# Algebra 1

## Course Summary

Learn how to use algebra to solve everyday life problems, from calculating how much gasoline is needed for a summer road trip to graphing college tuition costs. Students gain an in-depth understanding of algebraic principles, including variables, equations, graphs, number properties, polynomials, and more. In this introductory course, acquire the problem-solving skills to apply algebra to real-life situations.

**Course Prerequisite(s):**Students should have successfully completed middle school mathematics through grade 7.

## Curriculum

This is a 2-semester course. We do not recommend taking both semesters simultaneously.

##### Unit 1: Solving Equations and Inequalities

- Properties of Real Numbers
- The Distributive Property
- Solving Multi-Step Equations Part 1
- Solving Multi-Step Equations Part 2
- Solving Equations with Variables on Both Sides
- Literal Equations and Formulas
- Ratios, Rates, and Conversions
- Solving Proportions
- Solving Multi-Step Inequalities
- Compound Inequalities
- Absolute Value Equations
- Absolute Value Inequalities

##### Unit 2: An Introduction to Functions

- Using Graphs to Relate Two Quantities
- Patterns and Linear Functions
- Patterns and Nonlinear Functions
- Graphing a Function Rule
- Writing a Function Rule
- Formalizing Relations and Functions
- Arithmetic Sequences

##### Unit 3: Linear Functions

- Rate of Change and Slope
- Slope-Intercept Form
- Point-Slope Form
- Standard Form
- Slopes of Parallel and Perpendicular Lines
- Graphing Absolute Value Functions

##### Unit 4: Systems of Equations and Inequalities

- Solving Systems by Graphing
- Solving Systems Using Substitution
- Solving Systems Using Elimination
- Applications of Linear Systems
- Linear Inequalities
- Systems of Linear Inequalities

##### Unit 5: Exponential Functions

- Zero and Negative Exponents
- Exponential Functions
- Comparing Linear and Exponential Functions
- Exponential Growth and Decay
- Solving Exponential Equations
- Geometric Sequences
- Simplifying Radicals

##### Unit 6: Properties of Exponents

- Multiplying Powers with the Same Base
- More Multiplication Properties of Exponents
- Division Properties of Exponents
- Rational Exponents and Radicals

##### Unit 7: Polynomials and Factoring

- Adding and Subtracting Polynomials
- Multiplying and Factoring
- Multiplying Binomials
- Multiplying Special Cases
- Factoring x^2+bx+c
- Factoring ax^2+bx+c
- Factoring Special Cases

##### Unit 8: Quadratic Functions and Equations

- Quadratic Graphs and their Properties
- Graphing Quadratic Functions
- Solving Quadratic Equations
- Factoring to Solve Quadratic Equations
- Completing the Square
- The Quadratic Formula and the Discriminant
- Complex Numbers
- Linear, Quadratic, and Exponential Models
- Systems of Linear and Quadratic Equations

##### Unit 9: Other Types of Functions

- Properties of Exponential Functions
- Graphing Radical Functions
- Piecewise Functions
- Step Functions
- Combining Functions
- Composition and Inverse Functions

##### Unit 10: Data Analysis

- Frequency and Histograms
- Measures of Central Tendency and Dispersion
- Box-and-Whisker Plots
- Scatter Plots and Trend Lines
- Two-Way Frequency Tables