Algebra II and Trigonometry

Castle Learning Online's Algebra II and Trigonometry, targeted towards upper level high school students, is the third in a sequence that includes Integrated Algebra and Geometry.

The algebra portion of the course includes working with exponents, radicals and logarithms; solving exponential, radical and logarithmic equations; complex fractions; absolute value and summation notation; operations with complex numbers; and inverse variation. Also included are solving quadratic equations by factoring, completing the square, using the quadratic formula, and u-substitution. Data analysis topics include scatter plots, correlation coefficients and various types of regressions; working with the Bell curve and normal distributions; and measures of central tendency and the dispersion of data. Other topics include 2-outcome probability models and an introduction to functions and notation.

The trigonometry portion of the course starts with a review of right triangle trigonometry and its extension to the four quadrants; radian measure; the unit circle and reference angles; solving trigonometric equations; trigonometric identities; and graphing techniques. Applications of trigonometry include the Law of Sines and Cosines; ambiguous triangles; forces and resultants; and general area problems.

Units: (click to view Sections)

1. Exponents
   
   Sections:
   

   1. Laws of Exponents
   2. Expressions with Negative and Fractional Exponents
   3. Exponential Equations
   4. Exponential Functions
   5. Exponential Word Problems
2. Logarithms
   
   Sections:
   

   1. ELogarithmic Form of an Equation
   2. Logarithmic Rules
   3. Exponential Equations with Logarithmic Solutions
   4. Logarithmic Equations
   5. Logarithmic Functions
   6. Logarithmic Word Problems
3. Sequences, Series, and Summation Notation
   
   Sections:
   

   1. Sequences
   2. Arithmetic Sequences
   3. Geometric Sequences
   4. Recursive Rules for Sequences
   5. Arithmetic Series
   6. Geometric Series
   7. Summation (Sigma) Notation
4. Absolute Value
   
   Sections:
   

   1. Equations and Inequalities
5. Complex Numbers
   
   Sections:
   

   1. Simplifying and Operations of Imaginary Numbers
   2. Powers of i
   3. Addition and Subtraction of Complex Numbers
   4. Multiplication of Complex Numbers
   5. Multiplicative Inverses and Division of Complex Numbers
   6. Complex Roots of an Equation
6. Regressions
   
   Sections:
   

   1. Regressions
   2. Correlation Coefficient
7. Statistics
   
   Sections:
   

   1. Normal Distribution - Bell Curve
   2. Measures of Dispersion for Samples and Populations and Central Tendency
8. Probability
   
   Sections:
   

   1. Exactly, at Least, at Most
   2. Binomial Expansion and the nth Term
9. Radicals
   
   Sections:
   

   1. Operations with Radicals
   2. Radical Equations
   3. Rationalizing the Denominator
10. Functions
    
    Sections:
    

    1. Identify Relations and Functions
    2. Find Domain and Range
    3. Function Notation
    4. Compositions
    5. Inverses and One-to-One
11. Rational Expressions
    
    Sections:
    

    1. Reducing Rational Expressions
    2. Multiplying and Dividing Rational Expressions
    3. Adding and Subtracting Rational Expressions
    4. Simplifying Complex Rational Expressions and Fractions
    5. Solving Fractional Equations & Inequalities
12. Inverse Variation
    
    Sections:
    

    1. Solve for Unknown Values
    2. Graphs of Inverse Variation
13. Quadratics
    
    Sections:
    

    1. Discriminant - Nature of Roots
    2. Quadratic Inequalities
    3. Factoring
    4. Sum and Product of the Roots
    5. Completing the Square
    6. Quadratic Formula
    7. Quadratic Functions (Turning Point, AOS, Max, Min, TOV)
    8. Word Problems
    9. U-substitution
14. Introduction to Trigonometry
    
    Sections:
    

    1. Trigonometry of Right Triangles
    2. Terminating Quadrant
    3. Arcsin, Arccos, Arctan
    4. Radian Measure
    5. Exact Values for Special Angles
    6. Unit Circle
15. Trigonometric Equations and Expressions
    
    Sections:
    

    1. First Degree Trig Equations
    2. Second Degree Trig Equations
    3. Undefined Trig Fractions
16. Applications of Trigonometry
    
    Sections:
    

    1. Flaw of Sines and Cosines
    2. Ambiguous Case
    3. Forces
    4. Area of a Triangle and Parallelogram
    5. Arc, Radius, Central Angle
17. Trigonometry Identities
    
    Sections:
    

    1. Identities - Sum and Difference
    2. Identities - Double and Half Angles
    3. Pythagorean and Quotient Identities
18. Trigonometry Curves
    
    Sections:
    

    1. Graphs of sine and cosine
    2. Amplitude, Frequency, Phase shift and Period
    3. Graphs of secant, cosecant, tangent and cotangent
    4. Graphs of inverse trig functions
    5. Find the equation give the graphs of sine and cosine curves

Themes:

1. Number Systems
2. Number Theory
3. Operations
4. Variables and Expressions
5. Equations and Inequalities
6. Patterns, Relations, and Functions
7. Trigonometry
8. Coordinate Geometry
9. Organization and Display of Data
10. Analysis of Data
11. Predictions from Data
12. Probability

Attributes:

1. Diagram
2. Table
3. Graph
4. Word Problem
5. Short Answer Fill-in