Discovering Advanced Algebra: An Investigative Approach

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1: Patterns and Recursion

1.1: Recursively Defined Sequences

 Arithmetic Sequences
 Geometric Sequences

1.2: Modeling Growth and Decay

 Disease Spread
 Drug Dosage
 Dye Elimination
 Exponential Growth and Decay - Activity A
 Virus Life Cycle (Lytic)

1.5: Loans and Investments

 Half-life
 Simple and Compound Interest

2: Describing Data

2.1: Measures of Central Tendency and Box Plots

 Constructing Box-and-Whisker Plots
 Mean, Median and Mode

2.3: Histograms and Percentile Ranks

 Histograms

3: Linear Models and Systems

3.1: Linear Equations and Arithmetic sequences

 Arithmetic Sequences

3.3: Fitting a Line to Data

 Lines of Best Fit Using Least Squares - Activity A
 Solving Using Trend Lines

3.6: Linear Systems

 Modeling Linear Systems - Activity A
 Solving Linear Systems by Graphing

3.7: Substitution and Elimination

 Systems of Linear Equations - Activity A

4: Functions, Relations, and Transformations

4.2: Function Notation

 Introduction to Functions

4.3: Lines in Motion

 Slope-Intercept Form of a Line - Activity A
 Slope-Intercept Form of a Line - Activity B
 Translating and Scaling Functions

4.4: Translations and the Quadratic Family

 Quadratics in Vertex Form - Activity A
 Translating and Scaling Functions

4.5: Reflections and the Square Root Family

 Functions Involving Square Roots
 Reflections of a Linear Function
 Translating and Scaling Functions

4.6: Stretches and Shrinks and the Absolute-Value Family

 Absolute Value with Linear Functions - Activity B
 Quadratic and Absolute Value Functions

4.7: Transformations and the Circle Family

 Circles
 Ellipse - Activity A

5: Exponential, Power, and Logarithmic Functions

5.1: Exponential Functions

 Exponential Functions - Activity B

5.2: Properties of Exponents and Power Functions

 Exponents and Power Rules

5.4: Applications of Exponential and Power Equations

 Dye Elimination
 Half-life
 Simple and Compound Interest

5.6: Logarithmic Functions

 Logarithmic Functions - Activity A

5.7: Properties of Logarithms

 Logarithmic Functions: Translating and Scaling

6: Matrices and Linear Systems

6.5: Systems of Linear Inequalities

 Systems of Linear Inequalities (Slope-intercept form) - Activity A

6.6: Linear Programming

 Linear Programming - Activity A

7: Quadratic and Other Polynomial Functions

7.2: Equivalent Quadratic Forms

 Polynomials and Linear Factors
 Quadratics in Factored Form

7.3: Completing the Square

 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c

7.4: The Quadratic Formula

 Roots of a Quadratic

7.5: Complex Numbers

 Points in the Complex Plane - Activity A

7.7: Higher-Degree Polynomials

 Fourth-Degree Polynomials - Activity A

7.8: More About Finding Solutions

 Dividing Polynomials Using Synthetic Division

8: Parametric Equations and Trigonometry

8.3: Right Triangle Trigonometry

 Sine and Cosine Ratios - Activity B
 Sine, Cosine and Tangent
 Tangent Ratio

8.5: Projectile Motion

 Golf Range!
 Shoot the Monkey!

9: Conic Sections and Rational Functions

9.2: Circles and Ellipses

 Circles
 Ellipse - Activity A

9.3: Parabolas

 Parabolas - Activity B

9.4: Hyperbolas

 Hyperbola - Activity A

9.7: Graphs of Rational Functions

 General Form of a Rational Function
 Rational Functions

10: Trigonometric Functions

10.1: Defining the Circular Functions

 Unit Circle

10.3: Graphing Trigonometric Functions

 Cosine Function
 Sine Function
 Tangent Function

10.6: Fundamental Trigonometric Identities

 Simplifying Trigonometric Expressions
 Sum and Difference Identities for Sine and Cosine

12: Probability

12.1: Randomness and Probability

 Probability Simulations
 Theoretical and Experimental Probability

12.2: Counting Outcomes and Tree Diagrams

 Compound Independent Events
 Compound Independent and Dependent Events

12.5: Permutations and Probability

 Permutations

12.6: Combinations and Probability

 Binomial Probabilities
 Permutations and Combinations

13: Applications of Statistics

13.1: Probability Distributions

 Populations and Samples

13.5: Bivariate Data and Correlation

 Correlation
 Lines of Best Fit Using Least Squares - Activity A

Content correlation last revised: 3/30/2009