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College of DuPage FY Fall/17 ACTIVE COURSE FILE Curricular Area: Mathematics Course Number: 1428 Title: College Algebra with Applications Semester Credit Hours: 3 Lecture Hours: 3 Lab Hours: 0 Clinical Hours: 0 This course is not an IAI approved general education course. Changes from the present course must be accompanied by a yellow Course Revision or Deletion Form. Course description to appear in catalog: The study of algebra with emphasis on applications. This course should not be taken by students planning to enroll in calculus. Topics include, but are not limited to, matrices, functions, conic sections, polynomials, exponential and logarithmic functions, and sequences and series. Prerequisite: Demonstrated geometry competency (level 2), and Math 0482 (or college equivalent) with a grade of C or better or a qualifying score on the mathematics placement test or a qualifying A.C.T math sub-score A. General Course Objectives: Upon successful completion of this course, students should be able to do the following: 1. Determine the domain and range of relations and functions 2. Use function notation 3. Analyze graphs to determine the maximum and minimum values of a variety of relations and functions 4. Analyze graphs to determine when a variety of relations and functions are increasing and/or decreasing 5. Analyze graphs to determine the zeros of a variety of relations and functions 6. Determine the composite of two functions and the inverse of a one-to-one function 7. Construct the graphs of conic sections 8. Solve systems of linear equations 9. Perform matrix arithmetic 10. Determine the inverse of a nonsingular matrix 11. Solve exponential and logarithmic equations 12. Apply properties of logarithms 13. Determine terms of a sequence 14. Determine specific and general terms in arithmetic and geometric sequences 15. Determine sums of arithmetic and geometric series 16. Solve a variety of application problems relating to topics covered B. Topical Outline: This topical outline is not necessarily sequential. Applications are a major emphasis of this course. 1. Relations and functions a. Definition b. Determining domain and range c. Using tables of values d. Using function notation e. Forming the composite of two functions f. Graphing functions i. Determining if a graph is the graph of a function ii. Determining if a relation is symmetric to the x-axis, y-axis or origin. iii. Graphing using symmetry iv. Translating functions (horizontally and vertically) g. Analyzing functions (maximum/minimum, increasing/decreasing, zeros) i. Functions involving absolute value ii. Square root function iii. Functions defined by more than one formula depending on the value of the independent variable iv. Polynomial functions v. Rational functions h. Investigating the inverse of a function i. Determining a formula for f-l given f in ii. iii. function notation Determining the domain and range of f-l Graphing a function and its inverse 2. Analytic Geometry a. Parabolas i. Graphing quadratic functions and quadratic relations whose graphs are parabolas ii. Determining the coordinates of the vertex and the equation of the axis of a parabola b. Circles i. Determining the center-radius form of the equation of a circle ii. Determining the center and radius of a circle whose equation is given in general form iii. Graphing relations whose graphs are circles c. Ellipses d. Hyperbolas e. Systems of non-linear equations 3. Matrices a. Definition and dimension b. Operations with matrices i. Addition and subtraction ii. Scalar multiplication iii. Matrix multiplication c. Gaussian elimination to solve linear systems d. Gaussian elimination to find the inverse of a nonsingular matrix e. Use of the inverse of the coefficient matrix to solve a linear system 4. Exponential and logarithmic functions a. Exponential functions i. Definition ii. Analysis of the graphs of exponential functions iii. Exponential equations involving the same base iv. Applications b. Logarithmic functions i. Definition using the concept of function inversion on the exponential function ii. Analysis of the graphs of logarithmic functions iii. Properties of logarithms iv. Logarithmic equations v. Solution of exponential equations with different bases, using logarithms vi. The change of base formula vii. Applications 5. Binomial Expansion Theorem 6. Sequences and series a. Definitions b. Determination of the terms of a sequence given a c. d. C. formula for an or given a recursive definition Arithmetic sequences and series i. Determining if a given sequence is arithmetic ii. Determining any term of an arithmetic sequence iii. Determining a formula for an iv. Determining the sum of an arithmetic series Geometric sequences and series i. Determining if a given sequence is geometric ii. Determining any term of a geometric sequence iii. Determining a formula for an iv. Determining the sum of a geometric series v. Determining the sum (if it exists) of an infinite geometric series Methods of Evaluating Students: Unit tests at appropriate intervals; quizzes, homework, projects, and a comprehensive final examination, all at the discretion of the instructor. _______________________________ Initiator Date _______________________________ Sponsor Date _______________________________ Division Dean Date Textbook for Math 1428 Title: College Algebra, Graphs and Models, 6th edition Author: Bittinger, Beecher, Ellenbogen, Penna Publisher: Pearson Copyright: 2017 The following chapters and sections of the textbook should be covered. Chapter 1: All Sections 1.1 – 1.6 Chapter 2: Sections 2.1 (greatest integer function is optional), 2.2, 2.3, 2.4, 2.5 (cover basic functions, horizontal and vertical translations) Chapter 3: All Section 3.1 – 3.5 Chapter 4: Sections 4.1, 4.2, 4.5, 4.6 (Sections 4.3 and 4.4 Finding or approximating zeros for polynomial functions is optional) Chapter 5: All Sections 5.1 – 5.6 Chapter 6: Sections 6.1, 6.2, 6.3, 6.4, 6.5 Chapter 7: Sections 7.1 (determine coordinates of vertex, equation of axis, and graph), 7.2 (graph), 7.3 (graph), 7.4 Chapter 8: Sections 8.1 (omit sigma notation), 8.2, 8.3, 8.7 Applications are a major emphasis of this course. Please cover as many as time permits. Use of Technology in Math 1428 The mathematics faculty recommends to all mathematics instructors that any technology be allowed and encouraged in any level mathematics course when it can be used by a student to either 1. simplify calculations where the mechanics of the problem have already been mastered or 2. explore and experiment with concepts and problems that enrich the understanding of the material that is being taught. The use of either the TI-83 graphics calculator, TI-84 graphics calculator, or computer software is required in this course. This technology should be used to improve the speed and accuracy of complicated calculations and graphing in realistic modeling once the concepts of the problem have been developed. Videos for Math 1428 Instructional videos for Math 1428 are available within Student’s MyMathLab course. In all Mathematics courses, students with a documented learning disability that specifically requires a calculator as determined by Health Services, will be allowed to use a basic calculator for all test/quiz questions where arithmetic calculations are not the main objective. The specific disability must be verified with Health Services before the accommodation can be made.