math14 course syllabus

MAPUA INSTITUTE OF TEGHNOLOGYDepottment of Mqthemqticr

vtst0NThe Mapua lnstitute 0fTechnology shallbe a globalcenter of excellence in education by providing instructions thatare current

in content and state-of-the-ari in delivery; by engaging in cutting-edge, high impact research; and by aggresslvely taking on

presentday global concerns.

MISSION

a. The lUapua lnsiitute of Technology disseminates, generates, preserves and applies knowledge in various flelds of sludy.

b. The lnstitute, using the most effective and efficient means, provides its students with highly relevant professional and

advanced education in preparati0n for and furtherance of global praciice.

c. The lnstitute engages in research with high socio-economic impact and reports on the results of such inquiries.

d. The lnstiiute brings to bear humanity's vast store of knowledge on the pr0blems of industry and community in order to make

the Philippines and ihe world a better place.

BASIC STUDIES EDUCATIONAL OBJECTIVESMISSION

a b c d

1 To provide students with a solid foundation in mathematics, physics, general chemistry

and engineering drawing and to apply knowledge lo engineering, archltecture and

other relaied disciplines.

2. To complement the technical training of the students with proficiency in otal, witten,and qraphics communication.

3. To instill in the students human values and cultural refinement through the humanitiesand sociai sciences

4. To inculcaie high ethical standards in the students through its integration in the

learninq activities.

COURSE SYLLABUS

1. Course Code: Math 14

2. Course Title: Plane and Solid Analytic Geometry

3, Pre-requisite: MATH 10, MATH12

4. Co-requisite: none

5. Credit: 3 units

6. Course Description: This course covers topics on fundamental concepts and theorems intwo-dimensional and three-dimensional geometry using rectangular coordinate system, It also introduces thepolar coordinate system and polar curves. It tlso deals with the study of the properties and graphs of lines, thealgebraic curves, the circle, the conics, polar curves and different surfaces.

7. Student Outcomes and Relationship to Basic Studies Educational Objectives

Student OutcomesBasic Studies Educational

Obiectivesr-f --ls r4(a) an ability to apply knowledge of mathematics, science,

and enqineerinq

(b) an ability to design and conduct experiments, as well asto analyze and interpret from data A uThll )Rtl"

(c)an ability to design a system, component, or process iomeet desired needs

c( )Iz r

(d) an abilitv to function on multidisciplinary teams(e) an abilitv to identifv. formulate, and solve engineering

Course Title:PLANE AND SOLID ANALYTICGEOMETRY

Date Effeclive:l"tTermsY 2012-2013

Date Revised:

June 10,2012

lUUl^^_,4hproved by:y'LD SABINOSubject Chair

of 7

problemsan understanding ffiresponsibilityan ability to communicateffithe broad education necessary to unOersEnC fne irnpactof engineering solutions in the global and societal context

(f)

(s)

(h)

(i) a_recognition of the need for, and an ability to engage inlife-long learninga knowledge of contemporqlry issues

(k) an ability to use the techniques, skills, and modrernengineering tools necessary for engrneerinq practice

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

" Level: l- lntroduced, n- Reinforce4 D- Demonstrated

lhe course, the student must be able to:1. Apply principles garned from the prereqursrte coLrrses

2. Apply the fundamental concepts in solvGg applicationproblems in geometry; discuss comprehensively properties ofthe algebraic functions and apply these to sketCh algebraiccurves and lines.

3. Apply the properties of the algebraic-urrctioni to desiribe tfrccircles and the conics for the purpose of skelching and writinglhe equation lhat describes a particular geometryl Finally, tobe able to solve application problems involving these

coordinate svslem.

4. Apply the properties of the algebEic/non-a[ebraic fLLncLlin sketching the required graph in an appropriate 2_D t3-D

9. Course C

Mission and Vision ofMapua lnstitute ofTechnology

Orientation andlntroduction to theCourseDiscussion on COs,TLAs, and ATs of thecourse

Overview onstudent-centeredlearning and eclecticapproaches to be usedin the course

DIAGNOSTIC EXAMINATIONFundamental Corcepts (Definition and Application)- The Rectangular

Coordinate System- Directed Line Segment- Distance Between Two

Points

Guided Leaming One-on-One Interview #l

Class Produced Reviewer #lAr7tr


Date Effective:l"rTermsY 2012-2013

Exanples

co2

2

- Inclination and Slopes ofLines

- Angles Betw€en TwoIntersecting Lines

Locus of a MoYing PointDefining- Line- Circle- Conics

Guided Leaming

Lines and First l)egreeEquations- General Equation- Standard Forms

- Two- Point Form- Point- Slope Form

WorkingthroughExamples

Class Produced Reviewer #lBSlope-Intercept FormInter0ept FormNormal Form

3

Directed Distancefrom a Point to a LineDistance betweenParallel Lines

DyadicDiscussion

Algebraic Curves- PropertiesofAlgebraic

Curves- Extent of the graph

(Domain and Range)- X and Y - lntercepts- Symmetry with

respect to the X-axis,Y-axis and the Origin

- Asymptotes (Vertical, Horizontaland Slant)

- Sketching Graph of:- Polynomial Functions

(Type 1)

GroupDiscussior/ConcaptMapping

Mind Map: Outline of Procedure for Curve Tracing

Rational Function(Tvoe lI)

ClassArgumentation

4

Irrational Function (Type lll)Irrational Functions(Tlne IV)

Class Critique Class Produced Reviewer #lC

LONG QUIZ I

The Circles- Definition

General and StandardEquations

- Reduction of GeneralEquation to theStandard Form

CooperativeLeaming/GroupDiscussion

Class Produced Reviewer #2A

AuThi0!cole[1EFpY

Writing equations ofCircles Determined byGeometric ConditionsDetermination ofRadical AxisConditions andEquations DefiningFamily of Circles

DyadicDiscussion


Date Effective:'l"tTermsY 2012-2013

Date Revised:

June 10,2012"*\w'

ctJr{tcr llCo{nmittee

l,{#;; Y

i LD SABINO I Paqe 3 of 7Slrbject Chair I

5

co3

The Conics- The Parabola

- Definition- General Equation- Standard Equation

and Graph ofParabola withVertex at (0,0)

GuidedDiscovery /ClassDiscussion

Class Produced Reviewer #28Standard Equationand Graph ofParabola with Vertexat (h,k)Application Problemslnvolving theParabola

GuidedLeaming/Discovery

6

- The Ellipse- Definition- General Equation- Standard Equation and

Graph of Ellipse withCenter at (0,0)

CooperativeLeaming

Class Produced Revrewer #2C

Standard Equation andGraph of Ellipse withCenter at (h, k)Application ProblemsInvolving the Ellipse

DyadicDiscussion

- The Ilyperboh- Definition- General Equation- Standard Equation

and Graph ofl-Ilperbola withCenter at (0.0) Guided

Discovery

7

Standard Equationand Graph ofI{yperbola withCenter at (h, k)Application ProblemsInvolving the[Iyperbola

LONG OUIZ 2Simplification of Equations

- Simplification ofIquations byTranslation ofAxes

- The Gencral SecondDegree Equation(ldentification ofConics)

DyadicDiscussion

Class Produced Reviewer #3A

AUTI-[$Rf r'-\ r:.

iIUHD

8

Simplification ofEquation by RotationofAxes

GuidedDiscovery /ClassDiscussion

The Polar CurYes- The Polar Coordinate

System- Relationship Betwoen

Polar and RectangularCoordinate Systems

- Transforming PolarEouations to

GuidedDiscovery

PLANE AND SOLID ANALYTICGEOMETRY

1"r TermsY 2012-20't 3

Rectangular Form(vice versa)

co4

Properties of PolarCurves- Intercept- SymmetrySketching PolarCurves

DyadicDiscussion

9

The Parametric Equations- Definition- Elimination of

paralneter totransform equation to

the rectangular form.- Sketching Parametric

Equations

GuidedDiscovery

Three-DimensioualGeometry

- Space Coordinates- Plotting Points in 3-D- Distanca Between

Two Points in Space- Midpoint Formula

CooperativeLeaming / ClassDiscussion

Class Produced Reviewer #3BClassDiscussion

10

Equations and Graphsof Surfaces:- Planes- Cylindrical

Surfaces- Ouadric Surfaces

GuidedDiscovery

PROJECTReflective Journal

Poster/Proiect Output

LONG QUIZ 3

SUNINIATIVE ASSESSMtrNTFINAI, EXAMINATION

co1, co2,co3. co4

10. Opportunities to Develop Lifelong Learning Skill

To help students understand and apply the mathematical principles of Analytic Geometry and provide themwith the needed working knowledge of the different mathematical concepts and methods for them to fullyunderstand the relationship of Analytic Geometry with the increasingly complex world.

11. Gontribution of Course to Meeting the Professional Component

Engineering TopicsGeneral EducationBasic Sciences and Mathematics

12. Textbook:Analytic Geometry, 6th ed, 2006Douglas F. Riddle

13. Course Evaluation

0%o%

100%

AUTF$SM$flHAtr t\ c_*t \f1-" \-.!i i-- i

l"rTermsY 2012-2013

PLANE AND SOLID ANALYTICGEOMETRY

Student performance will be rated based on the following:

The final grades will correspond to the weighted average scores shown below:

Final Average Final Grade96< x < 100 1.00

933 x <96 't .2\90< x <93 1.50

86<x<90 1.7 s

83< x <86 2.0080< x <83 2.2576<x<80 2.50

73< x <76 2.75

70 < x<73 3.00Below 7O s.00 (Fail)

1 3.1 . Other Course Policies

a. AttendanceAccording to CHED policy, total number of absences by the students should not be more than20% of the total number of meetings or I hrs for a three-unit-course. Students incurring morethan I hours of unexcused absences automatically gets a failing grade regardless of classstanding.

b. Submission of Assessment TasksSubmission of students'work should be on time. Late submittals will not be accepted.

c. Written ExaminationLong quizzes and final examination will be as scheduled. No special examination will be given

unless for valid reason subject to approval of the Department Chairman.

d. Course PortfolioCourse portfolio will be collected at the end of the term.

e. Language of InstructionouuJ8ff1**

Assessment Tasks Weight(Y")

Minimum Average forSatisfactory Performance

(%l

Diagnostic Examination 10 7

co2 RLA3.6

1 5.1

Lonq Test 118

co3 RLAJ.l

14.a4

Lonq Test 218

co4RLA

1.)

15.54Lonq Test 3

14

Proiect5

Summative Assessmenl:Final Examination

17.5

TOTAL 100 70

Lectures, discussion, and documentation will be in English Written and

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

Date Revised:

June 10,2012PLANE AND SOLID ANALYTICGEOMETRY

f. Honor, Dress and Grooming CodesAll of us have been instructed on the Dress and Grooming Codes of the lnstitute. We have allcommitted to obey and sustain these codes. lt will be expected in this class that each of us willhonor the commitments that we have made.For this course the Honor Code is that there will be no plagiarizing on written work and nocheating on exams. Proper citation must be given to authors whose works were used in theprocess of developing instructional materials and learning in this course. lf a student is caughtcheating on an exam, he or she will be given zero mark for the exam. lf a student is caughtcheating twice, the student will be referred to the Prefect of Student Affairs and be given a failinggrdutr.

g. Consuliation ScheduleConsultation schedules with the Professor are posted outside the faculty room and in theDepartment's web-page (http://math.mapua.ed u.ph). lt is recommended that the student first setan appointment to confirm the instructor's availability.

14. Other References

14.1. Books

a. Plane Analytic Geometry, Mijares, 199'1

b. Analytic Geometry, Fuller and Taruater

14.2 WebsitesSciLab

15. Course Materials Made AvaitableCourse schedules for lectures and quizzes

Samples of assignmenUProblem sets of studentsSamples of written examinations of students

End-of-course self-assessment

16. Committee Members: Servando D. BernardoMaria Rosario C, ExcondeErnarnie C. De GuzmanReynatdo C. LanuzaGerardo G, UsitaAlberto C. Villaluz

AUTE:[*ffiq7' Effi


Date Effective:1'' TermsY 2012-2013

math14 course syllabus

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