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Topic A | Whole Numbers |

A.1 | Place Value and Names for Numbers |

A.2 | Addition with Whole Numbers |

A.3 | Rounding and Estimating Answers |

A.4 | Subtraction with Whole Numbers |

A.5 | Multiplication with Whole Numbers |

A.6 | Division with Whole Numbers |

A.7 | Powers and Exponents |

A.8 | Order of Operations |

Topic B | Introduction to Algebra |

B.1 | Positive and Negative Numbers |

B.2 | Addition with Negative Numbers |

B.3 | Subtraction with Negative Numbers |

B.4 | Multiplication with Negative Numbers |

B.5 | Division with Negative Numbers |

B.6 | Simplifying Algebraic Expressions |

Topic C | Fractions & Mixed Numbers |

C.1 | The Meaning and Properties of Fractions |

C.2 | Prime Numbers, Factors, and Reducing to Lowest Terms |

C.3 | Multiplication with Fractions |

C.4 | Division with Fractions |

C.5 | Addition and Subtraction of Fractions |

C.6 | Mixed-Number Notation |

C.7 | Multiplication and Division with Mixed Numbers |

C.8 | Addition and Subtraction with Mixed Numbers |

C.9 | Order of Operations |

C.10 | Complex Fractions |

Topic D | Solving Equations |

D.1 | The Distributive Property and Algebraic Expressions |

D.2 | The Addition Property of Equality |

D.3 | The Multiplication Property of Equality |

D.4 | Linear Equations in One Variable |

D.5 | Applications |

D.6 | Evaluating Formulas |

Topic E | Decimals |

E.1 | Decimal Notation, Place Value, and Rounding |

E.2 | Addition and Subtraction with Decimals |

E.3 | Multiplication with Decimals |

E.4 | Division with Decimals |

E.5 | Fractions and Decimals |

E.6 | Square Roots and the Pythagorean Theorem |

Topic F | Ratio & Proportion |

F.1 | Ratios |

F.2 | Rates and Unit Pricing |

F.3 | Solving Equations by Division |

F.4 | Proportions |

F.5 | Applications of Proportions |

F.6 | Similar Figures |

Topic G | Percent |

G.1 | Percents, Decimals, and Fractions |

G.2 | Basic Percent Problems |

G.3 | General Applications of Percent |

G.4 | Sales Tax and Commission |

G.5 | Percent Increase or Decrease, and Discount |

G.6 | Interest |

Topic H | Measurement |

H.1 | Unit Analysis I: Length |

H.2 | Unit Analysis II: Area and Volume |

H.3 | Unit Analysis III: Weight |

H.4 | Converting Between the Two Systems, and Temperature |

H.5 | Operations with Time and Mixed Units |

Topic A | Prealgebra Review |

A.1 | Factors and Simplifying Fractions |

A.2 | Operations with Fractions |

A.3 | Decimal Notation |

A.4 | Operations with Decimals |

A.5 | Percents, Decimals, and Fractions |

A.6 | Exponents and Order of Operations |

Topic B | Real Numbers and Algebraic Expressions |

B.1 | Real Numbers |

B.2 | Addition and Subtraction of Real Numbers |

B.3 | Multiplication of Real Numbers |

B.4 | Division of Real Numbers |

B.5 | Properties of Real Numbers |

B.6 | Simplifying Expressions |

Topic C | Linear Equations and Inequalities in One Variable |

C.1 | Addition Property of Equality |

C.2 | Multiplication Property of Equality |

C.3 | Solving Linear Equations in One Variable |

C.4 | Formulas |

C.5 | Applications: Number, Age, Perimeter, Coin Problems |

C.6 | Applications: Integer, Interest, Triangle, Miscellaneous Problems |

C.7 | Linear Inequalities in One Variable |

Topic D | Graphing Linear Equations and Inequalities in Two Variables |

D.1 | The Rectangular Coordinate System |

D.2 | Solutions and Graphs of Linear Equations |

D.3 | Graphing Linear Equations Using Intercepts |

D.4 | Graphing Linear Equations using Slope |

D.5 | Finding the Equation of a Line |

D.6 | Graphing Linear Inequalities in Two Variables |

Topic E | Exponents and Polynomials |

E.1 | Multiplication with Exponents and Scientific Notation |

E.2 | Division with Exponents and Negative Exponents |

E.3 | Operations with Monomials |

E.4 | Addition and Subtraction of Polynomials |

E.5 | Multiplication of Polynomials |

E.6 | Special Products |

E.7 | Dividing a Polynomial by a Monomial |

E.8 | Dividing a Polynomial by a Polynomial |

Topic F | Factoring Polynomials |

F.1 | The Greatest Common Factor |

F.2 | Factoring by Grouping |

F.3 | Factoring Trinomials of the Form x^{2}+bx+c |

F.4 | Factoring Trinomials of the Form ax^{2}+bx+c |

F.5 | The Difference of Two Squares and Perfect Square Trinomials |

F.6 | The Sum and Difference of Two Cubes |

F.7 | Factoring: A General Review |

F.8 | Solving Quadratic Equations by Factoring |

F.9 | Applications of Quadratic Equations |

Topic G | Rational Expressions and Equations |

G.1 | Simplifying Rational Expressions |

G.2 | Multiplication and Division of Rational Expressions |

G.3 | Unit Analysis with Rational Expressions |

G.4 | Addition and Subtraction of Rational Expressions |

G.5 | Equations Involving Rational Expressions |

G.6 | Complex Fractions |

G.7 | Proportions |

G.8 | Variation |

Topic H | Systems of Linear Equations |

H.1 | Solving Linear Systems by Graphing |

H.2 | The Substitution Method |

H.3 | The Elimination Method |

H.4 | Systems of Linear Inequalities |

H.5 | Applications of Systems of Equations |

Topic I | Radical Expressions and Equations |

I.1 | Radical Expressions |

I.2 | Simplifying Radicals |

I.3 | Addition and Subtraction of Radicals |

I.4 | Multiplication and Division of Radicals |

I.5 | Radical Equations |

I.6 | Rational Exponents |

I.7 | Graphs of Radical Equations |

Topic A | The Basics |

A.1 | The Ruler Postulate and Absolute Value |

A.2 | Lines and Angles |

A.3 | Midpoint Formula |

A.4 | Angle Pairs |

A.5 | The Distance Formula |

A.6 | Transformations |

Topic B | Inductive and Deductive Reasoning |

B.1 | Patterns and Inductive Reasoning |

B.2 | Conditional Statements |

B.3 | Deductive Reasoning |

B.4 | Biconditional Statements |

B.5 | Proofs with Algebra |

B.6 | Proofs with Segments and Angles |

Topic C | Parallel and Perpendicular Lines |

C.1 | Lines and Angles |

C.2 | Parallel Lines and Transversals |

C.3 | Proving Lines Parallel |

C.4 | Perpendicular Lines |

C.5 | Parallel and Perpendicular Lines in the Coordinate Plane |

Topic D | Congruent Triangles |

D.1 | Angles and Triangles |

D.2 | Congruence with Triangles |

D.3 | Proving Triangles are Congruent |

D.4 | Isosceles, Equilateral and Right Triangles |

Topic E | Properties of Triangles |

E.1 | Perpendicular and Angle Bisectors |

E.2 | Bisectors of Triangles |

E.3 | Medians and Altitudes of Triangles |

E.4 | Midsegments of Triangles |

E.5 | Inequalities of Triangles |

Topic F | Polygons and Quadrilaterals |

F.1 | Properties and Attributes of Polygons |

F.2 | Properties of Parallelograms |

F.3 | Properties of Special Parallelograms |

F.4 | Properties of Kites and Trapezoids |

Topic G | Similarity |

G.1 | Ratios and Proportions |

G.2 | Ratios and Similar Polygons |

G.3 | Triangle Similarity: AA, SSS, and SAS |

G.4 | Applying Properties of Similar Triangles |

G.5 | Using Proportional Relationships |

G.6 | Dialations and Similarity in the Coordinate Plane |

Topic H | Right Triangles and Trigonometry I |

H.1 | The Pythagorean Theorem |

H.2 | The Rectangular Coordinate System |

H.3 | Definition I: Trigonometric Functions |

H.4 | Introduction to Identities |

H.5 | More on Identities |

Topic I | Right Triangle And Trigonometry II |

I.1 | Definition II: Right Triangle Trigonometry |

I.2 | Calculators and Trigonometric Function of an Acute Angle |

I.3 | Solving Right Triangles |

I.4 | Applications |

I.5 | Vectors: A Geometric Approach |

Topic J | Extending Perimeter, Circumference and Area |

J.1 | Developing Formulas for Triangles and Quadrilaterals |

J.2 | Areas of Regular Polygons |

J.3 | Radians and Degrees |

J.4 | Circumference and Arc Length |

J.5 | Area of Circles and Sectors |

J.6 | Geometric Probability |

Topic K | Conic Sections |

K.1 | Parabolas |

K.2 | Ellipses |

K.3 | Hyperbolas |

K.4 | Nonlinear Systems of Equations and Inequalities |

Topic A | Real Numbers and Algebraic Expressions |

A.1 | The Real Numbers |

A.2 | Properties of Real Numbers |

A.3 | Arithmetic with Real Numbers |

A.4 | Exponents and Scientific Notation |

Topic B | Linear Equations and Inequalities in One Variable |

B.1 | Linear Equations |

B.2 | Formulas |

B.3 | Applications |

B.4 | Interval Notation and Linear Inequalities |

B.5 | Sets and Compound Inequalities |

B.6 | Absolute Value Equations |

B.7 | Absolute Value Inequalities |

Topic C | Graphs of Equations, Inequalities, and Functions |

C.1 | Graphs of Equations |

C.2 | Introduction to Functions |

C.3 | Function Notation |

C.4 | Algebra and Composition with Functions |

C.5 | Slope and Average Rate of Change |

C.6 | Linear Functions |

C.7 | Linear Inequalities |

Topic D | Systems of Equations |

D.1 | Solving Linear Systems |

D.2 | Systems of Linear Equations in Three Variables |

D.3 | Matrix Solutions to Linear Systems |

D.4 | Determinants and Cramer’s Rule |

D.5 | Applications of Systems of Equations |

D.6 | Systems of Linear Inequalities and Applications |

Topic E | Exponents and Polynomials |

E.1 | Sums and Differences of Polynomials |

E.2 | Multiplication of Polynomials |

E.3 | Greatest Common Factor and Factoring by Grouping |

E.4 | Factoring Trinomials |

E.5 | Factoring Special Products |

E.6 | Factoring: A General Review |

E.7 | Solving Equations by Factoring |

Topic F | Rational Expressions, Equations, and Functions |

F.1 | Basic Properties and Reducing to Lowest Terms |

F.2 | Multiplication and Division of Rational Expressions |

F.3 | Addition of Rational Expressions |

F.4 | Subtraction of Rational Expressions |

F.5 | Rational Equations |

F.6 | Applications |

F.7 | Complex Rational Expressions |

F.8 | Variation |

Topic G | Rational Exponents and Radicals |

G.1 | Rational Exponents |

G.2 | Simplifying Radicals |

G.3 | Addition and Subtraction of Radical Expressions |

G.4 | Multiplication and Division of Radical Expressions |

G.5 | Radical Equations and Functions |

G.6 | Complex Numbers |

Topic H | Quadratic Equations and Functions |

H.1 | Completing the Square |

H.2 | The Quadratic Formula |

H.3 | The Discriminant and Multiplicity |

H.4 | Equations Quadratic in Form |

H.5 | Graphing Quadratic Functions |

H.6 | Polynomials and Rational Inequalities |

Topic I | Exponential and Logarithmic Functions |

I.1 | Exponential Functions and Applications |

I.2 | Inverse Functions |

I.3 | Logarithmic Functions and Applications |

I.4 | Properties of Logarithms |

I.5 | Common and Natural Logarithms with Applications |

I.6 | Exponential Equations, Change of Base, and Applications |

Topic J | Conic Sections |

J.1 | The Distance Formula |

J.2 | Circles |

J.3 | Parabolas |

J.4 | Ellipses |

J.5 | Hyperbolas |

J.6 | Nonlinear Systems of Equations and Inequalities |

Topic K | Sequence and Series |

K.1 | Sequences and Recursion Formulas |

K.2 | Arithmetic and Geometric Series |

K.3 | Arithmetic Sequences |

K.4 | Geometric Sequences |

K.5 | The Binomial Expansion |

Topic A | The Six Trigonometric Functions |

A.1 | Angles, Degrees, and Special Triangles |

A.2 | The Rectangular Coordinate System |

A.3 | Definition I: Trigonometric Functions |

A.4 | Introduction to Identities |

A.5 | More on Identities |

Topic B | Right Triangle Trigonometry |

B.1 | Definition II: Right Triangle Trigonometry |

B.2 | Calculators and Trigonometric Function of an Acute Angle |

B.3 | Solving Right Triangles |

B.4 | Applications |

B.5 | Vectors: A Geometric Approach |

Topic C | Radian Measure |

C.1 | Reference Angle |

C.2 | Radians and Degrees |

C.3 | Definition III: Circular Functions |

C.4 | Arc Length and Area of a Sector |

C.5 | Velocities |

Topic D | Graphing and Inverse Functions |

D.1 | Basic Graphs |

D.2 | Amplitude Reflection and Period |

D.3 | Vertical Translation and Phase Shift |

D.4 | The Other Trigonometric Functions |

D.5 | Finding an Equation From its Graph |

D.6 | Inverse Trigonometric Functions |

Topic E | Identities and Formulas |

E.1 | Sum and Difference Formulas |

E.2 | Double-Angle Formulas |

E.3 | Half-Angle Formulas |

E.4 | Additional Identities |

Topic F | Equations |

F.1 | Solving Trigonometric Equations |

F.2 | More on Trigonometric Equations |

F.3 | Trigonometric Equations Involving Multiple Angles |

F.4 | Parametric Equations |

Topic G | Triangles |

G.1 | Law of Sines |

G.2 | The Ambiguous Case |

G.3 | The Law of Cosines |

G.4 | The Area of a Triangle |

G.5 | Vectors: An Algebraic Approach |

G.6 | Vectors: The Dot Product |

Topic H | Complex Numbers and Polar Coordinates |

H.1 | Complex Numbers |

H.2 | Trigonometric Form for Complex Numbers |

H.3 | Products and Quotients in Trigonometric Form |

H.4 | Roots of a Complex Number |

H.5 | Polar Coordinates |

H.6 | Equations in Polar Coordinates and Their Graphs |

Topic I | Introduction to Functions |

I.1 | Introduction to Functions |

I.2 | The Inverse of a Function |

Topic J | Exponential and Logarithmic Functions |

J.1 | Exponential Functions |

J.2 | Logarithms are Exponents |

J.3 | Properties of Logarithms |

J.4 | Common Logarithms and Natural Logarithms |

J.5 | Exponential Equations and Change of Base |

Topic A | Functions |

A.1 | Functions and Function Notation |

A.2 | Domain and Range |

A.3 | Rates of Change and Behavior of Graphs |

A.4 | Composition of Functions |

A.5 | Transformation of Functions |

A.6 | Absolute Value Functions |

A.7 | Inverse Functions |

Topic B | Linear Functions |

B.1 | Linear Functions |

B.2 | Graphs of Linear Functions |

B.3 | Modeling with Linear Functions |

B.4 | Fitting Linear Models to Data |

Topic C | Polynomial and Rational Functions |

C.1 | Complex Numbers |

C.2 | Quadratic Functions |

C.3 | Power Functions and Polynomial Functions |

C.4 | Graphs of Polynomial Functions |

C.5 | Dividing Polynomials |

C.6 | Zeros of Polynomial Functions |

C.7 | Rational Functions |

C.8 | Inverses and Radical Functions |

C.9 | Modeling Using Variation |

Topic D | Exponential and Logarithmic Functions |

D.1 | Exponential Functions |

D.2 | Graphs of Exponential Functions |

D.3 | Logarithmic Functions |

D.4 | Graphs of Logarithmic Functions |

D.5 | Logarithmic Properties |

D.6 | Exponential and Logarithmic Equations |

D.7 | Exponential and Logarithmic Models |

D.8 | Fitting Exponential Models to Data |

Topic E | Introduction to Trigonometric Functions |

E.1 | Angles |

E.2 | Unit Circle: Sine and Cosine Functions |

E.3 | The Other Trigonometric Functions |

E.4 | Right Triangle Trigonometry |

Topic F | Periodic Functions |

F.1 | Graphs of the Sine and Cosine Functions |

F.2 | Graphs of the Other Trigonometric Functions |

F.3 | Inverse Trigonometric Functions |

Topic G | Trigonometric Identities and Equations |

G.1 | Solving Trigonometric Equations with Identities |

G.2 | Sum and Difference Identities |

G.3 | Double-Angle, Half-Angle, and Reduction Formulas |

G.4 | Sum-to-Product and Product-to-Sum Formulas |

G.5 | Solving Trigonometric Equations |

G.6 | Modeling with Trigonometric Equations |

Topic H | Further Applications of Trigonometry |

H.1 | Non-right Triangles: Law of Sines |

H.2 | Non-right Triangles: Law of Cosines |

H.3 | Polar Coordinates |

H.4 | Polar Coordinates: Graphs |

H.5 | Polar Form of Complex Numbers |

H.6 | Parametric Equations |

H.7 | Parametric Equations: Graphs |

H.8 | Vectors |

Topic I | Systems of Equations and Inequalities |

I.1 | Systems of Linear Equations: Two Variables |

I.2 | Systems of Linear Equations: Three Variables |

I.3 | Systems of Nonlinear Equations and Inequalities: Two Variables |

I.4 | Partial Fractions |

I.5 | Matrices and Matrix Operations |

I.6 | Solving Systems with Gaussian Elimination |

I.7 | Solving Systems with Inverses |

I.8 | Solving Systems with Cramer’s Rule |

Topic J | Analytic Geometry |

J.1 | The Ellipse |

J.2 | The Hyperbola |

J.3 | The Parabola |

J.4 | The Rotation of Axes |

J.5 | Conic Sections in Polar Coordinates |

Topic K | Sequences, Probability, and Counting Theory |

K.1 | Sequences and Their Notations |

K.2 | Arithmetic Sequences |

K.3 | Geometric Sequences |

K.4 | Series and Their Notations |

K.5 | Counting Principles |

K.6 | Binomial Theorem |

K.7 | Probability |

Topic L | Introduction to Calculus |

L.1 | Finding Limits: Numerical and Graphical Approaches |

L.2 | Finding Limits: Properties of Limits |

L.3 | Continuity |

L.4 | Derivatives |

Topic A | Functions, Limits and Rates of Change |

A.1 | Introduction to Functions and Relations |

A.2 | Algebra and Composition with Functions |

A.3 | Slope, Rares of Change, and Linear Functions |

A.4 | Introduction to Limits |

A.5 | Functions and Continuity |

A.6 | Average and Instantaneous Rates of Change |

Topic B | Differentiation: The Language of Change |

B.1 | Derivative of a Function and Two Interpretations |

B.2 | Differentiating Products and Quotients |

B.3 | Higher Order Derivatives |

B.4 | The Chain Rule and General Power Rule |

B.5 | Implicit Differentiation |

Topic C | Applying the Derivative |

C.1 | The First Derivative and the Behavior of Functions |

C.2 | The Second Derivative and the Behavior of Functions |

C.3 | Applications of the Derivative: Optimization |

C.4 | Applications of the Derivative in Business and Economics |

Topic D | Derivatives of Exponential and Logarithmic Functions |

D.1 | The Exponential Functions |

D.2 | The Natural Logarithm Function |

D.3 | Differentiating the Natural Logarithm Function |

D.4 | Differentiating the Natural Exponential Function |

Topic E | Integration: The Language of Accumulation |

E.1 | Antidiffernetiation and the Indefinite Integral |

E.2 | Integration by Substitutions |

E.3 | The Definite Integral |

E.4 | The Definite Integral and Area |

E.5 | Improper Intergrals |

E.6 | Integration by Parts |

Topic F | Applications of Integration |

F.1 | Area of Regions in the Plane |

F.2 | Consumer’s and Producer’s Surplus |

F.3 | Annuities and Money Streams |

F.4 | Differential Equations |

F.5 | Applications of Differential Equations |

F.6 | Probability |

Topic G | Calculus of Functions of Several Variables |

G.1 | Functions of Several Variables |

G.2 | Partial Derivatives |

G.3 | Optimization of Functions of Two Variables |

G.4 | Constrained Maxima and Minima |

G.5 | The Total Differential |

G.6 | Double Intergrals as Volume |

G.7 | The Average Value of a Function |