Analytic+Geometry

COURSE SYLLABUS IN MATH 113 Subject Code: **MATHEMATICS 113** Subject Description: **Analytic Geometry** Credit: **3 units** Pre-Requisite: **Math 102, Math 105** Intended for: **DET Curriculum**

**COURSE DE**﻿**SCRIPTION:**  Math 213 - Analytic Geometry is a three-unit course which consists of the study of graphs and their equations, straight line, circle, parabola, ellipse, hyperbola, rotation of axis and higher plane curves fitting.

 It deals with the use of algebra (equations, formulas and their algebraic manipulations) as the main tool in investigation of interesting and useful properties of configurations involving points, straight lines, and curves other that straight line.

﻿ **COURSE OBJECTIVES:**  The main objective of this course is to provide students with skills in using algebra (equations, formulas and their algebraic manipulations) as a main tool in investigation of interesting and useful properties of configurations involving points, straight lines, and curves other that straight line.  After completing the course, the students should be able to:
 * Develop the skills and ability to work efficiently in this field.
 * Discuss categorically the principles embodied in each type of word problems.
 * Analyze and solve word problems in practical situations, and
 * <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 12pt;">Synthesize all the mathematical presentation of problems.

<span style="font-family: 'Arial Black',Gadget,sans-serif; font-size: 10pt;">**COURSE OUTLINE:**

<span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">**1. FUNDAMENTAL CONCEPTS AND METHODS (12 hours)** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;"> <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.1. Introduction <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.2. Directed Line Segments <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.3. Position of a Point on a Surface <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.4. Rectangular Coordinates <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.5. Distance Between Two Points <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.6. Midpoint of a Line Segment <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.7. Division of a Line Segment <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.8. Inclination and Slope <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.9. Parallel Lines and Perpendicular Lines <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.10. Angle Between Two Lines <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.11. Area of Triangle by Coordinate <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">1.12. Analytical Proofs of Theorem in Geometry

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">2. THE STRAIGHT LINE (15 hours) **  <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.1. Line Parallel to Coordinate Axes <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.2. Point Slope Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.3. Two-Point Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.4. Slope-Intercept Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.5. Intercept Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.6. The General Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.7. The Normal Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.8. Distance Between a Line and a Point <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">2.9. Families of Lines **<span style="font-family: 'Franklin Gothic Book',sans-serif;">3. THE CIRCLE (12 hours) ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">3.1. Center-Radius Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">3.2. The General Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">3.3. Circles Satisfying Three Conditions <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">3.4. Families of Circles <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">3.5. Tangent to a Circle

**<span style="font-family: 'Franklin Gothic Book',sans-serif;">4. PARABOLA, ELLIPSE AND HYPERBOLA (12 hours) ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.1. Conic Sections <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.2. The Parabola <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.3. Parabola with Vertex (h, k) <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.4. The Ellipse <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.5. Ellipse with Center at (h, k) <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.6. The Hyperbola <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.7. Hyperbola with Center at (h, k) <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.8. The General Form <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.9. Eccentricity <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">4.10. Tangent to a Conic

<span style="font-family: 'Arial Black',Gadget,sans-serif;">**METHODS OF TEACHING**

<span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">Classroom discussions, oral participation, seatwork and boardwork will be the primary means of classroom instruction for this course.

<span style="font-family: 'Arial Black',Gadget,sans-serif; line-height: 24px;">**COURSE REQUIREMENTS**

<span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">Quizzes, unit test, recitation, activities and term examinations shall be among the requirements of this course. The date of submission will be announce by the instructor.

<span style="font-family: 'Arial Black',Gadget,sans-serif; font-size: 10pt; line-height: 24px;">**CRITERIA FOR GRADING**

<span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">The following shall be used as the basis for giving grades. **<span style="font-family: 'Franklin Gothic Book',sans-serif;"> Class Standing 70% ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Quizzes 30% <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Attendance/Recitation 20% <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Projects/Assignments 20%

**<span style="font-family: 'Franklin Gothic Book',sans-serif;"> Term Examination __30%__ ** <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">100% <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">The final grade will be computed based on the 50-50 policy (50% of the Midterm + 50% of the tentative final grade)

<span style="font-family: 'Arial Black',Gadget,sans-serif; font-size: 10pt; line-height: 24px;">**TEXTBOOKS AND REFERENCES**

<span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 12pt;">Encyclopædia Britannica (2007//).// Analytic geometry. In //Encyclopædia britannica//. From: []. <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Feliciano, F. T. & Uy, F. B. (1992). //Modern analytic geometry//. Manila: Merriam & Webster, Inc. <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Love, C. E. & Rainville, E. D. (1981). //Analytic geometry.// Fifth Edition. New York: The Macmillan Company. <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Think Quest (2001). //Analytic geometry.// From http://library.thinkquest.org/C0110248/geometry.htm. <span style="font-family: 'Franklin Gothic Book',sans-serif; font-size: 16px; line-height: 24px;">Any Analytic Geometry Books