STANDARD COMPETENCIES:

 

 1.   Demonstrate an understanding of set notations, subsets of the real numbers and properties of real numbers.

 2.   Perform algebraic manipulations including working with exponents, radicals, polynomial operations, factoring and algebraic fractions.

 3.   Solve the following types of equations: linear, quadratic, rational, exponential, logarithmic equations involving radicals, equations in quadratic form and equations involving absolute value.

 4.   Demonstrate an understanding of formulas including formula evaluation and solving a formula for any of the variables.

 5.   Read and analyze problems in the form of word problem applications and obtain solutions using equations.

 6.   Solve and graph first degree inequalities, higher degree inequalities and inequalities involving absolute value.

 7.   Recognize and graph linear functions, rational functions, absolute value functions, and graph inequalities in two variables.

 8.   Work with function notation and demonstrate knowledge of the meaning of a function.

 9.   Demonstrate an understanding of function composition, one-to-one functions and inverse functions.

 10. Examine, evaluate and graph exponential and logarithmic functions.

 11. Use at least two of the following techniques to solve linear and non-linear systems of the equations: substitution, addition, Gaussian elimination, Cramer's rule.

 12. Perform operations with matrices and use a matrix operation.

 13. Graph systems of inequalities.

 14. Identify the conic section represented by a given second degree equation and graph conic sections including circles, parabolas, ellipses and hyperbolas.

 15. Explore various topics related to sequences and series including series notation, sequence formulas, counting principles, mathematical induction and the Binomial Theorem.

 16. Perform synthetic division.

 17. Use the Remainder Theorem and the Factor Theorem to factor and evaluate polynomials.

 18. Solve polynomial equations using the Rational Root Theorem and/or approximation techniques.

 19. Write and speak clearly and logically in presentations and essays.

 20. Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information.

 TOPICAL OUTLINE:

 

 I.      Review of Algebraic Concepts

         A.      Sets

         B.      Properties of Real Numbers

         C.      Exponents

         D.      Radical

         E.      Polynomial Operations

         F.      Factoring

         G.      Algebraic Fractions

 II.     Equations and Inequalities

         A.      Linear Equations

         B.      Complex Numbers

         C.      Quadratic Equations

         D.      Equations in Quadratic Form

         E.      Equations involving Radicals

         F.      Formulas

         G.      Applications

         H.      First Degree Inequalities

         I.      Equations and Inequalities Involving Absolute Value

         J.      Non-linear Inequalities

 III.    Functions and Their Graphs

         A.      The Cartesian Coordinate System

         B.      Linear Functions

         C.      Composition of Functions

         D.      One-to-one Functions

         E.      Inverse Functions

         F.      Absolute Value Functions

         G.      Rational Functions

         H.      Proportion and Variation (Functions of several variables)

         I.      Inequalities in two variables

 IV.     Exponential and Logarithmic Functions

         A.      Exponential Functions and Graphs

         B.      Logarithmic Functions

         C.      Properties of Logarithms

         D.      Logarithmic and Exponential Equations

 V.      Linear and Non-linear Systems

         A.      Substitution Method and Addition Method

         B.      Matrices & Guassion Elimination

         C.      Matrix Operations

         D.      Determinants and Cramer's Rule

         E.      Systems of Inequalities

         F.      Non-linear Systems

 VI.     Graphs and Equation Recognition of the Conic Sections

         A.      Circles

         B.      Parabolas

         C.      Ellipses

         D.      Hyperbolas

 VII.    Miscellaneous Topics

         A.      Sequences and Series

         B.      Arithmetic and Geometric Progressions

         C.      Permutations and Combinations

         D.      The Binomial Theorem

         E.      Math Induction

 VIII.   Theory of Equations

         A.      Synthetic Division

         B.      The remainder Theorem and the Factor Theorem

         C.      The Fundamental Theorem of Algebra

         D.      The Rational Root Theorem

         E.      Approximation of Real Roots