Lesson 1 Geometry Review Lesson 2 More on Area * Cylinders and Prisms * Cones and Pyramids * Spheres Lesson 3 Pythagorean Theorem * Triangle Inequalities (1) * Similar Polygons * Similar Triangles Lesson 4 Construction Lesson 5 Exponents and Radicals * Complex Numbers * Areas of Similar Geometric Figures * Diagonals of Rectangular Solids Lesson 6 Fractional Equations * Radical Equations * Systems of Three Linear Equations Lesson 7 Inductive and Deductive Reasoning * Logic * The Contrapositive * Converse and Inverse Lesson 8 Statements of Similarity * Proportional Segments * Angle Bisectors and Side Ratios Lesson 9 Congruent Figures * Proof Outlines Lesson 10 Equation of a Line * Rational Denominators * Completing the Square Lesson 11 Circles * Properties of Circles * The Quadratic Formula Lesson 12 Angles and Diagonals in Polygons * Proof of the Chord-Tangent Theorem Lesson 13 Intersecting Secants * Intersecting Secants and Tangents * Products of Chord Segments * Products of Secant and Tangent Segments Lesson 14 Sine, Cosine, and Tangent * Angles of Elevation and Depression * Rectangular and Polar Coordinates * Coordinate Conversion Lesson 15 Assumptions * Proofs Lesson 16 Complex Fractions * Abstract Equations * Division of Polynomials Lesson 17 Proofs of the Pythagorean Theorem * Proofs of Similarity Lesson 18 Advanced Word Problems Lesson 19 Nonlinear Systems * Factoring Exponentials * Sum and Difference of Two Cubes Lesson 20 Two Special Triangles Lesson 21 Evaluating Functions * Domain and Range * Types of Functions * Tests for Functions

Quarter 2

Lesson 22 Absolute Value * Reciprocal Functions Lesson 23 The Exponential Function * Sketching Exponentials Lesson 24 Sums of Trigonometric Functions * Combining Functions Lesson 25 Age Problems * Rate Problems Lesson 26 The Logarithmic Form of the Exponential * Logarithmic Equations Lesson 27 Related Angles * Signs of Trigonometric Functions Lesson 28 Factorial Notation * Abstract Rate Problems Lesson 29 The Unit Circle * Very Large and Very Small Fractions * Quadrantal Angles Lesson 30 Addition of Vectors * Overlapping Triangles Lesson 31 Symmetry * Reflections * Translations Lesson 32 Inverse Functions * Four Quadrant Signs * Inverse Trigonometric Functions Lesson 33 Quadrilaterals * Properties of Parallelograms * Types of Parallelograms * Conditions for Parallelograms * Trapezoids Lesson 34 Summation Notation * Linear Regression * Decomposing Functions Lesson 35 Change in Coordinates * The Name of a Number * The Distance Formula Lesson 36 Angles Greater Than 360° * Sums of Trigonometric Functions * Boat-in-the-River Problems Lesson 37 The Line as a Locus * The Midpoint Formula Lesson 38 Fundamental Counting Principle and Permutations * Designated Roots * Overall Average Rate Lesson 39 Radian Measure of Angles * Forms of Linear Equations Lesson 40 The Argument in Mathematics * The Laws of Logarithms * Properties of Inverse Functions Lesson 41 Reciprocal Trigonometric Functions * Permutation Notation Lesson 42 Conic Sections * Circles * Constants in Exponential Functions Lesson 43 Periodic Functions * Graphs of Sin and Cos Lesson 44 Abstract Rate Problems Lesson 45 Conditional Permutations * Two-Variable Analysis Using a Graphing Calculator Lesson 46 Complex Roots * Factoring Over the Complex Numbers Lesson 47 Vertical Sinusoid Translations * Arctan Lesson 48 Powers of Trigonometric Functions * Perpendicular Bisectors Lesson 49 The Logarithmic Function * Development of the Rules for Logarithms Lesson 50 Trigonometric Equations

Semester 2:

Textbook: The Mooculus Textbook Written by Jim Fowler, and Bart Snapp, Professors at Ohio State University

## Semester 1:

Text: SaxonAdvanced Mathematics, Second EditionQuarter 1Lesson 1Geometry ReviewLesson 2More on Area * Cylinders and Prisms * Cones and Pyramids * SpheresLesson 3Pythagorean Theorem * Triangle Inequalities (1) * Similar Polygons * Similar TrianglesLesson 4ConstructionLesson 5Exponents and Radicals * Complex Numbers * Areas of Similar Geometric Figures * Diagonals of Rectangular SolidsLesson 6Fractional Equations * Radical Equations * Systems of Three Linear EquationsLesson 7Inductive and Deductive Reasoning * Logic * The Contrapositive * Converse and InverseLesson 8Statements of Similarity * Proportional Segments * Angle Bisectors and Side RatiosLesson 9Congruent Figures * Proof OutlinesLesson 10Equation of a Line * Rational Denominators * Completing the SquareLesson 11Circles * Properties of Circles * The Quadratic FormulaLesson 12Angles and Diagonals in Polygons * Proof of the Chord-Tangent TheoremLesson 13Intersecting Secants * Intersecting Secants and Tangents * Products of Chord Segments * Products of Secant and Tangent SegmentsLesson 14Sine, Cosine, and Tangent * Angles of Elevation and Depression * Rectangular and Polar Coordinates * Coordinate ConversionLesson 15Assumptions * ProofsLesson 16Complex Fractions * Abstract Equations * Division of PolynomialsLesson 17Proofs of the Pythagorean Theorem * Proofs of SimilarityLesson 18Advanced Word ProblemsLesson 19Nonlinear Systems * Factoring Exponentials * Sum and Difference of Two CubesLesson 20Two Special TrianglesLesson 21Evaluating Functions * Domain and Range * Types of Functions * Tests for Functions## Quarter 2

Lesson 22Absolute Value * Reciprocal FunctionsLesson 23The Exponential Function * Sketching ExponentialsLesson 24Sums of Trigonometric Functions * Combining FunctionsLesson 25Age Problems * Rate ProblemsLesson 26The Logarithmic Form of the Exponential * Logarithmic EquationsLesson 27Related Angles * Signs of Trigonometric FunctionsLesson 28Factorial Notation * Abstract Rate ProblemsLesson 29The Unit Circle * Very Large and Very Small Fractions * Quadrantal AnglesLesson 30Addition of Vectors * Overlapping TrianglesLesson 31Symmetry * Reflections * TranslationsLesson 32Inverse Functions * Four Quadrant Signs * Inverse Trigonometric FunctionsLesson 33Quadrilaterals * Properties of Parallelograms * Types of Parallelograms * Conditions for Parallelograms * TrapezoidsLesson 34Summation Notation * Linear Regression * Decomposing FunctionsLesson 35Change in Coordinates * The Name of a Number * The Distance FormulaLesson 36Angles Greater Than 360° * Sums of Trigonometric Functions * Boat-in-the-River ProblemsLesson 37The Line as a Locus * The Midpoint FormulaLesson 38Fundamental Counting Principle and Permutations * Designated Roots * Overall Average RateLesson 39Radian Measure of Angles * Forms of Linear EquationsLesson 40The Argument in Mathematics * The Laws of Logarithms * Properties of Inverse FunctionsLesson 41Reciprocal Trigonometric Functions * Permutation NotationLesson 42Conic Sections * Circles * Constants in Exponential FunctionsLesson 43Periodic Functions * Graphs of Sin and CosLesson 44Abstract Rate ProblemsLesson 45Conditional Permutations * Two-Variable Analysis Using a Graphing CalculatorLesson 46Complex Roots * Factoring Over the Complex NumbersLesson 47Vertical Sinusoid Translations * ArctanLesson 48Powers of Trigonometric Functions * Perpendicular BisectorsLesson 49The Logarithmic Function * Development of the Rules for LogarithmsLesson 50Trigonometric Equations## Semester 2:

Textbook: The Mooculus Textbook Written by Jim Fowler, and Bart Snapp, Professors at Ohio State UniversityTopics Covered Spring 2014:

0 - Functions

- One-to-one functions
- Inverse functions

1 - Limits- The definition of a limit
- Limit laws

2 - Infinity and Continuity- Infinite limits
- Limits at infinity
- Continuity

3 - Basics of Derivatives- Slope of a tangent line via limits
- Basic derivative rules

4 - Curve Sketching- Extrema
- The first derivative test
- Concavity and inflection points
- The second derivative test
- Sketching the plot of a function

5 - The Product Rule and Quotient Rule- The product rule
- The quotient rule

6 - The Chain Rule- The chain rule
- Implicit differentiation
- Logarithmic differentiation

8 - Applications of Differentiation