# Algebra

## GENERAL STUDIES

### Algebra

### Course Description:

Students will explore a variety of methods to solve equations, graph functions, use mathematical symbols to represent aspects of the physical world, and learn to communicate effectively using mathematical notation. The course covers the following topics: basic operations on polynomial expressions, solutions to linear and quadratic equations, linear functions (graphing, the slope and y-intercepts of lines, writing the equations of lines), systems of linear equations and inequalities, quadratic and exponential functions (graphing and their properties), properties of exponents, properties of rational and irrational numbers, and simplification of radical expressions. 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.

### Course Objectives:

- Students will translate, evaluate and simplify expressions, order of operation; Words to symbols and graph on a coordinate plane: ordered pairs, linear equations, linear inequalities, relations and functions.
- Students will solve equations and inequalities involving angle measures.
- Students will classify numbers into their appropriate systems.
- Students will calculate the probability and odds of a simple event using the results to predict the outcome of future events, and differentiate between odds and probability of a simple event.
- Students will recognize, analyze and extend patterns and recognize and use properties of Algebra.
- Students will formulate a linear equation or inequality given a word problem and vice versa.
- Students will determine if a relation is a function and evaluate a function for a given value and will identify the domain, range, and inverse of a relation showing the relation as sets of ordered pairs, tables, mappings and graphs.
- Students will perform the four basic operations on rational numbers.
- Students will determine the slope of a line given two points, a linear equation or a graph.
- Students will compare and order real numbers including square roots.
- Students will solve and graph compound inequalities.
- Students will determine the x and y intercepts of linear graphs from their equations and will solve linear equations and inequalities and graph solutions on a number line.
- Students will classify polynomials and determine the degree for any polynomial.
- Students will solve quadratic equations by factoring.
- Students will solve rational equations and identify and solve proportions using them in applications.
- Students will simplify polynomials using appropriate exponent rules and give answers in either descending or ascending order of exponents.
- Students will multiply polynomials using FOIL on the distributing property and appropriate exponent rules and give answers in either descending or ascending order of exponents.
- Students will factor out the GCF of a polynomial and factor polynomials completely using difference of two squares, perfect square trinomials, trial and error, or regrouping.
- Students will simplify rational expressions using the four basic operations and determine the undefined values.

### Assessments:

Attendance and participation: 15%

Assignments and homework: 25%

- Nightly homework will be given as a review of what was covered in class

Tests and quizzes: 30%

- Quizzes will be given half way through each unit.
- Tests will be given at the end of each unit.

Midterm or final: 30%

### Scope and Sequence:

**Exploring Expressions, Equations, and Functions**

- Variables and Patterns
- Order of Operations
- Properties
- Identity and Equality
- Distributive
- Associative and Commutative

**Exploring Rational Numbers**

- Integers and Number Line
- Rational Numbers
- Adding/Subtracting
- Multiplying/Dividing
- Square Roots and Real Numbers

**Solving Linear Equations**

- With Addition/Subtraction
- With Multiplication/Division
- Multi-Step Equations and with Variables on Both Sides
- Formulas

**Proportional Reasoning**

- Ratios and Proportions
- Percent and Percent Change
- Probability and Odds
- Direct and Inverse Variation

**Graphing Relations and Functions**

- The Coordinate Plane
- Relations and Functions
- Graphing Linear Equations
- Writing Equations from Patterns

**Analyzing Linear Equations**

- Slope
- Writing Linear Equations
- Point Slope and Standard Form
- Slope Intercept From
- Graphing Linear Equations
- Midpoints
- Perpendicular and Parallel Lines

**Solving Linear Inequalities**

- With Addition/Subtraction
- With Multiplication/Division
- Multi-Step
- Compound Inqualities
- Absolute Value
- Graphing Inequalities with Two Variables

**Solving Systems of Linear Equations and Inequalities**

- Using Graphing
- Using Substitution
- With Elimination Using Addition/Subtraction and Multiplication
- Graphing Systems of Inequalities

**Exploring Polynomials**

- Multiplying and Dividing Monomials
- Scientific Notation
- Polynomials
- Addition/Subtraction
- Multiplying by a Monomial
- Multiplying by another Polynomial
- Special Products

**Using Factoring**

- GCF and Distributive Property
- Factoring Trinomials
- Difference of Squares and Perfect Squares
- Solving Equations by Factoring

**Exploring Quadratic and Exponential Functions**

- Graphing Quadratic Functions
- Solving Quadratics by Graphing
- The Quadratic Formula
- Exponential Functions and Growth and Decay

**Exploring Rational Expressions and Equations**

- Simplifying
- Multiplying/Dividing
- Dividing Polynomials
- Rational Expressions with Like and Unlike Denominators
- Mixed Expressions and Complex Fractions
- Solving Rational Equations

**Exploring Radical Expressions and Equations**

- Simplifying
- Operations with Radical Expressions
- Radical Equations
- Completing the Square