Intermediate Algebra

1. Basics of Algebra and Graphing.


Some Basics of Algebra.



Operations with Real Numbers.



Equivalent Algebraic Expressions.



Exponential and Scientific Notation.



Graphs.



Mathematical Models and Problem Solving.



2. Functions, Linear Equations, and Models.


Functions.



Solving Linear Equations.



Applications and Formulas.



Linear Functions: Slope, Graphs, and Models.



Another Look at Linear Graphs.



Introduction to Curve Fitting: Point-Slope Form.



Domains and the Algebra of Functions.



3. Systems of Linear Equations and Problem Solving.


Systems of Equations in Two Variables.



Solving by Substitution or Elimination.



Solving Applications: Systems of Two Equations.



Systems of Equations in Three Variables.



Solving Applications: Systems of Three Equations.



Elimination Using Matrices.



Business and Economics Applications.



4. Inequalities and Problem Solving.


Inequalities and Applications.



Intersections, Unions, and Compound Inequalities.



Absolute-Value Equations and Inequalities.



Inequalities in Two Variables.



5. Polynomials and Polynomial Functions.


Introduction to Polynomials and Polynomial Functions.



Multiplication of Polynomials.



Polynomial Equations and Factoring.



Equations Containing Trinomials of the Type x² + bx + c.



Equations Containing Trinomials of the Type ax² + bx + c, a 1.



Equations Containing Perfect-Square Trinomials and Differences of Squares.



Equations Containing Sums or Differences of Cubes.



Applications of Polynomial Equations.



6. Rational Expressions, Equations, and Functions.


Rational Expressions and Functions: Multiplying and Dividing.



Rational Expressions and Functions: Adding and Subtracting.



Complex Rational Expressions.



Rational Equations.



Solving Applications Using Rational Equations.



Division of Polynomials.



Synthetic Division.



Formulas, Applications, and Variation.



7. Exponents and Radical Functions.


Radical Expressions, Functions, and Models.



Rational Numbers as Exponents.



Multiplying Radical Expressions.



Dividing Radical Expressions.



Expressions Containing Several Radical Terms.



Solving Radical Equations.



Geometric Applications.



The Complex Numbers.



8. Quadratic Functions and Equations.


Quadratic Equations.



The Quadratic Formula.



Applications Involving Quadratic Equations.



Studying Solutions of Quadratic Equations.



Equations Reducible to Quadratic.



Quadratic Functions and Their Graphs.



More About Graphing Quadratic Functions.



Problem Solving and Quadratic Functions.



Polynomial and Rational Inequalities.



9. Exponential and Logarithmic Functions.


Composite and Inverse Functions.



Exponential Functions.



Logarithmic Functions.



Properties of Logarithmic Functions.



Natural Logarithms and Changing Bases.



Solving Exponential and Logarithmic Equations.



Applications of Exponential and Logarithmic Functions.



10. Sequences, Series, and the Binomial Theorem.


Sequences and Series.



Arithmetic Sequences and Series.



Geometric Sequences and Series.



The Binomial Theorem.



Appendix A: Conic Sections: Parabolas and Circles.


Appendix B: Conic Sections: Ellipses and Hyperbolas.


Appendix C: Nonlinear Systems of Equations.