# Algebra 2

## GENERAL STUDIES

### Algebra 2

### Course Description:

This course extends the skills and concepts introduced in Algebra 1 and covers the

following topics: absolute value inequalities; linear, quadratic and absolute value

functions (their graphs and defining features); properties of exponents including

negative, zero and fractional values; systems of linear and quadratic equations and

inequalities; quadratics equations with complex number solutions; exponential and

logarithmic functions (properties, graphs, solving equations and applications);

polynomial functions (graphing, finding zeros and important theorems); square root and

cube root functions; rational functions (graphing, finding zeros, and asymptotes); and

conic sections. Also, since problem solving is an integral part of this course, students

spend a considerable amount of time translating problems presented in written form to

equivalent statements in mathematics. Then, the students find solutions to the

problems and express the results in written form. Algebra 2 is a prerequisite for all

advanced math courses.

### Course Objectives:

- Students will be able to analyze and evaluate the characteristics of step, piece-wise,

exponential, and quadratic functions, as well as inverses of functions - Students will interpret and apply the characteristics of functions with regard to a given

context and analyze and evaluate rates of change, both constant and variable, within

the basic function families. - Students will be able to analyze and evaluate geometric and arithmetic sequences as

functions. - Students will analyze and solve quadratic equations using a variety of techniques and

represent, simplify, and operate with complex numbers. - Students will be able to analyze and solve problems involving probabilities,

permutations, and combinations, as well as analyze and evaluate sample data,

making inferences about population means and standard deviations and using these

inferences to compare data sets. - Students will understand and apply algebraic models to quantify the association

between two quantitative variables.

### Scope and Sequence:

**Analyzing Equations and Inequalities**

- Expressions, formulas, and properties of real numbers
- Graphs and measures of central tendency
- Solving equations and solving absolute value equations
- Solving inequalities and solving absolute value inequalities

**Graphing Linear Relations and Functions**

- Relations and functions
- Linear equations
- Slope
- Writing linear equations
- Scatter plots
- Special functions
- Linear inequalities

**Solving Systems of Linear Equations and Inequalities**

- Graphing systems and solving systems algebraically
- Cramer’s Rule
- Graphings systems of inequalities
- Linear programming and applications
- Systems in three variables

**Matrices**

- Adding, subtracting, and multiplying matrices
- Determinants
- Identity and inverse
- Using matrices to solve systems of equations
- Using augmented matrices
- Box and whisker plots

**Exploring Polynomials and Radical Expressions**

- Monomials and polynomials
- Dividing polynomials and factoring
- Roots of real numbers and radical expressions
- Rational exponents
- Solving radical equations and inqualities
- Complex numbers and simplifying expressions with complex numbers

**Exploring Quadratic Functions and Inequalities**

- Solving by graphing, factoring, and completing the square
- Quadratic formula and discriminant
- Sum and product of roots
- Analyzing graphs of quadratic functions
- Graphing and solving quadratic inequalities
- Standard deviation and the normal distribution

**Analyzing Conic Sections**

- Parabolas, circles, ellipses, hyperbolas, conic sections
- Solving quadratic systems

**Exploring Polynomial Functions**

- Graphing and approximating zeros
- Roots and zeros
- Using quadratic techniques to solve
- Composition of functions
- Inverse functions and relations

**Exploring Rational Expressions**

- Graphing Rational Functions
- Direct, inverse, and joint variation
- Multiplying, dividing, adding, and subtracting rational expressions
- Solving rational equations and inequalities

**Exploring Exponential and Logarithmic Functions**

- Real exponents and exponential functions
- Logarithms and logarithmic functions
- Properties of logarithms, common logarithms, natural logarithms
- Solving exponential equations
- Growth and decay

**Investigating Sequences and Series**

- Arithmetic sequences and series
- Geometric sequences and series
- Infinite geometric series
- Recursion and special sequences
- Fractals and the binomial theorem

**Investigating Discrete Mathematics and Probability**

- The counting principle
- Permutations and combinations
- Probability
- Multiplying probabilities and adding probabilities