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ADVANCED ALGEBRA (Math III-Elective)
S.Y. 2004-2005

FIRST QUARTER

I. Relation and Function (pages 12-29, 186-191 and 351-355)

  1. Definition
  2. Domain and Range
  3. Function Notations
  4. Graphs of Functions
  5. Absolute-Value Function
  6. Step Function

II. Quadratic Functions (pages 357-407)

  1. The Graph-Translation Theorem
  2. Graphing y = ax2 + bx + c
  3. Completing the Square
  4. Fitting a Quadratic Model to Data
  5. The Quadratic Formula
  6. Imaginary Numbers
  7. Complex Numbers
  8. Analyzing Solutions to Quadratic Equations

 

SECOND QUARTER

III. Quadratic Relations (pages 748-758 and 771-798)

  1. Parabolas
  2. Circles
  3. Relationships Between Ellipses and Circles
  4. Equations for Some Hyperbolas
  5. Equations for More Hyperbolas
  6. Quadratic-Linear Systems
  7. Quadratic-Quadratic Systems

 

THIRD QUARTER

IV. Inverses and Radicals (pages 478-521)

  1. Composition of Functions
  2. Inverses of Relations
  3. Properties of Inverse Functions
  4. Radical Notation for nth Roots
  5. Products with Radicals
  6. Quotients with Radicals
  7. Powers and Roots of Negative Numbers
  8. Solving Equations with Radicals

V. Series and Combinations (pages 810-874)

  1. Arithmetic Series
  2. Geometric Series
  3. The S and ! Symbols
  4. Descriptive Statistics
  5. Pascals Triangle
  6. The Binomial Theorem
  7. Subsets and Combinations
  8. Probabilities and Combinations
  9. Lotteries
  10. Binomial and Normal Distributions
  11. Polls and Sampling

 

FOURTH QUARTER

VI. Exponential and Logarithmic Functions (pages 532-592)

  1. Exponential Growth
  2. Exponential Decay
  3. Continuous Growth or Decay
  4. Fitting Exponential Models to Data
  5. Common Logarithms
  6. Logarithmic Scales
  7. Logarithms to Bases Other Than 10
  8. Properties of Logarithms
  9. Natural Logarithms
  10. Using Logarithms to Solve Exponential Equations

 

VII. Trigonometry (pages 604-663)

  1. Three Trigonometric Functions
  2. More Right-Triangle Trigonometry
  3. Properties of Trigonometric Ratios
  4. Trigonometry and the Unit Circle
  5. Cosines and Sines in Quadrants II-IV
  6. The Law of Cosines
  7. The Law of Sines
  8. The Cosine and Sine Functions
  9. Solving sin q = k
  10. Radian Measure

 

Reference:
The University of Chicago School Mathematics Project ADVANCED ALGEBRA Integrated Mathematics

Authors :
Senk, Ahbel, Jaskowiak, Thompson, Levin, Flanders, Viktoria, Weinhold, Jakucyn, Usiskin, Rubenstein, and Pillsbury

TRIGONOMETRY (Pre-Calculus Approach) - Math IV
S.Y. 2004-2005

I. Circular Functions (pages 232-271)

  1. Measures of Angles and Rotations
  2. Lengths of Arcs and Areas of Sectors
  3. Sines, Cosines, and Tangents
  4. Basic Identities Involving Sines, Cosines, and Tangents
  5. Exact Values of Sines, Cosines, and Tangents
  6. The Sine, Cosine, and Tangent Functions

 

II. Trigonometric Functions (pages 310-320, 327-333, & 346-352)

  1. Trigonometric Ratios in Right Triangles
  2. The Law of Cosines
  3. The Law of Sines
  4. General Solutions to Trigonometric Equations

 

III. Further Work With Trigonometry (pages 806-819)

  1. The Secant, Cosecant, and Cotangent Functions
  2. Proving Trigonometric Identities
  3. Restrictions on Identities

 

IV. Matrices & Trigonometry (pages 721-730)

  1. Formulas for cos(a +b ) and sin(a +b )
  2. Formulas for cos2q and sin2q

 

V. Polynomial Functions (pages 556-611)

  1. Polynomial Models
  2. Graphs of Polynomial Functions
  3. Finding Polynomial Models
  4. Division and the Remainder Theorem
  5. The Factor Theorem
  6. Complex Numbers
  7. The Fundamental Theorem of Algebra
  8. Factoring Sums and Differences of Powers
  9. Advanced Factoring Techniques

 

VI. Functions and Models (pages 105-118)

  1. Exponential Functions
  2. Exponential Models

 

VII. Root, Power, and Logarithm Functions (pages 383-408)

  1. Logarithm Functions
  2. e and Natural Logarithms
  3. Properties of Logarithms
  4. Solving Exponential Equations

 

VIII. Topics in Calculus (Functions, Limits, and Continuity)

  1. Operation on Functions and Types of Functions
  2. Graphical Introduction to Limits of a Function
  3. Definition of the Limit of a Function and Limits Theorems
  4. One-Sided Limits
  5. Infinite Limits
  6. Continuity of a Function at a Number

 

IX. The Derivatives and Differentiation (For Honors Class)

  1. The Tangent Line and the Derivatives
  2. Differentiability and Continuity
  3. The Numerical Derivative
  4. Theorem on Differentiation of Algebraic Functions and Higher Order Derivatives

 

 

References:

  1. The University of Chicago School Mathematics Project FUNCTIONS STATISTICS, AND TRIGONOMETRY Integrated Mathematics

2.) The Calculus With Analytical Geometry Sixth Edition


Authors :

1.) Senk, Ahbel, Jaskowiak, Thompson, Levin, Flanders, Viktoria, Weinhold, Jakucyn, Usiskin, Rubenstein, and Pillsbury

2.) Louis Leithold