# 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
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 nth - 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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