STANDARD COMPETENCIES:

 

 1.   Illustrate a knowledge of algebraic concepts through algebraic manipulations.

 2.   Solve first and second degree equations and inequalities.

 3.   Demonstrate a knowledge of the concepts of functions and graphing.

 4.   Demonstrate a knowledge and usage of exponential and logarithmic functions.

 5.   Demonstrate a knowledge of topics in theory of equations.

 6.   Use the six trigonometric functions in problem solving.

 7.   Find complex roots.

 8.   Use analytic geometry techniques in problem solving.

 9.   Illustrate a variety of techniques used to solve linear and non-linear systems of equations.

 10. Demonstrate a knowledge of various topics related to sequences and series.

 11. Analyze conic sections and their graphs.

 TOPICAL OUTLINE:

 

 I.      Illustrate a knowledge of algebraic concepts through algebraic manipulations.

         A.      Annotate set notations, subsets of the real numbers and properties of real numbers.

         B.      Manipulate algebraic expressions including working with exponents, radicals, polynomial operations, factoring and algebraic fractions.

 II.     Solve first and second degree equations and inequalities.

         A.      Solve the following types of equations:  Linear, quadratic, equations involving radicals, equations in quadratic form and equations involving absolute value.

         B.      Analyze solutions to quadratic equations, ie., complex, real, distinct, etc.

         C.      Manipulate formulas including formula evaluation and solving a formula for any of the variables.

         D.      Analyze problems in the form of word problem applications and obtain solutions using equations.

         E.      Solve first degree inequalities, higher degree inequalities and inequalities involving absolute value.

 III.    Demonstrate a knowledge of the concepts of functions and graphing.

         A.      Manipulate and graph linear functions, rational functions, absolute value functions, and graph inequalities in two variables.

         B.      Demonstrate knowledge of the meaning of "function" and work with function notation.

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

 IV.     Demonstrate a knowledge and usage of exponential and logarithmic functions.

         A.      Evaluate and graph exponential functions.

         B.      Evaluate and graph logarithmic functions.

         C.      Solve equations containing exponential and logarithmic functions.

         D.      Solve word problems involving exponentials and logarithms.

 V.      Demonstrate a knowledge of topics in theory of equations.

         A.      Perform synthetic division.

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

         C.      Annotate the Fundamental Theorem of Algebra.

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

 VI.     Use the six trigonometric functions in problem solving.

         A.      Graph any to the trigonometric functions or any variations in them.

         B.      Graph the inverses of the trigonometric functions and solve equations using these inverses.

         C.      Solve trigonometric equations.

         D.      Prove trigonometric identities.

         E.      Solve triangles for missing parts using trigonometry.

 VII.    Find complex roots.

         A.      Perform the four operations with complex numbers as well as finding an inverse or conjugate of a given complex number.

         B.      Find all roots, real and complex, of a given equation.

         C.      Find the roots and powers of complex numbers by use of the trigonometric from of complex number.

 VIII.   Use analytic geometry techniques in problem solving.

         A.      Graph and identify a given conic section.

         B.      Manipulate axis by rotation and/or translate axis to simplify an equation.

         C.      Use polar coordinates and transfer between rectangular and polar coordinates.

 IX.     Illustrate a variety of techniques used to solve linear and non-linear systems of equations.

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

         B.      Demonstrate a knowledge of matrix operations.

         C.      Graph systems of inequalities.

 X       Demonstrate a knowledge of various topics related to sequences and series.

         A.      Illustrate series notation and sequence formulas, and counting principles.

         B.      Apply the Binomial Theorem.

         C.      Demonstrate an understanding of proof by mathematical induction.

 XI.     Analyze conic sections and their graphs.

         A.      Graph conic sections including circles, parabolas, ellipses and hyperbolas.

         B.      Identify the conic section represented by a given second degree equation.