Algebra 1
For Educators
Teachers can use the complete Plus course curriculum for flexible instruction.
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.
Curriculum
This is a two-semester course. Each semester requires a commitment of approximately 70 or more hours of coursework. While students may enroll in both semesters within the same term, UC Scout does not recommend this due to the intensive workload, especially during shorter terms like summer.
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