Mathematics

SYLLABUS

MATHEMATICS 55B - Intermediate Algebra, Part B

Effective Fall 2007

Text:   Algebra for College Students. Second Customized Chabot Edition. Robert Blitzer. Pearson Custom Publishing

Supplementary Material for the Student:

            Student Solutions Manual

Supplementary Material for the Instructor:

            Printed Test Bank

Note:  Instructor Joe Berland has written supplementary materials for this textbook. Each section for which there are materials is marked with an asterisk. Pages are attached to this syllabus on which a description is given of what is discussed in the supplementary material for each section. All the supplementary material is optional. See Alice to obtain an electronic or a hard copy of the supplement.

Chapter 3:  Systems of Linear Equations

section 3.3 is new material.  The rest is review from Math 65.

TOTAL HOURS:  5 

Chapter 4:  Inequalities

Section 4.1-4.3 is review from Math 55A.

TOTAL HOURS:  5 

Chapter 5:  Polynomials and Factoring

Review solve quadratics by factoring.

TOTAL HOURS:  1 

Chapter 7:  Radicals and Rational Exponents

Review from Math 55A

TOTAL HOURS:  5 

Chapter 8:  Quadratic Equations and Functions and Review Rational Equations

Sections 8.1, 8.2, 6.6 are review from Math 55A. 

Section 6.6:  Rational equations—included after 8.2 to include those that reduce to quadratic equations that require quadratic formula..

TOTAL HOURS:  8.5 

Appendix:  Graphing Rational Functions

The method of translation presented here, involving changing the coordinate system, is also the one used in the supplementary materials for other sections that involve translation. You are of course free to use any method you wish.

TOTAL HOURS:  2.5 

Chapter 9:  Exponential and Log Functions

This is all new material.

TOTAL HOURS:  13 

Chapter 10:  Circles and non-linear Systems

New material. 

TOTAL HOURS:  2

TOTAL HOURS: 42

Note:  Much of the material in early chapters above is review from either Math 65 or 55A.  You may be able to cover some of these sections more quickly than indicated here, leaving yourself more time for the new material in sections 3.3, 4.4, 8.4, 8.5, Chapter 9 and Section 10.1 

In this schedule an “hour” means a 50-minute class period. Depending on holidays, the class meets for a total of 48 - 51 “hours”. So the schedule allows 6-9 “hours” for review and exams. If you would like more time for review and exams (more exams for example) reduce time allotted proportionally. 

Possible exam schedule: 

Exam 1:  Chapters 3-4

Exam 2:  Section 5.7 , Chapter 7 and Sections 8.1-8.4 (Lots of review material from Math 55A)

Exam 3:  Sections 8.5, appendix A and 9.1-9.2

Exam 4:  Sections 9.3-9.5 and 10.1 plus any optional topics.

Final Exam: Cumulative 

Milton Rube, May 2004

Revised Joe Berland, Fall 2006 and May 2007

DESCRIPTION OF SUPPLEMENTARY MATERIALS 

Section 7.1

Graphing square and cube root functions using translation techniques. Domain of even root function. Domain of cube root functions and odd root functions in general. Supplemental exercises. 

Section 7.2

Importance of positive base when simplifying rational exponent.  may not be true if base is negative; correction of wrong answer to text example that flows from this. 

Section 7.6

Deeper analysis than in the text of why extraneous solutions do or do not occur in root equations. 

Section 7.7

Discussion of the imaginary unit, correcting serious logical flaws in the text. 

Section 6.6

A deeper discussion than in the text on why extraneous roots in rational equations do or do not occur, using the concepts of domain and equivalent equations, can be found in the supplementary materials for Section 6.6 of the Elementary Algebra text. 

Section 8.3

Graphing quadratic functions using translation techniques (and completing the square when necessary). Suggestion about homework assignment. 

Appendix: Graphing Rational Functions

Simplified versions of the examples and exercises if you don’t want the students to have to factor or use any form of algebraic division. 

Section 9.1

Graphing exponential functions (including natural ones) using translation techniques. Suggestions about homework, including supplemental exercises. 

Section 9.2

More precise definition of a one-to-one function in a form that will be useful for further discussion in Section 9.5. 

Section 9.3

Graphing logarithmic functions (including natural ones) using translation techniques. Supplemental homework exercises. 

Section 9.5

Important properties of one-to-one functions that make them useful for solving equations, and particular versions of these properties for exponential functions. Discussion by example of use of exponential functions in equation solving, leading to an equivalence property for exponential equations. Editing and adding comments to an example in text to clarify logic and correct logical flaw. Particular versions of the one-to-one properties for natural logarithmic functions. Discussion by example of use of natural logarithmic functions in equation solving, leading to an equivalence property for natural logarithmic equations. Supplemental discussion of an example in text to examine deeply why, after isolating the variable in a logarithmic equation, some numbers are solutions and others are extraneous solutions.