**College Prep Algebra 1**

*Topics*

*All topics listed below are presented to the students in a way that is consistent with the vision of*

the NCTM (National Council of Teachers of Mathematics)the NCTM (National Council of Teachers of Mathematics)

**1. Introduction to Algebra**

**Variables, Grouping Symbols, and Equations.****Applications and Problem Solving****Translating words into symbols,****Translating sentences into equations,****Numbers on a Line****Number lines, and Absolute Value**

**2. Working with Real Numbers**

**Operations with Real Numbers,****Properties of Real Numbers**

**3. Solving Equations and Problems**

**Solving First Degree Equations,****Using equations to solve Cost-Income, and Value Problems.**

**4. Polynomials**

**Exponents,****Adding, Subtracting, Multiplying, and Dividing Polynomials****Transforming Formulas****Rate-Time-Distance,****Area Problems.**

**5. Factoring Polynomials**

**Multiplying Polynomials****Special Products**__Factoring Techniques__**G.C.F.****Foil****Reverse of Foil****Difference of two squares****Perfect square trinomials****Factoring by Grouping****Solving Equations by Factoring,****Using Factoring to Solve Problems.**

**6. Fractions**

**Simplifying, Multiplying, Dividing , and Adding Fractions****Mixed Expressions,****Polynomial Long Division.****Synthetic Division**

**7. Applying Fractions**

**Ratios, and Proportions,****Equations with Fractional Coefficients,****Fractional Equations,****Percent, and Percent Problems,****Mixture Problems,****Work Problems,****Negative Exponents, and Scientific Notation.**

**8. Introduction to Functions**

**Equations in Two Variables,****Points, Lines, and their Graphs,****Slope of a Line,****the Slope-Intercept Form,****Finding the Equation of a Line,****Different Forms of a Function,****Linear, and Quadratic Functions.****Direct, and Inverse Variation**

**9. Systems of Linear Equations.**

**Graphing, Substitution, and Elimination Methods****Solving Problems Involving Two Variables**

*10. Inequalities***Order of Real Numbers,****Solving Inequalities,****Solving Problems Involving Inequalities,****Solving Combined Inequalities,****Absolute Value in Open Sentence**

*11. Rational, and Irrational Numbers***Properties of Rational Numbers****Decimal Forms****Rational and Irrational Square Roots****Square Roots of Variable Expressions****The Pythagorean Theorem****Multiplying, Dividing, and Simplifying Radicals****Adding and Subtracting Radicals****Multiplying Binomials Containing Radicals****Solving Radical Equations.**

*12. Quadratic Functions***Quadratic Equations with Perfect Squares****Completing the Square Method****The Quadratic Formula****Graphs of Quadratic Equations:**

**a. Finding all key points algebraically and graphically**

**b. finding the Discriminant to predict type and number of solutions.**

**Word Problems/Applications**

**a. Types of Variation**

**Direct and Inverse Variation Involving Squares****Joint and Combined Variations.**

**b. Distance-Rate-Time Problems including current and wind**

**c. Work Problems**

**d. Coin Problems**

**etc.**

**Complex Numbers**

**The i-Form****Graphing complex numbers on the complex plane.****Adding, Subtracting, Multiplying, and Dividing**

**13. Probability and Data Analysis**

**Counting Principle****Permutations and Combinations****Dependent and Independent Events****Probability**