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Algebra Syllbus

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MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics

VISION
The Mapua Institute of Technology shall be a global center of excellence in education by providing instructions that are current in content and state-of-the-art in delivery; by engaging in cutting-edge, high-impact research; and by aggressively taking on present-day global concerns.

MISSION
The Mapua Institute of Technology disseminates, generates, preserves and applies knowledge in various fields of study. The Institute, using the most effective and efficient means, provides its students with highly relevant professional and advanced education in preparation for and furtherance of global practice. The Institute engages in research with high socio-economic impact and reports on the results of such inquiries. The Institute brings to bear humanity’s vast store of knowledge on the problems of industry and community in order to make the Philippines and the world a better place.

BASIC STUDIES EDUCATIONAL OBJECTIVES
1. To provide students with a solid foundation in mathematics, physics, general chemistry and engineering drawing and to apply knowledge to engineering, architecture and other related disciplines 2. To complement the technical training of the students with proficiency in oral, written, and graphics communication. 3. To instill in the students human values and cultural refinement through the humanities and social sciences. 4. To inculcate high ethical standards in the students through its integration in the learning activities

MISSION
a b c d

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COURSE SYLLABUS 1. Course Code 2. Course Title 3. Pre-requisite 4. Co-requisite 5. Credit 6. Course Description : MATH 10 : ALGEBRA : None : None : 3 units : The course covers discussion on wide range of topics necessary to
meet the demands of college mathematics. The course discussion starts with algebraic equations and inequalities in one variable and their applications, then progresses to ratio, proportion and variation, systems of linear and non-linear equations and inequalities, functions and relations, polynomial functions, and sequence and series.

Course Title:

Date Effective:

Date Revised:

Prepared by:

Approved by:

ALGEBRA

1st Quarter SY 2012-2013

June 2012

Cluster I Committee

LD SABINO Subject Chair

Page 1 of 9

7. Student Outcomes and Relationship to Program Educational Objectives

Student Outcomes An ability to apply knowledge of mathematics, science, and engineering An ability to design and conduct experiments, as well as to (b) analyze and interpret data An ability to design a system, component, or process to meet (c) desired needs (a) (d) An ability to function on multi-disciplinary teams (e) An ability to identify, formulate, and solve engineering problems

Program Educational Objectives 1 2 3 4 √ √ √  √ √ √ √ √ √ √ √ √ √ √ √ √  √ √ √ √ √ √ √ √ √ √ √ √ √ √  √

(f) An understanding of professional and ethical responsibility (g) An ability to communicate effectively The broad education necessary to understand the impact of (h) engineering solutions in a global and societal context A recognition of the need for, and an ability to engage in life(i) long learning (j) A knowledge of contemporary issues (k) An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.

8. Course Outcomes (COs) and Relationship to Student Outcomes: Course Outcomes The student should be able to: 1. Solve linear equations and its Student Outcomes* d E f g h D D D D D D D D D D

a I D D D D

b

c

i

j

k

applications. 2. Solve quadratic equations and inequalities and its application. 3. Solve systems of equations and inequalities and its applications. 4. Evaluate functions and relations, interpret its graphs, and find roots of polynomial functions. 5. Perform application problems involving sequence and series and find specific term of a binomial expansion.

* Level: I- Introduced, R- Reinforced,

D- Demonstrated

Course Title:

Date Effective:

Date Revised:

Prepared by:

Approved by:

ALGEBRA

1st Quarter SY 2012-2013

June 2012

Cluster I Committee

LD SABINO Subject Chair

Page 2 of 9

9. Course Coverage :
WEEK TOPIC TLA AT COURSE OUTCOME

Orientation and Introduction to the Course Discussion on COs, TLAs, and ATs of the course Overview on student-centered learning and eclectic approaches to be used in the course
1

Equations • Definition of terms - Equation - Linear and Nonlinear Equations - Root or Solution of an Equation - Solution set - Inconsistent equation • Properties of Equality • Equivalent Equations • Linear Equation in one variable • Equation leading to the form ax +b =0 - Fractional Equation - Literal Equation - Equations Involving Radicals - Absolute Value Equation Applications of Linear Equation in One Variable • Modeling with Equations • Solving Word Problems - Number Problems - Digit Problems - Geometric Problems - Money and Coin Problems - Investment Problems - Age Problems - Mixture Problems - Uniform Motion Problems - Work Problems - Clock Problems Ratio, Proportion and Variation  Ratio - Definition - Ways of Writing Ratio - Characteristics of Ratio  Proportion - Definition of Terms Proportion/ Extremes/ Means/ True Proportion - Solving a Proportion - Transformation of a Proportion a. By Alteration b. By Inversion c. By Addition d. By Subtraction
Course Title: Date Effective:

Working through examples

Class Produced Reviewer #1

Working through examples Guided Learning Group Dynamics Class Produced Reviewer #2

2

CO1

Classwork #1 Think-PairShare Class Produced Reviewer #3

Date Revised:

Prepared by:

Approved by:

ALGEBRA

1st Quarter SY 2012-2013

June 2012

Cluster I Committee

LD SABINO Subject Chair

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3

 Variation Definition of Terms: Variation, Constant of Proportionality Direct Variation Inverse Variation Joint Variation Combined Variation LONG QUIZ 1 Quadratic Equations in One Variable • Definition of Terms - Pure Quadratic Equation - Complete Quadratic Equation • Nature of Roots of Quadratic Equation - Discriminant - Introduction to Complex Numbers • Solving Quadratic Equation - Solution by Factoring (The Zero-Product Property) - Solution by Completing the Square - Derivation of Quadratic Formula by Completing the Square - Solution by Quadratic Formula - Sum and Product of Roots • Equations Leading to Quadratic Equations Equations Involving Radicals Equations Involving Fractional Expressions Equations of Quadratic Type Equations Involving Fractional Powers Fourth-degree Equations of Quadratic Type • Applications of Quadratic Equation in One Variable - Number Problems - Money and Coin Problems - Geometric Problems - Uniform Motion Problems

Guided Discovery (collaborative approach)

Classwork #2 Class Produced Reviewer #4

4

Class Interaction/ Concept Mapping (Advance Reading Using) Lecture Cooperative Learning/Group Discussion

CO2

Course Title:

Date Effective:

Date Revised:

Prepared by:

Approved by:

ALGEBRA

1st Quarter SY 2012-2013

June 2012

Cluster I Committee

LD SABINO Subject Chair

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5

Inequalities • Symbols of Inequalities • Kinds of Inequalities - Absolute Inequality - Conditional Inequality • Properties of Inequalities • Solutions Set of an Inequality in One Variable - Set Notation - Interval Notation - Graphical Representation • Linear Inequalities in One Variable • Nonlinear Inequalities in One Variable - Polynomial Inequalities - Rational Inequalities - Absolute Value Inequalities

Guided Discovery (collaborative approach)

Class Produced Reviewer #5

LONG QUIZ 2 Systems of Equations and Inequalities • Definition of Terms • Classifications of Systems of Equations - Linear System - Nonlinear System • Systems of Linear Equations in Two Variables • Types of Linear System of Equations in Two Variables as to the Nature of their Solutions - Consistent or Independent System - Inconsistent System - Dependent System • Solving Linear System of Equations in Two Variables - Algebraic Elimination by Addition and Subtraction - Substitution - Graphical • Systems of Nonlinear Equations • Applications of System of Linear Equations - Number Problems - Money and Coin Problems - Investment Problems - Geometric Problems - Age Problems - Mixture Problems - Uniform Motion Problems

Lecture Cooperative Learning/Group Discussion Guided Discovery (collaborative approach)

6

Class Produced Reviewer #6 Classwork #3

CO3

Course Title:

Date Effective:

Date Revised:

Prepared by:

Approved by:

ALGEBRA

1st Quarter SY 2012-2013

June 2012

Cluster I Committee

LD SABINO Subject Chair

Page 5 of 9


7

Solution Set of an Inequality in Two Variables • Rules in Sketching the Graph of an Inequality in Two Variables • Solving System of Inequalities in Two Variables • Applications of Systems of Inequalities in Two Variables Graphical Solution

Dyadic Discussion

Class Produced Reviewer #7

LONG QUIZ 3 Relations, Functions and Graphs • Definition of Terms – Functions and Relations • Ways to Represent a Function – List of Ordered Pairs – Table of Values (numerical) – Mapping Diagram – Equation – Graph • Types of Functions – One-to-One Function – Many-to-One Function • Evaluating a Function • Domain and Range of Function – Set Notation – Interval Notation • Kinds of Functions and its Graph – Linear Function – Quadratic Function • Operations of Functions – Sum, Difference, Product, and Quotient – Composite Functions • One-to-One Function and Its Inverse

8

Group Discussion/ Concept Mapping Guided Discovery (collaborative approach)

Class Produced Reviewer #8 Classwork #4
CO4

Polynomial Functions • Dividing Polynomials – Synthetic Division • The Remainder Theorem • The Factor Theorem and its Converse • Fundamental Theorem of Algebra • Zeros of Polynomials – Number of Zeros – Multiplicity of Each Zero – Complex Conjugate Zeros Polynomial with Specified Zeros Descarte’s Rule of Signs Rational Zeros

Lecture Cooperative Learning/Group Discussion

Class Produced Reviewer #9 Classwork #5

• • •

LONG QUIZ 4
9

Sequences and Series • Definition of Terms: Sequence, Progression, Series • Kinds of Sequences
Course Title: Date Effective:

Guided Discovery (collaborative approach)
Date Revised:

Portfolio

Prepared by:

Approved by:

ALGEBRA

1st Quarter SY 2012-2013

June 2012

Cluster I Committee

LD SABINO Subject Chair

Page 6 of 9

10

– Infinite Sequence – Finite Sequence • Finding the Terms of a Sequence • Finding the nth Term of a Sequence • Partial Sums of a Sequence Arithmetic Sequences • Definition • The nth Term of an Arithmetic Sequence • Partial sums of an Arithmetic Sequence • Applications Harmonic Sequence • Definition • The nth Term of a Harmonic Sequence Geometric Sequence • Definition • The nth Term of a Geometric Sequence • Partial Sums of a Geometric Sequence • Infinite Geometric Series The Factorial of a Number • Definition / Examples The Binomial Theorem • Expanding a Binomial Using Pascal’s Triangle • The Binomial Coefficients • Expanding a Binomial Using Binomial Theorem • Finding the Specific Term in a Binomial Expansion

CO5

Dyadic Discussion Guided Discovery (collaborative approach)

LONG QUIZ 5
11 SUMMATIVE ASSESSMENT FINAL EXAMINATION CO 1, CO 2, CO3,CO4,CO5

10. Opportunities to Develop Lifelong Learning Skill The primary Learning Outcome for this course to develop lifelong learning skill is the Student’s Quantitative Reasoning, which is to understand and apply the mathematical principles in Algebra that will provide students with the needed working knowledge of mathematical concepts and methods, and an awareness of their relationship to increasingly complex world. 11. Contribution of Course to Meeting the Professional Component: General Education: Engineering Topics: Basic Sciences and Mathematics: 0% 0% 100%

12. Textbook: Algebra and Trigonometry by Cynthia Young, 2nd Ed., 2010

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Date Effective:

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ALGEBRA

1st Quarter SY 2012-2013

June 2012

Cluster I Committee

LD SABINO Subject Chair

Page 7 of 9

13. Course Evaluation Student performance will be rated based on the following: Weight (%) 11 Class Produced Reviewer (3 sets at 1.5% each) Classwork Class Produced Reviewer (2 sets at 1.5% each) Classwork Class Produced Reviewer (2 sets at 1.5% each) Classwork Class Produced Reviewer (2 sets at 1.5% each) Classwork Portfolio 4.5 1.2 11 3 1.2 11 3 1.2 11 3 1.2 11 2.7 25 100 10.64 11.69 Minimum Average for Satisfactory Performance(%)

Assessment Tasks Long Quiz 1 CO1 Course Works Long Quiz 2 CO2 Course Works Long Quiz 3 CO3 Course Works Long Quiz 4 CO4 Course Works Long Quiz 5 Course Works

10.64

10.64

9.59

Summative Assessment Final Examination TOTAL

17.5 70

The final grades will correspond to the weighted average scores shown below Final Average 96  X < 100 93  X < 96 90  X < 93 86  X < 90 83  X < 86 80  X < 83 76  X < 80 73  X < 76 70  X < 73 Below 70 Final Grade 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 5.00 (Fail)

13.1 Other Course Policies a. Attendance According to CHED policy, total number of absences by the students should not be more than 20% of the total number of meetings or 9 hrs for a three-unit-course. Students incurring more than 9 hours of unexcused absences automatically gets a failing grade regardless of class standing. Submission of Assessment Tasks (Student Outputs) should be on time, late submittal of coursework’s will not be accepted. Written Major Examination (Long Quiz and Final Exams) will be administered as scheduled. No special exam will be given unless with a valid reason subject to approval by the Chairman of the Mathematics Department. Course Portfolio will be collected at the end of the quarter. Language of Instruction Lectures, discussion, and documentation will be in English. Written and spoken work may receive a lower mark if it is, in the opinion of the instructor, deficient in English.
Date Effective: Date Revised: Prepared by: Approved by:

b.

c.

d. e.

Course Title:

ALGEBRA

1st Quarter SY 2012-2013

June 2012

Cluster I Committee

LD SABINO Subject Chair

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f.

Honor, Dress and Grooming Codes All of us have been instructed on the Dress and Grooming Codes of the Institute. We have all committed to obey and sustain these codes. It will be expected in this class that each of us will honor the commitments that we have made. For this course the Honor Code is that there will be no plagiarizing on written work and no cheating on exams. Proper citation must be given to authors whose works were used in the process of developing instructional materials and learning in this course. If a student is caught cheating on an exam, he or she will be given zero mark for the exam. If a student is caught cheating twice, the student will be referred to the Prefect of Student Affairs and be given a failing grade. Grave misconduct other than cheating will likewise be given a failing grade.

g.

Consultation Schedule Consultation schedules with the Professor are posted outside the Math Faculty room and in the School’s web-page (http://.mapua.edu.ph). It is recommended that the student first set an appointment to confirm the instructor’s availability.

14. Other References 14.1 Books a. College Algebra and Trigonometry by Louis Leithold, International Ed., 2001 b. College Algebra and Trigonometry by Matk Dugopolski, 2 nd Ed. c. College Algebra, enhances with Graphing Utilities by Michael Sullivan and Michael Sullivan III, 2 nd Ed. d. College Algebra and Trigonometry by Nax Sobel and Lemer Norbert, 5th Ed., 1998 e. Applied Algebra and Trigonometry by Linda Davis, 3 rd Ed., 2003 f. Algebra and Trigonometry by James Stewart, Lothar Redlin and Saleem Watson, 2 nd ed, 2007 14.2 Websites a. www.homeschoolmath.net/online/algebra.php b. www.onlinemathlearning.com/college-algebra.html c. www.onlinemathlearning.com/algebra-math-games.html d. www.wtamu.edu/academic/anns/mps/math/.../col_algebra/index.html e. www.pct.edu/schools/is/coreCourses/mathLinks.html 15. Course Materials Made Available: Course schedules for lectures and quizzes Sample of assignments/problem sets of students Sample of written examination of students End-of-course self assessment

16.

Committee Members: Course Cluster Chair: Raquel B, Teodoro CQI Cluster Chair: Dionisia M. Lanuza Members: Linda B. Catan SheilaDorreen F. San Pedro Floro Deogracias G. Llacuna James Alfred M. Escalona

Course Title:

Date Effective:

Date Revised:

Prepared by:

Approved by:

ALGEBRA

1st Quarter SY 2012-2013

June 2012

Cluster I Committee

LD SABINO Subject Chair

Page 9 of 9

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