# MS-106 Technical Mathematics II

Course description:     This course is a continuation of MS104 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.

• Prerequisite Course: MS 104 Technical Math I
• #### A. PROGRAM LEARNING OUTCOMES (PLOs):

The student will be able to:

1. Demonstrate understanding and apply mathematical concepts in problem solving and in day to day activities.
2. Present and interpret numeric information in graphic forms.
3. Communicate thoughts and ideas effectively using proper mathematical terms.

#### B. STUDENT LEARNING OUTCOMES (SLOs) - GENERAL:

The student will be able to:
1. Analyze statistical data.
2. Graph linear equations, find the slope of a line, and find the equation of a line.
3. Solve systems of equations by graphing, substitution method, and addition method.
4. Define and describe the laws of exponents and perform basic operations with polynomials.
5. Simplify radicals and solve equations using one and two radical expressions.
6. Factor polynomials.
7. Define exponential and logarithmic functions and describe their relationship. Apply the change of base formula.
8. Perform operations with vectors, graph polar equations, and perform rectangular to polar conversions and vice versa.
9. Graph trigonometric functions.
10. Define the applications of trigonometry.
 SLO PLO 1 PLO 2 PLO 3 1 DM ID D 2 DM ID ID 3 IDM ID ID 4 DM ID D 5 IDM ID ID 6 IDM IDM ID 7 IDM IDM ID 8 IDM ID ID 9 DM ID ID 10 DM ID ID

I = Introduced
D = Demonstrated
M = Mastered

#### C. STUDENT LEARNING OUTCOMES - SPECIFIC:

The student will be able to:

General SLO 1.  Analyze statistical data.

 Student Learning Outcomes Assessment Strategies 1.1 Describe the role of statistics in industry. Written tests and oral recitations Written quizzes and homework 1.2 Explain the concepts of mean, median, mode, standard deviation, percentiles and quartiles. 1.3 Interpret the analysis of statistical data. 1.4 Describe the various statistical diagrams. 1.5 Contrast the various statistical histograms.

General SLO 2.  Graph linear equations, find the slope of a line, and find the equation of a line.

 Student Learning Outcomes Assessment Strategies 2.1 Describe the rectangular coordinate system. Written tests and oral recitations Written quizzes and homework 2.2 Locate points on the rectangular coordinate system. 2.3 Locate the coordinates of points on the rectangular coordinate system. 2.4 Graph linear equations. 2.5 Find the slope of a line. 2..6 Find the equation of a line.

General SLO 3.  Solve systems of equations by graphing, substitution method, and addition method.

 Student Learning Outcomes Assessment Strategies 3.1 Define a system of equations. . Written tests and oral recitations Written quizzes and homework 3.2 Solve systems of equations by graphing. 3.3 Identify consistent, inconsistent, and dependent systems by their graphs. 3.4 Solve systems of equations by substitution. 2.6 Identify consistent, inconsistent, and dependent systems by the results of substitution. 2.7 Solve systems of equations by addition. 2.8 Identify consistent, inconsistent, and dependent systems by the results of addition.

General SLO 4.  Define and describe the laws of exponents and perform basic operations with polynomials.

 Student Learning Outcomes Assessment Strategies 4.1 Define exponents and the laws of exponents. Written tests and oral recitations Written quizzes and homework 4.2 Define and describe monomials and polynomials. 4.3 Raise a power and a product or a quotient to a power. 4.5 Add, subtract, multiply, and divide monomials. 4.6 Add, subtract, multiply, and divide polynomials.

General SLO 5. Simplify radicals and solve equations using one and two radical expressions.

 Student Learning Outcomes Assessment Strategies 5.1 Factor  radicand terms. Written tests and oral recitations Written quizzes and homework 5.2 Simplify radicals using Product Property of Roots and  Quotient Property of Roots. 5.3 Rationalize denominators. 5.4 Multiply, divide, add and subtract radicals. 5.5 Solve equations containing radical expressions. 5.6 Define and describe complex numbers. 5.7 Perform the basic operations with complex numbers.

General SLO 6. Factor polynomials.

 Student Learning Outcomes Assessment Strategies 6.1 Factor by finding the greatest common factor. Written tests and oral recitations Written quizzes and homework 6.2 Factor by grouping. 6.3 Factor trinomials. 6.4 Factor by recognizing special binomial factors. 6.5 Solve polynomial equations by factoring. 6.6 Define quadratic equations and quadratic formulas. 6.7 Solve equations using the quadratic formula. 6.8 Solve word problems.

General SLO 7.  Define exponential and logarithmic functions and describe their relationship. Apply the change of base formula.

 Student Learning Outcomes Assessment Strategies 7.1 Define the exponential function. Written tests and oral recitations Written quizzes and homework 7.2 Describe the graph of the exponential function. 7.3 Evaluate exponential functions. 7.4 Define the logarithmic functions. 7.5 Describe the relationship exponential and logarithmic functions. 7.6 Describe the graph of the logarithmic functions. 7.7 Use the properties of logarithms. 7.8 Apply the change of base formula.

GENERAL SLO 8. Perform operations with vectors, graph polar equations, and perform rectangular to polar conversions and vice versa.

 Student Learning Outcomes Assessment Strategies 8.1 Define vectors and describe vector notation. Written tests and oral recitations Written quizzes and homework 8.2 Determine the magnitude and direction of a vector. 8.3 Determine the horizontal and vertical components of a vector. 8.4 Add, subtract, and multiply vectors. 8.5 Define and graph polar coordinates 8.6 Perform rectangular to polar conversions and vice-versa. 8.7 Define j-factor and write vectors in complex form.

General SLO 9.  Graph trigonometric functions.

 Student Learning Outcomes Assessment Strategies 9.1 Identify the basic graphs for the six trigonometric functions. Written tests and oral recitations Written quizzes and homework 9.2 Define period and amplitude. 9.3 Define the period and amplitude of sine and cosine functions. 9.4 Determine the amplitude of the sine and cosine functions. 9.5 Find the change in the period of a trigonometric function. 9.6 Determine the phase shift of a trigonometric function.

General SLO 10. Define the applications of trigonometry.

 Student Learning Outcomes Assessment Strategies 10.1 Identify an oblique triangle. Written tests and oral recitations Written quizzes and homework 10.2 Find the missing parts of an oblique triangle using the law of sines. 10.3 Describe the three possibilities resulting from the ambiguous case. 10.4 Find the missing parts of an oblique triangle using  the law of cosines . 10.5 Solve an oblique triangle using the laws of sines and cosines 10.6 Determine the area of an oblique triangle using trigonometric relationships.

#### D. COURSE CONTENT

1. introduction to statistics
2. algebra
3. complex numbers
4. logarithms
5. vectors
6. graphing polar equations
7. trigonometry

#### E. METHODS OF INSTRUCTION

Computer Aided Instruction

#### F. REQUIRED TEXT AND COURSE MATERIALS

Cleaves, Cheryl, and Margie Hobbs. College Mathematics: 2009 Update with MyMathLab.
Upper Saddle River, New Jersey: Prentice Hall, 2009 (or most recent edition)

None

None

#### I. EVALUATION

The student must achieve 70% mastery or a “C” grade to pass this course.

#### J. CREDIT BY EXAMINATION

None

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