Course Requirements for Math1414 and NCBM 0244

Course grades will be calculated according to the following criteria:

Math 1414 grade:

Tests 1 - 3 and Final Exam: 80%

Aleks HW: 10%

Quizzes: 10%

NCBM 0244 grade:

15% Participation

35% ALEKS Progress

50% Exit Exam Grade

A  90-100      B  80-89       C  70-79       D  60-69        F  <60

Students will work in an on-campus lab setting with faculty support. Students will take an initial knowledge check in the NCBM 0244  ALEKS pie, which will generate their individualized path through necessary just-in-time review topics.  Upon completion of NCBM 0244 with a C or higher (with concurrent enrollment in Math 1414), a student will be considered TSI complete in mathematics.

Exit Exam for NCBM 0244: The Exit Exam is worth 50% of your course grade. Students who pass MATH 1414 can substitute their final grade in MATH 1414 for the Exit Exam Grade. Students who are not doing well in MATH 1414 will want to take the exit exam after completing the prerequisite material through at least section 9.1 in the College Algebra textbook (systems of linear equations in two variables) in order to pass NCBM 0244 and become TSI complete (if not already TSI complete). Students may have TWO attempts to pass the exit exam and must request the second attempt only after completing their first attempt.

Specifics on whether you should prepare and how to prepare for the exit exam and the method of proctoring will be given later in the semester.  Review for the exit exam will be provided. This exam will be timed with a limit of 1 hour and 20 minutes and you are expected to show work. Receiving a grade of 70% or higher in this course and a 60% or higher on the exit exam are the requirements for passing this course. Students who do not meet these percentages will earn either a D or F in NCBM 0244.

Required Materials  

This is a First Day™ class. The cost of required course materials, including an online version of the textbook and ALEKS, has been added to your tuition and fees bill.   

Textbook: College Algebra & Trigonometry, 1st Edition by Miller & Gerken. McGraw-Hill (ALEKS software) ISBN: 9780078035623  

ALEKS: With First Day Access you will have access to the software program ALEKS. This will give you access to the online version of the textbook and to online homework.

Calendar for NCBM 0244

Course Content

Course Description for Math 1414

Credit Hours: 4, Contact Hours: 4

MATH 1414 – College Algebra for Precalculus (4-4-0). A course for students planning to take Precalculus (MATH 2412) and Calculus (MATH 2413). Content includes the rational, real, and complex number systems; the study of functions including polynomial, rational, radical, exponential, and logarithmic functions and related equations; inequalities; sequences and series; systems of linear equations using matrices.

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 are not planning to take Precalculus should take College Algebra MATH 1314.

Course 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).
• 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 extrema 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. 

Student Learning Outcomes

Upon successful completion of the course, a student should be able to:

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.

General Education Competencies

1. Communication Skills: Develop, interpret, and express ideas and information through written, oral, and visual communication that is adapted to purpose, structure, audience, and medium.
2. Critical Thinking: Gather, analyze, synthesize, evaluate, and apply information for the purposes of innovation, inquiry, and creative thinking.
3. Empirical and Quantitative Skills: Apply mathematical, logical, and scientific principles and methods through the manipulation and analysis of numerical data or observable facts resulting in informed conclusions.

Course Description for NCBM 0244

Credit Hours: 2, Contact Hours: 2

NCBM 0244 – Support for College Algebra for Precalculus (2-2-0). This course is designed to support students concurrently enrolled in MATH 1414 by providing additional focus on MATH 1414 topics and just-in-time review of prerequisite topics, as needed. Topics include review of properties of real numbers, functions, algebra of functions, inequalities, polynomials and factoring, rational expressions and equations, radical expressions and equations, quadratic functions and their graphs, solving quadratic equations, and exponential functions. This course is not for college-level credit.

Course Rationale

This course is intended to provide support to students who are taking MATH 1414.  It should be taken along with MATH 1414 and is required for students who do not meet the prerequisites to take MATH 1414 as a stand-alone course.  Upon completion of NCBM 0244 with a C or higher (with concurrent enrollment in MATH 1414), a student will be considered TSI complete in mathematics.

Student Learning Outcomes

Upon successful completion of the course, a student should be able to:

1. Demonstrate understanding and knowledge of properties of functions, which include evaluation, domain and range, related equations, and basic operations.
2. Simplify, factor, and perform basic operations on algebraic expressions, including polynomials, rational and radical expressions, complex fractions, and complex numbers.
3. Solve linear, absolute value, rational, and radical equations, quadratic equations by symbolic methods including completing the square, and linear inequalities.
4. Appropriately use forms and formulas, including quadratic formula, midpoint, distance, and equations of circles and lines.
5. Graph linear equations and inequalities, including systems of each, as well as quadratic functions, and circles.
6. Solve application problems using linear and quadratic models, direct and inverse variation, and 2x2 systems of linear equations.