MA105 COLLEGE ALGEBRA FOR CALCULUS PREPARATION (4 Cr.)

COURSE DESCRIPTION

Satisfies the foundations of natural science- mathematics requirement [Division III]

Prerequisite: MA 100 (B- or better) or satisfactory score on the Math Placement Exam. A graphing calculator or equivalent software is required.

Offered:  Fall, Winter

General Introduction and Goals

This course involves the continued development of students' abilities to manipulate algebraic statements and solve problems.  A study of functions, graphing, equation solving techniques, exponents and logarithms, and systems of equations.  Topics, applications and pace are tailored for those students intending to take calculus.

Course Content

1. Review of Algebra
   • The algebra of polynomials and rational expressions
   • Solving linear and quadratic equations
   • Radicals and rational exponents
   • The coordinate plane and graphing
   • Solving systems of linear equations
2. Real and Complex Numbers
   • Subsets of the real number system: naturals, integers, rationals, irrationals
   • Complex numbers: their inception and arithmetic
3. The Graphing Calculator
   • Drawing graphs
   • Approximating solutions to equations, determining extrema, etc.
4. Functions
   • The function concept and functional notation
   • Expressing functional dependence algebraically
   • Combinations of functions; inverse functions
   • Graphs, and transformations of graphs, of functions
   • Linear, quadratic, polynomial, and rational functions
   • Functions involving radicals
5. Solving Polynomial Equations and Inequalities
   • Algebraic and graphical methods
   • The theory of Equations
   • Solving literal equations
6. Exponents and Logarithms
   • Properties of the exponential and logarithmic functions
   • Solving exponential and logarithmic equations
   • Applications of the exponential and logarithmic functions
7. Systems of Equations
   • Solving linear systems algebraically
   • Solving non-linear systems algebraically and graphically
   • Applications of systems of equations
8. Other Topics
   • Matrices and determinants
   • Permutations and combinations