College of Dupage FY Fall/18

College of DuPage FY Fall/18

ACTIVE COURSE FILE Beginning Spring 2018

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:

Students will learn algebra with an 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

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. Domain and range c. Tables of values d. Function notation e. Composition of two functions f. Graphs i. Graphs of a function ii. Symmetry to the x-axis, y-axis or origin iii. Graphs with symmetry iv. Horizontal and vertical translations g. Functions i. Absolute value functions ii. Square root functions iii. Piecewise functions iv. Polynomial functions v. Rational functions h. Inverse of a function i. Function notation for f-1 ii. Domain and range of f-1 iii. Graphs of f and f-1 2. Analytic Geometry a. Parabolas i. Graphs of vertical and horizontal parabolas ii. Vertex and axis of symmetry b. Circles i. Center-radius form of the equation ii. General form of equation iii. Graphs 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 d. Inverse of a matrix e. Solution of a linear system using matrix inverse 4. Exponential and logarithmic functions a. Exponential functions i. Definition ii. Graphs iii. Exponential equations iv. Applications b. Logarithmic functions i. Definition ii. Graphs iii. Properties of logarithms iv. Logarithmic equations v. Exponential equations vi. Change of base formula vii. Applications 5. Binomial expansion theorem 6. Sequences and series a. Definitions b. nth term of a sequence c. Arithmetic sequences and series i. Definition ii. nth term of an arithmetic sequence iii. Formula for an iv. Sum of an arithmetic series d. Geometric sequences and series i. Definition ii. nth term of a geometric sequence iii. Formula for an iv. Sum of a geometric series v. Sum of an infinite geometric series C. Methods of Evaluating Students: Students will be evaluated by unit tests at appropriate intervals. Other methods may include quizzes, homework, projects, and a comprehensive final examination.

______Initiator Date Division Dean Date

______Sponsor 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.