Review of Basic Algebra. Pretest. I. OPERATIONS.
The Set of Real Numbers.
Operations with Real Numbers.
Exponential Notation and Order of Operations.
II. MANIPULATIONS.
Introduction to Algebraic Expressions.
Equivalent Algebraic Expressions.
Simplifying Algebraic Expressions.
Properties of Exponents and Scientific Notation.
1. Solving Linear Equations and Inequalities. Solving Equations.
Formulas and Applications.
Applications and Problem Solving.
Sets, Interval Notation, and Inequalities.
Intersections, Unions, and Compound Inequalities.
Absolute-Value Equations and Inequalities.
2. Graphs, Functions, and Applications. Graphs of Equations.
Linear Equations: Graphs and Slope.
More on Graphing Linear Equations.
Finding Equations of Lines.
Mathematical Modeling with Linear Equations.
3. Systems of Equations. Systems of Equations in Two Variables.
Solving by Substitution or Elimination.
Solving by Applications: Systems of Two Equations.
Systems of Equations in Three Variables.
Solving Applications: Systems of Three Equations.
Systems of Linear Inequalities in Two Variables.
Business and Economic Applications.
4. Polynomials and Polynomial Function. Introduction to Polynomials and Polynomial Equations.
Multiplication of Polynomials.
Introduction to Factoring.
Factoring Trinomials ax2 + bx + c, a
OE 1.Special Factoring.Factoring: A General Strategy.Applications of Polynomial Equations.5. Rational Expressions, Equations and Functions.
Rational Expressions: Multiplying, Dividing, and Simplifying.LCMs, LCDs, Addition and Subtraction.Division of Polynomials.Complex Rational Expressions.Solving Rational Equations.Applications and Problem Solving.Formulas and Applications.Variation and Applications.6. Radical Expressions, Equations and Functions.
Radical Expressions and Equations.Rational Numbers as Exponents.Simplifying Radical Expressions.Addition, Subtraction, and More Multiplication.More on Division of Radical Expressions.Solving Radical Equations.Applications Involving Powers and Roots.The Complex Numbers.7. Quadratic Equations and Functions.
The Basics of Solving Quadratic Equations.The Quadratic Formula.Applications Involving Quadratic Equations.More on Quadratic Equations.Graphs of Quadratic Functions of the Type f(x) = a(x - h)2 + k.Graphs of Quadratic Functions of the Type f(x) = ax2 + bx + c.Mathematical Modeling with Quadratic Functions.Polynomial and Rational Inequalities.8. Exponential and Logarithmic Functions.
Exponential Functions.Inverse and Composite Functions.Logarithmic Functions.Properties of Logarithmic Functions.Natural Logarithmic Functions.Solving Exponential and Logarithmic Equations.Mathematical Modeling with Exponential and Logarithmic Functions.9. Conic Sections.
Conic Sections: Parabolas and Circles.Conic Sections: Ellipses.Conic Sections: Hyperbolas.Nonlinear Systems of Equations.APPENDIXES.
A. Handling Dimension Symbols.
B. Determinants and Cramer's Rule.
C. Elimination Using Matrices.
D. The Algebra of Functions.
