Geometry+Trig+(Adv)

**//Grading and Assessment//**
Each Quarter 40% Final 20%

**//Quarter Grades://**
Tests 75% Homework 25%

Students have 90 to 100 problems per week. Students usually have 15 to 20 minutes per day to work on homework in class and to ask the teacher or other students for help on specific problems. Each student has access to a solution book as well to check their answers and methods of working the problems. Students are constantly encouraged to stay a lesson ahead of the class. Students have a three week assignment sheet detailing when lessons will be covered, when they are due and when tests will be given.
 * Homework** graded weekly by other students. (double off if problems are skipped or no work is shown)
 * Open book pop quizzes** with problems counting as test questions on the next test. (with time to study on their own and then seek help from other students before the quiz)
 * Weekly tests** given with extra credit or penalty (see next ) on the long period day of the week.
 * Average sheet** is kept by each student and signed weekly by parents. If the student brings the Avg sheet back signed the first day of the week, he gets 5 bonus points on the next test, with a penalty of a point per day. If the sheet is turned in without parent signature the student loses three points on the next test, If the sheet is not turned in at all 5 points are deducted from the test score.
 * Test Corrections** are required of any student making below an 80 on a test. A form is given for self assessment as to carelessness or lack of understanding. This is enforced by an additional 5 points deducted from the test score until the test corrections are turned in.


 * Text: //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

Quarter 3
Lesson 46 Complex Roots * Factoring Over the Complex Numbers
 * Lesson 44** Abstract Rate Problems
 * Lesson 45** Conditional Permutations * Two-Variable Analysis Using a Graphing Calculator
 * 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
 * Lesson 51** Common Logarithms and Natural Logarithms **Lesson 52** The Inviolable Argument * Arguments in Trigonometric Equations
 * Lesson 53** Review of Unit Multipliers * Angular Velocity
 * Lesson 54** Parabolas
 * Lesson 55** Circular Permutations * Distinguishable Permutations
 * Lesson 56** Triangular Areas * Areas of Segments * Systems of Inequalities
 * Lesson 57** Phase Shifts in Sinusoids * Period of a Sinusoid
 * Lesson 58** Distance from a Point to a Line * "Narrow" and "Wide" Parabolas
 * Lesson 59** Advanced Logarithm Problems * The Color of the White House
 * Lesson 60** Factorable Trigonometric Equations * Loss of Solutions Caused by Division
 * Lesson 61** Single-Variable Analysis * The Normal Distribution * Box-and-Whisker Plots
 * Lesson 62** Abstract Coefficients * Linear Variation
 * Lesson 63** Circles and Completing the Square
 * Lesson 64** The Complex Plane * Polar Form of a Complex Number * Sums and Products of Complex Numbers
 * Lesson 65** Radicals in Trigonometric Equations * Graphs of Logarithmic Functions

Quarter 4

 * Lesson 66** Formulas for Systems of Equations * Phase Shifts and Period Changes
 * Lesson 67** Antilogarithms
 * Lesson 68** Locus Definition of a Parabola * Translated Parabolas * Applications * Derivation
 * Lesson 69** Matrices * Determinants
 * Lesson 70** Percentiles and z Scores
 * Lesson 71** The Ellipse (1)
 * Lesson 72** One Side Plus Two Other Parts * Law of Sines
 * Lesson 73** Regular Polygons
 * Lesson 74** Cramer's Rule
 * Lesson 75** Combinations
 * Lesson 76** Functions of (-x) * Functions of the Other Angle * Trigonometric Identities (1) * Rules of the Game
 * Lesson 77** Binomial Expansions (1)
 * Lesson 78** The Hyperbola
 * Lesson 79** De Moivre's Theorem * Roots of Complex Numbers
 * Lesson 80** Trigonometric Identities (2)
 * Lesson 81** Law of Cosines
 * Lesson 82** Taking the Logarithm of * Exponential Equations
 * Lesson 83** Simple Probability * Independent Events * Replacement
 * Lesson 84** Factorable Expressions * Sketching Sinusoids
 * Lesson 85** Advanced Trigonometric Equations * Clock Problems
 * Lesson 86** Arithmetic Progressions and Arithmetic Means
 * Lesson 87** Sum and Difference Identities * Tangent Identities
 * Lesson 88** Exponential Functions (Growth and Decay)
 * Lesson 89** The Ellipse (2)
 * Lesson 90** Double-Angle Identities * Half-Angle Identities
 * Lesson 91** Geometric Progressions
 * Lesson 92** Probability of Either * Notations for Permutations and Combinations
 * Lesson 93** Advanced Trigonometric Identities * Triangle Inequalities (2)
 * Lesson 94** Graphs of Secant and Cosecant * Graphs of Tangent and Cotangent
 * Lesson 95** Advanced Complex Roots
 * Lesson 96** More Double-Angle Identities * Triangle Area Formula * Proof of the Law of Sines * Equal Angles Imply Proportional Sides
 * Lesson 97** The Ambiguous Case
 * Lesson 98** Change of Base * Contrived Logarithm Problems
 * Lesson 99** Sequence Notations * Advanced Sequence Problems * The Arithmetic and Geometric Means
 * Lesson 100** Product Identities * More Sum and Difference Identities
 * Lesson 101** Zero Determinants * 3 x 3 Determinants * Determinant Solutions of 3 x 3 Systems * Independent Equations
 * Lesson 102** Binomial Expansions (2)
 * Lesson 103** Calculations with Logarithms * Power of the Hydrogen
 * Lesson 104** Arithmetic Series * Geometric Series
 * Lesson 105** Cofactors * Expansion by Cofactors

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