COURSE DESCRIPTION

MATH 1414 COLLEGE ALGEBRA FOR PRECALCULUS.

• Credit Hours: 4

• Classroom Contact Hours per week: 4

• Laboratory Contact Hours per week: 0*

A course designed for students planning on taking Precalculus and then Calculus, majoring in business, mathematics, science, engineering, or certain engineering-related technical fields. Content includes the rational, real, and complex number systems; the study of functions including polynomial, rational, exponential, and logarithmic functions and related equations; inequalities; systems of linear equations; arithmetic, geometric sequences and series. Prerequisites: MATD 0390 or satisfactory score on the ACC Assessment Test. (MTH 1743)

Course Prerequisite: Current knowledge of high school algebra as measured by the TSI Assessment Test or a C or higher in NCBM 0214 or MATD 0390. Students who have a great deal of difficulty with the Pretest and/or review should consider signing up for the paired courses MATH 1414 and NCBM 0214.

Calculator: Students need either a scientific or business calculator. (Has log or ln key.) If a student cannot purchase one, calculators are available from the library. Graphing calculators are not required, but you will use graphing technology in most sections of the book. Graphing calculators are also available in the library. Most ACC faculty are familiar with the TI family of graphing calculators. Hence, TI calculators are highly recommended for student use.  Other calculator brands can also be used.  Your instructor will determine the extent of calculator use in your class section.

 

Communication with your Instructor:  All e-mail communication to students will be sent solely to the student’s ACCmail account or math software if applicable, with the expectation that such communications will be read in a timely fashion.  Likewise, students should use their ACCmail account or math software when communicating with instructors.  Instructors will respond to student emails within 3 business days.  If no response has been received by the end of that time, then the student should send a reminder to the instructor.  

 

INSTRUCTIONAL METHODOLOGY

This course is taught in the classroom primarily as a lecture/discussion course. We will be using Blackboard Collaborate to interact during classtime. I want this to be an online class that has a very “in person” feel. That means I want to hear from you. You need to stay at your computer the whole class. You need to answer questions when asked, participate in groups, let the class see your face on occasion. My teaching is very interactive. Class will not be me talking all the time

COURSE RATIONALE

This course is designed to teach students the functional approach to mathematical relationships that they will need for a calculus sequence. Other courses, such as MATH 1314, MATH 1332, or MATH 1342 are more appropriate to meet a general mathematics requirement. Check with your degree plan as to what math course your college requires.

Note: Students who have a degree requirement for College Algebra, but not planning to take Precalculus should take College Algebra MATH 1314.

 COMMON COURSE OBJECTIVES

Common course objectives are attached. They can also be found at:

https://sites.google.com/a/austincc.edu/math-students/documents/objectives

Note: include these in your syllabus.

MATH 1414 College Algebra Objectives

Functions:

• Use and interpret functional notation.

• Find the domain of polynomial, rational, radical, exponential, and logarithmic functions.

• Find a symbolic representation of the sum, difference, product, quotient, and composition of two functions.

• Evaluate the sum, difference, product, quotient, and composition of two functions at a given value of the respective domain for functions represented symbolically, graphically, and numerically.

• Find the inverse of a function represented symbolically, graphically, or numerically.

• Interpret the graphs of functions.

• Recognize and evaluate arithmetic/geometric sequences and series.

Graphing functions:

• Sketch the graphs of the following functions: Lines, x2, x3, x1/2, 1/x, 1/x2, |x|, factored polynomials of degree 3 or more, ax, logax, and rigid transformations of these functions.

• Describe the short run and end behavior of polynomial and rational functions.

• Approximate the zeros of a function from its graph.

• Solve an inequality involving a function from its graph.

• Graph a piece-wise defined function.

Symbolic Adeptness:

• Solve polynomial, rational, exponential, and logarithmic equations symbolically.

• Solve equations involving radicals symbolically.

• Solve equations with rational exponents symbolically.

• Solve equations with negative exponents symbolically.

• Solve polynomial and rational inequalities symbolically.

• Use the Fundamental Theorem of Algebra and the Conjugate Zeros Theorem to find zeros of polynomials of degree three or greater.

• Find the vertex of a parabola written in standard form by using the formula  h = -b/2a.

• Perform algebraic operations on complex numbers (addition, subtraction and multiplication (division?)).

• Convert an exponential equation to logarithmic form, and a logarithmic equation to exponential form.

• Solve Exponential and Logarithmic equations symbolically.

• Evaluate exponential and logarithmic functions using the change of base formula and a calculator.

• Use the properties of logarithms to expand a logarithmic expression, and to write an expanded logarithmic expression as a single logarithm.

• Solve a system of linear equations using Gaussian elimination.

• Perform algebraic operations on matrices, including addition, scalar multiplication, matrix multiplication.

• Find the determinant of a matrix and apply Cramer’s Rule.

Applications

• Recognize and use applications of linear functions.

• Recognize and use applications of quadratic functions, including falling object problems and extremea problems.

• Recognize and use applications of exponential and logarithmic functions, including exponential growth and decay, doubling time, and half-life problems.

• Recognize and use applications of systems of linear equations.

COURSE DESCRIPTION

MATH 1414 COLLEGE ALGEBRA FOR PRECALCULUS.

• Credit Hours: 4

• Classroom Contact Hours per week: 4

• Laboratory Contact Hours per week: 0*

A course designed for students planning on taking Precalculus and then Calculus, majoring in business, mathematics, science, engineering, or certain engineering-related technical fields. Content includes the rational, real, and complex number systems; the study of functions including polynomial, rational, exponential, and logarithmic functions and related equations; inequalities; systems of linear equations; arithmetic, geometric sequences and series. Prerequisites: MATD 0390 or satisfactory score on the ACC Assessment Test. (MTH 1743)

Course Prerequisite: Current knowledge of high school algebra as measured by the TSI Assessment Test or a C or higher in NCBM 0214 or MATD 0390. Students who have a great deal of difficulty with the Pretest and/or review should consider signing up for the paired courses MATH 1414 and NCBM 0214.

Calculator: Students need either a scientific or business calculator. (Has log or ln key.) If a student cannot purchase one, calculators are available from the library. Graphing calculators are not required, but you will use graphing technology in most sections of the book. Graphing calculators are also available in the library. Most ACC faculty are familiar with the TI family of graphing calculators. Hence, TI calculators are highly recommended for student use.  Other calculator brands can also be used.  Your instructor will determine the extent of calculator use in your class section.

 

Communication with your Instructor:  All e-mail communication to students will be sent solely to the student’s ACCmail account or math software if applicable, with the expectation that such communications will be read in a timely fashion.  Likewise, students should use their ACCmail account or math software when communicating with instructors.  Instructors will respond to student emails within 3 business days.  If no response has been received by the end of that time, then the student should send a reminder to the instructor.  

 

INSTRUCTIONAL METHODOLOGY

This course is taught in the classroom primarily as a lecture/discussion course. We will be using Blackboard Collaborate to interact during classtime. I want this to be an online class that has a very “in person” feel. That means I want to hear from you. You need to stay at your computer the whole class. You need to answer questions when asked, participate in groups, let the class see your face on occasion. My teaching is very interactive. Class will not be me talking all the time

COURSE RATIONALE

This course is designed to teach students the functional approach to mathematical relationships that they will need for a calculus sequence. Other courses, such as MATH 1314, MATH 1332, or MATH 1342 are more appropriate to meet a general mathematics requirement. Check with your degree plan as to what math course your college requires.

Note: Students who have a degree requirement for College Algebra, but not planning to take Precalculus should take College Algebra MATH 1314.

 COMMON COURSE OBJECTIVES

Common course objectives are attached. They can also be found at:

https://sites.google.com/a/austincc.edu/math-students/documents/objectives

Note: include these in your syllabus.

MATH 1414 College Algebra Objectives

Functions:

• Use and interpret functional notation.

• Find the domain of polynomial, rational, radical, exponential, and logarithmic functions.

• Find a symbolic representation of the sum, difference, product, quotient, and composition of two functions.

• Evaluate the sum, difference, product, quotient, and composition of two functions at a given value of the respective domain for functions represented symbolically, graphically, and numerically.

• Find the inverse of a function represented symbolically, graphically, or numerically.

• Interpret the graphs of functions.

• Recognize and evaluate arithmetic/geometric sequences and series.

Graphing functions:

• Sketch the graphs of the following functions: Lines, x2, x3, x1/2, 1/x, 1/x2, |x|, factored polynomials of degree 3 or more, ax, logax, and rigid transformations of these functions.

• Describe the short run and end behavior of polynomial and rational functions.

• Approximate the zeros of a function from its graph.

• Solve an inequality involving a function from its graph.

• Graph a piece-wise defined function.

Symbolic Adeptness:

• Solve polynomial, rational, exponential, and logarithmic equations symbolically.

• Solve equations involving radicals symbolically.

• Solve equations with rational exponents symbolically.

• Solve equations with negative exponents symbolically.

• Solve polynomial and rational inequalities symbolically.

• Use the Fundamental Theorem of Algebra and the Conjugate Zeros Theorem to find zeros of polynomials of degree three or greater.

• Find the vertex of a parabola written in standard form by using the formula  h = -b/2a.

• Perform algebraic operations on complex numbers (addition, subtraction and multiplication (division?)).

• Convert an exponential equation to logarithmic form, and a logarithmic equation to exponential form.

• Solve Exponential and Logarithmic equations symbolically.

• Evaluate exponential and logarithmic functions using the change of base formula and a calculator.

• Use the properties of logarithms to expand a logarithmic expression, and to write an expanded logarithmic expression as a single logarithm.

• Solve a system of linear equations using Gaussian elimination.

• Perform algebraic operations on matrices, including addition, scalar multiplication, matrix multiplication.

• Find the determinant of a matrix and apply Cramer’s Rule.

Applications

• Recognize and use applications of linear functions.

• Recognize and use applications of quadratic functions, including falling object problems and extremea problems.

• Recognize and use applications of exponential and logarithmic functions, including exponential growth and decay, doubling time, and half-life problems.

• Recognize and use applications of systems of linear equations.

First Day Access

To enhance your learning experience and provide affordable access to the right course material, this course is part of an inclusive access model called First Day™. You can easily access the required materials for this course through Blackboard, at a discounted price, and benefit from single sign-on access with no codes required. Austin Community College includes the discounted price as a course fee in your registration fees for this course.
It is NOT recommended that you Opt Out, as these materials are required to complete the course.
You can choose to Opt Out on the first day of class, but you will be responsible for purchasing your course materials at the full retail price and access to your materials may be suspended.
See your course in Blackboard for details.

Textbook:  College Algebra and Trigonometry, 1st edition, Miller and Gerken; published by McGraw-Hill. The textbook is accessible online as an eBook and there is no need to purchase a hard copy of the textbook but you may do so if you choose.

Hardcover option (not required):  ISBN 978-0078035623

Online Component: ALEKS will be required. Access to ALEKS is included in the First Day Access version of the text.

Learning Outcomes

Upon successful completion of this course, students will be able to do at least 70% of the following:

1. Demonstrate understanding and knowledge of properties of functions, which include domain and range, operations, compositions, and inverses.

2. Recognize and apply polynomial, rational, exponential, and logarithmic functions and solve related equations.

3. Apply graphical, symbolic and numeric techniques.

4. Evaluate all roots of higher degree polynomial and rational functions.

5. Recognize, solve and apply systems of linear equations using matrices.

6. Perform algebraic operations on matrices, evaluate the determinant and apply Cramer’s Rule

7. Recognize and evaluate arithmetic/geometric sequences and series.

The General Education Competency of:

1. Critical Thinking: gathering, analyzing, synthesizing, evaluating and applying information is covered in every SLO.

2. Quantitative and Empirical Reasoning: applying mathematical, logical, and scientific principles and methods is covered in every SLO.

3. Technology Skills: using appropriate technology to retrieve, manage, analyze, and present information is covered in SLOs # 1, 2, 3, 4, and 5.

4. Written, Oral and Visual Communication: communicating effectively adapting to purpose, structure, audience and medium is covered in every SLO.