VISION

The Mapua Institute of Technology shall be a global center of excellence in education by providinginstructitns that are cunent in content and state-of-the-art in delivery; by engaging in cuttrng-edge,high-impact research; and by aggressively takrng on present-day global concems.

MISSIONThe 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 ofglobal practice.ThJ institute engages in research with high socio-cconomic 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 p1ace.

BASIC STUDIES EDUCATIONAL OBJECTIVES MISSIONa b c d

I . To provide sludents with a solid foundation in mathematics, pltysics, generalchemistry and engineering drawing ar.rd to apply knowledge to engineering,architechrre and other related disciplines2. To conplement the tecbnical training of the students with proficiency in oral,written. and sranlics commur cation.3. To instill in the students human values and cultural reFtnernent tluough thehumanities and social sciences.4. To inculcate high ethical standards in the sludents through its integration inthe Ieamins activities

1. Course Code

2. Course Title

Pre-requisitc

Co-requisite

Credit

6. Course Description

3.

4.

:1.

MAPTA INSTITUTE OF TECHNOLOGYDepartmenl of Malhemal ics

COt]RSE SYLLABUS

MATII 10

ALGEBRA

None

None

3 units

The course covers discussion on wide range of topics necessary tomeet the demands of college mathematics. The course discussionstarts with algebraic equations and inequalities in one variable andtheir applications, then progresses to ratio, proportion andvariation, systems of linear and non-linear equations andinequalities, functions and relations, polynomial functions, and

AUThIORSZEDCOPYCourse Title:

ALGEBRA

sequence and series.

Student Outcomes

Basic StudiesEducationalObiectives

1 1 3 4

(a) An ability to apply knowledge of mathematics, science, andengineering

(b) An ability to design and conduct experiments, as well as tornalyze and interpret data

(") An ability to design a system, component, or process to meetdesired needs(d) An ability to function on n-rulti-disciplinary teams

(e) An ability to identify, formulate, and solve engineeringoroblems

(0 An understanding of professional and ethical responsibility(e) An abilitv To communicate eflectivelv(h) Ihe broad education necessary to understand the impact of

engineering solutions in a global and societal context

(D A recognition of the need for, and an ability to engage in life-long leamins

0) A knowledge of contemporary rssues(k) An ability to use the techniques, skills, and modem engineering

lools necessary for engineering practice.

7, Student Outcomes and Relationship to Basic Studies Educational Objectives

8. Course Outcomes (COs) and Relationship to Student Outcomes:

* Level: I- Introduced, R- Reinforced, D- Demonstrated

Course OutcomesThe student should be able to:

Student Outcomes*a b d E f h 1 k

1. Solve linear equations and itsa DDlications. I D D

2. Solve quadratic equations andineq ualities and its application. D

D D

3. Solve systems of equations andineo ualities and its aDDlications.

D D D

4, Evaluate functions and relations,interpret its graphs, andfind roots of oolvnomial functions.

D D D

5, Perform application problems involvingsequence and series and find specificterm of a binomial exDansion.

D D D

Course Title:

ALGEBRA

AUTr.f Offirf,EF

9. Course Cov

Ft#fr?i:8,OF'Y

Orientation and Introduction tothe CourseDiscussion on Cos, TLAS, and ATs ofthe cou rseOverview on stu d e nt-ce nte redlearning and eclectic approaches tobe used in the course

Class ProducedReviewer # 1

Workingthrough

examples

Equations. Definition of terms

- Equation- Linear and N o n linear

Eq u atio ns- Root or Solution of an

Equation- Solution set- Inconsistent eq uation

. Properties of Eq u a lity

. Equ iva lent Equations

. Linear Equation in one variable

. Equation leading to theform ax *b =0

- Fractional Eq uation- Litera I Eq uation- Eq uations Involving

Rad ica ls- Absolute Value Equ ation

Class Prod ucedReviewer #2

Applications of Linear Equation inOne variable

. Modeling with Eq uations

. Solving Word Problems- Number Problems- Digit Problems- Geometric Problems- Money and Coin Problems- Investment Problems- Age Problems- Mixture Problems- Uniform lYotion Problems- Work Problems- Clock Problems

Workingth roug h

examples

GuidedLea rn ing

GroupDynamics

Classwork # 1

class ProducedReviewer #3

Ratio, Proportion and variationr Ratio

- Defin itionWays of Writing Ratio

- Characte ristics of Ratro. Proportion

- Defin ition of TermsProportion/ Extremes/Means/ True Proportion

- Solving a Proportion- Transformation of a ProPortion

a. By Alterationb. By Inversionc. By Additiond. By Su btraction

Think-Pair-Share

Course Titlei

ALGEBRA

. va riatio n- Definition of Terms:

Variation, Consta nt ofProportiona litY

- Direct Va riation- Inverse Va riation- Jo int Variation- Combined Variation

Classwork #2

ClassP rod u ced

Reviewer #4

GuidedDiscovery

(colla borativeapproach)

Quadratic Equations in OneVariable

r Definition of Terms- Pure Quad ratic Equation- Complete Quad ratic

Eq u atio n. Nature of Roots of Quadratic

Eq u atio n- Discriminant- Introd uctio n to Complex

Numbers. Solving Quad ratic Equation

- Solution by Factoring(The Ze ro- Prod uct

ProPerty)- Solution by Completing

the Sq ua re- De rivation of Quadratic

Formula by Completingthe Square

- Solution by QuadraticFormula

- Sum and Product of Roots

ClassInteraction/

ConceptMa pping(Advance

Reading Using )

Lectu reCooperative

Lea rn ing/G rou pDiscussion

. Equations Leading toQuadratic Equations- Eq u atio ns Involving

Radicals- Eq uations Involving

Fractional Expressions- Eq uations of Quadratic

Type- Eq uations Involving

Fractional Powers- Fourth-degree Eq uations

of Quad ratic Type. Ap plications of Quadratic

Equation in One Variable- N umber Problems- Money and coin

Problems- Geometric Problems- U niform Motion Problems

Cours Titlel

ALGEBRA

AUT HSTqE S,HN

5Inequalities. Symbols of Inequalities. Kinds of Inequ a lities

- Absolute Ineq u a lity- Conditional InequalitY

. Properties of I neq ua lities

. Solutions Set of an Inequalityin One Variable

- Set Notation- Interval Notation- Graphical Representation

. Linear Inequalities in OneVariable

. Nonlinear Inequalities in OneVariable

- Polynomial Inequalities- Rationa I I neq ualities- Absolute Value Inequa lities

GuidedDiscovery

(collaborativeapproach)

Class ProducedReviewer #5

LONG QUIZ 2

6

Systems of Equations andInequalities

. Definition of Terms

. Classifications of Systems ofEquations

- Linear System- Nonlinear System

. Systems of Linear Equations inTwo Va ria bles

. Types of Linear System ofEquations in Two Variables asto the Nature of their Solutions

- Consistent or IndependentSystem

- I nconsiste nt System- Dependent System

. Solving Linear System ofEq uatio ns in Two Va riables

- Algebraic Elimination byAddition and Subtraction

- Su bstitution- Graphical

. Systems of Nonlinear Equations

Lectu re

CooperativeLea rning/Group

D iscu ssio n

Gu idedDiscovery

(colla boraliveapproach)

Class ProducedReviewer #6

Classwork #3

co3

. Applications of System ofLinea r Eq uatio ns

- Number Problems- Money and Coin Problems- Investment Problems- Geometric Problems- Age Problems- Mixture Problems- Uniform Motion Problems

AUT14ffigtETffiD

Course Titlel

ALGEBRA

CQPY

7. Solution Set of an Inequality inTwo Variables

. Rules in Sketching the craph ofan Inequality in Two Variables

. Solving System of lnequalitiesin Two Va ria bles

. Applications of Systems ofInequalities in Two VariablesGraphical Solution

DyadicDiscussion

Class Prod ucedReviewer #7

LONG QU tz3

a

Relations, Functions and Graphs. Definition of Terms

- Fu nctions and Relations

. Ways to Represent a Function- List of Ordered Pairs- Table of Values (numerical)- Mapping Diagram- Eq uation-

Graph. Types of Fu nctions

- One-to-One Function- f4 a ny-to- One Function

. Eva luating a FunctionI Domain and Range of Function- Set Notation- Interval Notation

o Kinds of Functions and itsGraph- Linear Fu nction- Quad ratic Fu nction

. O perations of Functions-

Sum, Differe nce, product,and Qu otient

- Composite Fu nctions. One-to-One Function and Its

Inverse

Grou pDiscussion/

ConceptMa pp ing

cuidedDiscovery

(collaborativeapproach)

Class Prod ucedReviewer #8

Classwork #4

co4

Polynomial Functions. Dividing Polynomials

- Synthetic Division. The Remainder Theorem. The Factor Theorem and its

Converse. Fundamental Theorem of

AlgebraLecture

CooperativeLearning/croup

Discussion

Class ProducedReviewer #9

Classwork # 5

9

. Zeros of Polynomials-

Number of Zeros- Multiplicity of Each Zero- Complex Conj ugate Zeros

. Polynomial with SpecifiedZeros

. Descarte's Rule of Signs

. Rationa I Zeros

LONG QUIZ 4

Sequences and Series. Definition of Terms: Sequence,

Progression, Se ries. Kinds of Seq ue n ces

GuidedDiscovery

(colla bo rativeapproach )

Portrotio A ! J-rHflFs?-'.1'"/"{;"'

,tt' ':\ 'Course Titlei

ALGEBRA

Date Effctiv:

1st QuartersY 2012 2013

June 2012l\Jfio&a

dh,lster ICommittee

oowl;^*,4 o sasrruo

Subject Chair

(-Page 6 of 9

t\

- Infinite Sequence

- Finite Sequence

. Finding the Terms of aSequence

. Finding the nth Term of aSequence

. Partial Sums of a SequenceArithmetic Sequences

. Defin itiono The nth Term of an Arithmetic

Sequenceo Partial sums of an Arithmetic

Sequence

DyadicDiscussion

GuidedDiscovery

(colla bo rativeapproach)

Harmonic Sequence. Defin ition. The nth Term of a Harmonic

Sequence Geometric Sequence. Defin itiono The nth Term of a Geometric

Sequencer Partial Sums of a Geometric

Seq u ence. Infinite Geometric Series

The Factorial of a Number. Defin ition / Examples

The Binomial Theorem. Expanding a Binomial Using

Pascal's Tria ng le. The Binomial Coefficie nts. Expanding a Binomial Using

Binomial Theorem. Finding the Specific Term in a

Binomial ExoansioLONG QUIZ 5

co I, co 2l

10. Opportunities to Develop Lifelong Learning Skill

The primary Leaming Outaome for this course to develop lifelong leaming skill is the Student's Quantitative Reasoning,whici is to unclerstand and apply ttre rnathematical principles in Algebra that wilt provide snrdents with the needed workingknowledge of mathematical concepts and methods, and an awareness of their relationship to increasingly complex world.

11. Contribution of Course to l\{eeting the Professional Component:

0%jyotoo"/"

General Education:Engineering Topics:Basic Sciences and Mathematics:

12. Textbook: Algebra and Trigonometry by Cyntlia Young, 2"d Ed., 2010

AUTFI*n'! ? Fn1.r

Course Title:

ALGEBRA

Date Effective:

1st QuartersY 2012-2013

Date Revisdi

lune 2012

Prepared by:lWta&d

rrtrkter ICommittee

LD SABINO -Page 7 of 9

Assessment Tasks Weight(%\Minimum Average for

SatisfactoryPerformance(Yo)

co1Lons Ouiz I ll

I1.69Course lVorks

Class Produced Reviewer(3 sets at 1.57o each) 4.5Classrvork 1.2

c02Lous Ouiz 2 11

10.64Course WorksClass Produced Revielver(2 sets at 1.57o each) 3Classwork 1.2

cC)3Long Ouiz 3 ll

10.64Course WolksClass Produced Reviewer(2 sets at 1.59lo each)Classrvork

31.2

c()4Lonq Quiz 4 11

10.64Course WorksClass Produced Revieryer(2 scts at 1.59lo ach) 3

1.2Classw0rkLons Ouiz 5 1l

9.s9Course Works Portfolio 2.7

Summative AsscssmentFinal Examination 25 17.5

I'OTAL 100 '70

13. Course EvaluationStudent perfonnance will be rated based on the following:

The final grades will conespond to the weighted average scores shown below

13.1 Other Corrse Policies

b.

AttendanceAccording to CHID policy, total number ofabsences by the students should not be more than 20olo ofthetotal number of meetings or t hrs for a three-unit-course. Shrdents incurring more than I hotlrs ofunexcused absences automatically gets a failing grade regardless ofclass standing.

Submission of Assessment Tasks (Student Outputs) should be on time, late submittal of coursework'swill not be accepted.

Written Major [xamination (Long Quizspecial exam will be given unless with aMathematics Department.

and Final Exams) will be administered as scheduled. Novalid reason subject to approval by the Chairman of the

d. Course Portfolio rvill be collected at the end of the quarter. AUTI'i0Rl Li:i)" iSlf,iJr:".:i"tJr::il]t1""'i 0"""-.","tion wi* be in Enslish. written and ,oou"" *s-s,fft

lower mark if it is, in the opinion ofthe instructor, deficient in English.

Final Averase Final Grade96< X < 100 L0093< X

f.

14, Other References

14.1 Booksa. College Algebra and Trigonontetry by Louis Leithold, lntemational Ed., 2001b. College Algebra and Trigonometry by Matk Dugopolskr, 2"'Edc. College Algebra, enhances with c;aphing Utillties by tr.lichael Sullivan and Michael Sullivan III, 2'd Ed.d. College Algebra and Trigonometry by Nax Sobel and I-enrer Norbert, 5'h Ed., 1998e. Applied Algebra and frigonometry by Lrnda Davrs. l'" [d . 2003f. Algebra and Trigonometry by Jarnes Stewart, Lothar Recllin and Saleem Watson, 2'd ed, 2007

14.2 Websitesa. www. hom eschool nnath.levqn Ljne/al gebE.phpb. www.onlinemathlearninq.con'l/qQllqge-dgebra.htmlc. wlwv.o n |jnCllathEalong. com/al g ebra-m ath-o alres htlnld. uaalry-rrylarnu.eddapad e m ic/an ns/m ps/math/.,,/Eq Lalgebtalildcx. hlllle. vwvw.Dct.eglu/schools/islcorecourses/mathLinks.html

15. Course Materials Madc Available:

Course schedules for lectures and quizzesSample of assignments/problem sts of studentsSample of written examination of studentsEnd-of-course self assessment

Honor, Dress and Grooming CodesA1l of us have been instructed on the Dress ancl Grooming Codes of the Institute We have all committedto obey and sustain these codes. It will be expected in this class that each of us will honor thecommitments that we have n]ade.

For this course the Honor code is that there will be no plagiarizing on written work and no cheating onexams. Proper citation must be given to authors whose works were used in the process of developinginstructional materials and leaming in this course. If a student is caught cheating on an exam, he or shervill be given zero mark tbr the exam. If a student is caught chcating twice, the shrdent rvi1l be refened tothe preiect of Student Affairs and be given a failing grade. Grave misconduct other than cheating willlikewise be given a failing grade.

Consrltation Scheduleconsultation schedules with the Pfofessor are posted outside the Math Faculty loom and in the School'sweb-page (httplLlrt4puffdlLp|l). It is recommended that the student first set an appointment to confirmthe instructor's availability.

16. Committee Members:Cours Cluster Chair:CQI Cluster Chair:Menrbersl

Raquel B, TeodoroDionisia M. LanuzaT.inda B. CataSheilaDorreen F. San PedroFloro Deogracias G. LlacunaJames Alfred M. Escalona

AUThIGRX '{ H};;

Course Titlel

ALGEBRA

C Oj:r Y