Algebra II

Polynomial Arithmetic 

• Introduction to polynomials. Average rate of change of polynomials. Adding and subtracting of polynomials. Multiplying monomials by polynomials. Multiplying binomials by polynomials. Special products of polynomials.

Complex Numbers

• The imagery unit i. Complex numbers introduction. The complex plane. Adding and subtracting complex numbers. Multiplying complex numbers. Quadratic equations with complex solutions. 

Polynomial Factorization

• Factoring monomials. Greatest common factor. Taking common factors. Factoring higher degree polynomials. Factoring using structure. Polynomial identities. Polynomial identities. Geometric series. 

Polynomial Division

• Dividing polynomials by x. Dividing quadratics by linear factors. Dividing polynomials by linear factors. Polynomial Remainder Theorem. 

Polynomial Graphs

• Zeros of polynomials. Positive and negative intervals of polynomials. End behavior of polynomials. Putting it all together.

Rational Exponents & Radicals

• Rational exponents. Properties of exponents. Evaluating exponents and radicals. Equivalent forms of exponential expressions. Solving exponential equations using properties of exponents.

Exponential Models

• Interpret sting the rate of changed exponential models. Constructing exponential models according to rate of change. Advanced interpretation of exponential models.

Logarithms 

• Introduction to logarithms. The constant e and the natural logarithm. Properties of logarithms. The change of base formula for logarithms. Solving exponential equations with logarithms. Solving exponential models.

Transformations of Functions

• Shifting functions. Square-root equations. Extraneous solutions. Cube-root equations. Quadratic systems. Solving equations by graphing.

Equations

• Rational equations. Square-root equations. Extraneous equations. Cube-root equations. Quadratic systems. Solving equations by graphing.
  

Trigonometry

• Unit circle introduction. Radians. The Pythagorean identity. Trigonometric values of special angles. Graphs os sin(x), cos(x), and tan(x). Amplitude, midline and period. Transforming sinusoidal graphs. Graphing sinusoidal functions. Sinusoidal models.

Modeling

• Modeling with function combination. Interpreting features of functions. Manipulating formulas. Modeling with equations and inequalities. 

Rational Functions

• Cancelling common factors. End behavior of rational functions. Discontinuities of rational functions. Graphs of rational functions. Modeling with rational functions. Multiplying and dividing rational expressions. Adding and subtracting rational expressions introduction. Adding and subtracting rational expressions (factored and not factored).