# Algebra II

Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

## Manipulating functions

A great cook knows how to take basic ingredients and prepare a delicious meal. In this topic, you will become function-chefs! You will learn how to combine functions with arithmetic operations and how to compose functions. You will also learn how to transform functions in ways that shift, reflect, or stretch their graphs. Finally, you will learn about inverse functions and how to find them!

- Combining functions
- Composing functions
- Shifting functions
- Stretching functions
- Modeling situations by combining and composing functions
- Introduction to inverses of functions

## Introduction to complex numbers

Learn about complex numbers and how to add, subtract, and multiply them. This will come in useful when working with polynomials.

- What are the imaginary numbers?
- What are the complex numbers?
- The complex plane
- Adding and subtracting complex numbers
- Multiplying complex numbers

## Arithmetic with polynomials

Learn how to add, subtract, multiply, and even divide polynomials.

- Adding and subtracting polynomials
- Multiplying polynomials
- Long division of polynomials
- Synthetic division of polynomials
- Practice dividing polynomials with remainders
- Polynomial Remainder Theorem

## Polynomial expressions, equations, and functions

Learn how to manipulate polynomials in order to prove identities and find the zeros of those polynomials. Use this knowledge to solve polynomial equations and graph polynomial functions. Learn about symmetry of functions.

- The binomial theorem
- Understanding the binomial theorem
- Factoring polynomials - Quadratic forms
- Factoring polynomials - Special product forms
- Advanced polynomial factorization methods
- Proving polynomial identities

## Radical equations and functions

In this topic you will learn how to solve radical equations (which are equations with radical expressions in them) while avoiding extraneous solutions. You will also learn how to graph radical functions.

- Solving square-root equations
- Analyzing extraneous solutions of square-root equations
- Solving cube-root equations
- Domain of radical functions
- Graphs of radical functions

## Rational expressions, equations, and functions

Rational expressions are like fractions, but instead of integers in the numerator and the denominator, you have variable expressions! Learn how to work with such expressions. Namely, simplify, add, subtract, multiply, and divide them (much like fractions!). Then, solve some equations with rational expressions in them, and analyze the behavior of rational functions.

- Simplifying rational expressions
- Multiplying and dividing rational expressions
- Adding and subtracting rational expressions
- Nested fractions
- Solving rational equations
- Direct and inverse variation

## Exponential growth and decay

Learn how to analyze and manipulate exponential functions and expressions in order to study their rate of change.

- Equivalent forms of exponential expressions
- Solving exponential equations using properties of exponents
- Introduction to rate of exponential growth and decay
- Interpreting the rate of change of exponential models
- Constructing exponential models according to rate of change
- Advanced interpretation of exponential models

## Exponential and logarithmic functions

Learn about logarithms, which are the inverses of exponents. Use logarithms to solve various equations. Then analyze both logarithmic and exponential functions and their graphs.

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

## Trigonometric functions

Learn about the definition of the basic trigonometric functions (sin(x), cos(x), and tan(x)), and use advanced trigonometric functions for various purposes.

- Introduction to radians
- The unit circle definition of sine, cosine, and tangent
- The graphs of sine, cosine, and tangent
- Basic trigonometric identities
- Trigonometric values of special angles
- The Pythagorean identity

## Advanced equations and inequalities

Learn how to approximate the solution to any kind of equation by graphing; Learn how to solve non-linear inequalities; Learn how to solve systems with more than two equations.

- Solving equations by graphing
- Quadratic inequalities
- Rational inequalities
- Systems with three variables

## Advanced functions

Learn how to determine the domain, the range, and the graph of relatively advanced functions. Learn how to interpret advanced features of functions (like symmetry, end behavior, and periodicity) in terms of their context, and compare features of various types of functions. Learn about two-variable functions.

- Determining the domain of advanced functions
- Determining the range of a function
- Graphing nonlinear piecewise functions
- Interpreting the symmetry of algebraic models
- Interpreting the end behavior of algebraic models
- Interpreting the periodicity of algebraic models

## Sequences and series

Review sequences and then dive into arithmetic and geometric series.

- Arithmetic sequences
- Basic sigma notation
- Finite arithmetic series
- Geometric sequences
- Finite geometric series
- Finite geometric series applications

## Modeling with algebra

Practice modeling problems with a variety of function types.

## Introduction to conic sections

Learn about two basic conic sections and their equations: Circle and Parabola.

- Introduction to conic sections
- The features of a circle
- Standard equation of a circle
- Expanded equation of a circle
- Focus and directrix of a parabola

## Miscellaneous

Algebra II: Questions

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