COPPIN STATE COLEGE



COPPIN STATE UNIVERSITY

DEEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

2500 WEST NORTH AVENUE

BALTIMORE, MARYLAND 21216

_______________________________________________________________________

COURSE SYLLABUS

For

MATH131 COLLEGE ALGEBRA FOR MATHEMATICS AND SCIENCE MAJORS

3 CREDITS

GENERAL INFORMATION

1. Office __________________________

2. Office Hours __________________________

3. Telephone 410-951____________________

4. Class Meeting time _____________________

5. Class Room __________________________

REQUIRED TEXT

Larson, Ron and Hostetler, Robert P. College Algebra: Concepts and Models. 5th. Ed. New York: Houghton-Mifflin, 2006.

COURSE DESCRIPTION

Real numbers field; sets of real numbers; linear equations and inequalities, absolute value; exponents; radicals; polynomials and roots of polynomial equations; complex numbers; linear, quadratic, rational and radical functions; systems of equations with two variables; methods of combining functions; inverse functions, the Cartesian plane and graphs of equations and inequalities; exponential and logarithms functions and equations.

Prerequisite: DVMT 109 (Intermediate Algebra) TI-83 Graphing Calculator is required.

COURSE CONTENT AND BEHAVIORAL OBJECTIVES

UNIT I: FUNDAMENTAL CONCEPTS OF ALGEBRA (Prerequisites)

A. Topics

R1.1 Real Numbers: Order and Absolute Value

R1.2 The Basic Rules of Algebra

R1.3 Integer Exponents

R1.4 Radicals, Rational Exponents, and Roots

R1.5 Polynomials and Special Products

6.4 Binomial Theorem (Expansion Only)

R1.6 Factoring

R 1.7 Fractional Expression, Complex Fraction, and Domain

R 2.1 Linear equations

R 2.5 Absolute Value Equations

R 2.6 Absolute Value Inequalities

B. Behavioral Objectives: Upon successful completion of this unit, the student shall be able to:

1. Identify different sets of real numbers, locate real numbers on real number line, and ordering of real numbers.

2. Absolute value and distance.

3. Solve and graph linear equations and inequalities.

4. Note difference between algebraic expression and equations.

5. Identify Basic Rules of Algebra

6. Identify properties of exponents and Scientific notation.

7. Identify properties of radicals and simplify radicals.

8. Identify polynomials and perform operations with polynomials.

9. Special products.

10. Factoring common factors, special polynomial forms, trinomials with binomial factors, and by grouping.

11. Evaluate algebraic and rational expressions.

12. Determine the domains of algebraic expressions and simplify rational expressions and complex fractions.

13. Expanding a binomial using binomial coefficients from Pascal’s Triangle.

14. Use algebraic techniques common in Calculus.

15. Solve Absolute value equations and inequalities

Unit II: THE FUNCTION CONCEPT AND LINEAR FUNCTION

A. Topics

4. Functions.

1.1 The Cartesian plane, Graphs of Equations.

1.2 Lines in the plane.

1.3 Linear Modeling.

B. Behavioral Objectives: Upon successful completion of this unit, the student shall be able to:

1. Determine if an equation or a set of order pair represents a function.

2. Use function notation.

3. Evaluate a function.

4. Find domain of a function.

5. Plot points in the Cartesian plane.

6. Find distance between two points in a plane.

7. Use Distance Formula to solve distance in geometry problems.

8. Find the midpoint of line segment.

9. Determine whether a point lies on the graph of an equation.

10. Find x- and y- intercepts of the graph of an equation.

11. Determine the symmetry of a graph.

12. Use the point-slope and slope-intercept forms to find equations and graphs of lines.

13. Find and use slopes of lines to write and graph linear equations in two variables.

14. Determine slopes and write equations of parallel or perpendicular lines.

15. Analyze graphs of functions.

16. Solve and graph linear equations and inequalities.

UNIT III: THE QUADRATIC FUNCTION AND CONIC SECTION

Topics

R2.3 Quadratic Equations.

R2.4 Quadratic Formula.

2.1 Quadratic Functions and Models.

1.1 Graphs of Equations.

B.1 Conic Sections.

B.2 Conic Sections and Translations.

4.1 System of Nonlinear Equations (Substitution)

4.2 System of Nonlinear Equations (Elimination)

4.4 System of Nonlinear Inequalities.

Behavioral Objectives: Upon successful completion of this unit, the student shall be able to:

1. Solve a quadratic equation by factoring.

2. Solve a quadratic equation by extracting square root.

3. Develop the Quadratic Formula by completing the square.

4. Use discriminant to determine the number of real or type of solutions to a quadratic equation.

5. Solve a quadratic equation using Quadratic Formula.

6. Sketch the graph of a quadratic function and identify its vertex and intercepts.

7. Find a quadratic function given its vertex and a point on the graph.

8. Find equation of a circle and its translations.

9. Completing the square to graph a circle.

10. Completing the square to identify different conic sections.

11. Vertical and horizontal shifts of conic sections.

12. Writing equations of conic section in standard form.

13. Solve a nonlinear system by the methods of elimination and substitution.

14. Interpret the solution of s nonlinear system graphically.

15. Sketch the graph of an inequality in two variables.

16. Solve a system of inequalities.

Unit IV: POLYNOMIAL, RATIONAL AND RADICAL FUNCTIONS

Topics

6. Transformations of Functions.

2.2 Polynomial Functions of Higher Degree.

2.3 Polynomial Division.

2.4 Real Zeros of Polynomial Functions.

2.6 The Fundamental Theorem of Algebra.

2.7 Rational Functions.

Behavioral Objectives: Upon successful completion of this unit, the student shall be able to:

1. Identify rigid and nonrigid transformations.

2. Sketch the graph of a function using transformations and common graphs.

3. Write the equation of a function using transformations and common graphs.

4. Solve a polynomial equation by factoring.

5. Rewrite and solve an equation involving radicals and rational exponents.

6. Identify the characteristics of polynomial function.

7. Apply the Leading Coefficient Test to determine right and left behavior of the graphs of a polynomial function.

8. Find the real zeroes of a polynomial functions.

9. Sketch the graph of a polynomial function.

10. Divide one polynomial by a second polynomial using long division.

11. Simplify a rational expression by using long division.

12. Use synthetic division to divide two polynomials.

13. Use the Remainder Theorem and synthetic division to evaluate a polynomial.

14. Use Factor Theorem to factor a polynomial function.

15. Find all possible real zeroes of a function using the Rational Zero Test.

16. Approximate the real zeros of a polynomial function using the Intermediate Value Theorem.

17. Use the Fundamental Theorem of Algebra and the Linear Factorization Theorem to a write a polynomial as the product of linear factors.

18. Find polynomial with integer coefficients whose zeros are given.

19. Factor a polynomial over the real and complex numbers.

20. Find all real and complex zeros of a polynomial.

21. Find domain of rational function.

22. Find the vertical and horizontal asymptotes of the graph of a rational function.

23. Sketch the graph of a rational function.

Unit V: The Algebra of Calculus and Inverse Functions

Topics

R1.4 Radicals and Rational Exponents.

2.5 Complex Numbers.

1.4 Functions.

1.7 The Algebra of Functions.

1.8 Inverse Functions.

3.1 Exponential Functions.

3.2 Logarithmic Functions.

3.3 Properties of Logarithms.

3.4 Solving Exponential and Logarithmic Equations.

3.5 Exponential and Logarithmic Models.

Behavioral Objectives: Upon successful completion of this unit, the

student shall be able to:

1. Find principal root of a real number.

2. Understand properties of radicals.

3. Perform operation and simplify radicals.

4. Understand the definition of rational exponents.

5. Perform operation with radical by use of calculator.

6. Perform operations with complex numbers and write the result in standard form.

7. Find the complex conjugate of a complex number.

8. Solve polynomial equations.

9. Definition of functions is revisited.

10. The Algebra of Functions revisited.

11. Inverse functions revisited.

12. Evaluate an exponential function.

13. Sketch the graph of exponential function.

14. Use an exponential model to solve an application problem. (Compounded interest, bacteria and population growth, demand function, and radioactive Decay).

15. Evaluate a logarithmic expression.

16. Find the domain, vertical asymptote, x-intercept of a logarithmic function.

17. Evaluate a logarithm using the change-of-base formula.

18. Rewrite logarithmic expression using the properties of logarithms.

19. Solve an exponential equation.

20. Solve a logarithmic equation.

21. Identify common mathematical models involving exponential and logarithmic functions.

22. Construct and use a model for exponential growth or exponential decay.

23. Use a base 10 logarithmic model to solve an application problem.

MODES OF EVALUATION

Chapter tests (5) 50%

Quizzes, Homework and attendance 20%

Final Exam 30%

_____

Total 100%

GRADE DISTRIBUTION

Grade A – 90% and above

Grade B – 80% to 89%

Grade C – 70% to 79%

Grade D – 60% to 69%

Grade F – under 60%

PLAGIARISM POLICY

Academic honesty is required of all students at all times. It will be taken for granted that any work, oral or written that a student does for the course is his/her original work. Any violation of this rule constitutes plagiarism. Plagiarism includes any form of cheating in exams, tests, and quizzes, unacknowledged/undocumented use of another’s writing or ideas published or unpublished. A student who plagiarizes will receive an F for the course as determined by the instructor.

CLASS RULES AND EXPECTATIONS

1. Respect and courtesy will be observed at all times during class session.

2. Smoking, eating and drinking are prohibited in class.

3. Attendance and punctuality policy and rules are strictly enforced (see college attendance policy in handbook).

4. All absences EXCUSED and UNEXCUSED will be indicated on the FINAL GRADE SHEET.

5. Attendance will be taken at the beginning of class. Any student who is not present at the time of roll call must contact the instructor immediately after class to inform of their presence.

6. Any excused absence must be reported via phone call within 24 hours of absence in order to be considered as excused.

7. Three late days will be counted as one absent.

8. If you are absent, it is your responsibility to find out what new material was covered in class during your absence. It is also your responsibility to make up any missed assignment/homework.

9. Absolutely NO MAKE-UP EXAM will be given. All exams will be announced well in advanced. If you are not able to take an exam on the scheduled date, then arrangement must be made with the instructor to take the exam prior to that date.

MODES OF INSTRUCTION

Various modes of instruction will be used. Among these are lecture, small and large group discussions, demonstrations, group and individual projects.

SUPPLEMENTARY TEXTS

Fowler, H. Ramsey. The Little Brown Handbook. Boston: Little, Brown and Company.

Lial, Hornsby, and McGinnis. Intermediate Algebra. Addison Wesley.

Larson, Ron and Hostetler, Robert P. Precalculus. 6th. Ed. New York: Houghton-Mifflin, 2003.

|Attendance Policy   |

|Coppin State College is dedicated to providing you with a quality educational experience. As a part of that experience, we know |

|that regular class attendance and the interaction between the faculty and the students is vital. On September 24, 1990, Coppin |

|State College implemented an Institutional Undergraduate Class Attendance Policy (IUCAP) which identifies the criteria that govern|

|a grade of AW/FX based on unsatisfactory class attendance. |

|The Institutional Undergraduate Class Attendance Policy |

|The Institutional Undergraduate Class Attendance Policy (IUCAP) identifies the criteria that govern a grade of AW or FX based on |

|unsatisfactory class attendance. |

|The instructor determines whether a student absence is excused or unexcused. A student who has unexcused absences exceeding two |

|times the number of lecture hours for a course has surpassed the number of allowable unexcused absences and is in violation of the|

|IUCAP. The instructor is authorized to issue a grade of AW (when the unexcused absence occurs within the withdrawal period) or FX |

|(when the unexcused absence occurs after the withdrawal period). The Institutional Class Attendance Policy is universal unless an |

|individual class attendance policy permits fewer absences. |

|The grade of AW or FX is considered official and effective upon receipt of the Grade Notification Form by the Office of Records. |

|Students who receive official grades of AW or FX forfeit the right to withdraw themselves from those classes despite the |

|withdrawal date. |

|NOTE: |

|The Institutional Undergraduate Class Attendance Policy refers to the number of lecture hours, not the number of class meetings. |

|For 3-credit MWF classes, there is equivalence, and the number of allowable unexcused absences is six (6). For 3-credit TR classes|

|(which meet 75 minutes each day), each class meeting equals one-and-one-half lecture hours, and the number of allowable unexcused |

|absences is four (4). For 3-credit evening classes which meet once a week, each class meeting equals three lecture hours, and the |

|number of allowable unexcused absences is two. |

|Ms. Michelle Reynolds, who is currently the Coordinator of the program, monitors and does intervention to assist the student |

|through phone calls, letters and counseling interaction for all undergraduate students. For questions or concerns you contact her |

|at 410-951-3939. |

 

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