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A premier university in CALABARZON, offering academic programs
and related services designed to respond to the requirements of the
Philippines and the global economy, particularly, Asian countries.




The University shall primarily provide advanced education,
professional, technological and vocational instruction in agriculture,
fisheries, forestry, science, engineering, industrial technologies, teacher
education, medicine, law, arts and sciences, information technology and
other related fields. It shall also undertake research and extension
services, and provide a progressive leadership in its areas of
specialization.




                                     ii
In pursuit of college mission/vision the college of education is committed
to develop the full potential of the individuals and equip them with
knowledge, skills and attitudes in teacher education allied fields
effectively responds to the increasing demands, challenge and
opportunities of changing time for global competitiveness.




   1. To serve as positive and powerful role models in the pursuit of
      learning thereby maintaining high regards to professional growth.

   2. Focus on the significance of providing whole some and desirable
      learning environment.

   3. Facilitate learning process in diverse types of learners.

   4. Use varied learning approaches and activities, instructional
      materials and learning resources.

   5. Use assessment data plan and revise teaching – learning plans.
   6. Direct and strengthen the links between school and community
      activities.

   7. Conduct research and development in Teacher Education and
      other related.




                                     iii
This Teacher’s Guide Module entitled “Advanced Algebra for fourth year
High School Module in Polynomial and Rational Function” is part of the
requirements in Educational Technology 2 under the revised curriculum for Bachelor
in Secondary Education based on CHED Memorandum Order (CMO)-30, Series of
2004. Educational Technology 2 is a three (3)-unit course designed to introduce both
traditional and innovative technologies to facilitate and foster meaningful and
effective learning where students are expected to demonstrate a sound
understanding of the nature, application and production of the various types of
educational technologies.

        The students are provided with guidance and assistance of selected faculty
members of the College through the selection, production and utilization of
appropriate technology tools in developing technology-based teacher support
materials. Through the role and functions of computers especially the Internet, the
student researchers and the advisers are able to design and develop various types
of alternative delivery systems. These kinds of activities offer a remarkable learning
experience for the education students as future mentors especially in the preparation
of instructional materials.

         The output of the group’s effort may serve as an educational research of the
institution in providing effective and quality education. The lessons and evaluations
presented in this module may also function as a supplementary reference for
secondary teachers and students.



                                                          FOR-IAN V. SANDOVAL
                                                        Computer Instructor / Adviser
                                                         Educational Technology 2




                                                            LYDIA R. CHAVEZ
                                                          Dean College of Education

                ACKNOWLEDGEMENT

                                          iv
The authors wish to express their sincerest gratitude to the following persons
who gave their support, cooperation and assistance in accomplishing this module.

       To Mrs. Delia F, Mercado, their co-author, for her profound help and
assistance, support and professional expertise to us.

      To Prof. Corazon N. San Agustin, for her guidance and supervision In
Educational Technology 1.

      Their instructor, Mr. For-Ian V. Sandoval, for his untiring effort, suggestion,
guidance and supervision.

        Lastly, the authors wish to extend their gratitude to their families for giving
their love, prayers, inspiration and financial support. And for all the sacrifices
hardships of all the authors to finish their module.

       Above all the authors give their overwhelming gratitude to our God Almighty,
through His guidance, spiritual strength and for wisdom He has extensively
showered us.




                                           v
Advanced Algebra for fourth year high school was essentially prepared

for the student’s/learner’s utility in achieving their aims to become a good conqueror

in Mathematics for our daily living.

          As the problems in learning mathematics, this module gives you a promising

knowledge that can fulfill your learning capacity to much gain and understand the

thought of learning Mathematics.

       This module includes the following chapters as the contents of this:

                Chapter 1 Polynomial Function

                Chapter 2 Rational Function

       In every chapter there are lessons which discuss some specific and applied

topics to promote learners knowledge enhancement.

       Also in each chapter, at the lessons there are challenges formed for the

students’ application of their skills and progressive knowledge after analyzing each

lesson.

       It is therefore the ultimate aim of the authors is to prepare and make the

students/learners a good individual dealing with mathematical problem particularly

Functions.




                                           vi
vii
PERSONAL INFORMATION

Name:                  Maria Wilnes Magno Calalo
Address:               Palacio Ext. Balian, Pangil, Laguna
Date of Birth:          November 18, 1988
Civil Status:          Single

Parents:

       Father:         Wilfredo Magnaye Calalo
       Mother:         Cocepcion Magno Calalo

EDUCATIONAL ATTATINMENT:

Elementary:       Victor O. De Guia Memorial Elementary School
                 Candelaria St. Balian, Pangil, Laguna
                 2000-2001

Secondary:       Balian National High School
                 Candelaria St. Balian Pangil, Laguna
                  2004-2005

Tertiary:         Laguna State Polytechnic University
                 Siniloan Campus
                 Siniloan, Laguna
                 2007-2011

Course:          Bachelor of Secondary Education
Major:            Mathematics




                                       viii
PERSONAL INFORMATION

Name:                Jennilyn Fabul Balbalosa
Address:             167 Gen. Luna St. Siniloan, Laguna
Date of Birth:        September 25, 1990
Civil Status:         Single

Parents:

       Father:         Wilson Pangito Balbalosa
       Mother:         Pilita Fabul Balbalosa

EDUCATIONAL ATTATINMENT:

Elementary: Angelo Ong Javier Memorial Elementary School
                Siniloan, Laguna
                2002-2003
Secondary:      Laguna State Polytechnic College
                Siniloan, Laguna
                2006-2007

Tertiary:         Laguna State Polytechnic University (LSPU)
                 Siniloan Campus
                 Siniloan, Laguna
                 2007-2011

Course:          Bachelor of Secondary Education ( BSE)

Major:            Mathematics




                                      ix
PERSONAL INFORMATION

Name:                  John Wilson Magno Calalo
Address:               Palacio St. Balian, Pangil, Laguna
Date of Birth:          September 27, 1990
Civil Status:           Single

Parents:

         Father:        Wilfredo Magnaye Calalo
         Mother:        Concepcion Magno Calalo

EDUCATIONAL ATTATINMENT:

Elementary:          Carmona Elementary School
                   Cavite
                   2002-2003

Secondary:         Balian National High School
                   Candelaria St. Balian, Pangil, Laguna
                   2006-2007

Tertiary:           Laguna State Polytechnic University
                   Siniloan Campus
                   Siniloan, Laguna
                   2007-2011

Course:            Bachelor of Secondary Education

Major:              Mathematics




                                          x
PERSONAL INFORMATION

Name:                 Daryl Natividad Sacay
Address:                  Southern Homes Subd. Siniloan, Laguna
Date of Birth:     September 30, 1990
Civil Status:          in relationship

Parents:

       Father:     Daniel Romero Sacay
       Mother:     Estelita Natividad Sacay

EDUCATIONAL ATTATINMENT:

Elementary:         Siniloan Elementary School
                 Siniloan, Laguna
                 2002-2003

Secondary:       Laguna State Polytechnic College
                 Siniloan, Laguna
                 2006-2007

Tertiary:         Laguna State Polytechnic University
                 Siniloan Campus
                 Siniloan, Laguna
                 2007-2011

Course:          Bachelor of Secondary Education

Major:                 Mathematics




                                       xi
xii
PERSONAL INFORMATION:


Name:          For-Ian Villanueva Sandoval
Address:       # 8 Rizal St. Siniloan Laguna
Birthday:       April 5, 1979
Contact No.: (0916) 221-77-11
E-mail Add: fvsandoval@yahoo.com
               Educational Background
Elementary: Palasan Elementary School, Sta. Cruz Laguna
               (1985-1992)
Secondary: Union College of Laguna, School, Sta. Cruz Laguna
               (1992-1996)
Tertiary:     Far Eastern University
Course:        Bachelor of Science in Math
Major:        Computer Science




                                xiii
PERSONAL INFORMATION:

Name:          Delia F. Mercado
Address:       Bagong Pook, Sta. Maria, Laguna
Birthday:      April 24, 1955
Contact No.: 09282794326


              Educational Background
Elementary: Sta. Maria Elementary School
               Sta. Maria, Laguna
               (1967-1968)
Secondary: Sta Maria Academy
               Sta. Maria, Laguna
               (1971-1972)
Tertiary:      San Pablo Colleges
Course:         Bachelor in Secondary Education
Major:           Mathematics


                                xiv
xv

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002 Vmg Os

  • 1. A premier university in CALABARZON, offering academic programs and related services designed to respond to the requirements of the Philippines and the global economy, particularly, Asian countries. The University shall primarily provide advanced education, professional, technological and vocational instruction in agriculture, fisheries, forestry, science, engineering, industrial technologies, teacher education, medicine, law, arts and sciences, information technology and other related fields. It shall also undertake research and extension services, and provide a progressive leadership in its areas of specialization. ii
  • 2. In pursuit of college mission/vision the college of education is committed to develop the full potential of the individuals and equip them with knowledge, skills and attitudes in teacher education allied fields effectively responds to the increasing demands, challenge and opportunities of changing time for global competitiveness. 1. To serve as positive and powerful role models in the pursuit of learning thereby maintaining high regards to professional growth. 2. Focus on the significance of providing whole some and desirable learning environment. 3. Facilitate learning process in diverse types of learners. 4. Use varied learning approaches and activities, instructional materials and learning resources. 5. Use assessment data plan and revise teaching – learning plans. 6. Direct and strengthen the links between school and community activities. 7. Conduct research and development in Teacher Education and other related. iii
  • 3. This Teacher’s Guide Module entitled “Advanced Algebra for fourth year High School Module in Polynomial and Rational Function” is part of the requirements in Educational Technology 2 under the revised curriculum for Bachelor in Secondary Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies. The students are provided with guidance and assistance of selected faculty members of the College through the selection, production and utilization of appropriate technology tools in developing technology-based teacher support materials. Through the role and functions of computers especially the Internet, the student researchers and the advisers are able to design and develop various types of alternative delivery systems. These kinds of activities offer a remarkable learning experience for the education students as future mentors especially in the preparation of instructional materials. The output of the group’s effort may serve as an educational research of the institution in providing effective and quality education. The lessons and evaluations presented in this module may also function as a supplementary reference for secondary teachers and students. FOR-IAN V. SANDOVAL Computer Instructor / Adviser Educational Technology 2 LYDIA R. CHAVEZ Dean College of Education ACKNOWLEDGEMENT iv
  • 4. The authors wish to express their sincerest gratitude to the following persons who gave their support, cooperation and assistance in accomplishing this module. To Mrs. Delia F, Mercado, their co-author, for her profound help and assistance, support and professional expertise to us. To Prof. Corazon N. San Agustin, for her guidance and supervision In Educational Technology 1. Their instructor, Mr. For-Ian V. Sandoval, for his untiring effort, suggestion, guidance and supervision. Lastly, the authors wish to extend their gratitude to their families for giving their love, prayers, inspiration and financial support. And for all the sacrifices hardships of all the authors to finish their module. Above all the authors give their overwhelming gratitude to our God Almighty, through His guidance, spiritual strength and for wisdom He has extensively showered us. v
  • 5. Advanced Algebra for fourth year high school was essentially prepared for the student’s/learner’s utility in achieving their aims to become a good conqueror in Mathematics for our daily living. As the problems in learning mathematics, this module gives you a promising knowledge that can fulfill your learning capacity to much gain and understand the thought of learning Mathematics. This module includes the following chapters as the contents of this: Chapter 1 Polynomial Function Chapter 2 Rational Function In every chapter there are lessons which discuss some specific and applied topics to promote learners knowledge enhancement. Also in each chapter, at the lessons there are challenges formed for the students’ application of their skills and progressive knowledge after analyzing each lesson. It is therefore the ultimate aim of the authors is to prepare and make the students/learners a good individual dealing with mathematical problem particularly Functions. vi
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  • 7. PERSONAL INFORMATION Name: Maria Wilnes Magno Calalo Address: Palacio Ext. Balian, Pangil, Laguna Date of Birth: November 18, 1988 Civil Status: Single Parents: Father: Wilfredo Magnaye Calalo Mother: Cocepcion Magno Calalo EDUCATIONAL ATTATINMENT: Elementary: Victor O. De Guia Memorial Elementary School Candelaria St. Balian, Pangil, Laguna 2000-2001 Secondary: Balian National High School Candelaria St. Balian Pangil, Laguna 2004-2005 Tertiary: Laguna State Polytechnic University Siniloan Campus Siniloan, Laguna 2007-2011 Course: Bachelor of Secondary Education Major: Mathematics viii
  • 8. PERSONAL INFORMATION Name: Jennilyn Fabul Balbalosa Address: 167 Gen. Luna St. Siniloan, Laguna Date of Birth: September 25, 1990 Civil Status: Single Parents: Father: Wilson Pangito Balbalosa Mother: Pilita Fabul Balbalosa EDUCATIONAL ATTATINMENT: Elementary: Angelo Ong Javier Memorial Elementary School Siniloan, Laguna 2002-2003 Secondary: Laguna State Polytechnic College Siniloan, Laguna 2006-2007 Tertiary: Laguna State Polytechnic University (LSPU) Siniloan Campus Siniloan, Laguna 2007-2011 Course: Bachelor of Secondary Education ( BSE) Major: Mathematics ix
  • 9. PERSONAL INFORMATION Name: John Wilson Magno Calalo Address: Palacio St. Balian, Pangil, Laguna Date of Birth: September 27, 1990 Civil Status: Single Parents: Father: Wilfredo Magnaye Calalo Mother: Concepcion Magno Calalo EDUCATIONAL ATTATINMENT: Elementary: Carmona Elementary School Cavite 2002-2003 Secondary: Balian National High School Candelaria St. Balian, Pangil, Laguna 2006-2007 Tertiary: Laguna State Polytechnic University Siniloan Campus Siniloan, Laguna 2007-2011 Course: Bachelor of Secondary Education Major: Mathematics x
  • 10. PERSONAL INFORMATION Name: Daryl Natividad Sacay Address: Southern Homes Subd. Siniloan, Laguna Date of Birth: September 30, 1990 Civil Status: in relationship Parents: Father: Daniel Romero Sacay Mother: Estelita Natividad Sacay EDUCATIONAL ATTATINMENT: Elementary: Siniloan Elementary School Siniloan, Laguna 2002-2003 Secondary: Laguna State Polytechnic College Siniloan, Laguna 2006-2007 Tertiary: Laguna State Polytechnic University Siniloan Campus Siniloan, Laguna 2007-2011 Course: Bachelor of Secondary Education Major: Mathematics xi
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  • 12. PERSONAL INFORMATION: Name: For-Ian Villanueva Sandoval Address: # 8 Rizal St. Siniloan Laguna Birthday: April 5, 1979 Contact No.: (0916) 221-77-11 E-mail Add: fvsandoval@yahoo.com Educational Background Elementary: Palasan Elementary School, Sta. Cruz Laguna (1985-1992) Secondary: Union College of Laguna, School, Sta. Cruz Laguna (1992-1996) Tertiary: Far Eastern University Course: Bachelor of Science in Math Major: Computer Science xiii
  • 13. PERSONAL INFORMATION: Name: Delia F. Mercado Address: Bagong Pook, Sta. Maria, Laguna Birthday: April 24, 1955 Contact No.: 09282794326 Educational Background Elementary: Sta. Maria Elementary School Sta. Maria, Laguna (1967-1968) Secondary: Sta Maria Academy Sta. Maria, Laguna (1971-1972) Tertiary: San Pablo Colleges Course: Bachelor in Secondary Education Major: Mathematics xiv
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