Math 4 Intermediate Algebra II
I. COURSE DESCRIPTION
Math 4 is a developmental course covering second year algebra.
II. PREQUSITES
Successful completion of MTH 3 or appropriate score on the placement test.
Students will not be
allowed in the course without the required prequisites .
III. INTRODUCTION
This course is designed to introduce and develop basic algebraic concepts and
skills listed
in the outline below. A student must have an 80% average to complete the course
successfully
and receive a grade of "S" – satisfactory; otherwise, the student will receive a
grade of "R" -
reenroll, or "U" - unsatisfactory and have to repeat the course.
IV. INSTRUCTIONAL MATERIALS
Textbook: Introductory and Intermediate Algebra, by Miller, O'Neill and Hyde;
McGraw Hill,
2006. ISBN: 0073298077 REQUIRED
Student's Solution Manual, ISBN: 0073305235 OPTIONAL
See Section IX for material available in the Math Lab and LRC.
V. MATERIAL TO BE COVERED
Unit I | Review Chapter 3 (sections 3.2 -3.5) | 2.5 weeks |
Chapter 7 (omit section 7.6) | ||
Unit II | Chapter 8 & Section 12.1 | 2 weeks |
Unit III | Chapter 9 | 3 weeks |
Unit IV | Review Chapter 5 | 3 weeks |
Chapter 10 (omit 10.4) | ||
Unit V | Chapter 11 | 2 weeks |
Unit VI | Chapter 12 | 2.5 weeks |
VI. BASIC CONCEPTS
Unit 1 | Systems of Linear Equations |
3.2-3.5 Review of Graphing Linear Equations (see Notes to the Instructor #1) | |
7.1 Solving Systems of Linear Equations by Graphing | |
7.2 Solving Systems of Equations by Using the Substitution Method | |
7.3 Solving Systems of Equations by Using the Addition Method | |
7.4 Applications of Systems of Linear Equations in Two Variables | |
7.5 Systems of Linear Equations in Three Variables and Applications | |
7.6 OMIT | |
Unit II | Introduction to Relations and Functions |
8.1 Introduction to Relations | |
8.2 Introduction to Functions (see Notes to the Instructor #2) | |
8.3 Graphs of Basic Functions (see Notes to the Instructor #3) | |
12.1 Algebra and Composition of Functions | |
8.4 Variation | |
Unit III | Radicals and Complex Numbers |
9.1 Definition of an n^{th} - Root | |
9.2 Rational Exponents (see Notes to the Instructor #4) | |
9.3 Simplifying Radical Expressions | |
9.4 Addition and Subtraction of Radicals | |
9.5 Multiplication of Radicals | |
9.6 Rationalization | |
9.7 Radical Equations | |
9.8 Complex Numbers (see Notes to the Instructor #5) | |
Unit IV | Quadratic Equations and Quadratic Functions |
5.1-5.6 Review of Factoring (see Notes to the Instructor #6) | |
10.1 Completing the Square and Square Root Property (see Notes to the Instructor #7) | |
10.2 Quadratic Formula (see Notes to the Instructor #8) | |
10.3 Equations Quadratic in Form | |
10.4 OMIT | |
10.5 Vertex of a Parabola and Applications (see Notes to the Instructor #9) | |
Unit V | More Equations and Inequalities |
11.1 Compound Inequalities | |
11.2 Polynomial and Rational Inequalities (see Notes to the Instructor #10) | |
11.3 Absolute Value Equations | |
11.4 Absolute Value Inequalities | |
11.5 Linear Inequalities in Two Variables | |
Unit VI | Exponential and Logarithmic Functions |
12.2 Inverse Functions | |
12.3 Exponential Functions | |
12.4 Logarithmic Functions | |
12.5 Properties of Logarithims | |
12.6 The Irrational Number e | |
12.7 Exponential and Logarithmic Equations (see Notes to the Instructor #11) |
VII | Suggested Weekly Schedule - 15 Week Semester | |
Week 1 | Review 3.2 – 3.5, 7.1, 7.2 | |
Week 2 | 7.3 – 7.5 (omit 7.6) | |
Week 3 | Test 1, 8.1, 8.2 | |
Week 4 | 8.2, 8.3, 12.1 | |
Week 5 | 8.4, Test 2, 9.1, 9.2 | |
Week 6 | 9.3 – 9.5 | |
Week 7 | 9.6 – 9.8 | |
Week 8 | Test 3, Review Chapter 5 | |
Week 9 | 10.1, 10.2 | |
Week 10 | 10.3, 10.5 (omit 10.4) | |
Week 11 | Test 4, 11.1, 11.2 | |
Week 12 | 11.3 – 11.5 | |
Week 13 | Test 5, 12.2, 12.3 | |
Week 14 | 12.4 – 12.6 | |
Week 15 | 12.7, Test 6 | |
Final Exam to be given during scheduled exam period. | ||
VIII | Suggested Weekly Schedule - 10 Week Semester | |
Week 1 | Review 3.2 – 3.5, 7.1 – 7.4 | |
Week 2 | 7.5, Test 1, 8.1, 8.2 (omit 7.6) | |
Week 3 | 8.3, 12.1, 8.4, Test 2 | |
Week 4 | 9.1 – 9.5 | |
Week 5 | 9.6 – 9.8, Test 3, Review of Chapter 5 | |
Week 6 | Review Chapter 5, 10.1, 10.2 | |
Week 7 | 10.3, 10.5, Test 4 (omit 10.4) | |
Week 8 | 11.1 -11.4 | |
Week 9 | 11.5, Test 5, 12.2 – 12.4 | |
Week 10 | 12.5 – 12.7, Test 6, Final Exam |
IX ADDITIONAL MATERIAL AVAILABLE TO STUDENTS
TCC Student ID Required to Use the First 3 Resources
1. Complete Solutions Guide, available in the Math Lab
2. Videos available on DVD in LRC, Media Resources
3. MathZone Web Site
X NOTES TO THE INSTRUCTOR
1. Students should be familiar with chapter 3. Cover this
material as a quick review. Stress
graphing linear equations using Slope -Intercept form.
2. Section 8.2 contains a lot of material. It will take several classes to cover
the material.
3. Students should be able to graph basic functions by “ plotting points .” Do not
cover the graphs of
rational functions (omit problems 14, 51, 52 on page 650).
4. In section 9.2, students should be able to convert from rational exponents to
radical form and
vice-versa. Objective 3 (properties of rational exponents) is optional.
5. In section 9.8, omit Objective 2 (powers of “i”).
6. Chapter 5 should be reviewed quickly (at most use about half of a week).
7. Section 10.1 should be covered as two lectures. One on the square root
property and one on
completing the square.
8. Emphasize section 10.2. Several classses should be used for students to
master this topic.
9. Omit section 10.4. In section 10.5, students should be able to graph
quadratic functions using the
vertex formula (Objective 2). In section 10.5, objective 1 should not be
covered.
10. In section 11.2, omit Objective 1 (solving inequalities graphically).
11. Section 12.7 should be covered as two sections. Solve logarithmic equations
in one lecture and
exponential equations in another.
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