College of Micronesia – FSM

P.O. Box 159

Kolonia, Pohnpei

Course Outline Cover Page

Technical Mathematics II                                                                             VMS 101

        Course Title                                                                                  Department and Number

Course Description:   This course is a continuation of VMS100 and is designed to provide vocational students with the mathematical tools needed to succeed in selected higher level technical occupational programs.  Topics covered include exponents and monomials, polynomials, roots and radicals, graphing trigonometric functions, angle formulas, and the applications of trigonometry, vectors, complex numbers and logarithms.   

Prepared by: Brent Villiers                                                      State: National Campus

                        Hours per Week           No. Of Weeks             Total Hours                  Semester Credits

Lecture             4/8                          16/8                             64                                     4

Laboratory      

                                                                        Total Semester Credits:                                     4

Purpose of Course                 Degree Requirement     _______________________________________

                                                Degree Elective            ______________________________________

Advanced Certificate    _______________________________________

                                                Certificate                     ________________XX____________________

                                                Remedial                      _______________________________________

                                                Other (Workshop)        _______________________________________

Prerequisite Course(s): VMS100

_______________________________________                              ___________________________

Signature, Chairman, Curriculum Committee                                                             Date Approved by Committee

_______________________________________________                                  ________________________________

Signature, President, COM-FSM                                                                                    Date Approved by the President

General Objective:

This course is designed to give the students entering the more technical occupational programs the mathematical skills to succeed in their chosen field of study.  There is an emphasis on the electronic and telecommunications applications.

Learning Outcomes:              Upon successful completion of this course the student will be able to:

• Define exponents, multiply and divide powers, raise a power to a power and a product or a quotient to a power. 
• Define exponents, multiply and divide powers, raise a power to a power and a product or a quotient to a power. 
• Describe, add, subtract, multiply and divide polynomials. 
• Factorize polynomials.
• Simplify radicals and solve equations using one and two radical expressions.
• Graph linear equations, find the slope of a line and find the equation of a line.
• Solve systems of equations by graphing, substitution and addition.  Identify consistent, inconsistent and dependent systems by their graphs, substitution or addition.
• Analyze statistical data.
• Graph trigonometric functions.
• Find the trigonometric function of an angle using a reciprocal or ratio identity, or Pythagorean and related identities.
• Find the exact trigonometric function value of a given angle using the sum and difference formulas and use the proper formula to find the exact trigonometric value of a given angle.
• Define the applications of trigonometry.
• Graph polar equations.
• Add vectors using the analytical method.
• Perform rectangular to polar conversions and vice versa, add, subtract, multiply and divide complex numbers.
• Define exponential and logarithmic functions and describe their relationship.  Apply the change of base formula.

Outline of Content:                            This course contains:

• Algebra
• Exponents and Monomials.
• Polynomials.
• Factoring Polynomials.
• Roots and Radicals.
• Graphs.
• Systems of Linear Equations.
• Introduction to Statistics.
• Trigonometry
• Graphing trigonometric functions.
• Trigonometric identities.
• Angle formulas.
• Applications of trigonometry.
• Graphing Polar Equations.
• Vectors
• Complex numbers.
• Logarithms.           

Learning Outcomes:              On completion of this course the learner will be able to:

Learning Outcome 1              Define exponents multiply and divide powers, raise a power to a power and a product or a quotient to a power. 

Assessment Criteria                  a.         Define exponents.        

• Multiply and divide powers with the same base.
• Raise a power to a power.
• Raise a product or a quotient to a power.

Assessment Method                             Multiple choice questions

Short answer questions

Learning Outcome 2              Define exponents, multiply and divide powers, raise a power to a power and a product or a quotient to a power. 

Assessment Criteria                a.           Describe monomials.

• Add, subtract, multiply, divide monomials.
• Use the four step process to solve problems.
• Solve word problems that use monomials.

Assessment Method                 Multiple choice questions

                                                            Short answer questions

Learning Outcome 3              Describe, add, subtract, multiply and divide polynomials. 

Assessment Criteria                a.           Define polynomials.

• Add and subtract polynomials.
• Multiply monomials and polynomials.
• Multiply polynomials.
• Describe special binomial products.
• Divide polynomials by monomials.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Learning Outcome 4              Factorize polynomials.

Assessment Criteria                  a.         Factorize by finding the greatest common factor.

• Factor by grouping.
• Factor trinomials.
• Factor by recognizing special binomial factors.
• Solve polynomial equations by factoring.
• Define quadratic equations and quadratic formulas.
• Solve equations using the quadratic formula.
• Solve word problems.

Assessment Method                 Multiple choice questions

Short answer questions

Learning Outcome 5              Simplify radicals and solve equations using one and two radical expressions.

Assessment Criteria                  a.         Factor radicand terms.

b.         Simplify radicals using Product Property of Roots and Quotient Property of Roots.

• Rationalize denominators.
• Multiply, divide, add and subtract radicals.
• Use the Squaring Property of Equations to solve for the unknown. 
• Solve equations containing one or two radical expressions.

Assessment Method                 Multiple choice questions

Short answer questions

Learning Outcome 6              Graph linear equations, find the slope of a line and find the equation of a line.

Assessment Criteria                  a.         Describe the rectangular coordinate system.

• Locate points on the rectangular coordinate system.
• Locate the coordinates of points on the rectangular coordinate system.
• Graph linear equations.
• Find the slope of a line.
• Find the equation of a line.

                                             

Assessment Method                 Multiple choice questions

Short answer questions

Learning Outcome 7              Solve systems of equations by graphing, substitution and addition.  Identify consistent, inconsistent and dependent systems by their graphs, substitution or addition.

Assessment Criteria                a.           Define a system of equations.

• Solve systems of equations by graphing.
• Identify consistent, inconsistent, and dependent systems by their graphs.
• Solve systems of equations by substitution.
• Identify consistent, inconsistent, and dependent systems by the results of substitution.
• Solve systems of equations by addition.
• Find the slope of a line.
• Identify consistent, inconsistent, and dependent systems by the results of addition.

Assessment Method                 Multiple choice questions

Short answer questions

Learning Outcome 8              Analyze statistical data.

 

Assessment Criteria                a.           Describe the role of statistics in industry.

• Explain the concepts of mean, median, mode, standard deviation, percentiles and quartiles.
• Interpret the analysis of statistical data.
• Describe the various statistical diagrams.
• Contrast the various statistical histograms.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Learning Outcome 9              Graph trigonometric functions.

Assessment Criteria                a.           Identify the basic graphs for the six trigonometric functions.

• Define period and amplitude.
• Define the period and amplitude of the six trigonometric functions.
• Determine the amplitude of the sine and cosine functions.
• Find the change in the period of a trigonometric function.
• Determine the phase shift of a trigonometric function.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Learning Outcome 10            Find the trigonometric function of an angle using a reciprocal or ratio identity, or Pythagorean and related identities.

Assessment Criteria                a.           Examine the origins of the reciprocal and ratio identities.

• Find the trigonometric of an angle using either a reciprocal or ratio identity.
• Find the trigonometric function of an angle using combinations of reciprocal and ratio identities.
• State the origins of Pythagorean and related identities.
• Find the trigonometric function of an angle using the Pythagorean and related identities.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Learning Outcome 11            Find the exact trigonometric function value of a given angle using the sum and difference formulas and use the proper formula to find the exact trigonometric value of a given angle.

Assessment Criteria                a.           State the sum and difference formulas for sine, cosine and tangents.

• Find the exact trigonometric function value for a given angle using the sum and difference formulas.
• State the double angle formulas for sine, cosine and tangent.
• State the power reducing formulas for sine, cosine and tangent.
• Use the correct formula to find the exact trigonometric value for a given angle.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Learning Outcome 12            Define the applications of trigonometry.

Assessment Criteria                a.           Identify an oblique triangle.

• Use the Law of Sines to find the missing parts of oblique triangles.
• Describe the four possibilities resulting from the ambiguous case.
• Use the law of cosines to solve oblique triangle given two sides and the included angle.
• Use the law of cosines to solve oblique triangles when given three sides.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Learning Outcome 13            Graph polar equations.

Assessment Criteria                a.           Define the polar coordinate pair.

b.         Graph polar coordinates.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Learning Outcome 14            Add vectors using the analytical method.

Assessment Criteria                a.           Define vector terms.

• Explain vector notation.
• Determine the magnitude and direction of a vector.
• Determine the horizontal and vertical components of a vector.
• Add vectors using the analytical method.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Learning Outcome 15            Perform rectangular to polar conversions and vice versa, and add, subtract, multiply and divide complex numbers.

Assessment Criteria                a.           Define j-operator and complex numbers.

• Describe the complex plane.
• Graph complex numbers.
• Perform rectangular to polar conversions.
• Perform polar to rectangular conversions.
• Add and subtract complex numbers.
• Multiply and divide complex numbers.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Learning Outcome 16            Define exponential and logarithmic functions and describe their relationship.  Apply the change of base formula.

Assessment Criteria                a.           Define the exponential function.

• Describe the graph of the exponential function.
• Evaluate exponential functions.
• Define the logarithmic functions.
• Describe the relationship exponential and logarithmic functions.
• Describe the graph of the logarithmic functions.
• Use the properties of logarithms.
• Apply the change of base formula.

Assessment Method                 Multiple choice questions

                                                Short answer questions

Required Course Materials:

           1. Instructor:

                       a. CAI Classroom with whiteboard or chalkboard

                       b. Text, Teacher’s Resource Guide, workbook

                       c. Overhead projector, transparencies

           2. Student:

                       a. Text(s), handouts provided by instructor

                       b. Ring binder

                       c. College ruled note sheet, pencil or pen

                       d. Scientific calculator

                      

Reference Materials:?

          

Method of Instruction:

• Computer Aided Instruction

          

Evaluation:

Final Grade for this course will be based on meeting the course requirements at the following

percentage rates:

                                   96% - 100%    A – Superior

                                   90% - 95%      B – Above Average

                                   80% - 89%      C – Average

                                   69% - 79%      D – Below Average

                                   0 %  - 69%      F – Failure

Attendance:

The COM-FSM vocational educational attendance policy will apply.