to
rewrite/simplify expressions involving negative radicands; perform operations
with complex numbers, writing results in standard form.TRI-COUNTY TECHNICAL COLLEGE
COURSE SYLLABUS
Course Prefix & Number: MAT 110_________________
Course Title: College Algebra__________
Class Hours Lab Hours Credits
Per week: _3_ Per Week: _0_ Awarded: _3_
Catalog Description: This course includes the following the following topics: polynomial, rational, logarithmic, and exponential functions; inequalities; systems of equations and inequalities; matrices; determinants; simple linear programming; solutions of higher degree polynomials; combinatorial algebra, including the binomial theorem; and introduction to probability.
Entry Level Skills: A student entering MAT 110 should be able to factor by any method, determine equations of lines, understand the function concept, solve systems of two equations, solve equations and inequalities (linear, absolute value, rational, and quadratic), simplify algebraic expressions (polynomial, exponential, radical, and rational).
Pre-requisites: MAT 102 with a grade of C or better or satisfactory score on mathematics placement exam
Co-requisites: None
Text(s)/Required Materials: A Graphical Approach to Algebra and Trigonometry, by John Hornsby, Margaret L. Lial, and Gary K. Rockswold, 4th edition, Pearson Addison-Wesley, 2007.
E = mc2 Excellence through Mathematics Communication and Collaboration Student
Handbook by Herbert Riedel, Gerald Marshall, and Susan Smith, 2001.
Equipment: Graphing Calculator (TI-83 Plus, TI-84 Plus, or TI-89 Titanium recommended)
Course Competencies and Objectives/Major Course Topics:
Unit 1: Functions: Basic Concepts, Graphs, and Applications
Upon completion of this unit (sections 1.2, 2.1-2.6) the student should be able to:
1. Determine whether an equation or graph represents a function, and determine the domain and range.
2. Find the value of a function from an equation or graph.
3. Use a graph to determine intervals over which a function is increasing, is decreasing, or is constant.
4. Identify symmetry and even or odd functions from a graph or equation.
5. Identify and graph functions using transformation techniques (shifts, reflections, compressions/stretches).
6. Graph functions involving absolute value.
7. Graph piecewise-defined functions.
8. Perform algebraic operations and compositions on functions and state the resulting domain.
Unit 2: Polynomial and Rational Functions
Upon completion of this unit (sections 3.1-3.2, 3.4-3.5, 3.8, 4.1-4.3) the student should be able to:
1.
Use the imaginary unit to
rewrite/simplify expressions involving negative radicands; perform operations
with complex numbers, writing results in standard form.
2. Identify key characteristics of quadratic functions and draw graphs.
3. Use quadratic functions to model applications and determine extreme values.
4. Analyze the graph of a polynomial function through intercepts, end behavior, and local maxima and minima.
5. Use polynomial functions to model applications and determine extreme values.
6.
Graph transformations of the reciprocal function and the rational
function 
.
7. Find the domain and asymptotes of a rational function.
8. Analyze and draw the graph of a rational function through features such as intercepts, asymptotes, key points, and end behavior.
9. Use rational functions to model applications.
Unit 3: Exponential and Logarithmic Functions
Upon completion of this unit (sections 5.1 – 5.6) the student should be able to:
1. Determine whether a function is one-to-one.
2. Find the inverse of a one-to-one function, graph both the function and its inverse, and give the domain and range of the function and its inverse.
3. Use transformations to graph exponential functions, and determine the domain, range, and horizontal asymptote.
4. Use properties of logarithms to rewrite, simplify, and evaluate logarithmic expressions.
5. Evaluate logarithms without using a calculator, using LOG and LN keys on a calculator, and using the change of base formula.
6. Use transformations to graph logarithmic functions, and determine the domain, range, and horizontal asymptote.
7. Solve exponential and logarithmic equations by hand using exponential and logarithmic properties; approximate solutions using a graphing utility.
8. Use exponential and logarithmic functions to model and solve a variety of applications such as compound interest, pH, exponential growth and decay.
Unit 4: Systems of Equations and Inequalities
Upon completion of this unit (sections 7.1 – 7.8) the student should be able to:
1. Solve systems of two or more linear equations by a variety of methods such as substitution, elimination, matrix row operations, determinants, and matrix inverses.
2. Use systems of equations to model and solve applications.
3. Perform basic algebraic operations on matrices by hand and/or with the aid of a graphing utility.
4. Graph inequalities in two variables and systems of inequalities by hand and/or with the aid of a graphing utility.
5. Find the maximum/minimum value of the objective function of a linear programming problem.
6. Find the partial fraction decomposition for rational expressions.
Unit 5: Miscellaneous Topics
There will not be a unit test for this material, although it may be included on the final exam. Upon completion of this unit (Sections 11.4, 11.6, and 11.7) the student should be able to:
1. Use Pascal’s Triangle and the Binomial Theorem to expand a binomial expression.
2. Solve counting problems using the fundamental principle of counting, permutations, and combinations.
3. Compute basic probabilities.
Grade Calculation Method: The exact method of calculating your grade will be distributed by your instructor at the beginning of the course, based on these guidelines:
4 Unit Tests, 12-18% each 60-72%
Cumulative Final Exam 15-18%
E=mc2 Project 10%
Other 0-15%
Total 100%
Prepared by Robin Pepper Date written or revised: May 9, 2006