Pretest Understanding Whole Numbers: 0 through 10 Greater Than, Less Than, Equal To Ordinal Numbers: First through Tenth Understanding Place Value: Ones and Tens Comparing Whole Numbers: 10 through 99 Understanding Place Value: Hundreds Understanding Addition and Subtraction 1 (with Assessments) Understanding Addition and Subtraction 1: Pretest Understanding Addition Understanding Addition: Number Line and Hundreds Chart Finding the Missing Number in Addition Understanding Subtraction Understanding Subtraction: Number Line and Hundreds Chart Finding the Missing Number in Subtraction Adding and Subtracting Whole Numbers 1 (with Assessments) Adding and Subtracting Whole Numbers 1: Pretest Adding 0 through 2: Addition Basic Facts Adding 3 through 9: Addition Basic Facts Adding Two 2-Digit Numbers: Sums Less Than 100 Adding Three or Four Numbers Subtraction Basic Facts Subtracting a 1-Digit Number from a 2Digit Number Subtracting Two 2-Digit Numbers Adding Two 2-Digit Numbers: Sums Greater Than 99 Understanding Whole Numbers 2 (with Assessments) Understanding Whole Numbers 2: Pretest Understanding Place Value: Thousands Reading and Writing Numbers in Word Form Understanding Place Value: Millions, Billions, and Beyond Representing Millions and Billions Understanding Addition and Subtraction 2 (with Assessments) Understanding Addition and Subtraction 2: Pretest Addition and Subtraction Fact Families Checking Subtraction by Addition Using the Identity Property of Addition Using the Commutative Property of Addition Using the Associative Property of Addition Adding and Subtracting Whole Numbers 2 (with Assessments) Adding and Subtracting Whole Numbers 2: Pretest Adding Multi-Digit Numbers Subtracting Multi-Digit Numbers with Regrouping Subtracting Multi-Digit Numbers with Consecutive Regrouping Subtracting across Zeros Solving Addition and Subtraction Story Problems Understanding Multiplication (with Assessments) Understanding Multiplication: Pretest Understanding Multiplication as Repeated Addition Understanding Multiplication as an Array Using the Identity Property of Multiplication Using the Commutative Property of Multiplication Using the Associative Property of Multiplication Using the Distributive Property of Multiplication over Addition Finding the Missing Number in Multiplication Identifying Multiples Finding Common Multiples and the Least Common Multiple Multiplying Whole Numbers (with Assessments) Multiplying Whole Numbers: Pretest -1- Multiplying by 0 through 5: Multiplication Basic Facts Multiplying by 6 through 10: Multiplication Basic Facts Multiplying a 2-Digit Number by a 1Digit Number Multiplying by a Multiple of 10 or 100 Multiplying a 3-Digit Number by a 1Digit Number Multiplying a Multiple of 10 by a Multiple of 10 Multiplying a 2-Digit Number by a 2Digit Number Solving Multiplication Story Problems Understanding Division (with Assessments) Understanding Division: Pretest Understanding Division as Repeated Subtraction Understanding Division as Fair Sharing Multiplication and Division Fact Families Dividing Whole Numbers (with Assessments) Dividing Whole Numbers: Pretest Division Basic Facts Dividing by a 1-Digit Number Dividing by a 2-Digit Number Dividing Multiples of 100 Writing a Quotient as a Mixed Number Solving Division Story Problems Understanding Fractions (with Assessments) Understanding Fractions: Pretest Understanding Fractions: Equal Parts of an Object Understanding Fractions: Equal Parts of a Collection Fraction Notation: Numerator and Denominator Proper Fractions and Improper Fractions Renaming Improper Fractions as Whole or Mixed Numbers Finding Equivalent Fractions Simplifying Fractions Working with Common Denominators and the Least Common Denominator Comparing Fractions Ordering Fractions Renaming Mixed Numbers as Improper Fractions Adding and Subtracting Fractions (with Assessments) Adding and Subtracting Fractions: Pretest Adding and Subtracting Fractions: Like Denominators Adding and Subtracting Fractions: Unlike Denominators Adding Mixed Numbers Subtracting Mixed Numbers: Like Denominators Subtracting Mixed Numbers: Unlike Denominators Multiplying and Dividing Fractions (with Assessments) Multiplying and Dividing Fractions: Pretest Multiplying Two Fractions Multiplying Whole Numbers and Mixed Numbers Dividing a Fraction by a Fraction Dividing Fractions, Whole Numbers, and Mixed Numbers Finding the Reciprocal Solving Fraction Story Problems Understanding Decimals (with Assessments) Understanding Decimals: Pretest Understanding Decimals: Tenths Understanding Decimal Place Value: Tenths and Hundredths Understanding Decimal Place Value: Thousandths and Ten-Thousandths Relating Decimals, Fractions, and Mixed Numbers Comparing and Ordering Decimals Performing Operations with Decimals (with Assessments) Performing Operations with Decimals: Pretest Adding and Subtracting Decimals Multiplying Decimals Multiplying Decimals by 10 or 100 Dividing Decimals Dividing a 2-Digit Number by 10 or 100 Renaming a Fraction as a Decimal Rounding Decimals Solving Decimal Story Problems Working with Percent (with Assessments) Working with Percent: Pretest Understanding Percent Relating Fractions, Decimals, and Percents Finding a Percent of a Whole Number Finding a Percent of a Decimal Number Understanding Ratio and Proportion (with Assessments) Understanding Ratio and Proportion: Pretest Understanding Ratio Equivalent Ratios Understanding Proportion Solving Proportions Solving Ratio, Proportion, and Percent Story Problems Plane and Solid Figures (with Assessments) Plane and Solid Figures: Pretest Lines, Parts of Lines, and Angles Lines in a Plane Introduction to Triangles Introduction to Quadrilaterals Introduction to Circles Exploring Congruent Figures Exploring Similar Figures Line Symmetry in Plane Figures Introduction to Solid Figures Using Geometry (with Assessments) Using Geometry: Pretest Area: Counting Square Units Calculating the Area of Rectangles and Squares Calculating the Area of Triangles Calculating the Volume of a Rectangular Prism Measurement (with Assessments) Measurement: Pretest Measuring Length: Metric Units Measuring Length: Customary Units Telling Time to the Minute Measuring Temperature: Fahrenheit Measuring Temperature: Celsius Solving Measurement Story Problems Math Fundamentals 95 Hours 671 Objectives Skill Level: Basic Target Audience; M, H, PS This beginning Math curriculum is designed to provide instruction in all the computation skills . from counting through beginning geometry. Basic Number Ideas Beginning -2- (with or without assessment test) Whole Numbers 0-9 Counting Numbers Whole Numbers 0-9 Review Whole Numbers 10-99 Whole Numbers 100-999 Numbers 10-999 Review Hundreds and Thousands Millions/Billions and Trillions Addition (with or without assessment test) Meaning of Addition Addition Facts 1 Addition Facts 2 Addition Properties Addition Skills 1 Addition Skills 2 Addition Skills 3 Addition Skills 4 Addition Review Subtraction (with or without assessment test) Meaning of Subtraction Subtraction Facts Subtraction Skills 1 Subtraction Skills 2 Subtraction Skills 3 Subtraction Skills 4 Subtraction Review Problem Solving 1 Multiplication (with or without assessment test) Meaning of Multiplication Multiplication Facts 1 Multiplication Facts 2 Multiplication Properties 1 Multiplication Properties 2 Multiplication Skills 1 Multiplication Skills 2 Multiplication Skills 3 Multiplication Skills 4 Multiplication Review I Multiplication Skills 5 Multiplication Skills 6 Multiplication Skills 7 Multiplication Review II Problem Solving 2 Division (with or without assessment test) Meaning of Division Division Facts Division Skills 1 Division Skills 2 Division Skills 3 Division Review I Division Skills 4 Division Skills 5 Division Skills 6 Division Skills 7 Division Skills 8 Division Review II Problem Solving 3 Fractions (with or without assessment test) Meaning of Fractions Equivalent Fractions Multiples and Common Denominators Comparing Fractions Improper Fractions and Mixed Numbers Basic Terms Review Adding and Subtracting Fractions 1 Adding and Subtracting Fractions 2 Adding Mixed Numbers Subtracting Mixed Numbers 1 Subtracting Mixed Numbers 2 Adding and Subtracting Fractions Review Multiplying Fractions Dividing Fractions 1 Dividing Fractions 2 Multiplying and Dividing Mixed Numbers 1 Multiplying and Dividing Mixed Numbers 2 Multiplication and Division Review Problem Solving 4 Decimals (with or without assessment test) Decimal Fractions 1 Decimal Fractions 2 Adding and Subtracting Decimals Multiplying Decimals Dividing Decimals Decimals Review Problem Solving 5 Ratio/Proportion/Percent (with or without assessment test) Ratio Concepts Proportion Concepts Percent Concepts 1 Percent Concepts 2 Ratio/Proportion/Percent Review Problem Solving 6 Geometry and Measurement (with or without assessment test) Plane Figures 1 Plane Figures 2 Figure Comparison Common 3-Dimensional Figures Basic Figures Review Linear Measurement Area Measurement Volume and Capacity Measurement Measurement Review Problem Solving 7 Math Problem Solving 57 Hours 19 Objectives Skill Level: Basic - Advanced Target Audience: M, H, PS This powerful math courseware features nineteen interactive scenarios that encourage learners to explore and apply mathematical concepts from basic computation to advanced algebra. Math Fundamentals: Math Problem Solving Building a Highway Smart Shopping Car Costs Running a Business Beginning Algebra: Math Problem Solving Plan for a Fishing Trip Tunnel through Bald Mountain Bean-Counting Intermediate Algebra: Math Problem Solving Video Rental Running a Race Advanced Algebra: Math Problem Solving Car Rental Building Boats Saving the Birds Geometry and Measurement: Math Problem Solving Planning a Park Shelf Space Probability and Statistics: Math Problem Solving The Fund Raiser Making the Grade Statistics for Quality Data Skills: Math Problem Solving Growing Lilies Planning a Playground Applied Math (with or without assessment test) 14 Hours 24 Objectives Skill Level: Basic Target Audience: M, H, PS Part of PLATO Workskills, this course teaches the practical mathematics skills essential for success in the modern workplace. Time Applications Clocks and Time Zones Estimating Math Conversions Using Base, Rate, and Portion Converting Linear Measurements Converting Weight Measurements Converting Volume Measurements Using Linear Measurement Tools Data Skills 35 Hours 84 Objectives Skill Level: Intermediate Target Audience: M, H, PS Part of PLATO® WorkSkills, this curriculum teaches both reading and math skills essential to students. success in today.s fast-paced workplace. Reading Graphical Data (with or without assessment test) Reading Pie Charts Introduction to Line Graphs Reading Line Graphs Introduction to Bar Graphs Reading Bar Graphs Introduction to Data in Tables Reading Data in Tables Introduction to Flowcharts Computing Graphical Data (with or without assessment test) Graphing and Charting Tables Using Pictographs Using Line Graphs Using Bar Graphs Using Pie Charts Using Histograms Reading Complex Charts and Graphs (with or without assessmenttest) Reading Histograms Reading Complex Tables Reading Complex Flowcharts Constructing Graphs and Charts (with or without assessment test) Constructing Line Graphs Constructing Pie Charts -3- Constructing Bar Graphs Constructing Histograms Selecting Graphs and Charts ALGEBRA 1 (part 1) Basic Number Ideas Odd and Even Numbers Prime and Composite Exponents: Exponential Form Exponents: Product Rule Exponents: Power Rule The Additive Inverse of Integers Adding Integers Subtracting Integers Multiplying Integers Dividing Integers Square Roots of Perfect Squares Square Roots of Imperfect Squares Multiplying Common Fractions Adding and Subtracting Fractions Adding and Subtracting Mixed Numbers Dividing Fractions Multiplying and Dividing Mixed Numbers Using Basic Number Ideas Mental Math with Whole Numbers Mental Math with Fractions and Percents Math Sentences Order of Operations Expressions in 1 Variable Expressions in 2 or More Variables Determining the True Value of a Statement Adding Monomials Subtracting Monomials Multiplying Monomials Dividing Monomials Adding Binomials and Monomials Subtracting Binomials and Monomials Multiplying Binomials and Monomials Dividing Binomials and Monomials Linear Equations in 1 Variable: Solving by Inspection Linear Equations in 1 Variable: Isolating the Variable Linear Inequalities in 1 Variable, Part 1 Linear Inequalities in 1 Variable, Part 2 More Difficult Linear Inequalities in 1 Variable Special Quadratic Equations, Part 1 Special Quadratic Equations, Part 2 Using Linear Equations to Solve Problems Using Quadratic Equations to Solve Problems Graphing Basics Coordinate Plane Identifying Points on a Coordinate Plane Ordered Pairs as Solutions to a Linear Equation Graphing Linear Equations in 2 Variables Solving and Graphing Systems of Equations Solving Problems with Systems of Linear Equations Equations and Formulas Literal equations Adapting and Using Formulas Special Topics Visualizing Percents Less than 1% Converting Percents Less Than 1% to Decimals Converting a Decimal to a Fraction of a Percent Finding the Amount with Percents Less than 1% Visualizing Percents Greater than 100% Converting Percents Greater than 100% to Decimals Converting a Number Greater than 1 to a Percent Mean, Median, and Mode Probability and Possible Outcomes Probability of an Event Solving Problems with Percents Solving Problems with Mean, Median, and Mode Solving Problems with Probability Estimation Basics Estimation by Clustering Scaling and Proportion, Part 1 Scaling and Proportion, Part 2 Introduction to Functions Patterns and Sequences Functions Describing Functions with Equations, Tables, and Graphs Linear Patterns Graphs, Slopes and yIntercepts Equations, Graphs, Slopes, and y-Intercepts Interpreting Graphs to Solve Problems ALGEBRA 1 (part 2) Sets and Numbers Additive Inverse of an Integer Integer Sum Integer Difference Integer Product Integer Quotient Adding Fractions -4- Subtracting Fractions Multiplicative Inverse of a Fraction Product of Fractions Quotient of Fractions Basic Set Concepts: Elements in a Set Basic Set Concepts: Finite or Infinite Basic Set Concepts: Subsets Basic Set Concepts: Roster and Set builder Forms Union of Two Sets Intersection of Two Sets Positive and Negative Exponents Integer Exponents and the Product Rule Integer Exponents and the Quotient Rule Integer Exponents and the Power Rule, Part 1 Integer Exponents and the Power Rule, Part 2 Square Roots of Integers Multiplication Rule for Radicals Division Rule for Radicals Simplifying Radicals, Part 1 Simplifying Radicals, Part 2 Review: Fractions and Sets Review: Exponents and Radicals Polynomials and Factoring Classifying Polynomials Additive Inverse of a Monomial Monomial Sum Monomial Difference Monomial Product Monomial Quotient Binomial Sum Additive Inverse of a Binomial Binomial Difference Value of a Polynomial Polynomial Sum Polynomial Difference Product of a Monomial and Polynomial Simplifying Polynomial Expressions Product of Polynomials Quotient of a Monomial and Polynomial Quotient of a Binomial and Polynomial Greatest Common Factor of Monomials Monomial Factors of Polynomials Binomial Factors of Polynomials, Part 1 Binomial Factors of Polynomials, Part 2 Factoring the Difference of Squares Factoring Perfect Square Trinomials Factoring Trinomials, Part 1 Factoring Trinomials, Part 2 Review: Polynomials and Factoring Equations and Inequalities Simple Equations in 1 Variable: Using Inspection Simple Equations in 1 Variable: Isolating the Variable More Difficult Linear Equations in 1 Variable Absolute Value of a Number Equations with Absolute Values Graphing a Solution Set on a Number Line Solving and Graphing Equations in 1 Variable Solving Problems with Linear Equations in 1 Variable Linear Inequalities in 1 Variable, Part 1 Linear Inequalities in 1 Variable, Part 2 Linear Inequalities in 1 Variable, Part 3 Solving Simple Quadratic Equations Solving Quadratic Equations by Factoring, Part 1 Solving Quadratic Equations by Factoring, Part 2 Solving Quadratic Equations by Factoring, Part 3 Quadratic Formula Solving Problems With the Quadratic Equations Review: Equations and Inequalities Algebra 2 (part 1) Rational Expressions Evaluating Rational Expressions Restrictions on Rational Expressions Equivalent Forms of Rational Expressions Simplifying Rational Expressions Sum of Rational Expressions, Part 1 Difference of Rational Expressions: Part 1 Product of Rational Expressions Quotient of Rational Expressions Common Denominators of Rational Expressions Sum of Rational Expressions: Part 2 Difference of Rational Expressions: Part 2 Review: Rational Expressions Graphs and Linear Equations The Coordinate Graphing Ordered Pairs Solutions of Linear Equation as Ordered Pairs Graphing a Linear Equation in 2 Variables Graphing Linear Inequality in 2 Variables Slope of a Line from 2 Points The y-Intercept of a Line Using the Slope and yIntercept to Graph a Line Finding the Slope and yIntercept from an Equation Writing Equations in SlopeIntercept Form Identifying Graphs from Their Equations Parallel Lines and Their Slopes Perpendicular Lines and Their Slopes Equations of Parallel or Perpendicular Lines Review: Graphs Linear Systems of Equations and Inequalities Solving Linear Systems of Equations: Graphs Classifying Linear Systems Solving Linear Systems of Inequalities: Graphs Solving Linear Systems of Equations: Substitution Solving Linear Systems of Equations: Addition Solving Linear Systems of Equations: Matrices 1 Solving Linear Systems of Equations: Matrices 2 Solving Problems with Linear Systems Review: Linear Systems Probability Chance Experiments and Probability Determining the Probability of an Event Multiplication Principle of Counting Review: Probability Vectors Introduction to Vectors Vector Addition Algebra 2 (part 2) Numbers and Their Properties Rules for Exponents and Radicals Rationalizing the Denominator in Rational Expressions Applying Rules for Exponents and Radicals Scientific Notation Simplifying Algebraic Expressions Multiplying Algebraic Expressions -5- Factoring Algebraic Expressions Factoring Sums and Differences of Perfect Cubes Factoring or Using Quadratic Formulas Rational Expressions: Simplify Rational Expressions: Add and Subtract Rational Expressions: Multiply and Divide Special Equations and Inequalities Evaluating Expressions With Absolute Value Absolute Value, Inequalities, and Interval Notation Graphing Linear Inequalities in 1 Variable Graphing with Restrictions on the Variable Graphing Solution Sets of Associated Inequalities Coordinates and Curves Calculating the Slope of a Line Point-Slope and Slope-Intercept Forms of Equations Equation of a Line Given a Point and Parallel Line Equation of a Line Given a Point and Perpendicular Line Perpendicular Bisector of a Line Segment Distance between 2 Points Distance between a Point and a Line Distance and Circles Parabola and Its Intercepts Parabola and Its Vertex Ellipse Hyperbola Equations of Ellipses and Hyperbolas Functions and Their Graphs Defining a Function with Its Rule Finding Values of a Function Using Its Rule Equations and Graphs of Functions, Part 1 Equations and Graphs of Functions, Part 2 Functional Values Composite Functions Domain Values of Composite Functions Inverse of a Function Determining if a Function Has an Inverse Solving Problems with Linear Functions Solving Problems with Quadratic Functions Beginning Algebra Exponential and Logarithmic Functions Properties of Exponential Functions Properties of Logarithmic Functions Recognizing Graphs of Types of Functions Solving Problems: Exponential and Logarithmic Exponential Growth Exponential Decay Pre-Algebra 23 Hours 177 Objectives Skill Level: Intermediate Target Audience: M, H, PS This curriculum provides students with the foundation skills they.ll need to understand and apply algebraic concepts. Basic Number Ideas -PreAlgebra (with or without assessment test) Odd/Even/Prime/Composite Numbers Exponents - Pre-Algebra Adding and Subtracting Integers Multiplying and Dividing Integers Square Roots - Pre-Algebra Common Fractions Using Basic Number Ideas Math Sentences, Part 1 (with or without assessment test) Variables Monomials Binomials Linear Equations: 1 Variable Linear Inequalities: 1 Variable Special Quadratic Equations Using Math Sentences, Part 1 Math Sentences, Part 2 (with or without assessment test) Coordinate Plane Linear Equations: 2 Variables Systems of Equations - Pre-Algebra Using Math Sentences, Part 2 Special Topics (with or without assessment test) Percents, Part 1 Percents, Part 2 Mean, Median, and Mode Probability - Pre-Algebra Using Special Topics 36 Hours 282 Objectives Skill Level: Intermediate Target Audience: M, H, PS Building on the information presented in Pre-Algebra, these courses continue students. ntroduction to algebra with instruction for sets and numbers, polynomials and factoring, and math sentences, following up with application exercises. Sets and Numbers (with or without assessment test) Integer Sum Integer Difference Integer Product and Quotient Fractional Numbers: Add & Subtract Fractional Numbers: Multiply & Divide Basic Set Concepts Set Union and Intersection Exponents - Beginning Algebra Quotient and Power Square Roots - Beginning Algebra Roots and Radicals Review: Sets and Numbers Polynomials and Factoring (with or without assessment test) Monomial Sum and Difference Monomial Product and Quotient Binomial Sum and Difference Polynomial Sum and Difference Polynomial Product Polynomial Quotient Common Factors Factoring II Factoring Special Cases Factoring Trinomials I Factoring Trinomials II Review: Polynomials/Factoring -6- Math Sentences (with or without assessment test) Simple Equations Solving Equations Absolute Value Graphing Word Problems I Inequalities I Inequalities II Simple Quadratics Quadratic Equations Quadratic Formula Word Problems II Review: Math Sentences Intermediate Algebra 20 Hours 140 Objectives Skill Level: Intermediate Target Audience: M, H, PS Starting where Beginning Algebra left off, this curriculum provides instruction in the core algebra topics usually required to fulfill high school course requirements. Rational Expressions (with or without assessment test) Evaluating Equivalent Forms Rational Sum and Difference Rational Product and Quotient Unlike Denominators Review: Rational Expression Graphs (with or without assessment test) Points in a Plane Linear Equations and Inequalities Slope and Y-Intercept Slope - Intercept Form Parallel and Perpendicular Lines Intermediate Review: Graphs Linear Systems of Equations and Inequalities (with or without assessment test) Linear Systems Systems - Substitute Systems - Addition Word Problems Review: Linear Systems Probability (with or without assessment test) Probability I Probability II Review: Probability Advanced Algebra 27 Hours 75 Objectives Skill Levels: Advanced Target Audience: H, PS This college-level course prepares students for the high-technology jobs of today. Numbers and Their Properties (with or without assessment test) Exponents and Radicals Algebraic Operations Factoring Algebraic Fractions Equations and Inequalities (with or without assessment test) Intervals, Distance and Absolute Values Inequalities Coordinates and Curves (with or without assessment test) Lines and Slopes Parallel and Perpendicular Lines Advanced Distance and Circles Parabolas Ellipses and Hyperbolas Functions and Their Graphs (with or without assessment test) Definitions of Functions Graphs of Functions More on Graphing Functions Composite and Inverse Functions Applications of Functions Exponential Functions (with or without assessment test) Exponential and Logarithmic Functions Exponential Growth and Decay Geometry and Measurement 1 10 Hours 78 Objectives Skill Level: Intermediate Target Audience: M, H, PS This curriculum offers students a powerful introduction to basic geometric and measurement concepts. Geometry (with or without assessment test) Special Angles, Part 1 Special Angles, Part 2 Circles/Arcs/Circumferences The Pythagorean Theorem 1 Using Geometry Measurement (with or without assessment test) Metric Measurement Area, Part 1 Area, Part 2 Volume Using Measurement Geometry and Measurement 2 45 Hours 156 Objectives Skill Level: Intermediate Target Audience: M, H, PS This curriculum provides instruction required in most high school-level geometry courses. Introduction to Geometry (with or without assessment test) Postulates and Theorems Points, Lines and Planes Intersecting Lines and Planes Congruent Angles Supplementary and Complementary Angles Two of a Kind Triangles and Lines (with or without assessment test) Congruent Triangles, Part 1 Congruent Triangles, Part 2 Congruent Triangle Problems Angles in Pairs Transitive Properties of Lines The Sum of the Angles in a Triangle The Pythagorean Theorem 2 Solving Right Triangle Problems 30-60 Right Triangles Proportionality A Sense of Proportion Not Everything is Created Equal Polygons (with or without assessment test) Introduction to Polygons -7- Summing up Angles Angles in Regular Polygons Parallelograms: Part 1 Parallelograms: Part 2 Rhombuses and Trapezoids Transformations, Symmetry, and Area (with or without assessment test) Symmetry Translations Rotations Area of Right Triangles and Parallelograms Area of Any Triangle Area of Trapezoids and Rhombuses Circles (with or without assessment test) Introduction to Circles Tangents Arcs and Chords Inscribed Angles Circles and Angles Circles and Segments Measuring Circumference The Length of Arcs The Area of Circles Solids and Coordinate Geometry (with or without assessment test) Prisms Area and Volume of Cylinders Area and Volume of Cones The Distance Formula Slope Coordinates in Three Dimensions Trigonometry 16 Hours 36 Objectives Skill Level: Advanced Target Audience: H, PS This college-level curriculum provides students with the skills necessary to understand concepts such as right angle trigonometry, circular functions, trigonometric identities, and equations. Trigonometric Functions (with or without assessment test) Right Angle Trigonometry Radian Measure Circular Functions Three More Trigonometric Functions Graphing Trigonometric Functions Trigonometric Identities and Equations (with or without assessment test) Trigonometric Identities of a Single Variable Trigonometric Identities II Trigonometric Equations Inverse Trigonometric Functions Law of Sines and Cosines Polar Coordinates Calculus 1 38 Hours 135 Objectives Skill Level: Advanced Target Audience: H, PS An introduction to the fundamentals of differential and integral calculus, this curriculum provides a foundation for further study in calculus, or in other fields where a knowledge of calculus is required. Limits I Introduction to Limits - Tutorial Introduction to Limits - Exercises Limits of Rational and Transcendental Functions- Tutorial Limits of Rational and Transcendental FunctionsExercises Limits at Infinity - Tutorial Limits at Infinity - Exercises Limits II Definition and Proofs of LimitsTutorial Definition and Proofs of LimitsExercises Use of Limit Theorems- Tutorial Use of Limit Theorems- Exercises Continuity - Tutorial Continuity . Exercises The Derivative Derivative: Approximating Rates and Definition - Tutorial Derivative: Approximating Rates and Definition - Exercises Derivative: Instantaneous Rates Tutorial Derivative: Instantaneous Rates . Exercises Techniques of Differentiation Differentiation of Polynomials and Rational Functions - Tutorial Differentiation of Polynomials and Rational Functions - Exercises Uses of the First DerivativeTutorial Uses of the First DerivativeExercises The Second Derivative Tutorial The Second Derivative Exercises Finding Maxima and Minima of Functions - Tutorial Finding Maxima and Minima of Functions - Exercises Derivatives of Trigonometric Functions Concavity and the Second Derivative Test - Tutorial Concavity and the Second Derivative Test - Exercises Graphing Rational FunctionsTutorial Graphing Rational FunctionsExercises Narrative Max-Min ProblemsTutorial Narrative Max-Min Problems-Exercises The Pinching Theorem Tutorial The Pinching Theorem Exercises Differentiation of Trigonometric Functions - Tutorial Differentiation of Trigonometric Functions . Exercises Chain Rule and Related Rates Derivatives of Composite Functions - Tutorial Derivatives of Composite Functions - Exercises More on the Chain Rule - Tutorial More on the Chain Rule - Exercises Implicit Differentiation Tutorial Implicit Differentiation Exercises Related Rates - Tutorial Related Rates - Exercises Tangent Line Approximations and Differentials Tangent Line ApproximationTutorial Tangent Line ApproximationExercises Differentials at a Point Tutorial Differentials at a Point – Exercises Applications of the First Derivative The Behavior of a Function as Related to the Sign of the Derivative - Tutorial The Behavior of a Function as Related to the Sign of the Derivative - Exercises -8- Applications of the Second Derivative General Properties of Continuous and Differentiable Functions Basic Theorems - Tutorial Basic Theorems . Exercises The Indefinite Integral The Indefinite Integral: Physical and Geometrical Interpretation of the Antiderivative - Tutorial The Indefinite Integral: Physical and Geometrical Interpretation of the Antiderivative - Exercises Integration by Substitution- Tutorial Integration by SubstitutionExercises Definite Integral Introduction to the Definite Integral: Approximations and Areas - Tutorial Introduction to the Definite Integral: Approximations and Areas - Exercises Introduction to the Definite Integral: Definition and Applications - Tutorial Introduction to the Definite Integral: Definition and Applications . Exercises The Fundamental Theorem The Fundamental Theorem of Calculus - Tutorial The Fundamental Theorem of Calculus – Exercises Derivatives of Integrals with Functions as Limits - Tutorial Derivatives of Integrals with Functions as Limits – Exercise Geometrical Applications of the Definite Integral Other Logarithm and Exponential Functions Area Between Curves - Tutorial Area Between Curves - Exercises Volumes of Solids of Revolution by the Method of Disks - Tutorial Volumes of Solids of Revolution by the Method of Disks - Exercises Volumes of Solids of Revolution by the Method of Shells - Tutorial Volumes of Solids of Revolution by the Method of Shells - Exercises Properties and Graphs of the General Exponential and Logarithm Functions Applications of the Common Logarithm Physical Applications of the Definite Integral Work Done by Moving an Object Horizontally or by Stretching or Compressing Spring - Tutorial Work Done by Moving an Object Horizontally or by Stretching or Compressing Spring - Exercises Work Done by Lifting an Object or Pumping a Liquid - Tutorial Work Done by Lifting an Object or Pumping a Liquid - Exercises Force Due to Hydrostatic PressureTutorial Force Due to Hydrostatic PressureExercises Center of Mass - Tutorial Center of Mass - Exercises Calculus 2 35 Hours 77 Objectives Skill Level: Advanced Target Audience: H, PS This curriculum is intended as the second semester of a course in the fundamentals of differential and integral calculus. Introduction to Inverse Functions Properties of Inverse Functions Derivatives of Inverse Functions Inverse Trigonometric Functions The Arcsine Function The Arctangent Function The Natural Logarithm Properties of the Natural Logarithm The Natural Exponential Function The Natural Exponential Function Exponential Growth and Decay Hyperbolic Functions L.Hopital.s Rule L.Hopital.s Rule Further Indeterminate Forms Integration by Substitution and by Parts Integration by Substitution Integration by Parts Techniques of Integration Involving Trigonometric Functions Trigonometric Integrals Integration by Trigonometric Substitution Partial Fractions Partial Fractions Integration by Partial Fractions Numerical Integration Riemann Sums and the Trapezoidal Rule Simpson.s Rule Improper Integrals Improper Integrals Lengths of Curves Lengths of Graphs of Functions Introduction to Sequences Polynomial Approximation and Taylor.s Theorem Sequences Further Properties of Convergent Sequences Introduction to Series Introduction to Series Preliminary Results on Infinite Series -9- Tests of Convergence on Non-negative Series The Integral Test and the Comparison Tests The Ratio Test and the Root Test Additional Topics on Convergence and Divergence of Series The Alternating Series Tests Absolute and Conditional Convergence Power Series The Radius and Interval of Convergence of Power Series Differentiation and Integration of Power Series Taylor Series The Binomial Series