Mathematics

SYLLABUS

 MATHEMATICS 55A - Intermediate Algebra, Part A

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 1:  Basic Concepts

If you are going to use the supplementary materials for Section 1.3, you should either delay that section until immediately after Section 2.2, or teach Section 1.3 as in the text now and then teach the new topics in the supplementary materials after Section 2.2

TOTAL HOURS:  3

 Chapter 2:  Functions and Linear Functions

Some of the supplementary material for Section 1.3 focuses on techniques of translation. Some supplementary material for later sections assumes knowledge of these techniques, so if you want to use that material you will need to teach the supplemented version of 1.3 here. The supplemented version of Section 1.3 takes about 1 ½ hours of class time.

If you skipped Section 1.3 during Chapter 1, then when you teach Section 2.1 you may wish to review basic graphing by point-plotting (if you want to assign any of problems

19 – 28.) In Section 2.1, you may also wish to introduce identification from a graph of domain and range.

In Chapter 2, the material on functions is new. The material on lines is review, but very important.

TOTAL HOURS:  5

 Chapter 4:  Inequalities

Section 4.1 is review.  The rest is new material.

TOTAL HOURS:  4

 Chapter 5:  Polynomials and Factoring

Section 5.1 and 5.5 contain some new material.  The rest is review.

TOTAL HOURS:  8 

Chapter 6:  Rational Functions and Expressions

Everything after 6.1 is review.

TOTAL HOURS:  7

 Chapter 7:  Radicals and Rational Exponents

This is basically all new material.

TOTAL HOURS:  9.5

Chapter 8:  Quadratic Equations and Functions

This is mostly new material. 

TOTAL HOURS:  5.5 .

TOTAL HOURS: 42

 Note:  Much of the material in chapters 1 – 6 is covered in Math 65 so it should be  review for the students.  You may be able to cover some of these sections more quickly than indicated here, leaving yourself more time for the new material in chapters 7 – 8. 

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 1, 2 and 4 (12 hrs)

Exam 2:  Chapter 5 and Sections 6.1-6.2 (10 hrs)

Exam 3:  Sections 6.3, 6.6, 6.7, 6.8  and sections 7.1-7.4 (10.5 hrs)

Exam 4:  Sections 7.5-7.7 and Ch 8  (9.5 hrs)

Final Exam: Cumulative

Milton Rube, May 2004

Revised Joe Berland, Fall 2006 and May 2007

DESCRIPTION OF SUPPLEMENTARY MATERIALS

Section 1.3

 Meaning of the graph of an equation. Graphing , , and  by point-plotting. Identifying the domain and range of a function from its graph. Graphing using techniques of translation. Exercises.

 Later supplemental material that deals with translation will assume knowledge of the techniques discussed in this section. I highly recommend teaching graphing by translation at each section of the book where the supplemental material discusses translation, even if you choose to vary from my technique.

 Sections 2.3 and 2.4

Suggestions for proving slope-intercept form, avoiding the errors and incomplete argument in the text and using the concept of translation. Suggestion to prove the graph of (A and B not both zero) is a line if the graph of slope-intercept form is a line. Suggestion to prove point-slope form by translation arguments.

 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 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 8.3 

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