COURSE SYLLABUS
MATH 125 – CALCULUS I
PHILOSOPHY Total human development with appropriate competencies.
VISION A premier and globally competitive university.
MISSION Provide relevant quality instruction, research and extension.
GOAL To lead in transforming human resources into productive self-reliant citizens and responsible leaders.
Course Name Calculus I
Course Credits 3 units
Course Description This course introduces to students the fundamentals of Calculus: limits, continuity, and derivatives. This course assumes a
thorough understanding of concepts on analytic geometry and trigonometry. The use of graphing calculators and computer algebra
systems is highly encouraged.
Contact Hours/Week 3 hours
Prerequisite Math 113 - Trigonometry
Course Objectives At the end of the semester, the students should be able to:
1. Show thorough mastery of the fundamental concepts of calculus 1 like limits, continuity, and derivatives.
2. Apply these concepts to problem situations
3. Relate math concepts to real-life situations
Course Outline and
Timeframe
Course Content / Subject Matter
Week 1-18 UNIT I : FUNCTIONS, LIMIT AND CONTINUITY
1. Functions and their Graphs
2. Types & Operations on Functions
3. Functions as Mathematical Models
4. Graphical Introduction to Limits of Functions
5. Limit of a Function & limit Theorems
6. Continuity of a Function
7. Continuity of a Composite Function
8. Continuity of the Trigonometric Functions and the Squeeze theorem
UNIT II: DERIVATIVES AND DIFFERENTIATION
1. The Tangent Line and the Derivative
2. Differentiability and Continuity
3. Differentiation of Algebraic Functions and Higher Order Derivatives
4. Rectilinear Motion
5. The Derivatives as a Rate of Change
6. Derivatives of Trigonometric Functions and the Chain Rule
7. Derivatives of Trigonometric Functions and the Chain Rule
8. The derivative Power Functions for Rational Exponents and Implicit Differentiation
9. Related Relates
UNIT III. Behavior of Functions & Their Graphs; Extreme Function Values; Approximation
1. Maximum and minimum Function Values
2. Applications of Absolute Values
3. Rolle’s Theorem and the Mean Value Theorem
4. Increasing and decreasing Functions and the First Derivative Test
5. Concavity, Points of Inflection, and the Second Derivative Test
6. Sketching Graphs of Functions
7. Limits at infinity
8. Additional Applications of Absolute Extreme
9. Approximations by Newton’s Method, the Tangent line and Differentials
Prepared by:
LEONARDO F. GRAYCOCHEA , Ph.D.
Faculty
Recommending Approval: Approved:
MYAL A. GUBA, MATE-TVSM MA.CLEOFE F. BELLO, Ed.D
Chairman, BSIE Dean, CTED
LEARNING PLAN
MATH 125 – CALCULUS I
Philosophy
Total human development with appropriate competencies.
Vision
A premier and globally competitive university.
Mission
Provide relevant quality instruction, research and extension.
Goal of the University
To lead in transforming human resources into productive self-reliant citizens and responsible leaders.
Objectives
1. To train and prepare high school and technology teachers who are effective , efficient and committed in the pursuit of quality education through:
a. The development of critical thinking and manipulative skills;
b. The conduct of research, extension and production activities; and
c. The inculcation of moral values and safe work habits.
2. To develop entrepreneurs and produce industrial manpower with experience in the democratic way of life for enlightened, productive and
environmentally responsive citizenry.
Degree Program : Bachelor of Science in Industrial Education
Course Code : Math 125
Course Title : Calculus I
Prerequisite : Math 113 – Trigonometry
Requisite to :
Credit Units : 3 Total no. of Hrs: 54 Total No. of Hrs. Per Week : 3
Course Description : This course introduces to students the fundamentals of Calculus: limits, continuity, and derivatives. This course assumes
a thorough understanding of concepts on analytic geometry and trigonometry. The use of graphing calculators and computer
algebra systems is highly encouraged.
Course Objectives
General : To determine the correct principles on analytic geometry and triginometry
Specific : At the end of the course, the students must have:
1. Show thorough mastery of the fundamental concepts of calculus 1 like limits, continuity, and derivatives.
2. Apply these concepts to problem situations
3. Relate math concepts to real-life situations
Values to be Integrated : Punctuality, Honesty, Orderliness, Decisiveness, Creativity, Accuracy, Innovativeness, Enthusiasm and
Cheerfulness.
Course Requirements : 1. Seatwork, Assignments, Quizzes, Attendance
2. Term Examinations: There will be one written examination each term
3. Class Recitation and Participation
4. Projects
Methodology : Lecture/Discussion, interactive learning, collaborative and experiential teaching strategies.
Grading : Class Standing/Midterm Exam and Final Term
1. Quizzes 25%
2. Seatwork/Recitation/Board Work 20%
3. Problem Sets/Assignments 15%
4. Midterm Exam/Final Exam 40%
The grading formula to be used is: [(Score/Total number of Items)* 50] + 50
Midterm Grade: 60% class standing + 40% Midterm Examination
Final Term Grade: 60% class standing + 40% Final Examination
Final Grade: 40% Midterm Grade + 60% Final Grade
LEARNING PLAN
Desired Learning Outcomes Course Content/ Subject Textbooks/ Teaching and Assessment Resource Time
(DLO ) Matter References Learning Tasks (ATs) Materials Table
Activities (TLAs)
1. Discuss & generalize the 1. Orientation VGMOs Lecture Monitoring VGMOs
VGMO 1.1 VGMO Student Handbook Discussion Sensory Student 1 hour
student handbook and course 1.2 Student Handbook Syllabi Experiential Integration Handbook
content. 1.3 Course Content Learning Syllabi
2. 2. Functions, Limits, & Burtgmeier, James Discussion Group Textbook
Define a function, limit and Continuity W., Monte B. Group Activity Activity Graphing
continuity of a function 2.1 Functions and their Graphs BOisen Jr., and Max Question- Seat Work Paper 17
Sketch the graph of a 2.2 Types & Operations on D. Larsen. 1990. generation Board Work Ruler, hours
function Functions Calculus with strategies Quizzes Colored
Determine the limit of a 2.3 Functions as Mathematical Applications. New Pens
function Models York: McGraw-Hill Calculators
Present proofs of the Publishing Co. Worksheets
theorems on limits and 2.4 Graphical Introduction to
continuity of a function Limits of Functions Kuhfttig, Peter K.F.
logically and intuitively 2.5 Limit of a Function & limit 1983. Technical
Solve word problems Theorems Calculus with
involving functions as 2.6 Continuity of a Function Analytic Geometry.
mathematical models 2.7 Continuity of a Composite Monterey,
Show a working knowledge Function California:
on the continuity of 2.8 Continuity of the Brooks/Cole
trigonometric functions and Trigonometric Functions and Publishing Co.
the squeeze theorem the Squeeze theorem
3. 3. The Derivatives & Larson, Roland E. Lecture Discussion Textbook
Show the geometric Differentiation and Robert P. Demonstration Oral Graphing
interpretation of the 3.1 The Tangent Line and the Hosteler. 1987. Problem Recitation Paper 15
derivative as the slope of Derivative Brief Calculus with Solving Pair Work Ruler, hours
the tangent line to the 3.2 Differentiability and Applications.2nd
graph of a function Continuity Edition.Toronto: D.C Group Work Activity Colored
Define derivative and 3.3 Differentiation of Algebraic Heath and Co. Independent Group Pens
differentiation Functions and Higher Order Study Activity Calculators
Discuss the relationship Derivatives Ostebee, Arnold and Seat Work Worksheets
between differentiability 3.4 Rectilinear Motion Paul Zorn. 1997. Board Work LCD
and continuity 3.5The Derivatives as a Rate of Calculus: From Quizzes Projector
Determine the derivatives Change Graphical,
of functions 3.6 Derivatives of Trigonometric Numerical, and
Apply the derivatives as a Functions and the Chain Rule Symbolic Points of
rate of change in solving 3.7 Derivatives of Composite View. Flofida, USA:
problems in rectilinear Functions and the Chain Rule Harcout Brace
motion, population growth, 3.8 The derivative Power and Company.
decay, and applications in Functions for Rational
economics Exponents and Implicit
Apply the concepts of Differentiation
determinants in solving 3.9 Related Relates
systems of equations
Differentiate implicitly
4. 4. Behavior of Functions & Discussion Oral Drill Textbook
Define and determine Their Graphs; Extreme Purcell, Edwin J. Group Activity and Graphing
minimum and maximum Function Values; 1978. Calculus Question- Exercises Paper 20
function values Approximation with Analytic generation Written Quizzes Ruler, hours
Solve minima and 4.1 Maximum and minimum Geometry. 3rd strategies Colored
maxima problems Function Values Edition. Englewood, Pens
Apply concepts on 4.2 Applications of Absolute Cliffs, N.J: Prentice- Calculators
derivatives in graphing Values Hall, Inc Worksheets
functions 4.3 Rolle’s Theorem and the
Apply limits at infinity in Mean Value Theorem Thomas, George Jr.
determining horizontal 4.4 Increasing and decreasing B and Ross L.
asymptotes of graphs Functions and the First Finney.1993.
Solve problems on Derivative Test Calculus and
absolute extremes. 4.5 Concavity, Points of Analytic
Approximate function Inflection, and the Second Geometry.8th
values using numerical Derivative Test Edition. Philippines:
processes 4.6 Sketching Graphs of Addison-Wesley
Functions Publishing Co., Inc.
4.7 Limits at infinity
4.8 Additional Applications of
Absolute Extreme
4.9 Approximations by
Newton’s Method, the Tangent
line and Differentials
Supplementary Reading Materials
1. Math Magazines
On-Line References
1. http://www.isu.edu/academic-info/majors/calculus.html
2. http//:www.variablecalculus.fullerton.edu/undergraduate/geometry.html
3. http://www.analyticgeometry.edu/dept/math/
Prepared by: Recommending Approval : Approved:
LEONARDO F. GRAYCOCHEA, Ph.D. MYAL A. GUBA, MATE-TVSM MA.CLEOFE F. BELLO, Ed.D
Faculty Chairman, BSIE Dean, CTED
