Curriculum

1. Foundations of Algebra

• Review of Arithmetic and Pre-Algebra: Basic operations, fractions, decimals, integers, and order of operations.

• Properties of Real Numbers: Identity, inverse, commutative, associative, and distributive properties.

2. Solving Equations and Inequalities

• Linear Equations: Solving one-variable linear equations, including word problems.

• Equations with Variables on Both Sides: Techniques for solving and applications.

• Systems of Linear Equations: Solving by graphing, substitution, and elimination methods; applications in word problems.

• Linear Inequalities: Solving and graphing one-variable inequalities; compound inequalities.

• Systems of Linear Inequalities: Graphing and interpreting solutions.

3. Functions

• Understanding Functions: Definitions, domain and range, evaluating functions.

• Linear Functions: Graphing linear functions, slope-intercept and point-slope forms, modeling with linear functions.

• Function Notation and Operations: Using function notation, adding, subtracting, and composing functions.

• Inverse Functions: Understanding and finding inverse functions.

4. Linear Equations and Their Graphs

• Slope and Rate of Change: Understanding and calculating slope, interpreting slope in real-world contexts.

• Forms of Linear Equations: Standard form, converting between forms, graphing linear equations in different forms.

• Graphing and Writing Linear Equations: Using intercepts, slope, and applications to write and graph equations.

5. Polynomials and Factoring

• Polynomial Operations: Adding, subtracting, multiplying, and dividing polynomials (excluding division by a polynomial).

• Special Products: Square of a binomial, difference of squares, sum and difference of cubes.

• Factoring: Factoring by grouping, factoring trinomials, and special factoring techniques.

• Solving Quadratic Equations by Factoring

6. Rational Expressions and Equations

• Simplifying Rational Expressions: Finding excluded values, simplifying complex fractions.

• Operations with Rational Expressions: Addition, subtraction, multiplication, and division.

• Solving Rational Equations: Techniques and applications in word problems.

7. Radicals and Connections to Geometry

• Simplifying Radical Expressions: Basic operations with square roots and higher-order roots.

• Pythagorean Theorem and Distance Formula: Applications in solving problems involving right triangles and distance between two points in a coordinate plane.

• Solving Quadratic Equations: Using square roots, completing the square, and the quadratic formula.

8. Quadratic Functions and Equations

• Graphing Quadratic Functions: Understanding parabolas, vertex form, and transformations.

• Solving Quadratic Equations by Completing the Square

• The Quadratic Formula: Derivation and applications.

• Applications of Quadratic Functions: Projectile motion and other real-world problems.

9. Data Analysis and Probability

• Descriptive Statistics: Mean, median, mode, range, and standard deviation.

• Interpreting Graphs and Tables: Reading and analyzing data from various sources.

• Simple Probability: Basic probability concepts and counting principles.