Semester 1:

Text: Saxon Advanced Mathematics, Second Edition

Quarter 1

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

Topics 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
  • L'Hôpital's Rule
  • The derivative as a rate
  • Rated rates problems